Math Institute: Building Structure, Fluency, and Mathematical Reasoning

Adaptable to your schedule! 

Join us for this four-day institute with leading researchers in math instruction. Create a personalized learning experience by attending a single session or the full institute.

Dates: July 20-23, 9:00 am- 12:00 pm EST
Location: Virtual
Credits: NYCTLE credits – 3 hours per workshop

Day 1: Mathematics Vocabulary: What do words have to do with it?

Presenter: Elizabeth Stevens, PhD

Description:
Mathematics vocabulary can be challenging for students, especially those with mathematics difficulty, because so many terms carry multiple meanings both across subjects and within math itself. Yet research consistently shows that strong math vocabulary is tightly linked to stronger math performance, making it essential for helping students communicate their thinking, make sense of word problems, and engage confidently with new content. This session invites teachers to dig into the complexity of math language, explore different types of vocabulary, and understand why using precise terms (like numerator instead of “top number”) truly matters. Educators will learn how to identify high‑impact words using a database of critical math terms, and learn five practical instructional routines designed to make vocabulary instruction more powerful and engaging. Through hands‑on practice, collaborative planning, and ready‑to‑use digital resources, teachers will leave equipped to strengthen students’ mathematical language and elevate classroom discourse.

Key Learning Objectives:

• Explain why mathematics vocabulary knowledge supports understanding of mathematics concepts
• Explain how to prioritize terms for instruction
• Identify and learn practices for teaching and reviewing mathematics vocabulary
• Plan ways to implement and apply content learned in your instructional setting (e.g., classroom, small group, coaching)

 Day 2: A Structured Approach to Solve Addition Math Word Problems

Presenter: Elizabeth Hughes, PhD

Description:
This session introduces participants to the principles of schema-based instruction, an approach that helps students make sense of word problems by recognizing underlying mathematical structures rather than relying on superficial keywords. We will explore the major additive problem types, including join, separate, part–part–whole, and compare, and discuss how to guide students in identifying these structures across varied contexts. Participants will learn how to use visual models to represent thinking, support problem comprehension, and strengthen conceptual understanding. The session will also include a brief introduction to worked examples as an effective tool for building clarity and reducing cognitive load as students internalize problem schemas.

Key Learning Objectives:

• understand what schema-based instruction is and why it supports deeper mathematical comprehension
• identify and explore the four major additive problem types
• gain strategies for helping students recognize problem structure rather than relying on keywords
• gain practical ways to use visual models to represent thinking and support problem-solving
• explore how worked examples can build conceptual clarity and reduce cognitive load for learners

Day 3: The Power of Structure: Understanding Multiplicative Thinking

Presenter: Jonté Meyers, PhD

Description:
This session will deepen participants’ understanding of multiplicative reasoning and how it differs fundamentally from additive reasoning. We will explore key multiplicative structures, including equal groups, comparison situations using “times as many,” arrays and fundamental differences, rate problems, to build a solid conceptual foundation. Participants will examine how students form composite units and why this shift in thinking is essential for fluent multiplication and division. The session will highlight a range of representations that make multiplicative structure visible, supporting stronger reasoning and problem solving. Finally, we will look at worked examples that clearly connect visual models to procedures, helping learners internalize the logic behind efficient strategies.

Key Learning Objectives:

• understanding how multiplicative reasoning fundamentally differs from additive reasoning, and why this shift matters for students’ mathematical development
• familiarity with major multiplicative structures, including equal groups, “times as many” comparison problems, arrays/area models, and rate situations
• insight into how learners build composite units and how to support this critical cognitive move
• strategies for using representations that reveal multiplicative structure, helping students see and make sense of relationships
• explore worked examples that connect visual models to formal procedures, building conceptual and procedural fluency

Day 4: The Science of Math: Turning Research into High-Impact Classroom Practices

Presenter: Paul Riccomini, PhD

Description:
This workshop covers spaced learning, varied practice types, and information recall, three evidence-based methods to enhance student learning. Educators will receive frameworks and develop a clear understanding of the scientific principles underlying these approaches. Participants will examine cognitive processes that support long-term retention and acquire techniques to deepen students’ understanding and application of math knowledge. Through interactive activities and collaborative planning, educators will learn to incorporate these strategies into mathematics instruction.

Key Learning

• explain key cognitive processes related to memory and retention within math concepts
• identify and understand the research supported techniques of Spaced learning, Interleaved Practice, and Practice Test Retrieval
• analyze how retention strategies can vertically align with K–12 mathematics instruction
• apply evidence-based techniques to authentic classroom scenarios by designing lesson components, tasks, and review routines
• gain a toolkit of instructional scaffolds that integrate into math lessons