1. Before we get started… Jot down notes about how you solved this problem. Solve 18 x 5 in your head. If you’d like, you can download the materials for this webinar from the GoToTraining dashboard now. Otherwise, we will email you a link tomorrow to access them along with the recording of the webinar.

2. Webinar Series Outcomes Know recommended practices for students struggling to learn math Access math intervention research and resources Connect with practitioners across the state Create a plan to improve your school's math interventions

3. Webinar Series Topics October Overview and Screening February Systematic planning November Motivational Strategies March Fact fluency December Intervention content April Monitoring progress January Use of visual representations May Next steps / networking

4. What the research says How it looks in practice Reflection & resources Q&A Agenda Today’s Featured Practice: The Use of Visual Representations

5. Today’s featured practice …interventionists should be proficient in the use of visual representations of mathematical ideas. Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and…

6. Effective Mathematics Teaching Practices 1.Establish mathematics goals to focus learning. 2.Implement tasks that promote reasoning and problem solving. 3.Use and connect mathematical representations. 4.Facilitate meaningful mathematical discourse. 5.Pose purposeful questions. 6.Build procedural fluency from conceptual understanding. 7.Support productive struggle in learning mathematics. 8.Elicit and use evidence of student thinking.

7. Last month’s featured practice Interventions should focus intensely on in- depth treatment of whole numbers in grades K - 5 and on rational numbers in grades 4 - 8.

8. What the research says How it looks in practice Reflection & resources Q&A Agenda

9. “A major problem for students who struggle with mathematics is weak understanding of the relationships between the abstract symbols of mathematics and the various visual representations.”

10. "Mathematics requires representations. In fact, because of the abstract nature of mathematics, people have access to mathematical ideas only through the representations of those ideas.” Why representations?

11. Think back to the problem you solved at start of this webinar Boaler, J. (2015). Visual math Improves math performance. How did you solve 18 x 5 in your head?

12. Provide multiple entry points and access to the study of mathematics Support students’ ability to justify and explain their reasoning.Promote transfer Visual representations can… UDL; LD online; Center on Technology and Disability; NCTM; IES Practice Guide; EDC SolveMe puzzles

13. Focus students’ attention on the structure or essential features of mathematical ideas The “right” visual representation can…

14. Focus students’ attention on the structure or essential features of mathematical ideas The “right” visual representation can… Use visual representations such as number lines, arrays, and strip diagrams.

15. “Occasional and unsystematic exposure* is insufficient and does not facilitate understanding of the relationship between the abstract symbols of mathematics and various visual representations.” *the norm in many classrooms

16. Provide a graduated framework for students to make meaningful connections Support students in moving from informal to formal representations of mathematical ideas Blend conceptual and procedural understanding in a structured way The right visual representations scaffolded along a learning progression can… University of Kansas Special Connections: Concrete – Representational – Abstract Instruction; LD Online

17. Everyday experiential informal knowledge: words and quantities in the real world Formal school math knowledge: Words, notations, methods Example Instructional Progression Framework Image from Moving with Math Scaffolding language and visual representations

18. Really Good Results Children’s Math Worlds

19. What the research says How it looks in practice Reflection & resources Q&A Agenda

20. Today’s featured presenters Dina Mendola Instructional Coach, Math Recovery Jamie Neary Third Grade Mathematics Teacher, Cudahy Schools Ken Davis Math Consultant, Wisconsin Department of Public Instruction

21. What the research says How it looks in practice Reflection & resources Q&A Agenda

22. Additional Resources Resource categories General Teacher Resources for Using Visual Representations Online Visual Representation Tools Outcome Studies Discourse Strategies

23. Reflection Make a connection! Enter it in the chat box. Screen all students to identify those at risk for potential mathematics difficulties Focus intensely on in-depth treatment of whole numbers (K-5) and rational numbers (gr 4-8) Include opportunities for students to work with visual representations of mathematical ideas Include motivational strategies in tier 2 and tier 3 interventions.

24. What the research says How it looks in practice Reflection & resources Q&A Agenda

25. Upcoming Webinars February 16 – Systematic Instructional Planning March 17 April 20 May 17

26. Thank you for attending! Featured presenters Dina Mendola, dina@mathrecovery.org, Math Recoverydina@mathrecovery.org Jamie Neary nearyj@cudahysd.org, Cudahy School Districtnearyj@cudahysd.org Ken Davis, kenneth.davis@dpi.wi.gov, Wisconsin DPIkenneth.davis@dpi.wi.gov Wisconsin RtI Center Technical Assistance Coordinators Sara Summ, summs@wisconsinrticenter.orgsumms@wisconsinrticenter.org Heidi Erstad, erstadh@wisconsinrticenter.orgerstadh@wisconsinrticenter.org Please complete the exit survey as a way to say thank you to our guest presenters!