Best Practices in MathUsing the Habits of Mind and Interaction

Integrating effective math instruction

(think Common Core Mathematical

Practices) with district curriculum

(Engage New York).

The Big Picture

Where to begin? Locate your first unit of study

Found on the CIA: https://salkeiz-cia.orvsd.org/

Be sure to log in first username: lastname_firstname

password: the same as you use to log in for the district

Open your first unit of study under your grade’s “instruction” tab

Take time to look through the unit of study (curriculum map)

Focus on the “Big Ideas”

Engage New York All grades will use Engage New York (ENY).

As a PLC, you may decide to supplement with other

resources.

You should have:

Paper copy of each unit’s teacher’s guide/lessons

Electronic teacher’s guides are on U drive and also uploaded

on Digital Storefront.

Non-consumable workbooks (student Problem Sets), not to

be written in.

Engage New York Exit Tickets: you will need to order print or decide as a

PLC how you’d like to assess

Homework: Also, as a PLC, decide what you’d like to

do. Use the ENY homework as is? Modify? Use

something else?

Mid-module and end-of-module assessments: you will

need to look at these with your PLC, and order print

ENY and Student Mathematical Practices

All grades are required to implement the Student

Mathematical Practices.

Located on the CIA site: https://salkeiz-cia.orvsd.org/math

How can we be sure that they are a part of our

everyday math instruction/learning?

How can we get our students to understand these

practices and eventually start implementing them on

their own?

What is a way to teach these practices in a “student-

friendly” way?

Mathematical Productive

Thinking Routines

Explain your thinking/reasoning in a

variety of ways.

Explain why your

ideas/solutions/conjectures are always,

sometimes ,or never true.

Clarify, deepen, and expand thinking by

making conjectures based on the math

you know combined with relationships

noticed.

Mathematical Habits of Mind

CONNECTIONS

I notice and reason about connections within and across

mathematical representations, other math ideas, and

everyday life.

MATHEMATICAL REPRESENTATIONS

I create and reason from mathematical representations-

visual models, graphs, numbers, symbols and equations,

and situations.

REGULARITY, PATTERNS, STRUCTURE

I notice and reason about mathematical regularity in

repeated reasoning, patterns, and structure (meanings,

properties, definitions).

MISTAKES & STUCK POINTS

I explore mistakes and stuck points to start new lines of

reasoning and new math learning.

METACOGNITION & REFLECTION

I use metacognition and reflection. I think about my math

reasoning and disequilibrium– how my thinking is

changing and how my ideas compare to other

mathematicians’ ideas.

PERSEVERE & SEEK MORE

I welcome challenging math problems and ideas, and

after I figure something out, I explore new possibilities.

Mathematical Habits of Interaction

When I do math with other mathematicians, we:

Use PRIVATE REASONING TIME

Honor each other’s right to private reasoning time before

talking about our ideas.

EXPLAIN

Explain how we think and reason mathematically.

LISTEN TO UNDERSTAND

Listen to understand each other’s math reasoning about

problems, conjectures, justifications, and generalizations.

Ask GENUINE QUESTIONS

Use genuine questions to inquire about each other’s math

reasoning about problems, conjectures, justifications, and

generalizations.

Use MULTIPLE PATHWAYS

Explore multiple pathways by applying each other’s lines

of reasoning.

COMPARE LOGIC & IDEAS

Compare our math logic and ideas to figure out how they

are mathematically the same and different.

CRITIQUE & DEBATE

Critique and debate the math logic and truth in each

other’s reasoning.

Remember that MATH REASONING IS THE

AUTHORITY

Use math reasoning as the authority for deciding what is

correct and makes sense.

Question of the Day

Focus lesson around one main problem. This gives you

freedom to go “off script” from the teacher’s guide.

It would most likely come from your ENY lesson for the

day (modify if needed)

The problem would be one that is focused on your “big

idea.”

The problem would lend itself to integrating one or

more of the habits of mind and interaction.

Strategies and

Representations Do the math!

Plan ahead of time for what strategies and representations you’d like to feature (sketch out on your plans).

Think about what mistakes/stuck points may come up and how to approach that.

Write out “genuine questions” that you plan to ask.

Think about the habits of mind and interaction you’d like to focus on for the lesson.

Some of these habits will come naturally, especially after implementing them regularly.

Student Math-Talk Let’s try it…

Math Task Brock makes 21 jars of tomato sauce with the tomatoes

from his garden. He puts 7 jars in each box to sell at

the farmers’ market. How many boxes does Brock

need?

Step 1: Take private reasoning time to work through

this problem using mathematical representations.

Student Math Talk

Step 2: Student Math Talk

Strategy: Listen & Compare: Partner A

speaks while Partner B listens without

interrupting. When teacher announces

“Finish your thought and switch roles,”

Partner B speaks, including comparative

language (sentences frames would come in

handy with this one).

More Strategies

Strategy: Revoice & Compare:

As with the previous strategy, Partner A shares

while Partner B listens silently. Instead of

immediately switching roles, Partner B revoices

Partner A’s ideas without modifying them.

Partner A clarifies as needed. The partners

then switch roles and the process is repeated.

Strategic “Share” As students are working, teacher circulates. When s/he

sees a strategy or representation to highlight with the

group, the teacher places a sticky note near the

student.

The teacher then helps transition back to whole-group

time, and asks the students with sticky notes to share.

Often, the teacher uses these ideas to construct a

public record (anchor chart).

Creating “Public Records” Part of “doing the math” ahead of time is envisioning

how you want the public record (aka anchor chart) to

look.

Think about the representations you want students to

use. They should discover them on their own, but if

they don’t, how will you guide them without directly

feeding it to them?

Hint: “I once saw a student do it this way…”

More Application Solve the following the problem….and you can’t “invert

and multiply….”

12 ÷ ¼ =

Use Private Reasoning Time and create a

mathematical representation.

So…… How did that feel? Was it comfortable?

Welcome to…Productive Disequilibrium!

This is an example of using Mistakes and Stuck Points

to further learning. It’s a paradigm shift to view being

stuck as a positive part of learning. As teachers, we

need to remember to not jump in and give them the

answer to alleviate our own discomfort.

Planning a Lesson Use created template or some other method you

decide on as a PLC.

Walk through…

Final Thoughts This is a shift to student-centered mathematics

instruction. Think of yourself as the facilitator. Plan

ahead for what you want the students to understand

and what strategies you want them to discover. Have a

plan for facilitating these things if they don’t naturally

discover them. Ask genuine questions that will lead to

sense-making and generalizing.