Maximizing the Mathematical Proficiency

1. Maximizing the Mathematical Proficiency Setting the Focus of TAL

2. Learning Intention and Success Criteria • We are learning to… • Develop a common understanding of the word intervention. • We will be successful when we… • Make connections from our previous work in Math Alliance and explain how that supports intervention ideas.

3. Thinking about students…

4. Setting the groundwork for Intervention ReadChapter 2 The Landscape of Learning: A Framework for Intervention • How does the information in the chapter connect to what we’ve been doing in Math Alliance? • What are two ideas you connected with as you read the chapter? • What’s the message the author is asking us to think about when it comes to Interventions? Share out with your table group How does this affect your own definition of intervention?

5. Another perspective on Intervention Read the draft position paper from NCTM (National Council of Teachers of Mathematics) What is the Council’s position on Intervention? • Identify their key components • Discuss them with your table group do you agree or disagree • In what way does this position on intervention effect your definition?

6. Thinking back on our studies Use the set of cards at your table. • Pull out a card, read the idea. • Discuss the idea – make sure everyone at the table is clear on what it is or means. • Develop an example to clarify it. • Decide if the card is a strategy, a big idea, or a type of mathematical modeling. • Use the note taking sheet to help you keep track of your conversation.

7. Representations:Models for Thinking pictures manipulative models oral language written symbols Real-world situations Strengthening the ability to move between and among representations improves the growth of children’s conceptual understanding. Vandewalle, J. Elementary and Middle School Mathematics Teaching Developmentally. Pearson Education, 2007. .

8. Concrete-Representational-Abstract • Concrete The “doing” stage using concrete objects to model problems • Representational - The “seeing” stage using representations of the objects to model problems • Abstract - The “symbolic” stage using abstract symbols to model problems

9. CRA • Research-based studies show that students who use concrete materials develop more precise and more comprehensive mental representations, often show more motivation and on-task behavior, understand mathematical ideas, and better apply these ideas to life situations • (Harrison & Harrison, 1986; Suydam & Higgins, 1977).

10. Where to start? Capturing Intelligence …we must find ways to structure subject matter so as to enable learners to get their thoughts about it. We must take those thoughts seriously and set out helping students pursue them in greater depth and breadth. This is the way to capture the intelligence of our students. E. Duckworth, 1996

11. Guidelines for planning and implementing mathematics instruction • Should promote all aspects of mathematics proficiency in an intertwined manner. • CMF • Teaching and learning principles apply to all children “students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge” p. 20 PPSM

12. Guidelines for All Learners of Mathematics • Instructional tools such as activities, manipulatives, group work, and calculators must be used carefully and reflectively • Instruction should be based on a child’s individual pattern of informal and formal mathematical strengths and weaknesses.

13. Summer Focus Teaching All Learners Revisiting – Big Ideas, Strategies and Mathamatical Models Focusing on Assessment Deepening understanding about math instruction as intervention Exploring the CCSS and it’s connection to student learning. Leadership – Deepening understanding of collaboration models and skills.