Prep

Watch DMT Insights DMT Insight 01 Taking Students Ideas Seriously This DMT Insight describes how taking students' initial ideas seriously, building on their intuitive knowledge, and engaging in crucial cognitive processes improve long-term understanding and skills. Watch DMT Insights DMT Insight 02 How Math Models Transform Learning This DMT Insight shows how a few models used again and again, such as the bar model, number line, and area model, make the underlying mathematical relationships visible, so students reason with structure. Watch DMT Insights DMT Insight 03 Prioritizing Conceptual Learning This DMT Insight shows why building conceptual understanding before the procedure gives students something to reason from, so a forgotten step can be rebuilt rather than simply lost. Watch DMT Insights DMT Insight 04 Focusing on Mathematical Structure This DMT Insight shows how a small set of structural actions, naming the unit and composing, decomposing, iterating, and partitioning it, recurs across every topic and grade, so that structure becomes what stays the same when the mathematics changes. Watch DMT Insights DMT Insight 05 Harnessing Misconceptions This DMT Insight shows why a misconception is a good idea when it no longer applies, and how to reorganize the reasoning behind a wrong answer instead of simply correcting it. Watch DMT Insights DMT Insight 06 Early Predictors of Math Success This DMT Insight explains how six areas of early mathematics (number sense, number facts, contextual problems, relational thinking, measurement, and spatial reasoning) help teachers decide what to teach next. Watch DMT Insights DMT Insight 07 The Learning Trifecta This DMT Insight explains how productive struggle, restraint with hints, and mixed practice leave more mathematical decisions to students, so they retain and use what they learn. Watch DMT Insights DMT Insight 08 Foundations in Number Sense Early mathematics education shapes students' long-term mathematical understanding and problem-solving abilities. A key component of this is developing number sense. Watch DMT Insights DMT Insight 10 The Power of Division This DMT Insight examines division as a relationship among a total, a unit, and an iterator, showing why the same equation can ask two different questions and why students need to know what the quotient counts. Division Multiplication / Division (3-5) Watch DMT Insights DMT Insight 11 Percent Is a Relationship This DMT Insight explains percent as a relationship between a quantity and a reference quantity (100%) and shows how bar models, double number lines, ratio tables, and benchmark percentages help students reason about that relationship. Number (6-8) Watch DMT Insights DMT Insight 12 Building Place Value Understanding This DMT Insight explains why naming places is not the same as understanding place value, and shows how students learn to read a multi-digit number as a single quantity composed of nested base-ten units that they can compose, decompose, rename, and l Place Value (3-5) Place Value (K-2) Watch DMT Insights DMT Insight 14 Math Fact Fluency This DMT Insight explains math fact fluency as accurate, increasingly efficient recall or derivation of facts from known relationships, and shows how students build unknown facts from known ones and practice those relationships until many become auto Algebra (6-8) Fluency and Flexibility Watch DMT Insights DMT Insight 15 Fraction Understanding This DMT Insight examines why fraction errors are rarely careless, showing how a student who reads a fraction as a count of units of a named size rather than as two whole numbers estimates before computing, and how each predictable misconception name Fraction Fraction Concepts (3-5) Watch DMT Insights DMT Insight 18: Why Measurement Matters: The Building Blocks of Math This DMT Insight explains how measurement gives numbers meaning: students compare attributes, iterate equal-sized units, and coordinate unit size with unit count. That same structure extends to rulers, number lines, fractions, decimals, and place val Measurement Measurement (3-5) Watch DMT Insights DMT Insight 19 The Five Counting Principles This DMT Insight explains the five counting principles and shows how students coordinate number words, units, and quantity, so teachers can distinguish reciting the counting sequence from counting a set and see what a student's counting reveals. Number Whole Numbers (K-2) Watch DMT Insights DMT Insight 20 Rethinking Powers of Ten This DMT Insight explains why multiplying by ten is not "adding a zero," and shows how students come to understand powers of ten as the ×10 structure of base-ten units, where each unit is ten times the one to its right and one-tenth the one to its le Middle School Number (6-8) Watch DMT Insights DMT Insight 21 Developing Multiplicative Reasoning This DMT Insight examines how students develop multiplicative reasoning by identifying units and iterations, using bar and area models to connect decomposition and the distributive property to efficient procedures. Multiplication / Division (3-5) Multiplication Fluency Watch DMT Insights DMT Insight 22 Understanding State Mathematics Assessments This DMT Insight examines what state mathematics assessments measure, distinguishes DMTI’s assessment categories from Webb’s Depth of Knowledge, and explains how teachers can use state results. Read this one DMT Insights DMT Insight 23 Assessing Mathematical Understanding This DMT Insight shows how teachers can use the DMT assessment framework to examine students’ strategies, representations, and explanations, and to use the resulting evidence to plan instruction. Watch DMT Insights DMT Insight 24 Beyond the Core Curriculum This DMT Insight examines why some students need intervention that takes a different mathematical approach than the core curriculum, one that develops conceptual understanding, procedural fluency, and flexibility together rather than repeating core l Read this one DMT Insights DMT Insight 25 Beyond Borrowing This DMT Insight reviews research on how students understand place value, develop multi-digit subtraction strategies, and understand regrouping as the decomposition of equivalent quantities rather than as borrowing. Addition / Subtraction (3-5) Addition / Subtraction (K-2)

PD Video Developing Mathematical Thinking Framework PD Video Addition and Subtraction Fluency: Introduction to the Strategies PD Video Fractions: Visual Model Progression PD Video Measurement: Length Misconceptions and the Broken Ruler PD Video Geometry: Quadrilateral Hierarchy PD Video Decimal Concepts: Introduction PD Video Modeling Compare Problems PD Video Ratio and Proportion: Using Context, Ratio Tables, and Models