# DCSD K-12 Mathematics Initiative

### Your Menu to Math Success!!

## Greetings Wonderful Math Teachers!

## ...Mistakes are RESPECTED, EXPECTED, and INSPECTED

**INSTRUCTIONAL RIGOR**is "creating an environment in which each student is

__expected__to learn at high levels, each student is expected to learn at high levels, each student is

__supported__so he or she can learn at high levels, ad each student

__demonstrates__learning at high levels (Blackburn, 2012)."

__Rigorous and Relevant Lessons - Answers the listed student questions...__

What am I learning?

Why am I learning it?

How will I apply/use it?

## Mathematics Process

- originated from PDCA: Plan-DO-Check-Act
- PDCA is a cyclical method for continuous improvement of processes
- DCSD: PLAN - ENGAGE - ASSESS
- We are continuously asking, "What are we trying to accomplish?"; "How will we know that a change is an improvement?"; and "What changes can we make that will result in improvement?"

## Mathematics Design

## Concrete-Representational-Abstract (C-R-A)

- C-R-A are the fundamental stages to development content mastery.
- Instruction includes deep conceptual understanding and procedural fluency. Initial teaching can either be explicit instruction or student exploration that leads to conceptual understanding.
- Mathematical vocabulary is developed throughout the lesson.

## Multiple Representation

- Verbally
- Algebraically
- Numerically
- Graphically

## Number Talks

A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation. A Number Talk is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply and divide.

Number Talks should be structured as short sessions alongside (but not necessarily directly related to) the ongoing math curriculum. It is important to keep Number Talks short, as they **are not intended to replace current curriculum or take up the majority of the time spent on mathematics**. In fact, teachers need to spend only 5 to 15 minutes on Number Talks. Number Talks are most effective when done every day.

The primary goal of Number Talks is computational fluency.

The National Council for Teachers of Mathematics states that "Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently. The computational methods that a student uses should be based on mathematical ideas that the student understands well, including the structure of the base-ten number system, properties of multiplication and division, and number relationships.” Principal and Standards for School Mathematics, NCTM, Reston, VA 2000, p.152

## Math Talks

Math Talk provides students an opportunity for deeper understanding through communication. Individually or in groups, students articulate and defend their ideas and analyze the reasoning of others.

Teachers will gain the ability to assess student knowledge through asking “good questions,” and align instruction to ensure each student understands how to use math skills through thinking, talking, and doing.

Five Major Reasons That Talk Is Critical to Teaching and Learning

- Talk can reveal understanding and misunderstanding.
- Talk supports robust learning by boosting memory.
- Talk supports deeper reasoning.
- Talk supports language development.
- Talk supports development of social skills.

Using communication in the classroom to **represent, explain, justify, agree,** and **disagree** shapes the way students learn mathematics. Classroom dialogue engages students, encourages them to learn more, and allows for the exploration of **ideas, strategies, procedures, facts,** and more.

Affecting the way ideas are exchanged and developed, Math Talk supports a social learning environment for children—creating a community of **encouragement, respect, and the exchange of ideas.**

## Note-taking

## Polya's Problem Solving Process

https://math.berkeley.edu/~gmelvin/polya.pdf

http://study.com/academy/lesson/polyas-four-step-problem-solving-process.html

## Constructing a Response in Math with Close Reading

A strategy that allows readers to dig deeper into a text by:

- Reading and re-reading the text to gather meaning and determine purpose
- Highlighting important vocabulary words and other essential details that help to determine purpose and meaning.
- Providing evidence and support for answers to comprehension questions by using the information from the text.