DMT Insights
The research behind how children actually learn mathematics
Short, readable overviews of the research DMTI builds on, published every other week. Every one is free to read, watch, and share.
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Three ways in
Pick the one that matches your question. They overlap, and an Insight can belong to more than one.
Foundations
How students think, learn, reason, and represent mathematics. These ideas apply in every grade and every topic you teach.
9 insightsMathematics
The mathematics itself, from counting and place value through algebraic reasoning.
13 insights · 8 domainsMath Learning Profiles
The research behind identifying what students understand and what they are ready to learn next.
5 insightsRecently added
Recently added Insights
Scaling and Comparing
This DMT Insight explains why the move from adding to scaling, from asking how many more to how many times as much, is one of...
Number Lines Should Be Built
This DMT Insight shows how letting students build number lines, not just use them, strengthens their structural understanding by...
The Struggle with Rounding and Estimation
This DMT Insight explains why rounding and estimation are about reasoning about proximity and magnitude rather than about a rule...
Rethinking Powers of Ten
This DMT Insight synthesizes key insights on teaching powers of 10, emphasizing its foundational role in mathematics education,...
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By the mathematics
22 insights across 8 topics, with one more in development.
Foundations
How students think, learn, reason, represent, and develop understanding
9 insightsNumber & Quantity
Quantity, counting, cardinality, subitizing, unitizing, composing and decomposing
2 insightsPlace Value
Units and unit relationships, base-ten structure, composing and decomposing, magnitude
4 insightsAddition & Subtraction
Quantitative relationships, properties, composing and decomposing, benchmark reasoning, comparison
1 insightMultiplication & Division
Equal groups, arrays, units and unit relationships, multiplicative reasoning, factors and multiples
1 insightFractions & Decimals
Partitioning and iterating units, the unit of 1, unit fractions, equivalence, magnitude, operations
2 insightsRatio & Proportional Reasoning
Multiplicative comparison, ratios, rates, proportions, percent, scaling
2 insightsGeometry & Measurement
Spatial reasoning, attributes and units, length, area, volume, angle, geometric structure
1 insightAlgebraic Reasoning
Equivalence, generalized relationships, expressions, patterns, variables, functions
In development