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DMT Insights
All 52 are free to read and print. No account needed.
Grade
Topic
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DMT Insights
Are Your Students Really Understanding Line Plots?
This DMT Insight examines why students commonly misinterpret line plots, focusing on confusion between quantities and counts as well as misunderstanding symbols like X marks. It shares research-based strategies—such as clear language, visual mo
Watch
DMT Insights
Are Your Students Really Understanding Line Plots?
This DMT Insight examines why students commonly misinterpret line plots, focusing on the confusion between quantities and counts, as well as misunderstandings of symbols like X marks.
DMTI Overviews
Geometry / Measurement / Data (3-5)
Watch
DMT Insights
Assessing Student Understanding
This unit overview presents the DMT assessment framework, which guides educators in assessing student understanding in mathematics through a multi-level approach encompassing skill-based, problem-solving, conceptual, and reasoning tasks to identify m
Watch
DMT Insights
Bridging Core and Intervention Curricula
This DMT Insight clarifies the distinct roles, structures, and best practices of core and intervention math curricula, highlighting how their purposeful alignment and integration can better meet diverse student needs and address persistent gaps
Watch
DMT Insights
Building Stronger Math Thinkers Through Progressive Formalization
This DMTI Insight explains how progressive formalization guides students from intuitive, hands-on math experiences toward a deep understanding of formal mathematical concepts.
DMTI Overviews
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 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 38 Building the Number Line
This DMT Insight shows how students build a number line by defining a unit, iterating it, partitioning it as needed, and establishing a scale so each number represents both a location and a distance from zero.
Watch
DMT Insights
Are Your Students Really Understanding Line Plots?
This DMT Insight examines why students commonly misinterpret line plots, focusing on the confusion between quantities and counts, as well as misunderstandings of symbols like X marks.
DMTI Overviews
Geometry / Measurement / Data (3-5)
Watch
DMT Insights
Assessing Student Understanding
This unit overview presents the DMT assessment framework, which guides educators in assessing student understanding in mathematics through a multi-level approach encompassing skill-based, problem-solving, conceptual, and reasoning tasks to identify m
Watch
DMT Insights
Bridging Core and Intervention Curricula
This DMT Insight clarifies the distinct roles, structures, and best practices of core and intervention math curricula, highlighting how their purposeful alignment and integration can better meet diverse student needs and address persistent gaps
Watch
DMT Insights
Building Stronger Math Thinkers Through Progressive Formalization
This DMTI Insight explains how progressive formalization guides students from intuitive, hands-on math experiences toward a deep understanding of formal mathematical concepts.
DMTI Overviews
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 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 38 Building the Number Line
This DMT Insight shows how students build a number line by defining a unit, iterating it, partitioning it as needed, and establishing a scale so each number represents both a location and a distance from zero.
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