Math

The IFL helps teachers, coaches, and administrators to enhance, define, and work towards a common vision of what it means to know, learn, and teach mathematics. 

We support teachers and instructional leaders to implement and maximize cognitively demanding tasks and refine the use of effective teaching practices called for by the National Council of Teachers of Mathematics (NCTM).

Professional Development

Our Professional Development related to mathematics instruction engages educators as learners. The sessions are designed to shift pedagogical practice, leading to more equitable learning opportunities for students. After each session, teachers are encouraged to plan, implement, and return with classroom artifacts to reflect on their practice.

Our professional development provides opportunities for mathematics educator to

    • Select cognitively demanding tasks.
    • Engage students in cognitively demanding tasks in ways that keep the thinking and reasoning with the hands and minds of students.
    • Use targeted questions to assess and advance student learning.
    • Plan for and facilitate mathematically meaningful Accountable Talk® discussions to make sense of mathematical concepts and connect mathematical representations to form generalizations.
    • Use formative assessment to identify student assets and ensure growth in understanding.
    • Address instructional challenges related to interrupted learning, significant amounts of unfinished learning, remote instruction.

“Professional development I’ve participated in seems like it just scratches the surface on important strategies or techniques. This workshop allowed us to really participate and apply what we were learning, such as a college course would instead of the professional development I’ve taken since leaving the university. The rigor was at a higher level than in-person workshops and there were many aspects which added to the rigor – reading articles, watching the videos, applying and receiving feedback.”

– Online Content-Focused Coaching® Workshop participant

Our professional development sessions range from short, targeted learning opportunities to those embedded in multi-year school, district, or state partnerships. Our sessions are most effective when teachers work side-by-side with professionals who support classroom instruction, such as coaches, administrators, and central office educators. Additional professional development opportunities are available for leaders to support mathematics teaching and learning.

Math Planning Essentials Guide

Each Math Planning Essentials guide (MPE) pulls together key elements of lesson planning that are organized by a set of essential understandings— the underlying mathematical truths worth exploring for a given concept of study. MPEs can help make sense of these truths by providing information about how they might playout as students’ conceptual understanding develops.

Each MPE provides:

  • Essential Understandings that name what students need to know for a mathematical concept.
  • Tasks to contextualize the mathematics.
  • Ways students may Use & Explain Representations in response to the tasks, paired with suggestions to further elicit student thinking.
  • Prompts and questions that
    1. ask students to Connect Representations shown in and across student responses and
    2. require students to Explain Mathematical Reasoning about the ideas articulated in the essential understandings.
  • A generalized list of what Students Should be Able to Do and Say, if they have made sense of the essential understandings.

Accountable Talk Math Teacher’s Guide

The Accountable Talk® Mathematics Teacher’s Guide provides teachers and school leaders practical and actionable guidance for creating opportunities for students to engage in meaningful mathematics discussions.

The guide serves as a primer for teachers who want to begin using Accountable Talk practices with their students and also serves as a valuable resource for teachers well versed in the facilitation of  Accountable Talk mathematics discussions. The guide helps teachers enhance instruction by building knowledge related to the types of tasks conducive to talk, planning to ensure that the Accountable Talk features are present during a discussion, and ways of getting students talking in meaningful ways.

The guide includes access to videos and transcripts that can be studied, analyzed, and discussed with colleagues as a means to better understanding Accountable Talk practices. Additionally, you’ll receive a “Student Talk Moves” poster that provides students guidance on how they might respond to their peers and ask questions when they are engaged in small group and whole group discussions.

Content Overlapping Verbal-language and Efficacy Learning (COVE)

COVE is a set of mathematical learning experiences designed for educators to explore the development of content understanding, verbal-language skills, and efficacy in early learners, ages 3-6.

COVE sets clear expectations that students should communicate their thinking and reasoning about mathematical concepts through actions and expressive language. These materials provide educators insights about how to leverage students’ natural curiosity and interests related to foundational mathematical ideas (sorting and categorizing, conservation, and counting and cardinality) and offers educators opportunities to deepen their understanding of mathematical content, content pedagogy, and student thinking.

Supporting Ongoing Achievement Responsibility (SOAR)

SOAR focuses on surfacing and supporting students’ ability to make sense of, represent, and explain mathematical concepts. SOAR can be used across all levels of tiered support to identify assets and areas of need related to students’ mathematical understanding and provide additional learning opportunities to solidify understanding.

Each SOAR toolkit includes:

  • Survey Tools that provides interview prompts, follow-up questions and a checklist that outlines evidence that should be looked and listened for during the interview.
  • Instructional Activities that provide additional learning opportunities focused on thinking and reasoning and guidance for those engaging students in the activities.

Available for the following domains:

  • Operations and Algebraic Thinking – Addition & Subtraction
  • Operations and Algebraic Thinking – Multiplication & Division
  • Numbers in Base Ten
  • Fractions
  • Ratios & Proportions
  • Expressions & Equations

Kindergarten Math Running Record

The math running record focuses on surfacing student understanding and reasoning related to kindergarten numeracy domains: Counting and Cardinality, Operations and Algebraic Thinking, and Number and Operations in Base Ten.

The KMRR includes a

    • Teacher Guide that provides prompts and follow-up questions to identify where students are in their understanding of the content.
    • Checklist that outlines evidence that should be looked and listened for during the running record and provides a place for observations to be recorded.
    • Student display book that serves as a student copy of running record prompts.

Lesson Sets

A lesson set includes a sequence of 8 high-level mathematics tasks. For each task, there is a lesson guide that provides anticipated solution paths, as well as questioning strategies for both small-group work and whole-group discussions. Each lesson set also provides application problems and Quick Writes. A lesson set may take 8-15 days of instruction. 

Instructional Units

An instructional unit contains an overview of the unit and the concept(s) of study, a series of at least 14 related tasks with lesson guides, checkpoints at strategic points in the unit paired with student support activities, and final performance-based assessment. An instructional unit may take 3-6 weeks of instruction.