Teaching Math for Learning: Standards-Aligned System, Secondary Mathematics, Year 2

Team Pierogi Head Complete the team activity entitled Team Pierogi Head Be prepared to share your poster and team name

Goals for Year 2 Become familiar with a process for planning a lesson which includes thoughtful consideration of selecting and setting up a task, supporting students’ exploration of the task, and sharing and discussing student solutions of the task Utilize the PA Standards-Aligned System as a tool in lesson design

Math & Science Collaborative4 Concept Map and Conceptual Flow Find the concept map and conceptual flow documents behind the Guiding Documents tab

Math & Science Collaborative Norms for Learning What can you do to make this a good learning experience for yourself? What can you do to make this a good learning experience for others?

Algebra I Keystone Exams Assessment Anchors Review the assessment anchors and eligible content for the Algebra I Keystone Exam on the SAS portal How do these ideas relate to our year 1 academy?

Assessment Anchors and Eligible Content Assessment Anchor A Simplify expressions involving polynomials. Eligible Content A Add, subtract, and/or multiply polynomial expressions (express answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial

Algebra Tiles Task Use algebra tiles to show these multiplications and make a sketch of your model. Write the product. 2x(x-1) (x+1)(x+2) (x-2)(3x+3) (x-3)(x+3) (2x+2)(2x-2) (x+3)(x+3) Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2009). Implementing standards-based mathematics instruction: A casebook for professional development (2 nd ed.). New York: Teachers College Press.

Task Analysis How would you categorize this task according to the Task Analysis Guide? Low-Level Tasks memorization procedures without connections High-Level Tasks procedures with connections doing mathematics

Based on work by Dr. Margaret S. Smith, University of Pittsburgh Linking to Literature/ Research: The QUASAR Project The Mathematical Tasks Framework TASKS as they appear in curricular/ instructional materials TASKS as set up by the teachers TASKS as implemented by students Student Learning Stein, Smith, Henningsen, & Silver, 2000, p. 4

The Case of Monique Butler Read the Case of Monique Butler on pages in Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development (Stein, Smith, Henningsen, and Silver, 2009)

The Case of Monique Butler 1.What issues was Monique concerned about in this lesson? a) What were the mathematical issues Monique was concerned about? b) What do you think Monique wanted her students to learn? c) Were there any nonmathematical issues of concern to Monique? 2.What do you think Monique’s students were learning in the lesson? a) Were they making connections between the area representations and the symbolic procedures? b) Was Malcolm’s explanation at the end of class a good mathematical explanation ? Why or why not?

The Case of Monique Butler 3.How did the set-up of the task, both prior to and during the lesson, affect the implementation of the task? 4.What factors may have influenced whether students were making the connections Monique was hoping they would make? a) Were there things Monique was doing to support or inhibit the students’ engagement in high-level thinking? b) What were the students doing that might have influenced their own learning?

The Case of Monique Butler 5.What do you think Monique should do next? (Or if Monique had more time in the lesson, how do you think she should have responded to Malcolm?)

Bag of Marbles Task Based on work by Dr. Margaret S. Smith, University of Pittsburgh

Task Analysis How would you categorize this task according to the Task Analysis Guide? Low-Level Tasks memorization procedures without connections High-Level Tasks procedures with connections doing mathematics

Homework Read the article, Thinking Through a Lesson: Successfully Implementing High-Level Tasks Focus question: What are some implications for teaching and learning that the article implies?

Reflection What is one idea from our work today that you are now considering for your classroom practice? Why?