**Week Eight 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)

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.

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

- I can implement tasks that promote reasoning and problem-solving. (#NCTMP2A)

- I can make sense of tasks and persevere in solving them.

**Tasks:**

- Open Middle: Biggest Product
- Illustrative Mathematics: Overlapping Squares
- Open Middle: Finding Equivalent Fractions

**What the research says:**

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

Too often students see mathematics as isolated facts and rules to be memorized. … students are expected to develop deep and connected knowledge of mathematics and are engaged in learning environments rich in use of multiple representations.

Mathematics learning is not a one size fits all approach …, meaning not every child is expected to engage in the mathematics in the same way at the same time. … the diversity of their sense-making approaches is reflected in the diversity of their representations.[p. 140]

##### 08_Strengthen Mathematical Flexibility_ Use and Connect Mathematical Representations by Jill Gough on Scribd

[Cross posted at Experiments in Learning by Doing]

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.