Monthly Archives: April 2016

Aleta May’s EDET637 UbD Unit Internship Reflection Spring, 2016

Understanding by Design (UbD) Fractions Unit Reflection

For EDET 637: Differentiating Instruction through Technology

Instructor: Lee Graham

By Aleta May

Please refer to artifact links in reference section at the end of this paper. Padlet showcases evidence of gaming, next steps after the Brainpop battleship numberline game (numberline worksheet samples from a referenced website) and the math chart used by students for converting and reducing fractions. Also, there is a dropbox link to show pre- and posttest artifacts with work samples between that were scanned to my computer and placed into dropbox. Additionally, I have blogged throughout the course with students regarding learning in this class and specifically giving and receiving feedback for my unit design and progress as the unit was taught.

Contributing to Individual Paths for Learning

Students were taught in a small Response to Intervention (RTI) group. Three students in the group were ready for learning how to convert fractions to like denominators and reduce fraction. Three other students in the group were placed on a learning path that allowed them to practice their multiplication tables and applying this understanding to multiplying fractions to give applied practice to using multiplication tables as a reference tool.

Within my UbD Fractions Converting and Reducing Unit, students were given individualized help as needed. Students were given opportunities to correct errors not corrected during the group time-frame on the following day, since the RTI time is shorter than the usual full 90 minute block.

Planning and Customization

Planning in the beginning was very through. Daily monitoring of progress allowed me to adjust learning according to specific learning needs. Sometimes students did not complete all the problems in one session. Although a dropbox link is provided in the below to show these worksheet types of artifacts, students completed much more work than shown. This is a sampling of the progress of students, pre- and posttests, and structure of the unit.

There are practice exercises with applied problem solving exercises in Chapter 3 Fractions in my Basic Math Skills book by AGS Publishing (known for age appropriate but lower readability and explanations).

Student Learning

Student progress was significant, as can be seen on student pre- and posttests. Much of this is because of monitoring, adjusting and reviewing material as needed. Also, gaming in the class gave them an engaging opportunity to learn skills more fluently and to get a break from worksheets, though the concepts were connected between.

Following is a reflection I wrote on Week 10 where we discussed our units in a weekly Twitter session:

By learning to use TweetDeck for weekly Twitter sessions, I was able to schedule with two colleagues, Amber Novak (from another state location) and Jeff Clay, to host the last week of class. I feel empowered now to communicate with teachers “the modern way.”

One very important point was made: I wanted to figure out how to find time to reflect on student learning throughout the unit. What came to my mind was to use some class time to model writing a reflection on my teaching, while asking students to write a reflection on their learning. Dr. Graham wrote that this is an idea that she has applied and that she learned it from Nancy Atwell. As I think back to my Reading Specialist training, I remember watching DVDs of Donald Graves. He taught that the best way to teach writing is to model writing as an adult; such as using a mini-lesson think-aloud approach. He also spoke about just writing in class while students write. So if I want to teach students to reflect on their learning, I need to model this for them.

We also discussed the value of teaching deeper, rather than wide/broad. We tend to feel the push as teachers to cover the curriculum. It is important to touch on as much of that curriculum that is tied to the standards as is possible, but it is not possible to try to make kids learn faster than they are ready to learn. We can engage, motivate, redesign instruction, and review—all with a forward momentum. But particularly in subject areas, such as the fractions unit my students are learning, it does no good to move on if they do not have the foundations down yet! I commented that we need persistence without frustrating our students.

To demonstrate further Twitter discussion thinking, here are questions I spent much time coming up with for our Week 13 session:

  1. Differentiated instruction —-Aleta

#diffimooc How much did available technology affect your customization of standards or curriculum

#diffimooc In what ways did you use technology to modify existing materials to make a better fit for your students? (Matuk, Linn, & Eylon, 2015, p. 231).

#diffimooc How was your students’ thinking made visible to you when using technology

4.  Assistive technology —–Aleta

#diffimooc Did tech. help any of your students with visual, auditory, being able to perceive and make meaning better than no tech.?

#diffimooc In what ways did you use technology to illustrate content in a way that is more comprehensible to their own lives?

#diffimooc Are there examples of how technology brought the outside world to the students?

#diffimooc Were there certain digital apps that helped your more advanced students explore beyond the norm?

  1. Problem-based learning —-Aleta

#diffimooc Why does PBL begin with learning outcomes instead of traditional information transmission?

(It is student-centered instruction, and begins with real questions to real problems. It is self-directed. —Begin planning, thinking about specific learning outcomes students should gain by analyzing and discussing. Rico Ertmet (p. 97)

#diffimooc What various student configurations, were used to inspire students to cooperate?  (Examples can be: small group activities, role play, students chatting in online games, and blogging.)

#diffimooc In PBL, how does collaborating affect student engagement?

#diffimooc Since the teacher assumes the role of facilitator in a PBL instruction model, what were some scaffolds you provided.

#diffimooc In PBL, did you notice your students engaging group talk: describing, questioning, elaborating, predicting, explaining?

  1. Creating, implementing, and evaluating a unit on differentiation –

#diffimooc Did you use reflective journals as exit tickets? If so, how did this help you evaluate teaching & learning?

#diffimooc How you think having students reflect on their learning helps them take ownership & set personal goals?

As my classmates responded to these questions, I was simply amazed at the level of dissusion we were having regarding applications of technology applied to our well designed UbD units! References for the studies I read just to prepare for this Twitter session reflect the amount of thinking that has gone into planning for this unit.

3-28-16

Pre-Test: 20 problems possible– Please refer to artifacts in dropbox link in references at the end of this paper

Turn in assignment, then practice identifying types of fractions at:   http://coolmath-games.com/0-fraction-splat

JW:     6/20

PJ:     14/20

MC:   15/20

AI:       6/20

TE:     4/20

4-19-16 Posttest for Three Who Participated in UbD Fractions Converting and Reducing Unit—Please refer to artifacts in dropbox link in references at the end of this paper:

JW:  90% correct (missed 2)

MC: 100% correct.

PJ: 90% correct (missed 2)

Students will need to continue practicing this skill with more difficult fractions to convert to like denominators and reduce. They will need more opportunities to apply these skills to real world applications through problem based learning in projects and word problems. I plan to search MobyMax http://www.mobymax.com  website for appropriate applied fractions lessons. I still want to explore the use of MineCraft for teaching math concepts, fraction measurement included.

Overall Unit Plan:

ESTABLISHED GOALS  

Instructional Focus: Sixth Grade Standards—

  1. “Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems.” (Alaska English/Language Arts & Mathematics Standards June 2012, p. 140)

Transfer

Students will be able to independently use their learning to…                                         

Reduce, calculate and conceptually apply fraction in addition and subtractions.

Recognize concepts and terminology related to reducing, calculating and applying fraction concepts.

Transfer their knowledge to pre-algebra concepts and understanding of how fractions are used in the real world.

Meaning—

Students will understand that . . .

Multiplication and division fluency directly impact their ability to calculate addition and subtraction of fractions.

Fluency in recognizing different types of fractions and how fractions relate to a whole helps them understand concepts and terminology.

ESSENTIAL QUESTIONS                         

How can reducing or increasing fractions, using least common multiple or greatest common factor, help me in the real world—at home, on the job? (cooking, sewing, construction, water treatment, computer coding. . .)

What type of math does knowing this prepare me for?

Acquisition

Students will know; based on standards

Students will know…                                 

Apply and extend previous understandings of multiplication and division to divide fractions by fractions 6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions (e.g., by using visual fraction models and equations to represent the problem).

Students will be skilled at . . .

According to individual needs: reducing and calculating fractions through addition and subtraction. They will work on multiplication and division fluency to help them complete fraction calculations with 95% or higher accuracy.

Stage 2- Evidence

Pre and post test PERFORMANCE TASK(S): Students will take a pretest and post test to demonstrate their strengths and weaknesses in adding and subtracting fractions, including a few word problems.   They will use a paper and pencil test for this.
Students will use computer games to increase skills in calculations.

Students will use worksheets to practice skills where they can practice their computation accuracy at an instructional skill level.

OTHER EVIDENCE:

The teacher will observe and track which games they are using to make sure students are working at an appropriate level for their skills as shown on the pretest.

Worksheets will be collected as evidence of calculation for accuracy.

Students will be observed for engagement, understanding, and motivation.

Increases math fact fluency will be noted through timed multiplication / division paper pencil tests.

Stage 3 – Learning Plan

Summary of Key Learning Events and Instruction

Coolmath.com for visual support and discuss this concept with the teacher.

Three days per week of paper pencil practice at individualized levels.

Two days per week of game practice. Students will choose a game that will strengthen personal areas of need.

To begin with, students will complete pretest activities using worksheet and pencil. Then they will start using gaming to get started with fluency. When fraction concepts need to be further clarified, students will view and go over mini-lessons that are presented in Coolmath.com for visual support and discuss this concept with the teacher.

Three days per week of paper pencil practice at individualized levels.

Two days per week of game practice. Students will choose a game that will strengthen personal areas of need.

Aleta May’s Week 10 – Week of March 28, 2016

Update to Week 1 of my UbD Fractions Unit:

During this week, I have a paper/pencil pre-assessment on paper.  The post assessment will replicate the pre-assessment with different problems.  As an initial incentive, students used fraction games found on Coolmath.com; it has initially been used as a draw in motivator and fluency for my lowest students.There are other games I want to use.  Ideally, I could get MathBlaster to work on our iPads soon.

Student self assessment is through watching their progress in games, and using the visual fraction strategy called Radial Fractions.  McMullen, C. Ph.D. (2010).  Radial Fractions math workbook (addition and subtraction):  A fun & creative visual strategy to practice adding and subtracting fractions.  CreateSpace. This can be found on amazon.com The students use this visual that looks like the spokes of a bicycle wheel to add or subtract.

My step-by-step plan is now (after noting their progress) in the visual strategy as follows:

This week they added or subtracted without reducing, using the wheel; since students were sometimes getting adding and subtracting mixed up.

Next week, they will subtract more than they did the first week; and they will begin reducing within this visual strategy.

This is looking more and more like a 3 week (instead of a 2 week unit plan).

I’ll be able to really focus more deeply on all the “embellishments”. . . as there will be less school-wide assessment focus!

Here is a new link I found that will include the more challenging fractions (such as reducing) fractions online (PacMan games):

http://www.sheppardsoftware.com/math.htm

Presently, students are using a visual strategy that even though it is paper based, it is a brightly colored bicycle wheel.

Week 2 of Fractions Unit

Essential question: What are my challenges and successes in implementing my unit? Students solidifying basic math facts.

Looking ahead: This week and next week  (through April 15) will be dedicated to teaching your unit as much as possible in your classroom.

Students will go onto an internet site to practice math skills:

shepherdsoftware.com   choose ‘math games’

More specific at this site, students went to Math Man (a branch off of the former Pac Man game) during the end of week one and more so during week two: http://linkis.com/sheppardsoftware.com/vXPu1

Students practiced reducing fractions with the computer software program. They challenged each other to try to get to level 7.

During the allotted time students remained on task and improved with practice.

Make notes for yourself as you teach your unit this week. How did things go?

I was surprised to see how fast students caught on to the first step of adding fractions.

Was it as expected?

It went better than expected.

What challenges did you see?

I found that the students followed the first steps and are ready for the second step: Reducing, which includes dividing the top and bottom numbers by a common denominator.

Did you see evidence of learning?

Yes!  

What was this evidence?

Students followed one-step rules in week 1.

Will you need to change the unit in some way for the second week? I will only add step two, the reducing fractions this week and see how well they can follow a two-step rule.

Steps given by EDET 637 rubric are included as I respond, and reflect from week 2 then plan for week 3:

Reflection of the internship provides evidence that the teacher participated in and contributed to individual paths for learning for students engaged in the experience.

During the pretest I gave no help, support, or directions. During the first week of assignments, I demonstrated on the white board a simple method of adding fractions with out asking students to ‘reduce or simplify their answers.

 The teacher summarizes information from observations in the lesson about why students were making choices they did. – So, you need to make notes of the way that you helped individual students as they pursued their learning path (how your “scaffolded” student learning).

During actual assignment time, after demonstrating at the white board, I sat with the students looking busy. They would ask, “Is this right? Am I doing it right?” 

This is the support that new learners need to become expert in their new knowledge. So if a student asks for assistance – why did this happen? Was it appropriate at the time?

This is the normal method I use to energize and help students stay on track.

Is there a way that you could build in supports so that the next time you do this unit this issue is covered?

I could make a place near the teacher desk where a student could go to check their answers when finished.

Week 3

Students will be assigned web page to continue to practice reducing fractions prior to worksheet assignments:

http://www.sheppardsoftware.com/mathgames/fractions/reduce_fractions_shoot.htm

http://www.sheppardsoftware.com/mathgames/fractions/mathman_reduce_fractions.htm

I will incorporate gaming that is specifically geared to individual student needs. They will continue to practice skills using both radial and other practice worksheets

Additional Pieces to Original Plan:

Group Composition

Student Group is made up of one sixth grader, two seventh graders, and two eighth graders. They are sent to me for response to intervention (RTI) each day for extra practice in focus areas of math for them. Two students are on an IEP and are preparing for pre-algebra for next fall. The other three students will likely be in small group basic skills RTI math again next year.

Technology Resources for practicing terminology and fluency:

http://www.coolmath-games.com/0-fraction-splat

CoolMath Fraction Splat Instructions:

Click on the types of fractions for each round, (There are three rounds.) Click the finished button once you have found them all.

Round 1 Target: Mixed Numbers

Teaches terminology: improper fraction whole number mixed number

Round 2 Target: Fractions that are greater than or equal to 1

Round 3: Target=Fractions that are less than 1/2

http://www.coolmath-games.com/0-fractone

FractOne – Your goal is to get sums of 1. Get it? FractONE

Click on pairs of squares that add up to 1 and do it as fast as you can!

Technology Resources through Cool Math using simple explanations and visual representations for mini-lessons that will be used to individualize according to student needs:

http://www.coolmath.com/prealgebra

  1. Factors and Primes http://www.coolmath.com/prealgebra/00-factors-primes
  2. Divisibility Tests
  3. Factorizations
  4. Prime and Composite Numbers
  5. Prime Factorizations
  1. Intro to Fractions
  2. Mixed Numbers http://www.coolmath.com/prealgebra/01-fractions/fractions-02-mixed-numbers-01
  3. Equivalent Fractions Part 1 http://www.coolmath.com/prealgebra/01-fractions/fractions-04-equivalent-01
  4. The Magic 1 (fluency in matching fractions to make one whole)
  5. http://www.coolmath.com/prealgebra/01-fractions/fractions-03-magic-one-01
  1. Common Factors (Common Divisors)
  2. Greatest Common Factor (GCF)—Also known as Greatest Common Divisor (GCD)
  3. Common Multiples
  4. Least Common Multiple (LCM)

Game choices

Technology Resources for practicing terminology and fluency:

http://www.coolmath-games.com

http://www.coolmath-games.com/0-fraction-splat

CoolMath Fraction Splat Instructions:

Click on the types of fractions for each round, (There are three rounds.) Click the finished button once you have found them all.

Round 1 Target: Mixed Numbers

Teaches terminology: improper fraction whole number mixed number

Round 2 Target: Fractions that are greater than or equal to 1

Round 3: Target=Fractions that are less than 1/2

http://www.coolmath-games.com/0-fractone

FractOne – Your goal is to get sums of 1. Get it? FractONE

Click on pairs of squares that add up to 1 and do it as fast as you can!

Teaches fluency in adding numerators with a variety of denominators to equal one whole. Results produce how many seconds it took the player and what this adds up to in minutes and seconds.

Students will track their progress for fluency in games and paper pencil.

Game: The Clue Finders Math Adventures Ages 9-12 with multiplication, division, and fractions. The Learning Company—Windows & Macintosh. With 10 levels of difficulty; auto-leveling, 50 printable activities, personalized workbooks and rewards. Game to practice multiplication and division fluency and fractions: http://www.mathblaster.com

Game: MindTwister Math by Edmark. Increases math fact fluency and strengthens mental math skills.

Game: Math Blaster Hyper Blaster II-HD

Game: Fractions and Smart Pirates In App Store

Week of 4-11-16 

Essential question: What evidence am I collecting for my final project – and for what purpose?

The most obvious evidences are: pre- post- tests, a few screenshots of computer gaming levels / playing for padlet.com link, observation notes, and daily worksheets. On task behavior was not formally tracked, but was noted in observation notes.

We went from adding and reducing to subtracting & reducing fractions. Focused on a specific game.

As of 4-13-16, Students are getting the concept of adding and subtracting fractions with unlike denominators; but they are still having trouble with reducing. I will continue working on this with them next week, even though I know they are improving.

The kinds of evidence of contributing to individual learning paths are as follows: First, I have a small group, so it is easier to go from student to student. Second, checking their paper/pencil work regularly as soon as they leave gives me feedback for what to emphasize the next day. Third, I watch them as they play the reducing fractions game to see them move on to different game levels.

Evidence that students are being given individualized learning paths are staying on the same basic concept of adding fractions with unlike denominators; then gradually going into subtraction, all the while reducing. Some students seem to want to complete the entire sheet, even knowing they will be asked to go back to reduce these the next day. They are not penalized for this, since the entire concept of adding/subtracting fractions with unlike denominators was either new to them, they forgot what they had learned in the past, or they simply added denominators to get the same denominator in their answers. Then reducing fractions is yet another step for them. As long as they are focused, the pressure is not who gets what first, rather, the focus is on learning and progressing daily.

The pillar that bears the most weight of evidence of learning are the pre- and post-tests; as well as the fact that they are staying so on task! On task behavior is one definition of engagement and learning.

One way I am scaffolding learning is to have three students who need to learn their multiplication tables fluently are working on these to prepare them for adding and subtracting fractions with unlike denominators. As they learn multiplication tables, they will now, start multiplying fractions and using their multiplication chart to assist with this. Further scaffolding is allowing students to focus on the process of creating like denominators; then the process of reducing after—either one problem at a time or step one for all the problems then step two.

The kind of growth I expect on my post-test, based on observation and daily worksheet checks is; with such a short timeframe for the unit, they will grow in creating common denominators—and hopefully reducing fractions as well.

This is how the unit is set up:

Day One PreTest

Day Two Multiplication Facts/Practice

Day Three Computer Fractions Game

Day Four Adding Fractions Worksheet

Day Five Computer Reducing Fractions

Day Six Reducing/Adding Fractions Worksheet

Day Seven Computer Adding Fractions Game

Day Eight Subtracting Fractions

Day Nine Computer Subtracting Fractions Game

Day Ten PostTest

Evidence is collected daily through worksheets; teacher observation and reflections of the help needed; pre- post-test; and a padlet wall with screenshots of their Sheppardsofware.com fractions gaming. http://www.sheppardsoftware.com/mathgames/fractions/mathman_reduce_fractions.htm

See level screenshots at:  http://padlet.com/aleta_57/tq5v224rfbuk

3-28-16

Pre-Test: 20 problems possible

Turn in assignment, then practice identifying types of fractions at:

http://coolmath-games.com/0-fraction-splat

JW:     6/20

PJ:     14/20

MC:   15/20

AI:       6/20

TE:     4/20

4-4-16

Students will go onto an internet site to practice math skills:

shepherdsoftware.com   choose ‘math games’

Students practiced reducing fractions with the computer software program. They challenged each other to try to get to level 7.

During the allotted time students remained on task and improved with practice.

Ongoing Concept the students are learning: We don’t have to reduce any more because you cannot reduce 5/8.

Monday, 4-11-16

Lesson–Math Has Problems:

3= 1                1 + 1 = 7+ 3

6   2               3     7     2

2= 1                1+ 1 = 5 + 2

4   2               2   5     10

8  = 4             4 + 1 = 5

10 = 5             8     8     8

Practice and review

T.E. is getting his multiplication skills up in order to prepare for fractions reducing.

Sheppardsofware.com

  1. JW. 2 goes into 2 how many times so right here we put 2 over 2; what number goes into these; what number goes into those; how many times does this number go into this? Multiply the bottom; now we need to multiply the top. He got to level 4 on Math Man, then restarted (WTL18) 18 possible, 3 errors= 15/18 83%
  1. PJ. This number reduces further; this number has to be the same, if you divide the top, then the same for both numbers; this reduces further; (Mac 2). On the Math Man program, P. J. stayed at level 1. 18 possible 8 errors= 10/18 56%
  1. MC. Let’s look at this again and do it the other way; multiply and multiply; 4 goes into both those. 2 X 4 goes into there 3 times. M. C. has a very difficult time transitioning to the computer activity without getting sidetracked, however, he did begin working on Mac Man—he appeared to enjoy it and did not want to stop when class time was over. (P.C. Mac Pam’s). 18 possible, 3 errors= 15/18 83%

The students will make corrections on Tuesday, then access the Math Man reducing fractions game.

  1. PJ. will get individualized assistance in making corrections.

Tuesday, 4-12-16

Today the students made corrections on their worksheets from the previous day. They enjoy using the game after making corrections, so this was motivational to them to finish their work.

On Day 7: students came to class and reviewed yesterday’s work, making any needed corrections and then logged onto Sheppardsoftware.com; Math Games and played Fractions Games.

When asked how they could use Fractions, some of their reply were: Measuring things, calculating how much is needed for something, money has fractions (cents of a dollar), how much to order….

Wednesday, 4-13-16

Lesson–How to subtraction Fractions:

4   3_ = 16 -____­­_____

3         4             12

First multiply the two denominators (3×4=12) put a line above the 12

Second multiply the top first numerator (4) by the second denominator (4) and put the answer (16) on the line above the 12, followed by a subtraction sign. Thirdly, multiply the first denominator (3) times the second numerator (3), and put the answer (9) above the 12, after the subtraction sign. Fourthly, subtract the numerators and put the answer over the denominator:

16-9 =       7

12 =          12             Then for reducing ask: Is there number that can fit into both

the numerator and denominator evenly?

Another Problem:

5 _ 1 =     15 – 6_ =   9__ = 1      

6    3 =           18      18       2       Reduce: The biggest number that can fit into

both the numerator and denominator evenly is 9.

  1. MC.—Is very focused on completing the radial fraction worksheet. It is common for M. C. to get off track; but not today. M. C. will need to reduce tomorrow.
  2. JW.—Is pushing himself to be fast at radial fractions; subtraction. J. W. needs to reduce several problems tomorrow.
  1. PJ.—Is very focused on completing the radial fraction worksheet—at a slower pace. (Home factors; health of grandpa.) Preston / Joseph need occasional support; 3 goes into this and 3 goes into that. P. J.–is focusing on completing the process of creating like denominators.  He finished half the page, and plans to finish and reduce them tomorrow.  His Uppi (grandpa) whom he lives with is experiencing serious health problems, and P. J. came to school tired; napped earlier.  He helps take care of his Uppi.

They are not familiar that reducing is part of the process. They get correct answers, but in trying to complete the pages in a hurry, they reduce quickly.

  1. TE.—multiply to get ready for fractions. (Serious attendance problems lately.)
  2. AI.—Came in 20 minutes late; multiply to get ready for fractions.

T.E.—multiplication page

As a side note: Older students: 9th grade students also participated in the radial math fraction activities; from a separate group. This is helping them to build their fluency and skill in reducing fractions. A. A., C. C., N. A.

On Thursday, April 14, the students will go back to these same math problems to reduce fractions they completed on Wednesday.

Students will go onto an internet site to practice math skills:

shepherdsoftware.com and choose Math Man (reducing fractions in ‘math games.’ This allows them time to practice reducing fractions fluently.

Students practiced reducing fractions with the computer software program. They challenged each other to try to get to level 7.

During the allotted time students remained on task and improved with practice.

Updating notes on Thursday, 4-14-16:

Students have earned time to play Math Man for tomorrow, 4-15-16.

First, M. C., P. J., & J. W., created common denominators on 4-13-16.

Second, M. C., P. J., & J. W., reduced fractions using the following process:

To scaffold learning for M. C., P. J., & J. W., I provided a color coded multiplication chart that is set up in a linear way visually so students could refer to it when they ask themselves the following question: How many times does 6 go into 42? Looking at the linear chart, with each multiplication set up in rectangles and divided up by colors for each (6x is green; 7x is yellow, etc.), it is visually easy to find the highest number that will go into a numerator and denominator to reduce:

6 X 0= 0

6 X 1= 6

6 X 2 = 12

6 X 3 = 18

6 X 4 = 24

6 X 5 = 30

6 X 6 = 36

6 X 7 = 42

etc.

  1. MC. Finishing radial fractions, subtraction page and reducing problems he had created common denominators for yesterday. He was able to stay on task and really looks forward to raising his reducing fractions game time tomorrow using Math Man. He is at level 5 in the game.
  1. PJ. When he came in, he completed the steps for creating common denominators, then reduced fractions. P. J. looks forward to using Math Man to reduce fractions tomorrow. He is at level 1 in the game.
  1. JW. When he came in, he was surprised at first to have his page handed back to him from yesterday. He apparently completed the page on 4-13 forgetting that creating common denominators and subtracting was not the final step, unless that fraction answer could not be reduced further. He is working to complete level 4 with a higher score and reaching level 5.

To Scaffold learning for T.E. & A.I.:

  1. TE. & A. I. Completed multiplication practice sheet, then used this sheet to multiply fractions for. Here are examples 10/1 X 7/13 = 70/13 (I wrote next to his answer 70 divide by 13 and other problems that needed to be turned into mixed fractions, rather than reduced); here is another example 7/1 X 7/10= 49/10 and 49 divide by 10—converting to a mixed fraction.

T.E. & A.I. To differentiate game time tomorrow, 4-15-16, these students will use math gaming that increases multiplication skills and fluency.

Thursday, 4-15-16

Today students went to http://www.sheppardsoftware.com/math.htm and clicked on Math Man. Rather than selecting reducing fractions, they selected mixed operations where they were challenged to work through basic equations using mental math to do so. P. J. and J. W. were challenging themselves to get through the problems quickly. The answers are posted on the Math Man icon, and each time they select a correct answer, they received points and the choices were narrowed down for them for the next problem to solve. M. C. worked on completing a math project for another class, since this was the last day he could finish it.

As the students played, I talked with each of them about what they would like to do next. P. J. and J. W. miss using the Dreambox math computer program. M. C. wants to focus more on the Aleks computer program to help him keep up in his other math class where they use this as a center. P. J. and J. W. want to use both math programs. J. W. showed to me a section he can work on within Aleks that has problems like, round this fraction to the nearest hundredth: 41/13 = 3.15. There is a calculator provided on the program page, so his focus is on the process of dividing 41 by 13 and considering what the nearest hundredth means. In Dreambox, the students used visual tools to see hundreds, tens, ones, as well as tenths and hundredths. I observed J.W. processing what his own error was when he first answered 3.1 . This gave me the confidence that combining programs that individualize for them and my own mini-lessons in the fractions unit are indeed a great combination over the long run.

As I consider where they are with reducing fractions through assessing their progress in a variety of ways, I want to make sure they become automatic in changing unlike denominators to like denominators and then reducing. The computer programs are individualized for each of their needs. I think we can alternate days where we continue the fractions unit through the end of the school year (with Culture week coming up, the end of school is fast approaching—about mid-May for them). We can also have computer program days. This sounds like a good balance for an Response to Instruction/Intervention (RTI) program for then.

After reconsidering, on Monday, 4-18-16, the students will review and then spend some time on Brainpop using the numberline fraction game; an idea I received from Amy after reading her post on 4-16-16 and trying out the game:  https://www.brainpop.com/games/battleshipnumberline/  This game will give the students a more focused way to see and ask questions about where a fraction with a smaller denominator number vs. a faction with a larger denominator number falls on a line.

A note on looking forward:  When they continue working on reducing fractions beyond this UbD plan, the students will also use worksheets from  http://themathworksheetsite.com numberline fraction worksheets to see whole numbers (inches) with fractions of inches.  I believe they will start out doing okay in the Brainpop battleship online game, then as it gets more challenging, I will bring out the more visual worksheets to use with them.  We will work through these together, as I have a SmartKapp that allows me to present the worksheet on the board, go through a think aloud with them, and then save that lesson in case I need to bring it back up to help them visualize the line on the battleship fractions numberline game.

On Tuesday, 4-19-16, they will take the post test.  The process used in the visual radial fractions strategy; like the examples provided above from what was presented on the board for their lessons; will need to be reflected in the post test. Since students actually focused a lot more on the process of converting unlike denominators to like denominators, than on the end goal of reducing fractions, this should become part of the post assessment to reflect this and be clearly distinguished from reducing.  Reducing will be derived from the actual answer they get after converting unlike denominators (and adding or subtracting them).

 Updating notes on Thursday, 4-14-16:

 Students have earned time to play Math Man for tomorrow, 4-15-16.

First, M. C., P. J., & J. W., created common denominators on 4-13-16.

Second, M. C., P. J., & J. W., reduced fractions using the following process:

To scaffold learning for M. C., P. J., & J. W., I provided a color coded multiplication chart that is set up in a linear way visually so students could refer to it when they ask themselves the following question: How many times does 6 go into 42? Looking at the linear chart, with each multiplication set up in rectangles and divided up by colors for each (6x is green; 7x is yellow, etc.), it is visually easy to find the highest number that will go into a numerator and denominator to reduce.:

6 X 0= 0

6 X 1= 6

6 X 2 = 12

6 X 3 = 18

6 X 4 = 24

6 X 5 = 30

6 X 6 = 36

6 X 7 = 42

etc.

  1. MC. Finishing radial fractions subtraction page and reducing problems he had created common denominators for yesterday. He was able to stay on task and really looks forward to raising his reducing fractions game time tomorrow using Math Man. He is at level 5 in the game.
  2. PJ. When he came in, he completed the steps for creating common denominators, then reduced fractions. P. J. looks forward to using Math Man to reduce fractions tomorrow. He is at level 1 in the game.
  3. JW. When he came in, he was surprised at first to have his page handed back to him from yesterday. He apparently completed the page on 4-13 forgetting that creating common denominators and subtracting was not the final step, unless that fraction answer could not be reduced further. He is working to complete level 4 with a higher score and reaching level 5.

To Scaffold learning for T.E. & A.I.:

  1. E. & A. I. Completed multiplication practice sheet then used this sheet to multiply fractions for. Here are examples 10/1 X 7/13 = 70/13 (I wrote next to his answer 70 divide by 13 and other problems that needed to be turned into mixed fractions, rather than reduced); here is another example 7/1 X 7/10= 49/10 and 49 divide by 10—converting to a mixed fraction.

T.E. & A.I. To differentiate game time tomorrow, 4-15-16, these students will use math gaming that increases multiplication skills and fluency.

This group unit will extend to Monday, 4-18-16 where it will end with a post test.

 4-19-16

 Specific Lesson Taught

 Patterns: 3/? = 9/18; 5/? = 10/12; 1/5=?/10

Add or Subtract Top Numbers

Bottom Number Stays The Same

The bottom numbers stay the same

1/12 + 4/12 = 5/12   (be sure to add)

5/8 – 2/8= 3/8   (be sure to subtract)

Reduce= Make Smaller:

5/10 divide by 5/5 ½

Computer Game Accessed:

https://www.brainpop.com/games/battleshipnumberline/

References

Battleship Fraction Numberline Game: https://www.brainpop.com/games/battleshipnumberline/

Aleta May’s Artifact Padlet Wall for Technology Embedded Within the UbD Fractions Unit:    

http://padlet.com/aleta_57/tq5v224rfbuk

Aleta May’s Artifact in Dropbox for Visual and Other Worksheets to Show Students’ Progress Through the UbD Fractions Unit and Differentiation:

https://www.dropbox.com/s/atgf5n5iorcpt63/Aleta%20May%27s%20EDET%20637%20Pre%20Posttest%20with%20progressive%20worksheet%20artifacts%20in%20between.pdf?dl=0

MobyMax Retrieved on 4-23-16 at: http://www.mobymax.com

Treff, A. V. and Jacobs, D. H. (2003). Basic Math Skills. Circle Pines, MN: AGS Publishing.

The Mathworksheet Site On-line Math Worksheet Generator at: http://themathworksheetsite.com

Resources Read for UbD Fractions Unit Planning:

Alaska English/Language Arts and Mathematics Standards pp. 144-162. Retrieved on 3-27-16 from:   https://education.alaska.gov/akstandards/standards/akstandards_elaandmath_080812.pdf

Childre, A., Sands, J. R., & Pope, S. T. (2009). Backward design. Teaching Exceptional Children, 41(5), pp. 6-14.

 Twitter Session References:

Hutchison, A. & Woodward, L. (2014). A planning cycle for integrating digital technology into literacy instruction. The Reading Teacher, 67(6), pp. 455-464.

Matuk, C. F., Linn, M. C, & Eylon, B. (2015). Technology to support teachers using evidence from student work to customize technology-enhanced inquiry units. Instructional Science, 43, pp. 229-257. Springer Science & Business Media B.V.

Meij (van der) , H. (2011). Learning from games: Does collaboration help?   British Journal of Educational Technology, 42(4), pp. 655-664. Wiley-Blackwell.

Rico, R. & Ertmer, P. A. (2015). Examining the role of the instruction in problem-centered instruction. TechTrends, 59(4), pp. 96-103.

 

Differentiation Reflection; Replies to Peers in EDET 637, and A Valued Comment from One for Week 12

 

Week 12 Reflection for Differentiating Instruction through Technology

Instructor: Dr. Lee Graham

April 17, 2016

By Aleta May

Amy made a response to my post as shown below. Her comment to me was extremely helpful. We both designed a fractions unit, although she designed hers for 3rd grade students and mine were for middle school students. There is much overlap in the concepts we taught, and this week she shared a Brain Pop Battleship game link in her post that I will use with students on Monday after a review for a Tuesday unit post test. I shared a link with her, mathworksheetsite.com that I will be using to create fractions, numberline worksheets for students to use in conjunction with the game—after they have tried the game without worksheets. My goal is for them to notice where fractions (with smaller and larger denominators) fit on a number line; as well as to use this as a concept that applies to using a tape measure for real world applications; such as a measurement for carpentry construction.

Catherine got me thinking about how our assessments are purposeful when we reflect on our teaching, using this as a tool for monitoring and adjusting our instruction, as well as for students to take responsibility for their own learning! Kate’s post reminded me of the importance of keeping work at an appropriate level of challenge for students (whether they were high or low in that particular skill at the time). This is where behavior comes in. When students are appropriately challenged, their behavior changes from acting out, withdrawing, etc. to engage in the activity and learning! They feel successful.

Anastasia’s work with moon phases is such a beautiful example of engagement! When we look at astronomy, we see how very big the universe around us really is. Such a study as hers brings out the natural curiosity and questions kids have, when we listen. Now we are learning, or relearning, as teachers, that we can group students to research different aspects within their own groups of a topic, and share with other groups—like reading parts of an article and sharing out with other groups—jigsaw reading, and reciprocal teaching/learning.

Larissa also bravely focused on science. I was so inspired by her salmon life cycle and how that reaches out beyond to an entire food chain, that I researched and found a site for her students to practice the vocabulary of the food chain, as well as finding 3 to 4 minute video clips that shows a bear (carnivore) in action and asked a question as to whether the seagull and hawk become decomposers when they clean up the bear’s leftovers. Sara showed us how to teach heat conservation through hands on model building and thermal building. Sara and I teach students from very similar cultures, and attendance plays a major role in how we teach an ongoing unit with “come and go” student participation. However, they were obviously very engaged when they were shown putting models together and speaking about their project.

There are more student peer projects I had the privilege to view and respond to. I have many educational websites bookmarked now, and I have learned so much from my peers in this class about how they apply the UbD plan. As I move forward to write my final reflection for this UbD unit and internship, I have a much better idea of where to focus my own. I got ideas for organizing my paper. Reflecting on many student projects this week provided me with a sharpened awareness of how to make appropriate connections between my UbD and the application of it through internship.

4-16-16 Amy’s Comment made to my Week 12 Blog Evidence Collected:

One Response to Week 12 Blog Evidence Collected for Final Project

  tessiesim says: 
. April 16, 2016 at 7:06 pm

Aleta, I see so many positive aspects of DI happening in your unit! I love how you state that on-task behavior is one way to see engagement and learning. I agree with this statement 100%, as this is something I normally struggle with in my math group, but I am seeing less behavioral issues currently with the UbD unit. You cite several examples of how you’re differentiating for your students (computerized games at different levels, multiplication facts work, individual teacher assistance with corrections) so that each can be successful. The fact that all are engaged and wanting to continue with the unit speaks to the fact that it is well planned and is meeting their needs. I like how you’re using their worksheets as formative assessments, helping you to plan the next day’s lesson. Your mention of a student’s grandpa being ill and this affecting his performance at school is an important reminder of how we have to consider students’ social/emotional needs as we plan our academics. It sounds like having a small group is letting you reach each student where they need it with fractions, and I like the way you highlighted specific evidence that shows learning.

Below are responses I made to several students in this week’s blog.

4-14-16

Catherine,

I think the real purpose of assessment is for both students and teachers. Students become invested in their own learning and can make suggestions to their teacher about what they need next in the learning process.

I found that by looking at their progress and talking with them about it, we needed to focus longer on the process of creating like denominators (and treating reducing fractions as a separate more detailed lesson step) a lot more than I had originally anticipated.

aletakmay

4-15-16 Kate,

The pretest really served your more advanced learner well! He/She was likely kept engaged by having an appropriate level of challenge. The way you focus their attention on the physical appearance of organisms and “who” is not in the micro-habitats seems interesting to me as well. Are they drawing the different organisms and labeling unique features in their journals?

I found that even during school, there are so many time constraints. My small math group will complete a posttest on Monday. My plan is to use the same test problems that were on the pretest, but I wonder if it would be best to have multiple levels of evaluating what they learned. Since they did not know how to consistently convert fractions with unlike denominators before adding and subtracting them, this should be analyzed just as deeply (if not more so) than the ultimate goal of being able to reduce them as well.

I wonder if you could write about their reactions to the book(s) you read to them, either during the reading itself or at the beach as they examined differences between organisms in Alaska and beaches in other places. This seems like an evaluation of their understanding as well.

April 15, 2016 at 8:51 pm

Anastasia,

I have been collecting the radial visual worksheets my small group has been working on as well.

What a great way to use a KWL chart—it is a reflection chart anyway. I remember using this in a small reading group that I taught as a weekly measure.

What do your students use to put the moon phases in order? If this unit continued over time and in winter when it gets so dark during the daytime, it would be awesome to have them take camera phones or iPads out to get snapshots of the moon phases and date them; then ask questions about which side of the moon is shadowed over.

aletakmay

4-15-16

Genevieve,

If students were to bring their own device (BYOD), would they be able to incorporate Google maps onto these? I know some schools have a policy for BYOD, this might be a good example for the advantage of having their devices with them. Or was it an Internet filtering issue that you weren’t able to incorporate Google maps on the iPads?

What an excellent idea to incorporate art into your science lesson! When they matched the stages of the fish’s life cycle to definitions, they were getting plenty of practice with the vocabulary. This lesson will cross over into biomes (like the river, and on out into the ocean) where they will study the big picture of how each life cycle impacts the life cycle of other creatures.

The pictures with the sentences are so awesome! The matching stages of the life cycle to the definition is cool too.

I have not tried scanning in and attaching anything to the WordPress blog yet. It looks great! Thank you for providing that example.

APRIL 15, 2016 AT 9:05 PM

4-16-16 Sara,

I’m really glad I watched the watched the video link you put up about what you would have the students build. Now when I view your students insulating a house, I felt so proud for / with you.

We have attendance problems in our village school as well. Last month it was pike fishing. The ducks, geese and swans are just showing up since the middle of last week. Hunting for eggs. bird hunting. Our attendance sheet has—hunting, slept somewhere (meaning landed at a cousin’s house, stayed up late and sleeping in), and coming.

One student in my group is coming in tired. He lives with grandma/grandpa. Grandpa had a stroke recently and the student does a lot to take care of him. One girl told me last year that she stayed up all night to watch her grandma as she slept because she was afraid to sleep without being watched.

But—I must say, the video and pictures you posted speak a 1,000 words each. The students are engaged. They are willing to let you give them a sentence starter prompt to help them focus their speech on the content of the project and the why. We have very, very intelligent, kids, Sara J

But teaching around their lifestyle caused me to extend my unit a bit as well. I started a bit early to get that pretest data. And Monday will be review and post test. Out of 6 students, I am glad we only need to focus our assessment on 3. At this point, I have 3 students who are there consistently and can do this level of basic fractions work. My other 3 come and go, and 1 of these acts out a lot—so they are working on multiplication fluency and applying that to multiplying fractions now. Took some time, but I figured out what to do with them.

With your students building a project—it would be much more difficult to see the project partially built, and no student(s)! They are getting the concept of keeping the thermal energy in, from what the young man in the video spoke.

4-16-16

Amy,

The journals they had for reflecting their understanding makes me think about how important this step is. It is like they are going back and teaching themselves what they learned by writing or drawing what they learned. This helps students cement (fix) the understanding into their memory. The cake example is definitely something they can visualize in their mind; then hearing another student say that he wanted the piece with the smaller denominator brings their mind to a birthday party to ask themselves, “Why would this guy want that piece? He loves cake!”

Thank you for sharing the Brainpop Battleship numberline page idea. This looks fun. I work with students of a variety of ages. At http://themathworksheetsite.com numberline fraction worksheets can be downloaded.

The exit slip information that speaks to focusing on vocabulary sounds like perfect feedback. Since students were engaged, the one blurting out may be trying to get attention in part because students are more focused on the work than him/her.

The sentence frame you provided is excellent. Writing and speaking are both expressive forms of communication, so using that sentence frame for both connects their ability to see how these two are related. So often students will say, “I don’t know what to write.” Getting them to tell me what they are thinking is the start, as I start a word bank from their own speech, then we go back and write sentences.

For my older students who are learning very similar concepts, but being pushed at a higher rate, they gave me feedback yesterday that they miss the Dreambox math program we were using just before this unit. I am figuring out ways to use some of the time for this, another popular computer program called Alex, and continue converting and reducing fractions. The computer programs are individualized, so that is important as well to cover concepts they need to fill in the gaps they missed as building blocks for more math learning. The brainpop battleship numberline game has levels as well. This individualizes learning for your students.

4-16-16

Sally,

The Pizzaz self-correcting worksheets are a great tool that avoids that circular effect of having students say, I’m done, turn it in, only to have to receive it back for making corrections—when students are rushing through work. However, it is true, that catching their actual errors helps identify exactly where the misunderstandings in math are, so the teacher can use a think-aloud lesson to walk them through the process. One thing about math, is that we don’t want them to practice errors, because going back and undoing the habit of doing it the incorrect way is hard to reconcile.

Maybe your student who did not want to make the corrections could see (but maybe not admit to you) how important it is to get the order of operations down as you take them to the next level. The students exceeded your expectations—nice!

I have a student who “shuts down” in math too. He will work if it has a low enough challenge for him—he improves at a much more gradual rate. The option is that he will refuse to work; and even start damaging items in the room. Although I realize his behavior is not only a result from math, but from live at home as well, I am thinking about why so many of our middle school students are behind in math. All I really need to do is take a look at that spiral math curriculum program they were in during previous years. It was supposed to teach concepts, vocabulary, and revisit concepts learned—but the revisiting does not happen soon enough, and concepts are not mastered before moving on. The concepts are better learned on Dreambox math program, in my opinion.

Sounds like you have done an excellent job of communicating to the students that they Can do it!

4-16-16

Sarah,

The different scaffolding levels for the practice sheets are an excellent way to differentiate. What a great variety of assessments!

My unit is going into next week as well. As I think about it, they will need Monday to review, before giving the post test on Tuesday.

4-16-16

Larissa,

I have never heard of the traffic light system. What a great way for students to find out who may help them. Communicating with colors is so quick and the ask 3 before me tends to create wandering around the classroom without any real knowledge of who to ask. Greens could also seek out the yellows, and the teacher may focus on a small group mini-lesson with the red group.

I found this at Bright Hub Education that has animal pictures next to the definition: http://www.brighthubeducation.com/science-homework-help/47420-food-chains-and-food-webs/

I found this also: https://www.spellingcity.com/view-spelling-list.html?listId=6074868   There is a list of words under 3rd grade: decomposer, transfer, producer, herbivore, carnivore, compete, omnivore, and food chain. I tried clicking on ominivore—and it said click to get a quick lesson. There is a brief podcast that explains what it means. I clicked on flashcards, and print—it gave options like front side, flip side, definition, sentence, etc. Here is what it gave me when I clicked: https://www.spellingcity.com/flashcards-spelling-game.html

They could play an inside-outside circle game (from Kagan) to practice the vocabulary. Here is the site with detail directions: http://wvde.state.wv.us/strategybank/Inside-OutsideCircle.html

There is a game feature here as well. I clicked on the test and teach game. The game was focused on spelling—carve out Mt. https://www.spellingcity.com/tnt-spelling-game.html When it gives me the word, it says the word, uses it in a sentence, then I type in the spelling word (producer, compete, transfer (sun’s energy/photosynthesis), herbivore, foodchain (the food chain involves transfer of energy between predator and prey), carnivore (uses it’s teeth to tear meat), decomposer (is typically a fungus that …); I got a score of 7/8 88% and an option to play Again or play another game. There is an online wordsearch as well. What I really wanted was

Although you have already thought of this and applying wordparts to actually understanding the food chain can be difficult to transfer, I think teaching the word vore = eat and teaching herbi = plant, carni = animal with teeth, etc. could really help as well.

http://explore.org/live-cams/player/brown-bear-salmon-cam-brooks-falls

http://video.nationalgeographic.com/video/weirdest-salmon?source=searchvideo

This one is a perfect 3 min video that shows salmon jumping, salmon under water, spawning, baby fry; a hawk coming in to clean up (likely ran off the seagulls), http://video.nationalgeographic.com/video/weirdest-salmon?source=searchvideo

http://video.nationalgeographic.com/video/salmon_sockeye?source=searchvideo

This one shows the bear’s feet in the water trolling for fish. Once they start their own journey, the sockeye start to digest their own skin (although my husband, who used to be a commercial salmon fisherman, does not believe this; LOL, he likens this to a banana turning brown, and it is not because it digests its own skin).. It shows a female thrashing out a nest, laying thousands of eggs (return run in 5 years lowers odds of survival). Their death provides the gift of life

http://kids.nationalgeographic.com/explore/nature/live-cam-brown-bears/ If you have a smart board, this brown bear can be seen catching salmon – Pre-recorded live cam.

This is an off season view of Brooks Falls These 5 or 6 bears are patient carnivore predators. I wonder what those seagull predators are waiting for? Are segulls kind of like decomposers when they eat the left over salmon guts the bears leave behind?

http://video.nationalgeographic.com/video/alaska-salmon-forest-lex?source=searchvideo

Southeast Alaska Salmon Forests—ecosystems, original predator/prey eco system.   Salmon are born in fresh water, go to ocean then

Trees and forests are nourished by fish when they die. Fish nourish next generation of fish.

AT: http://www.nwf.org/Wildlife/Wildlife-Library/Amphibians-Reptiles-and-Fish/Chinook-Salmon.aspx I found what Chinook salmon eat: Diet:  Young Chinook salmon will eat small invertebrates, including crustaceans, and amphipods. Adult salmon dine on smaller fish.

http://www.defenders.org/salmon/basic-facts

Diet

In general, young salmon eat insects, invertebrates and plankton; adults eat other fish, squid, eels, and shrimp. Unlike all other salmon, the sockeye salmon has a diet that consists almost entirely of plankton.

Aleta May 4/16/2016 10:18:00 am

Sara,

I’m really glad I watched the watched the video link you put up about what you would have the students build. Now when I view your students insulating a house felt so proud for you.

We have attendance problems in our village school as well. Last month it was pike fishing. The ducks, geese and swans are just showing up since the middle of last week. Hunting for eggs. bird hunting. Our attendance sheet has—hunting, slept somewhere (meaning landed at a cousin’s house, stayed up late and sleeping in), and coming.

One student in my group is coming in tired. He lives with grandma/grandpa. Grandpa had a stroke recently and the student does a lot to take care of him. One girl told me last year that she stayed up all night to watch her grandma as she slept because she was afraid to sleep without being watched.

But—I must say, the video and pictures you posted speak a 1,000 words each. The students are engaged. They are will to let you give them a sentence starter prompt to help them focus their speech on the content of the project and the why. We have very, very intelligent, kids, Sara ☺

But teaching around their lifestyle caused me to extend my unit a bit as well. I started a bit early to get that pretest data. And Monday will be review and post test. Out of 6 students, I am glad we only need to focus our assessment on 3. At this point, I have 3 students who are there consistently and can do this level of basic fractions work. My other 3 come and go, and 1 of these acts out a lot—so they are working on multiplication fluency and applying that to multiplying fractions now. Took some time, but I figured out what to do with them.

With your students building a project—it would be much more difficult to see the project partially built, and no student(s)! They are getting the concept of keeping the thermal energy in, from what the young man in the video spoke.

 

 Jeff,

By having students watch you create examples, they could see someone think the steps out loud (think-aloud strategy). Then the step-by-step instructions brought them to trying it out together. The real world connections is what has been missing in math classes for so many years. I think textbooks try to cover this in the for of problem solving, but researching from preselected destinations is so much richer. Your group configuration seems so perfect.

When we are more observant of the processes are students use to get answers (right or wrong), we learn so much about how to analyze problem solving from the perspective of the student.

The way students come to you for making revisions and listen as you show them what they need to do to correct posters also shows you have built trust with them. I think going back and working on those errors is the teaching deeper rather than wider concept. Another way to word this is teaching to mastery. This seems especially important in content areas where one skill relies on a solid understanding of a lower skill.

The headings you used help me think about how to organize my final reflection.

4-17-16

Teresa,

As a special teacher, I was taught to analyze each math problem when I gave the Woodcock-Johnson test for academic achievement, the Key Math test, or other standardized individualized assessment. The overall score is more for norming (comparing with average scores across the country). To write the goals and annual objectives, and from there the group work sample plan, which resembles an UbD plan, we analyzed how the student came up with their answer (whether it was an error or not an error). The process for getting there speaks volumes about where misunderstands come from. Particularly, if the problem completed was a word / story problem, we asked ourselves to analyze the process they used in order to make a plan for taking them from what they know to perhaps an easier strategy for completing those problems. One standardized test I used to give even gave a rubric for helping the person giving the assessment to watch for certain steps students took. We were taught to observe the child’s behavior—finger counting (vs. automaticity) and getting lost in the process, mental math skills used that showed that the student almost came to the correct answer (therefore, the need would be not to focus on the process here, rather checking for ones own accuracy—self checking and awareness).

As I read about how you analyzed the pretests, this is exactly what special education teachers in my program were taught to do. Providing them with “scaffolding during the unit which consisted of and modeling and explicit mini-lessons” is using that information you gained from your analysis to teach and pair students up with one that can help them learn.

Isn’t the feedback and encouragement you provided what gives the student the ability to believe in themselves? I can hear a child thinking something like, “the teacher believes in me, I must be able to do this; she is sitting here patiently helping me!” This is contagious in a classroom too. Students mimic our attitude; in some cases, they may simply calm down in the positive environment that believes in each child’s ability to grow!

Any time you can get kids motivated to “read it again,” you are teaching them real comprehension skills—clarifying understanding! Thank you for the app idea: https://www.speakaboos.com I’ve already shared this with our full time sped teacher and daughter.

Week 12 Blog Evidence Collected for Final Project

Week 12 Blog                                                                                                                                                   EDET 637: Differentiating Instruction through Technology                                               Instructor: Dr. Lee Graham

By Aleta May

Essential question: What evidence am I collecting for my final project – and for what purpose?

The most obvious evidences are: pre- post- tests, a few screenshots of computer gaming levels / playing for padlet.com link, observation notes, and daily worksheets. On task behavior was not formally tracked, but was noted in observation notes.

We went from adding and reducing to subtracting & reducing fractions. Focused on a specific game.

As of 4-13-16, Students are getting the concept of adding and subtracting fractions with unlike denominators; but they are still having trouble with reducing. I will continue working on this with them next week, even though I know they are improving.

The kinds of evidence of contributing to individual learning paths are as follows: First, I have a small group, so it is easier to go from student to student. Second, checking their paper/pencil work regularly as soon as they leave gives me feedback for what to emphasize the next day. Third, I watch them as they play the reducing fractions game to see them move on to different game levels.

Evidence that students are being given individualized learning paths are staying on the same basic concept of adding fractions with unlike denominators; then gradually going into subtraction, all the while reducing. Some students seem to want to complete the entire sheet, even knowing they will be asked to go back to reduce these the next day. They are not penalized for this, since the entire concept of adding/subtracting fractions with unlike denominators was either new to them, they forgot what they had learned in the past, or they simply added denominators to get the same denominator in their answers. Then reducing fractions is yet another step for them. As long as they are focused, the pressure is not who gets what first, rather, the focus is on learning and progressing daily.

The pillar that bears the most weight of evidence of learning are the pre- and post-tests; as well as the fact that they are staying so on task! On task behavior is one definition of engagement and learning.

One way I am scaffolding learning is to have three students who need to learn their multiplication tables fluently are working on these to prepare them for adding and subtracting fractions with unlike denominators. As they learn multiplication tables, they will now, start multiplying fractions and using their multiplication chart to assist with this. Further, scaffolding is allowing students to focus on the process of creating like denominators; then the process of reducing after—either one problem at a time or step one for all the problems then step two.

The kind of growth I expect on my post-test, based on observation and daily worksheet checks is; with such a short time frame for the unit, they will grow in creating common denominators—and hopefully reducing fractions as well.

This is how the unit is set up:

Day One PreTest

Day Two Multiplication Facts/Practice

Day Three Computer Fractions Game

Day Four Adding Fractions Worksheet

Day Five Computer Reducing Fractions

Day Six Reducing/Adding Fractions Worksheet

Day Seven Computer Adding Fractions Game

Day Eight Subtracting Fractions

Day Nine Computer Subtracting Fractions Game

Day Ten PostTest

Evidence is collected daily through worksheets; teacher observation and reflections of the help needed; pre- post-test; and a padlet.com wall with screenshots of their Sheppardsofware.com fractions game.

http://www.sheppardsoftware.com/mathgames/fractions/mathman_reduce_fractions.htm

See level screenshots at:  http://padlet.com/aleta_57/tq5v224rfbuk

3-28-16

Pre-Test: 20 problems possible

Turn in assignment, then practice identifying types of fractions at:  http://coolmath-games.com/0-fraction-splat

J. W.:     6/20

P. J.:     14/20

M. C.:   15/20

A. I.:       6/20

T. E.:     4/20

4-4-16

Students will go onto an internet site to practice math skills:  shepherdsoftware.com   choose ‘math games’

Students practiced reducing fractions with the computer software program. They challenged each other to try to get to level 7

During the allotted time students remained on task and improved with practice.

Ongoing Concept the students are learning: We don’t have to reduce any more because you cannot reduce 5/8.

Weekly summary notes for the dates 3-28 through 4-1 and 4-4-4-8 are in the blog for Week 11.

Monday, 4-11-16

Math Has Problems:

3/6= 1/2               1/3 + 1/7 = 7+ 3  /2

2/4= 1/2                1/2+ 1/5 = 5 + 2  /10

8/10  = 4/5           4/8 + 1/8 = 5/8

Practice and review

T.E. is getting his multiplication skills up in order to prepare for fractions reducing.  Sheppardsofware.com

J. W. 2 goes into 2 how many times so right here we put 2 over 2; what number goes into these; what number goes into those; how many times does this number go into this? Multiply the bottom; now we need to multiply the top. He got to level 4 on Math Man, then restarted (WTL18) 18 possible, 3 errors= 15/18 83%

P. J. This number reduces further; this number has to be the same, if you divide the top, then the same for both numbers; this reduces further; (Mac 2). On the Math Man program.  P. J. stayed at level 1. 18 possible 8 errors= 10/18 56%

M. C. Let’s look at this again and do it the other way; multiply and multiply; 4 goes into both those. 2 X 4 goes into there 3 times. M. C. Has a very difficult time transitioning to the computer activity without getting sidetracked, however, he did begin working on Mac Man—he appeared to enjoy it and did not want to stop when class time was over. (P.C. Mac Pam’s). 18 possible, 3 errors= 15/18 83%

The students will make corrections on Tuesday, then access the Math Man reducing fractions game.

P. J.  will get individualized assistance in making corrections.

Tuesday, 4-12-16

Today the students made corrections on their worksheets from the previous day. They enjoy using the game after making corrections, so this was motivational to them to finish their work.

On Day 7: students came to class and reviewed yesterday’s work, making any needed corrections and then logged onto Sheppardsoftware.com; Math Games and played Fractions Games.

When asked how they could use Fractions, some of their reply were: Measuring things, calculating how much is needed for something, money has fractions (cents of a dollar), how much to order….

Wednesday, 4-13-16

How to subtraction Fractions:

4/3 – 3/4_ = 16 -_   /12

First multiply the two denominators (3×4=12) put a line above the 12.  Second multiply the top first numerator (4) by the second denominator (4) and put the answer (16) on the line above the 12, followed by a subtraction sign. Thirdly, multiply the first denominator (3) times the second numerator (3), and put the answer (9) above the 12, after the subtraction sign. Fourthly, subtract the numerators and put the answer over the denominator:

     16-9    / 12      =       7/12

Then for reducing ask: Is there number that can fit into both the numerator and denominator evenly?

Another Problem:

5 /6- 1/3 =     15 – 6_ /18 =   9/18 = 1 /2

Reduce: The biggest number that can fit into both the numerator and denominator evenly is 9.

M. C.—Is very focused on completing the radial fraction worksheet. It is common for M. C. to get off track; but not today. M. C. will need to reduce tomorrow.

J. W.—Is pushing himself to be fast at radial fractions; subtraction. J. W. needs to reduce several problems tomorrow.

P. J.—Is very focused on completing the radial fraction worksheet—at a slower pace. (Home factors; health of grandpa.) Preston / Joseph need occasional support; 3 goes into this and 3 goes into that.  P. J.–is focusing on completing the process of creating like denominators.  He finished half the page, and plans to finish and reduce them tomorrow.  His Uppi (grandpa) whom he lives with is experiencing serious health problems, and P. J. came to school tired; napped earlier.  He helps take care of his Uppi.

They are not familiar that reducing is part of the process. They get correct answers, but in trying to complete the pages in a hurry, they reduce quickly.

J. E.—multiply to get ready for fractions.  (Serious attendance problems lately.)

T. E.—multiply to get ready for fractions.

A. I.—Came in 20 minutes late; multiply to get ready for fractions.

As a side note: Older students: 9th grade students also participated in the radial math fraction activities; from a separate group. This is helping them to build their fluency and skill in reducing fractions. A. A., C. C., N. A.

On Thursday, April 14, the students will go back to these same math problems to reduce fractions they completed on Wednesday.

Students will go onto an internet site to practice math skills:  shepherdsoftware.com   and choose Math Man (reducing fractions) in ‘math games.’  This allows them time to practice reducing fractions fluently.

Students practiced reducing fractions with the computer software program. They challenged each other to try to get to level 7.

During the allotted time students remained on task and improved with practice.

Updating notes on Thursday, 4-14-16:

Students have earned time to play Math Man for tomorrow, 4-15-16.

First, M. C., P. J., & J. W., created common denominators on 4-13-16.

Second, M. C., P. J., & J. W., reduced fractions using the following process:

To scaffold learning for M. C., P. J., & J. W., I provided a color coded multiplication chart that is set up in a linear way visually so students could refer to it when they ask themselves the following question: How many times does 6 go into 42? Looking at the linear chart, with each multiplication set up in rectangles and divided up by colors for each (6x is green; 7x is yellow, etc.), it is visually easy to find the highest number that will go into a numerator and denominator to reduce.:

6 X 0= 0

6 X 1= 6

6 X 2 = 12

6 X 3 = 18

6 X 4 = 24

6 X 5 = 30

6 X 6 = 36

6 X 7 = 42

etc.

M. C. Finishing radial fractions, subtraction page and reducing problems he had created common denominators for yesterday. He was able to stay on task and really looks forward to raising his reducing fractions game time tomorrow using Math Man. He is at level 5 in the game.

P. J. When he came in, he completed the steps for creating common denominators, then reduced fractions. P. J. looks forward to using Math Man to reduce fractions tomorrow. He is at level 1 in the game.

J. W. When he came in, he was surprised at first to have his page handed back to him from yesterday. He apparently completed the page on 4-13 forgetting that creating common denominators and subtracting was not the final step, unless that fraction answer could not be reduced further. He is working to complete level 4 with a higher score and reaching level 5.

To Scaffold learning for T.E. & A.I.:

T. E. & A. I. Completed multiplication practice sheet, then used this sheet to multiply fractions for. Here are examples 10/1 X 7/13 = 70/13 (I wrote next to his answer 70 divide by 13 and other problems that needed to be turned into mixed fractions, rather than reduced); here is another example 7/1 X 7/10= 49/10 and 49 divide by 10—converting to a mixed fraction.

T.E. & A.I. To differentiate game time tomorrow, 4-15-16, these students will use math gaming that increases multiplication skills and fluency.

This group unit will extend into Monday, 4-18-16 where it will end with a post test.

To Scaffold learning for T.E. & A.I.:

A. E. & A. I. Completed multiplication practice sheet, then used this sheet to multiply fractions for. Here are examples 10/1 X 7/13 = 70/13 (I wrote next to his answer 70 divide by 13 and other problems that needed to be turned into mixed fractions, rather than reduced); here is another example 7/1 X 7/10= 49/10 and 49 divide by 10—converting to a mixed fraction.

T.E. & A.I. To differentiate game time tomorrow, 4-15-16, these students will use math gaming that increases multiplication skills and fluency.

Thursday, 4-15-16

Today students went to http://www.sheppardsoftware.com/math.htm and clicked on Math Man. Rather than selecting reducing fractions, they selected mixed operations where they were challenged to work through basic equations using mental math to do so. P. J. and J. W. were challenging themselves to get through the problems quickly. The answers are posted on the Math Man icon, and each time they select a correct answer, they received points and the choices were narrowed down for them for the next problem to solve. M. C. worked on completing a math project for another class, since this was the last day he could finish it.

As the students played, I talked with each of them about what they would like to do next. P. J. and J. W. miss using the Dreambox math computer program. M. C. wants to focus more on the Aleks computer program to help him keep up in his other math class where they use this as a center. P. J. and J. W. want to use both math programs. J. W. showed to me a section he can work on within Aleks that has problems like, round this fraction to the nearest hundredth: 41/13 = 3.15. There is a calculator provided on the program page, so his focus is on the process of dividing 41 by 13 and considering what the nearest hundredth means. In Dreambox, the students used visual tools to see hundreds, tens, ones, as well as tenths and hundredths. I observed J.W. processing what his own error was when he first answered 3.1 . This gave me the confidence that combining programs that individualize for them and my own mini-lessons in the fractions unit are indeed a great combination over the long run.

As I consider where they are with reducing fractions through assessing their progress in a variety of ways, I want to make sure they become automatic in changing unlike denominators to like denominators and then reducing. The computer programs are individualized for each of their needs. I think we can alternate days where we continue the fractions unit through the end of the school year (with Culture week coming up, the end of school is fast approaching—about mid-May for them). We can also have computer program days. This sounds like a good balance for an Response to Instruction/Intervention (RTI) program for then.

After reconsidering, on Monday, 4-18-16, the students will review and then spend some time on Brainpop using the numberline fraction game; an idea I received from Amy after reading her post on 4-16-16 and trying out the game:  https://www.brainpop.com/games/battleshipnumberline/  This game will give the students a more focused way to see and ask questions about where a fraction with a smaller denominator number vs. a faction with a larger denominator number falls on a line.

A note on looking forward:  When they continue working on reducing fractions beyond this UbD plan, the students will also use worksheets from  http://themathworksheetsite.com numberline fraction worksheets to see whole numbers (inches) with fractions of inches.  I believe they will start out doing okay in the Brainpop battleship online game, then as it gets more challenging, I will bring out the more visual worksheets to use with them.  We will work through these together, as I have a SmartKapp that allows me to present the worksheet on the board, go through a think aloud with them, and then save that lesson in case I need to bring it back up to help them visualize the line on the battleship fractions numberline game.

On Tuesday, 4-19-16, they will take the post test.  The process used in the visual radial fractions strategy; like the examples provided above from what was presented on the board for their lessons; will need to be reflected in the post test. Since students actually focused a lot more on the process of converting unlike denominators to like denominators, than on the end goal of reducing fractions, this should become part of the post assessment to reflect this and be clearly distinguished from reducing.  Reducing will be derived from the actual answer they get after converting unlike denominators (and adding or subtracting them).

Reflecting on Weekly Class Twitter Session and WordPress Blogging

Reflection for Week 11

Aleta May

Differentiating Instruction through Technology EDET

Instructor: Dr. Lee Graham

Reflecting on Weekly Class Twitter Session and WordPress Blogging

During the Twitter Session this Week :

By learning to use TweetDeck for weekly Twitter sessions, I was able to schedule with two colleagues, Amber Novak (from another state location) and Jeff Clay, to host the last week of class. I feel empowered now to communicate with teachers “the modern way.”

One very important point was made: I wanted to figure out how to find time to reflect on student learning throughout the unit. What came to my mind was to use some class time to model writing a reflection on my teaching, while asking students to write a reflection on their learning. Dr. Graham wrote that this is an idea that she has applied and that she learned it from Nancy Atwell. As I think back to my Reading Specialist training, I remember watching DVDs of Donald Graves. He taught that the best way to teach writing is to model writing as an adult; such as using a mini-lesson think-aloud approach. He also spoke about just writing in class while students write. So if I want to teach students to reflect on their learning, I need to model this for them.

We also discussed the value of teaching deeper, rather than wide/broad. We tend to feel the push as teachers to cover the curriculum. It is important to touch on as much of that curriculum that is tied to the standards as is possible, but it is not possible to try to make kids learn faster than they are ready to learn. We can engage, motivate, redesign instruction, and review—all with a forward momentum. But particularly in subject areas, such as the fractions unit my students are learning, it does no good to move on if they do not have the foundations down yet! I commented that we need persistence without frustrating our students.

Week 11 Blog Reflection:

As I read through the blogs of other students in my class, I learned about many different ways that teachers use the UbD planning method to bring out student-centered learning approaches. A common theme through the posts that I noticed was how students overall are still not accustomed to taking charge of their own learning. Sometimes I believe I am behind on this, but what I notice is that we are all in the same boat. As teachers, we may be at different points of facilitating, rather than using authoritarian approaches to teaching and learning. I think we work within a system that is experiencing change, yet at the same time budget cuts and higher expectations. It may seem easier to teach in a way that makes students more responsible, but the time involved is as intensive, if not more so, than teaching and expecting students to learn and apply with little support. As a facilitator of learning, we now focus our energies on using a variety of tools and platforms to reach students who come from a very wide range of backgrounds; ethnically, monetarily, ability and life experiences that allow them to visualize what they are learning to add to old schema.

Here are the responses I made to blog posts this week:

Jeff,

First, the structure of your paper makes me think about how to write my final reflection!

Challenges

Making connections from math work in direct instruction, technology and project work may seem unclear to students if they have not previously received such awesome instruction as what you are providing to them.

Maybe a block schedule would work better. I realize you do not have control over this, but many times it seems that a 50 minute class timeframe forces teachers into either/or situations; i.e., either we will go over the work to make it more clear, or get into the projects; and getting into projects means being interrupted to go to the next class when students are just getting into the project.

They are learning very valuable skills by inserting equations and tables into Microsoft Word documents; function tables and graphs. I’ve not heard of the Snipping Tool before! The technology skills are real world skills. I wonder if a small business owner or a manager in charge of creating charts for end of year tax reports for their business could come in and talk about how they make proposals communicating this way.

Successes

When giving direct instruction, what a great way to monitor and adjust! Once students stopped focusing on the instruction, this seems like the perfect time to have students pause to work together in groups to apply previous (or current) learning. I think when students feel successful at teaching others, they want to get up and go to other groups to share their understanding. Although it is important to redirect students to stick with their groups (sometimes because of the number of students in class), it looks like a good sign that students felt good about what they understood and wanted to help others.

I appreciate your sharing how some students kept that rubric right next to them as a guideline.

Evidence of Scaffolding

I know I like examples as an adult student! I’m sure your students appreciated the example. Over time, they can branch off and create their own examples. I’m thinking of the online mind mapping tools out there. Maybe they could use MindNode to explain the steps they used as a group to create their charts or solve problems.

Evidence of Planning

I think the letting go as a dispenser of knowledge is what students initially fear—just like us, they are so used to the traditional forms of instruction, that they likely react in ways that seem like they are confused, frustrated, or lost. Now that they’ve experienced this style of learning, going back to traditional methods will likely not satisfy them anymore.

Evidence of Using Data from Observations and/or Surveys

The posters will provide all the evidence of their engagement and application of learning.

Larissa,

I notice this in my own teaching as well—when I don’t let students in on what my goals or objectives are for them, they question me more as to why we are doing this. This is a legitimate question on their part. This used to be relegated to “teachers only.” Students were not supposed to question why they are learning this or that, they were just supposed to do it. I think we are still recovering from being taught this way and it impacts our practice today.

Catherine,

I think they call this interactive notebooks—as they place their work in it becomes a reference notebook for review and a tool to share with others. It is also so impressive that some students took off on the project on their own, leaving you time to help other students who were still unclear about the concept individually.

So cool—a theorem tattoo! This got their attention—and got them right back into noticing the need to use a ruler and grid paper to redesign a tattoo picture to scale. Yay, you got to keep your computers—no AMP. I looked up Mangahigh. This site looks fun! Thank you for sharing.

https://www.mangahigh.com/en-us/

Good idea having students use a Prezi site to learn from. I wonder if they could create a better Prezi for teaching other students out there what they learned in a much more inviting step-by-step student friendly mode of learning.

The exit tick with four quick questions sounds like a perfect way to check their understanding, and to reinforce to them what they now understand.

Kate,

What a great opportunity for the kindergarten student to learn from the 3rd grade student; differentiation right off!

The way you had them using their tablets and your camera to take pictures at the beach for observation, data collection is such a meaningful way for students to learn. The kindergarten student using the text app to record his observations sound like a perfect way for him to go back later and review what he saw in real time.

Incorporating children’s literature to teach science is so important. The way you used “What’s in the Tide Pool” to compare and contrast tide pools in the book to tide pools in Sitka is exactly how thematic approaches to learning take place! Science, non-fiction literature, recording/writing to compare and contrast, and incorporating technology tools to document research are learning that makes sense! It is holistic and meaningful. Thank you for sharing.

Amy,

It is interesting that many of your students, and even more so with three of your students, could communicate through drawing what they understood about fractions, but did not know how to explain in writing or orally about their learning. But this is why we are being taught to have students engage more with each other as we facilitate learning. What you are doing with them by having them talk about and write out what they know or need to know is so valuable. I know with our English Language Learners (ELLs), we use a lot of sentence frames to get them started. I think students who are not ELLs benefit from this strategy as well.

We have noticed in our school that students had not learned to help each other or to work independently; so this became a major district wide plan for improving instruction. Our dual language program reflects this by pairing students into bi-lingual pairs.

Folding shapes seems to be a perfect way to get kids to work together, help each other and talk about what they are doing. I believe your persistence will pay off. In fact, they are showing this in their reflective journals after only a couple of days. I use prompts and scribing to help kids see that writing is often just putting down in words what you explain verbally to the teacher and ultimately to each other.

Our ELLs struggle with the vocabulary piece as well. Where we live means that we may need to use different items than what is normally shown in a textbook or online lesson to communicate dividing a whole into fractional parts. The hands on activities sound so inviting.

Week 2 & Planning for Week 3 of Fractions Unit

Week 11 Blog for EDET 637: Differentiating Instruction through Technology

Instructor: Dr. Lee Graham

by Aleta May

Week 2 of Fractions

Steps given by EDET 637 rubric are included as I respond, and reflect from week 2 then plan for week 3:

Students will go onto an internet site to practice math skills:

shepherdsoftware.com   although there is some choice involved when using a variety of sites, the main focus at this point is more specific, at this site, students went to Math Man (a branch off of the former Pac Man game) during the end of week one and more so during week two: http://linkis.com/sheppardsoftware.com/vXPu1

Students practiced reducing fractions with the computer software program. They challenged each other to try to get to level 7.

During the allotted time students remained on task and improved with practice.  Make notes for yourself as you teach your unit this week. How did things go?

I was surprised to see how fast students caught on to the first step of adding fractions.

Was it as expected?

It went better than expected.

 What challenges did you see?

I found that the students followed the first steps and are ready for the second step: Reducing, which includes dividing the top and bottom numbers by a common denominator.

Did you see evidence of learning?

Yes!

 What was this evidence?

Students followed one-step rules in week 1.

Will you need to change the unit in some way for the second week? I will only add step two, the reducing fractions this week and see how well they can follow a two-step rule.

During the pretest I gave no help, support, or directions. During the first week of assignments, I demonstrated on the white board a simple method of adding fractions with out asking students to ‘reduce or simplify their answers.  – So, you need to make notes of the way that you helped individual students as they pursued their learning path (how your “scaffolded” student learning).

During actual assignment time, after demonstrating at the white board, I sat with the students looking busy. They would ask, “Is this right? Am I doing it right?”

 This is the support that new learners need to become expert in their new knowledge. So if a student asks for assistance – why did this happen? Was it appropriate at the time?

This is the normal method I use to energize and help students stay on track.

Is there a way that you could build in supports so that the next time you do this unit this issue is covered?

I could make a place near the teacher desk where a student could go to check their answers when finished.

Week 3

Students will be assigned web page to continue to practice reducing fractions prior to worksheet assignments:

http://www.sheppardsoftware.com/mathgames/fractions/reduce_fractions_shoot.htm

http://www.sheppardsoftware.com/mathgames/fractions/mathman_reduce_fractions.htm

I will incorporate gaming that is specifically geared to individual student needs. They will continue to practice skills using both radial and other practice worksheets.

During this week, I will focus as a teacher reflecting on students processes and progress.

This week students will focus on reducing fractions, subtracting fractions and end with a post-test.

Reflection for Week 10: Understanding by Design and Twitter Session

EDET 637: Differentiating Instruction through Technology with Dr. Lee Graham

by Aleta May

Two assignments this week helped me grow in my skills. The first was when I cohosted a Twitter session with Kate Mullins. Second was writing a fractions unit to be used with middle school students who need to learn adding/subtracting and reducing fractions in a way that is meaningful and motivational to them.

We did not have specific reading assigned to us this particular week, because it was the week for applying what we had read extensively throughout the semester and written to each other about to designing a unit for actual use in our schools. The Understanding by Design (UbD) developed by Jay McTighe and Grant Wiggins is the framework I used. This is one that is known as a backward design; but is better described as beginning with one or more essential questions. In order to help me review and gain new insight into what the UbD should focus on and how this looks in other content areas, as well as in teaching fractions, I looked up articles and websites to help me develop questions for our Wednesday, 3-10-16, class Twitter session. I wrote several questions from the resources that will be added to this reflection. Using Twitter and email, I presented these questions to Kate for consideration. She had a very similar focus in mind with questions she had thought of.   I asked her to interweave her questions into the list I had sent in a way that made sense to her. Then after conferring more, we decided to come to the Twitter session early enough to speak to each other with opening ice breaker questions, inviting people in our class to join into our conversation as they arrived. This worked really well! We were early to the session, yet we were both very thankful we had a plan to come early since we both had to quickly solve internet situations in our respective homes.

What I took away from this was: 1) a better understanding of how we should focus our teaching via a UbD unit, 2) the experience of cohosting allowed me to think about when to step to improvise our plan if need be (connectivity issues in our separate homes, etc.) and when to back up and not take over the session—we followed an alternating questioning pattern with some necessary modifications 3) I am much more confident that this is a really great way to teach because quiet people contribute, and we are all forced to make our responses concise, thereby preventing anyone from taking over a session 4) I can now utilize another tool for communicating with students that they are already accustomed to using in their every day lives.

Here are the questions Kate and I came up with and the references we used to come up with quality discussion:

Twitter Session:

Ice Breakers—

What kind of Alaska foods have you eaten? What Alaska foods should be added to school lunches?

 Did the volcano impact travel (airplanes not flying or backed up flights due to ash in the air) for anyone out there or someone close to you?

 Let’s generate a list of overarching or essential questions used in your unit design.

 What types of pre-tests are you using? Computer, observation, paper/pencil. . .?

 What hooks are you using in your unit to engage students initially?

What is an example of how your student learning goals and achievements will show understanding? 

Are these tailored to allow individual style to shine? If so, how?

What are good examples of ways students can use the information learned later; transfer?

Name a real-world situations or problems students can use their new knowledge for.

Tell about scenario goals, challenges, roles played in a scenario, … in your UbD.

Are there tools, resources, or strategies you are using that you’d like to share?

How are portions of your lessons personalized for students?

Examples of formative assessment, checking for understanding in your unit are …?

What are ways our students may rethink, reflect or revise their product? 

References

Donhouser, M., Hersey, H., Stutzman, C. & Zane, M. (2014). From lesson plan to learning plan: An introduction to the inquiry learning plan. School Library Monthly, 31(1), pp. 11-13.

Keeling, M. (2015). Backwards design considerations for the 21st-century school library. School Library Monthly, 31(4), pp. 22-24.

Lubiner, G. (2014). Understanding by design: A unit on color theory. Arts & Activities, 156(1), pp. 20-44.

McTighe, J. & Wiggins, G. (2013).   Essential questions: Opening doors to student understanding. Alexandria, VA: Association for Supervision & Curriculum Development (ASCD).  Ch. 1. What Makes a Question Essential?  Retrieved 3-27-16.

UbD in a Nutshell.   Retrieved 3-28-16.   http://jaymctighe.com/wordpress/wp-content/uploads/2011/04/UbD-in-a-Nutshell.pdf

Throughout the week, I blogged with students in class regarding our UbD units:

I wrote to Sara (she inspired me to take the UbD to the next level and help our science teacher apply the real world application to learning)—

Sara,

A bubble map is such a great way to review. With this visual, the students can see the connections between energy types and trigger memories from what they already know.

I had never heard of Actively Learn. Thank you for sharing this! I have the link bookmarked on my toolbar now. http://www.activelylearn.com

Edpuzzle.com is new to me too. Another awesome site with videos to use for teaching! https://edpuzzle.com Thank you again!

Kahoot https://kahoot.it/#/   to https://getkahoot.com   Thank you again! Games for any subject. I’m excited to go into these sites, especially to focus on my current UbD unit for reducing fractions.

By sharing your links and ideas, I am able to research specific games/activities my students can use this coming week to choose how they will want to improve their skills. This will be a student centered focus and I am truly becoming a more exciting facilitator / educator with a large technology tool bag.

Wow! Your performance plan assessment with transfer of energy, using simple models they build and using iPads. Here are video notes I took from your video post:

Step One: Take four images from different angles; and using contrasting color (light imaging camera using light lengths which is close to thermal imaging) images of their model to see where energy loss is.

Step Two: Taking temperatures using temperature probes.

Question: In step one: is there a special website you go to in order to take pictures using contrasting colors, or is it built into the camera that is on the iPad already.

Step Three:  Cotton for Insulation with hot glue to take a second round of thermal images. Compare to the first set of pictures, compare/contrast, make connections to heat transfer. Students experimented using tape instead of cotton. The scotch tape was better at keeping heat inside the model house than cotton.

Closing Reflections:

Temperature data sheet. Respond to what does the data show about energy transfer in model homes not insulated vs. insulated by different materials?

Energy conservation – how does it benefit you and your parents?

Big picture—how does this understanding help the environment?

Amy wrote to me and I replied:

Aleta,

Since we’re both doing fractions units, I was especially interested to check out your unit. Since it is geared for middle school RTI students, it gives me future ideas for my students, as we’re focusing on third and fourth grade skills right now. I like how you tie your fraction work to real-world activities, like cooking, sewing and coding. This will let your students see that what they’re learning has authentic uses in life and is worth mastering. I feel like this is an area that I will strengthen in my fractions unit and spend more time discussing how we use fractions in real life. Your students should be motivated by the use of online games, and it’s wonderful how you’re able to use the pretest results to differentiate games for each student. That is something that I love about small groups! I like how students will be doing self-assessment in your group so that they see their growth and are motivated to keep working. I’m going to try self-reflection journals in my group to help kids clarify their thinking during the unit, and that might be an idea for you to try also, so that students can ask questions or make connections. One thing I worry about with the journals, though, is the difference in writing ability that my students have, with some able to quickly jot down ideas and others laboring over their words. I will check out the radial fractions activity that you are doing, as it sounds like a good way for students to see their work visually. I like your update after teaching your unit for a few days and how your ideas will continue to grow as you assess your students’ needs. Thanks for sharing your thinking!

Amy, 4-2-16

I think your idea for trying self-reflection journals for asking questions or making connections is perfect! Thank you for your feedback and idea! Maybe this is where I can have them actually take notes and reflect on how fractions are used in real life situations. Although students at every age need to think about real life applications, it seems to become even more important as a way to give older students a reason to invest their time or to engage more deeply and try learning this again–it must be so discouraging to older students who have not learned a concept that many of their peers have already caught on to.

I wrote to Sally 4-1-16:

Sally,

I think Lee was telling us on our Twitter session last night that what you wrote here would be a perfect example of the concept of transfer, because it has real world applications:

“Use order to calculate cost when different factors are involved. For example: fees, taxes when purchasing items.”

When I was learning to use this the word transfer in my previous training for special education, it included the idea of transfer of learning from one subject to another. Naturally, we thought about transferring their skills to the job as we started students into a special education transition program at a high school I worked at. So ultimately, transfer is for the real world. Here’s another awesome example you provided in your plan:

“Students will be skilled at…

  • Finding the cost of joining a club with fee, purchase and taxes.”

Also, your day by day planning in Stage 2 looks perfect! I need to improve mine. Thank you for sharing! Your examples help me see the whole picture better.

Aleta

 I wrote to Sarah 4-3-16:

The way you built in choices “by taking in information about the behavior of gases” looks like a great plan mainly because the students are working together, then regrouping to discuss results. Students listen to, watch and talk to each other at different levels of understanding.

I looked up Poll Everywhere apps . Are you using the mobile app through student phones; or your phone as a clicker with a PowerPoint? Since this is new to me, I went to: https://itunes.apple.com/us/app/poll-everywhere/id893375312?mt=8

Thank you for sharing about this app and how you use it for formative assessment!

I wrote to Anastasia on 4-1-16—it was still awaiting moderation when I checked back on this on 4-3-16

aletakmay says:.comment-author

April 1, 2016 at 1:48 am.comment-metadata

Your comment is awaiting moderation.

Anastasia,

The student who is working far below his grade level is participating in a way that helps him to visualize nature in a way that may help him retain the information; especially with pictures to go by from books and websites. He likely loves to be in your classroom participating on the same subject with peers.

The individualized KWL chart is such a great idea! Fifth grade students can make really good use of this visual to set goals and note what they have learned.

Aleta

Post to Genevieve on 4-2-16:

Genevieve,

Wow, your UbD is wonderful! It is so detailed and easy to read. Everything is embedded in it from using a visual KWL to describe student understanding from the beginning throughout the end of your unit, to using Google Maps, QR codes, iPads and screenshots to apply technology to create engaging learning, to making it meaningful–the study of Salmon, a resource we depend on in Alaska! That rubric is such an excellent example of using assessment in a way that is detailed and descriptive to students–perfect for conferencing with students to help them set individual goals!

Week 1 of the Fractions Unit

EDET637:  Differenting Instruction Through Technology with Dr. Lee Graham

Aleta May’s Week 10 Update to  Week 1 of my UbD Fractions Unit:

During this week, I have a paper/pencil pre-assessment on paper.  The post assessment will replicate the pre-assessment with different problems.  As an initial incentive, students used fraction games found on Coolmath.com; it has initially been used as a draw in motivator and fluency for my lowest students.There are other games I want to use.  Ideally, I could get MathBlaster to work on our iPads soon.

Student self assessment is through watching their progress in games, and using the visual fraction strategy called Radial Fractions.  McMullen, C. Ph.D. (2010).  Radial Fractions math workbook (addition and subtraction):  A fun & creative visual strategy to practice adding and subtracting fractions.  CreateSpace.  This can be found on amazon.com

The students use this visual that looks like the spokes of a bicycle wheel to add or subtract.

My step-by-step plan is now (after noting their progress) in the visual strategy as follows:

This week they added or subtracted without reducing, using the wheel; since students were sometimes getting adding and subtracting mixed up.

Next week, they will subtract more than they did the first week; and they will begin reducing within this visual strategy.

This is looking more and more like a 3 week (instead of a 2 week unit plan).

I’ll be able to really focus more deeply on all the “embellishments”. . . as there will be less school-wide assessment focus!

Here is a new link I found that will include the more challenging fractions (such as reducing) fractions online (PacMan games):

http://www.sheppardsoftware.com/math.htm

Presently, students are using a visual strategy that even though it is paper based, it is a brightly colored bicycle wheel.