**Week Six of Embolden Your Inner Mathematician**

We commit to curation of best practices, connections between mathematical ideas, and communication to learn and share with a broad audience.

**Course Goals:**

At the end of the semester, teacher-learners should be able to say:

- I can work within NCTM’s Eight Mathematical Teaching Practices for strengthening the teaching and learning of mathematics.
- I can exercise mathematical flexibility to show what I know in more than one way.
- I can make sense of tasks and persevere in solving them.

**Today’s Goals**

At the end of this session, teacher-learners should be able to say:

- I can use and connect mathematical representations. (#NCTMP2A)
- I can make sense of tasks and persevere in solving them. (#SMP-1)
- I can show my work so that a reader understands without have to ask me questions.

From *Principles to Actions: Ensuring Mathematical Success for All: *

**Use and connect mathematical representations:** Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

From *Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5*

*In ambitious teaching, the teacher engages students in challenging tasks and collaborative inquiry, and then observes and listens as students work so that she or he can provide an appropriate level of support to diverse learners. The goal is to ensure that each and every student succeeds in doing meaningful, high-quality work, not simply executing procedures with speed and accuracy.*(*Smith, 4 pag.)*

**Learning Progressions for today’s goals:**

- I can use and connect mathematical representations. (#NCTMP2A)

- I can show my work so that a reader understands without have to ask me questions.

**Tasks:**

- Visual representation of multiplication, exponents, subtraction. (Connect 2nd-5th grade with Algebra I and II.)
- Apples and Bananas task (see slide deck)

**What the research says:**

*Not only should students be able to understand and translate between modes of representations but they should also translate within a specific type of representation. [Smith, pag. 139] *

*Equitable teaching of mathematics includes a focus on multiple representations. This includes giving students choice in selecting representations and allocating substantial instructional **time and space for students to explore, construct, and discuss external representations of mathematical ideas. *[Smith, pag. 141]

*Too often students see mathematics as isolated facts and rules to be memorized. *[Smith, pag. 141]

**\Anticipated work and thinking:**

[Cross posted at Sum it up and Multiply it out]

Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions.” *Experiments in Learning by Doing**or Easing the Hurry Syndrome.*WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Leinwand, Steve. *Principles to Actions: Ensuring Mathematical Success for All*. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

Smith, Margaret Schwan., et al. *Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5*. The National Council of Teachers of Mathematics, 2017.