Project Overview

The purpose of the Project MINE is to integrate professional noticing of children’s mathematical thinking with equitable teaching practices in mathematics.

Professional Noticing (PN) is a purposeful integration of these three components into teaching: attending (observing students’ mathematics thinking), interpreting (understanding what students know), and deciding (making instructional decisions based on evidence). We use Gutierrez’s (2009) four dimensions of Equity (access, achievement, identity, and power) to integrate topics related to critical math topics in the classroom. We strongly suggest the two brief readings, which provide an overview of PN and the dimensions of equity, which guide the modules. As preservice teachers engage in observations, discussions, and activities in the modules, the goal is for them to improve their teaching practices by attending not only to students’ mathematical strengths, but making learning meaningful by connecting to students’ personal identities and their communities.

Lesson Organization

This document contains overview information about the MINE project and the modules that compose it.

A brief description of the content of each module is listed here, along with a summary of the mathematical content, pedagogical content, equity dimensions, professional noticing component, and an approximate time to complete each module in class. Links to each Google Slides presentation as well as the accompanying guide are included as well. The guide for a specific module contains a link to the accompanying presentation and a link back to this document. All guides are organized the same way: an overview of the equity dimensions and the professional noticing (PN) components at the top of the document, and then all slides in the presentations are detailed in two columns. The left column contains images of the slides and the right column gives instructions on the slide activities, including an approximate time to be spent on that slide.

Each presentation contains an introductory overview slide and a concluding wrap-up slide that highlights the equity dimensions and PN components of that specific module.These are used in every presentation to illustrate the relevant themes, with the themes that are not being specifically focused on still present but in grey.


Icons are used in the instructor guides to help efficiently convey the contents of the modules as a whole and the activities of specific slides.

The top of the document for each module lists all the equity dimension and PN component icons, with the themes not discussed in a specific module in greyscale to match the overview and wrap-up slides. Slide and activity components are shown in red.

Slide Components:

Individual Activity

Partnered Activity

Small Group Activity

Discussion Prompt

Focus on Language


Other Component

Professional Noticing Components:




Equity Dimensions:






PN ComponentsEquity Dimensions
Introduction to Professional Noticing Components and Dimensions of EquityCheckedCheckedCheckedCheckedCheckedCheckedChecked
Number Talks and Smartness in MathematicsCheckedCheckedCheckedCheckedCheckedChecked
Ratios and Language in MathematicsCheckedCheckedCheckedCheckedCheckedCheckedChecked
Patterns and Student Work in MathematicsCheckedCheckedCheckedCheckedCheckedChecked
Cornhole Fractions and Productive Struggle in MathematicsCheckedCheckedCheckedCheckedChecked
Fractions and Representations in MathematicsCheckedCheckedCheckedCheckedCheckedChecked
Functions and Creating Inclusive Story Problems in MathematicsCheckedCheckedCheckedCheckedCheckedChecked
Social Justice and Standards in MathematicsCheckedCheckedCheckedChecked

Introduction to Professional Noticing Components and Dimensions of Equity

During this module, students will be introduced to both the professional noticing and equity frameworks used throughout the module set.  Students will have the opportunity to engage in professional noticing of a child’s mathematical activity in the context of number/operations as well as engage in connecting an instructional segment to different equity dimensions.  The module concludes with an examination of common language related to diversity and instructional experience.

Mathematical Content: Number/Operations; Percent
Pedagogical Content: Practices for orchestrating productive discussions
Equity Dimensions: all
PN Components: all
Approximate Lesson time: 30 minutes
*This is the 1 required first module for all who implement, then instructors can choose additional modules according to content or themes.

Number Talks and Smartness in Mathematics

This module focused on the attending and interpreting components of professional noticing as well as the identity, power, and achievement dimensions of equity. The video anchor for this module shows a teacher discussing how she empowers her students by allowing them to lead number talks. The video reveals how she provides instructions to the students regarding appropriate questioning and conversations about the problem as well as how she encourages reflections at the end of the lesson. This follows with a discussion of ways that students can be “smart” in math beyond just getting correct answers. The final discussion involves a discussion about how to use words such as “low” and “high” to describe student learning.

Mathematical Content: Subtraction
Pedagogical Content: Number Talks, Being “Smart” in Math
Equity Dimensions: Identity, Power, Achievement
PN Components: All
Approximate Lesson time: 20-25 min

Ratios and Language in Mathematics

This session focuses on challenging the notion that “math is a universal language” or that it is “culturally neutral” by highlighting an ELL perspective in math. Students will first be put in the position of reading and listening/viewing a math problem in Spanish to provide some disequilibrium. Then they will discuss how strategies can support multilingual learners in mathematics. The thinking about language further challenges students to think about assumptions they have about multilingual learners and how children’s backgrounds can be used as an asset in math.

Mathematical Content: Ratios and Proportions
Pedagogical Content: Strategies for Multilingual Learners and Language in Mathematics
Equity Dimensions: all
PN Components: all
Approximate Lesson time: 20-25 minutes

Patterns and Selecting Student Work in Mathematics

During this module students will exercise their professional noticing skills of all three components considering equitable practices as they do so. The focus, related to equity, is the critical axis (changing the game) dimensions of identity and power. Students will view a video with a stance of mathematics and equitable practices, then discuss what classroom changes can be considered to shift identities and power to be more equitable. Finally, a typical statement will be analyzed for language that may unintentionally impact the identity and power of students.

Mathematical Content: Multiplicative and Additive Patterns
Pedagogical Content: Practices for orchestrating productive discussions
Equity Dimensions: Access, Identity and Power
PN Components: Attend, Interpret, and Decide (all)
Approximate Lesson time: 25-30 minutes

Cornhole Fractions and Productive Struggle in Mathematics

In this module, the students will learn about disequilibrium and how/when a teacher can press for academic stress during those healthy struggles. It uses all three components of professional noticing and focuses on the achievement dimension of equity. The introduction of healthy struggle, is followed by some examples of children completing a fractions task that centers around painting a set of cornhole boards and how much paint they should buy. One task appears too simple and the next task appears too complex so it leads to a discussion on a better task. Finally, a typical statement heard in farming communities and its potential impact on childrens’ achievement is discussed.

Mathematical Content: Arithmetic and Reasoning with Fractions
Pedagogical Content: Healthy Struggles and Pressing for Academic Success
Equity Dimensions: Achievement & Power
PN Components: Attending, Interpreting, Deciding
Approximate Lesson time: 20-25 minutes

Functions and Creating Inclusive Story Problems in Mathematics

In this session, students will explore how identity (e.g. gender, race, family background) provides access to mathematics in varying ways. They will create story problem contexts that are more inclusive and meaningful as an application. A brief video of a second grade classroom discussing a patterns/functions idea will also extend the conversation of access and identity.

Mathematical Content: Functions and Word Problems
Pedagogical Content: Creating Inclusive and Meaningful Math Tasks
Equity Dimensions: Access, Identity
PN Components: Attending, Deciding
Approximate Lesson time: 25 minutes

Social Justice and Standards in Mathematics

In this session, students will explicitly consider how math can be used to explore the critical axes of equity of identity and power in the classroom. They will view a clip about how mathematics is used to understand and improve the world. Then, they will review two mathematics and social justice tasks (one more critical than the other) to discuss how such tasks and lessons can improve students’ mathematics skills and understanding of social justice.

Mathematical Content:
Pedagogical Content:
Equity Dimensions: Access, Identity, Power
PN Components: Decide
Approximate Lesson time: