1. Math Liaison Meeting for Elementary Schools October 2014 Presenter: Simi Minhas Math Achievement Coach, Network 204

2. Agenda Developing Effective Fractions Instruction for Kindergarten through Fifth Grade-Research Article Understanding the progression of fractions in grades K-5 Understanding the purpose of visual models in developing a deeper understanding of fractions, for students in elementary grades How to incorporate effective models in instructional units of study? Sharing best practices with colleagues

3. Let’s Have Fun With Math!!! Please Solve the ‘Dog Years Dilemma’ problem Show all your thinking on paper. Use models, equations, and justify your thinking in words.

4. Gallery Walk Walk around the room and take a look at how other people solved the problem. As you walk around the room to analyze the work of others, you may… Ask a clarifying question on a post-it Write a comment Provide feedback

5. Developing Effective Fractions Instruction for Kindergarten Through 8 th Grade Each group reads the introduction, and the other assigned pages. (Introduction-Pgs. 1-11) Reading and individual highlight: Participants read the assigned text and highlight the points that interest them as individual readers, and that they think others should attend to. (40 minutes)

6. Group Protocol Discussion and group highlighting: Each group has a discussion and constructs a list of key points for posting and sharing with others. Chart the highlights. (20 minutes)

7. Gallery walk: Groups move as a group to read the charts from other groups. Participants create and attach post-its to what they see in the gallery walk: with questions, affirmations, comments, examples.(10-15 minutes) Revisit and response: Participants return to their initial group to review and discuss comments posted on their chart by others. A spokesperson for each group shares reactions. (10 minutes)

8. Whole Group Debrief General discussion and debriefing: Participants share general comments about the topic of discussion and/or the process. (15 minutes) How can you use this protocol for professional development at your school? How could this protocol be used in the classroom with the students?

9. Relationships Between Visual Static Models and Students’ Written Solutions to Fraction Tasks Researchers hypothesize that students’ exposure to varied mathematical representations influences their ability to flexibly use static visual representations. They recommend that students have a solid understanding of real-world mathematics situations in order to successfully create and interpret visual static models of mathematics. Research done by: Utah State University and University of Colorado

10. What are visual static models? Visual static models: a still picture that is either printed or drawn on a page to represent mathematical concepts. Students are provided with the model in the question. They can manipulate the model to answer the question, or they are asked to interpret the model.

11. Mathematical Modeling-What’s the purpose? Overarching UnderstandingsOverarching Essential Questions Mathematicians create models to interpret and predict the behavior of real world phenomena. Mathematical models have limits and sometimes they distort or misrepresent. How can we best model this (real world phenomena)? What are the limits of this model? How reliable are its predictions?

14. Student #1Student #2

15. Student #3Student #4

17. Student #1 Student #2

18. Student #3

19. Another Student

20. Research Findings/ Discussion What types of misconceptions do students’ written solutions commonly reveal on fraction tasks involving either given or student-created visual static models? What is the relationship between given or student-created visual static models of fraction concepts and students’ written solutions on open-ended problems?

21. Conclusion High-achieving students often display the highest level of spatial visualization. Likewise, low-achieving students benefit from working with given visual static models. Essential Question: What are the instructional implications?

22. Let’s Share Math PD at our school Best practices Highlights Issues Questions and concerns

23. Questions, Comments and Feedback Please fill out the feedback form.