The Learning Trajectories for Everyday Computing (LTEC) team has worked to iteratively develop and test integrated fractions + computational thinking lessons and assessments for grades 3 and 4. These instructional materials are aligned with learning trajectories in the areas of sequencing, repetition, conditional logic, decomposition, and debugging. In this year of the project, we are conducting a study to investigate the extent to which these integrated lessons influence students' understanding of mathematics as well as their computational thinking.
Computer Science, Integrating STEM and CS, Research / Evaluation
Univ of Florida, Univ of Chicago, UI Urbana-Champ
STEM + Computing Partnerships (STEM+C)
Related Content for Learning Trajectories for Everyday Computing
Discussion from the 2020 STEM For All Video Showcase (18 posts)
Maya Israel
Lead Presenter Associate professor
May 5, 2020 | 09:13 a.m.
Thanks for checking out of video about the LTEC-2 project. We have been working hard at developing materials for integrating computational thinking (CT) into elementary mathematics with a focus on fractions instructions in grades 3 and 4. We were in the middle of a treatment/control study when COVID-19 began, but are grateful for the data that we did collect that we can now examine. We would love to hear how others are integrating CT into the content areas as well as how others are assessing CT.
Hi, Maya! Nice to see your video. I love the references to seeing patterns and looping in the different colored tiles on the floor. Check out our project Guitars, Rocketry, Robotics ATE. We're looking at how to engage rural community college students in problem solving and computational thinking through hands-on learning projects.
Maya Israel
Lead Presenter Associate professor
May 6, 2020 | 09:20 a.m.
Thanks for pointing me to your video. It is a powerful program and I would love to learn more about it.
Sarah Young
Facilitator Director of Strategic Initiatives
May 5, 2020 | 11:53 a.m.
I appreciate the focus on grades 3 and 4 related to fractions. Is there a public website where I can see the "Action Fraction" lessons from the video? I am interested in learning more about the specific lesson engagements you have created.
Maya Israel
Lead Presenter Associate professor
May 5, 2020 | 01:03 p.m.
Hi Sarah. The Everyday CS website (http://everydaycomputing.org/) has a few sample lesson plans. You can request access to other lessons here: https://www.canonlab.org/actionfractionslessons. Once we are done with our implementation study, we will host all the lessons on the Everyday CS website. Until then, we are being a bit more controlled in this dissemination.
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Found helpful:
Sarah Young
Jennifer Vermillion
Facilitator Director of Innovative Teaching and Learning
May 5, 2020 | 02:39 p.m.
This is an interesting project and a wonderful model for authentically integrating computer science into math instruction! I am curious to learn more about your team's approaches to assessing students' computational thinking competencies.
1
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Found helpful:
Maya Israel
Brian Gane
Co-Presenter Research Assistant Professor
May 5, 2020 | 04:45 p.m.
Hi Jennifer, assessing students' computational thinking competencies is a major focus of the LTEC-2 project and we have approached this challenge by building off of cognitive theories about how students develop computational thinking (CT), as represented by different CT learning trajectories. Using these learning trajectories as a starting point, we then used an evidence-centered design process to develop assessments that allow students to demonstrate their CT knowledge, skills and abilities. We are currently in the process of testing, refining, and validating these assessments with students that participated in the project.
1
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Interesting project, and great to see a multi-institution collaboration. I'm curious about a couple of things: (1) how did your multi-university collaboration originate and evolve; and (2) how are you measuring engagement that students have with the program/content?
Thank you for sharing your project. I'm going to check out the everydaycomputing and canonlab websites.
Janice Cuny
Facilitator Global DIrestor of Align
May 7, 2020 | 05:02 p.m.
Both interesting questions.
Diana Franklin
Co-Presenter Associate Professor
May 7, 2020 | 05:18 p.m.
Our multi-institution collaboration originated based on the expertise in the different sites. University of Chicago brought extensive mathematics and curriculum development experience (via Everyday Mathematics textbook series), and Maya Israel has extensive research experience with students with disabilities and technology. I joined UChicago right as the project began, and I have experience with researching computer science learning and developing CS curriculum. So between these three sets of expertise, we had what we needed. When we got further in the project, the second NSF grant, we added UIC for their assessment expertise. We meet often and move responsibilities around as peoples' interests and expertise morph.
We have done classroom observations and teacher interviews, but we don't have specific written measures for engagement for the students.
Janice Cuny
Facilitator Global DIrestor of Align
May 8, 2020 | 11:38 a.m.
Really nice blend of skills on the team!
Can you talk about how the research component has has added to the development and evolution of your project?
Gayithri Jayathirtha
Graduate Student
May 7, 2020 | 01:26 p.m.
Sounds like a promising project! It is very exciting to hear that students have this opportunity to program as they learn about fractions. This reminds me of Yasmin Kafai's (1995) work on fractions+Scratch with middle school students.
As an ex-math-teacher, I am curious to know if and how you see math learning changing in the process of integrating programming with it.
Diana Franklin
Co-Presenter Associate Professor
May 7, 2020 | 05:21 p.m.
Our vision is that mathematics instruction could change in two ways (though others can weigh in on other perspectives). First, we're able to provide virtual manipulatives that give another way of students interacting with those manipulatives. They can sit down with fraction circle pieces themselves, then they can program the computer as to which pieces to pick up and how many to place. This shows an animation and helps them make connections between the denominator and the size of the piece. In addition, we provide ways they can think about the rules associated with mathematics. For comparing fractions, we have them express how they compare fractions with like denominators or fractions with like numerators, hoping they notice the different rules involved.
Gayithri Jayathirtha
Graduate Student
May 7, 2020 | 07:02 p.m.
Sounds great! I love your idea of "virtual manipulatives" which can be so much more diverse than the traditional manipulatives in math learning context. And, the very diversity may invite conversations around unit fraction and its relation to the sizes of sprites that are being used. I am excited to learn more about this in the coming years! All the very best!
Really appreciate this work that you all are doing! I loved how the students began to notice loops and repeating patterns outside the classroom. Do you find students able to bring some of these CT ideas to other math topics that they're learning (besides fractions)?
Whet a great video, Maya! I was particularly interested in the assessment work/learning tasks mentioned toward the end. I appreciated how you all included/described different assessment item formats (e.g., some requiring verbal responses vs some requiring children to select from a set of visual options) and how you recorded children's thinking process/rationale in addition to their response. I'd be interested to hear more about what you learned from analyzing these data. Were some item formats more reliable? Did specific items yield more variability in responses? Did some perform better or allowed you to identify lower/higher performers? If children struggled how did you determine if the struggle came from math, CT or both?
Brian Gane
Co-Presenter Research Assistant Professor
May 9, 2020 | 05:54 p.m.
Great questions! We are in the process of analyzing the data now and have multiple sources of data -- some from students' responses on paper and some from students "thinking aloud" as they work through the assessment items. I can speak more about what we learned from the responses on paper, but maybe Maya or others can comment on the think aloud results.
After coding/scoring the paper responses we've learned that the items do indeed vary in terms of difficulty, with some being able to be answered correctly by a majority of students and some being more difficult. In addition, some of the items were more predictive of students' overall score, indicating that they can discriminate well between lower and higher performances. This seems to be true across a variety of items that test different content/learning trajectories. Although we can make these statements about the items in general, we did not use an experimental design that would allow us to separate out the effect of items' format on students' performance (doing so would have required varying the item format while holding the content constant and would have meant students had to complete many more assessment items).
Re: "If children struggled how did you determine if the struggle came from math, CT or both?" We approached this in two ways. First, we attempted to minimize struggles from math by using content that was learned in prior units or years. Second, we sometimes had to build the coding/scoring rubrics to allow for isolating math errors so that they did not negatively influence the judgements of students' CT proficiency.
1
Discussion is closed. Upvoting is no longer available
A great fusion of computational thinking and mathematics. Is there a formal curriculum connecting fractions (including parts-to-whole, decimal, percentage, ratio and scale) to the CT and programming? Is there a resource or a framework that you can expound upon. Thanks for sharing this work.
Maya Israel
Associate professor
Thanks for checking out of video about the LTEC-2 project. We have been working hard at developing materials for integrating computational thinking (CT) into elementary mathematics with a focus on fractions instructions in grades 3 and 4. We were in the middle of a treatment/control study when COVID-19 began, but are grateful for the data that we did collect that we can now examine. We would love to hear how others are integrating CT into the content areas as well as how others are assessing CT.
Cheryl Calhoun
Hi, Maya! Nice to see your video. I love the references to seeing patterns and looping in the different colored tiles on the floor. Check out our project Guitars, Rocketry, Robotics ATE. We're looking at how to engage rural community college students in problem solving and computational thinking through hands-on learning projects.
Maya Israel
Associate professor
Thanks for pointing me to your video. It is a powerful program and I would love to learn more about it.
Sarah Young
Director of Strategic Initiatives
I appreciate the focus on grades 3 and 4 related to fractions. Is there a public website where I can see the "Action Fraction" lessons from the video? I am interested in learning more about the specific lesson engagements you have created.
Maya Israel
Associate professor
Hi Sarah. The Everyday CS website (http://everydaycomputing.org/) has a few sample lesson plans. You can request access to other lessons here: https://www.canonlab.org/actionfractionslessons. Once we are done with our implementation study, we will host all the lessons on the Everyday CS website. Until then, we are being a bit more controlled in this dissemination.
Sarah Young
Jennifer Vermillion
Director of Innovative Teaching and Learning
This is an interesting project and a wonderful model for authentically integrating computer science into math instruction! I am curious to learn more about your team's approaches to assessing students' computational thinking competencies.
Maya Israel
Brian Gane
Research Assistant Professor
Hi Jennifer, assessing students' computational thinking competencies is a major focus of the LTEC-2 project and we have approached this challenge by building off of cognitive theories about how students develop computational thinking (CT), as represented by different CT learning trajectories. Using these learning trajectories as a starting point, we then used an evidence-centered design process to develop assessments that allow students to demonstrate their CT knowledge, skills and abilities. We are currently in the process of testing, refining, and validating these assessments with students that participated in the project.
Maya Israel
Dave Miller
Interesting project, and great to see a multi-institution collaboration. I'm curious about a couple of things: (1) how did your multi-university collaboration originate and evolve; and (2) how are you measuring engagement that students have with the program/content?
Thank you for sharing your project. I'm going to check out the everydaycomputing and canonlab websites.
Janice Cuny
Global DIrestor of Align
Both interesting questions.
Diana Franklin
Associate Professor
Our multi-institution collaboration originated based on the expertise in the different sites. University of Chicago brought extensive mathematics and curriculum development experience (via Everyday Mathematics textbook series), and Maya Israel has extensive research experience with students with disabilities and technology. I joined UChicago right as the project began, and I have experience with researching computer science learning and developing CS curriculum. So between these three sets of expertise, we had what we needed. When we got further in the project, the second NSF grant, we added UIC for their assessment expertise. We meet often and move responsibilities around as peoples' interests and expertise morph.
We have done classroom observations and teacher interviews, but we don't have specific written measures for engagement for the students.
Janice Cuny
Global DIrestor of Align
Really nice blend of skills on the team!
Can you talk about how the research component has has added to the development and evolution of your project?
Gayithri Jayathirtha
Sounds like a promising project! It is very exciting to hear that students have this opportunity to program as they learn about fractions. This reminds me of Yasmin Kafai's (1995) work on fractions+Scratch with middle school students.
As an ex-math-teacher, I am curious to know if and how you see math learning changing in the process of integrating programming with it.
Diana Franklin
Associate Professor
Our vision is that mathematics instruction could change in two ways (though others can weigh in on other perspectives). First, we're able to provide virtual manipulatives that give another way of students interacting with those manipulatives. They can sit down with fraction circle pieces themselves, then they can program the computer as to which pieces to pick up and how many to place. This shows an animation and helps them make connections between the denominator and the size of the piece. In addition, we provide ways they can think about the rules associated with mathematics. For comparing fractions, we have them express how they compare fractions with like denominators or fractions with like numerators, hoping they notice the different rules involved.
Gayithri Jayathirtha
Sounds great! I love your idea of "virtual manipulatives" which can be so much more diverse than the traditional manipulatives in math learning context. And, the very diversity may invite conversations around unit fraction and its relation to the sizes of sprites that are being used. I am excited to learn more about this in the coming years! All the very best!
Shuchi Grover
Really appreciate this work that you all are doing! I loved how the students began to notice loops and repeating patterns outside the classroom. Do you find students able to bring some of these CT ideas to other math topics that they're learning (besides fractions)?
Ximena Dominguez
Whet a great video, Maya! I was particularly interested in the assessment work/learning tasks mentioned toward the end. I appreciated how you all included/described different assessment item formats (e.g., some requiring verbal responses vs some requiring children to select from a set of visual options) and how you recorded children's thinking process/rationale in addition to their response. I'd be interested to hear more about what you learned from analyzing these data. Were some item formats more reliable? Did specific items yield more variability in responses? Did some perform better or allowed you to identify lower/higher performers? If children struggled how did you determine if the struggle came from math, CT or both?
Brian Gane
Research Assistant Professor
Great questions! We are in the process of analyzing the data now and have multiple sources of data -- some from students' responses on paper and some from students "thinking aloud" as they work through the assessment items. I can speak more about what we learned from the responses on paper, but maybe Maya or others can comment on the think aloud results.
After coding/scoring the paper responses we've learned that the items do indeed vary in terms of difficulty, with some being able to be answered correctly by a majority of students and some being more difficult. In addition, some of the items were more predictive of students' overall score, indicating that they can discriminate well between lower and higher performances. This seems to be true across a variety of items that test different content/learning trajectories. Although we can make these statements about the items in general, we did not use an experimental design that would allow us to separate out the effect of items' format on students' performance (doing so would have required varying the item format while holding the content constant and would have meant students had to complete many more assessment items).
Re: "If children struggled how did you determine if the struggle came from math, CT or both?" We approached this in two ways. First, we attempted to minimize struggles from math by using content that was learned in prior units or years. Second, we sometimes had to build the coding/scoring rubrics to allow for isolating math errors so that they did not negatively influence the judgements of students' CT proficiency.
Michael I. Swart
Michael I. Swart
A great fusion of computational thinking and mathematics. Is there a formal curriculum connecting fractions (including parts-to-whole, decimal, percentage, ratio and scale) to the CT and programming? Is there a resource or a framework that you can expound upon. Thanks for sharing this work.
Further posting is closed as the event has ended.