1.  EDUC 4334: J/I Mathematics Week Seven

2. J/I Math November 4 – 8 S7 Overview  Assignment 1 Handed Back Today  Final due date for PS Set II  Last Week’s Guest Speaker—Brief review  Picking Up on Problem Solving Again  Briefly: TTPS  Assessment: challenges and opportunities  BREAK  Lesson Planning-encouraging the use of multiple representation forms  Next Week: Into NSN for the rest of the term

3. J/I Math S7 Guest Speaker....  What are the main points you took away from the presentation by LNS Student Achievement Officer Doug Robidoux?

4. J/I Math S7 Problem Solving (TTPS) – review and evaluation  Recall the Three-Part Lesson (Before, During, After)  Now with an expanded “After”  After: Consolidation  After: Highlights/Summary  After Practice (newer)  In Ontario, a TTPS format called Bansho has become popular  See Small (2013) Chapter 4, p. 71 for a brief description.  Roughly, Bansho follows the pattern on next slide

5. Labels (e.g., mathematical strategies) BEFORE Activation DURING AFTER - Consolidation ( focused on knitting ideas together from one solution to another towards the learning goal – organized by groups that used a similar approach, and less to more mathematically in line with goal ) AFTER Highlights/ Summary - AFTER Practice mathematical annotations - either on the board or on the student solutions to make explicit mathematical ideas, strategies, and tools and to show relationships between the solutions - “ What information from the problem will we use to make a plan to solve the problem? Explain. Record the info In a list <problem or previous day solutions> Record 2 solutions to Highlight math ideas

6. J/I Math S 7 Problem Solving (TTPS) – evaluation  You will need to evaluate the work of individual children, even though they may often be working together. There are regular times when you want to see their personal mathematical understanding and ability to apply that to their own problem solving situations.  Think, for example, of EQAO context  (For me, TTPS is a mix of small group and individual opportunities)  Such evaluation can be challenging.

7. J/I Math Week 7 Problem Solving (TTPS) – evaluation  Let’s work on the following example:  “Cue the handout”  Evaluation approaches (older and newer)  A child’s work to evaluate  Then we’ll discuss.  BREAK!

8. J/I Math...... S 7 NSN: Using Representations  Several years ago (1987) the authors Lesh, Post, and Behr published an article in which they identified five major ways to represent a mathematical idea and emphasize the interconnectedness of these forms (especially at the elementary level).  The schematic on the next slide illustrates these representations and connections.  As Van de Walle and Folk (2005) note, these multiple ways of representing math “make it so powerful...”  They also say: “Students need to understand that these are useful ways of communicating mathematical ideas to other people” (p. 8). Van de Walle, J, & Folk, S. (2005). Elementary and Middle School Mathematics: Teaching developmentally (Can. ed.). Toronto: Pearson.

10. J/I Math...... S 7 NSN: Using Representations  An Activity: Your Small Groups Task (Table groups)  For at least one of the following two grade blocks: 4-6, 7-8 (Time dependent)  Identify a particular mathematics topic in Number Sense and Numeration (be specific)  Briefly Outline (on chart paper) how you might teach this topic in ways that draw upon the five major representation forms.  Identify grade, topic, outline of strategies, your representations.  Address at least three of the major forms  Think also of connections to other forms  Feel free to use the curriculum document, and materials in this room.

11. J/I Math...... S 7 NSN: Using Representations  I am also distributing the article “A Model for Understanding, Using, and Connecting Representations” by Clement (2004).  We will post and share/discuss some suggestions from each of the groups. Please make them legible so that they can be transcribed!

12. Mathematical Representations in the Classroom  Additional Notes (post-class)  As you rise through the grades, you increasingly want to further refine some of the forms—for example, “pictures” becomes forms such as diagrams, graphs, charts, both presented to students and created by students.  When preparing your lesson plans, I recommend that you always keep in mind the question of, “Is a variety of representational forms being used?”

13. J/I Math S 7 Closing  Hand back Assignment 1  Mark out of 20 is combination of individual and group (see your paper for individual mark /13)  Next week: Into NSN—Whole numbers and their operations