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Research overviews for K-8 mathematics
Understand the mathematics. Understand your students' thinking. Know what to do next.
Each DMT Insight is a short research overview on one idea in K-8 mathematics. Every Insight comes with a video, a 2-page newsletter for teachers, and a Companion for coaches and study groups. 56 are published, and all of them are free to read, watch, and share.
Where to start
Start with the newsletter.
2 pages: one classroom example, the central idea, 3 to 4 things to try, and questions to ask tomorrow. Then watch the video.
Four parts to every Insight
Insight Free
The research overview. About 3 pages, with references.
Video Free
A video introduction to the idea, for watching alone or with a team.
Newsletter Free
2 pages for teachers and families: one classroom example, the central idea, and things to try.
Companion In the free demo
For coaches and study groups: questions to ask, student work to analyze, and teacher moves to plan for.
Begin with your students
Does this sound familiar?
Choose what you are seeing in your classroom or school. Each one leads to the Insights that explain it and show what to do next.
Developing Multiplicative Reasoning
A student represents 3 × 4 as 3 iterations of the unit of 4. How can a bar model or an area model show this relationship?
Multiplication and Division (MLP)
A student knows 6 × 8 = 48. Can they represent 6 iterations of the unit of 8 and connect the relationship to division?
Math Fact Fluency
One student recalls 8 + 7 immediately; another reasons from 8 + 8. What evidence would you need to understand each student’s fluency?
Start here
Five ideas that apply in every grade
These Insights describe how students learn mathematics. Read them in order, or bring one to each team meeting.
Taking Students Ideas Seriously
A student says 9 + 6 = 14 after counting on from 9. What might their counting tell you about how they are coordinating the quantities?
How Math Models Transform Learning
Two students represent 24 ÷ 4 differently. What quantities and relationships does each representation make visible?
Prioritizing Conceptual Learning
A student adds 36 + 48 correctly but cannot explain the 1 recorded above the tens. What does the procedure tell us, and what remains to be investigated?
Focusing on Mathematical Structure
One student represents 28 as 2 tens and 8 ones; another as 4 iterations of 7. What structure does each representation reveal?
Harnessing Misconceptions
A student says 6 × ½ must be greater than 6 because multiplication makes numbers larger. What reasoning might be behind the response?
Study paths
Follow one idea across the grades
Each path puts related Insights in a teaching order. Coaches can use one Insight per meeting, with its Companion as the guide.
Multiplicative reasoning
From iterating a unit to scaling and equivalent ratios.
Fractions and decimals
From iterated units in measurement to fractions and decimals as numbers with magnitude.
Place value and whole-number operations
From number sense to units of ten and hundred, then to subtraction with regrouping.
Geometry and measurement
From attributes and units to area, perimeter, and the properties that define shapes.
Assessment and intervention
From evidence of student thinking to preteaching, reteaching, and intervention.
Decisions for school leaders
Research on teacher knowledge, spending, instructional time, and state assessments.
Library
All 56 Insights
Search by what you teach, or browse by pathway, topic, and grade band.
Showing 12 of 56 Insights
Taking Students Ideas Seriously
A student says 9 + 6 = 14 after counting on from 9. What might their counting tell you about how they are coordinating the quantities?
How Math Models Transform Learning
Two students represent 24 ÷ 4 differently. What quantities and relationships does each representation make visible?
Prioritizing Conceptual Learning
A student adds 36 + 48 correctly but cannot explain the 1 recorded above the tens. What does the procedure tell us, and what remains to be investigated?
Focusing on Mathematical Structure
One student represents 28 as 2 tens and 8 ones; another as 4 iterations of 7. What structure does each representation reveal?
Harnessing Misconceptions
A student says 6 × ½ must be greater than 6 because multiplication makes numbers larger. What reasoning might be behind the response?
Early Predictors of Math Success
Two students earn the same total score but use very different strategies. What might the score conceal?
The Learning Trifecta
Students answer correctly during a lesson. What evidence would show whether they can use the mathematics later?
Foundations in Number Sense
A child counts to 20 but starts at 1 to find 8 + 3. What does that strategy tell us?
Linear Models vs 100s Charts
A student locates 62 on a hundreds chart but cannot describe its distance from 40. What relationship is not yet visible?
The Power of Division
In 18 ÷ 3 = 6, the 6 might count coops or chickens, depending on the situation. How can students determine what the quotient counts?
Percent Is a Relationship
A student finds 25% of 80 but cannot explain what 25% refers to. What relationship needs attention?
Building Place Value Understanding
A student says 340 has 4 tens. How could you determine whether they mean the tens digit or the number of tens in 340?
In the full portal
Topical PD Videos
75+ focused videos on strategies and valuable classroom instruction information
Free coaching series
Check out our free Coaching Natalie series
Watch 5th grade teacher Natalie work with DMTI coaches Jackie and Jonathan through 8 coaching sessions.
The Insights explain the mathematics. Math Success gives you the materials to teach it.
One subscription opens everything, for kindergarten through grade 8. You can start today.
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- Prep materials: online video professional development
Who writes DMT Insights
Jonathan Brendefur, PhD
Jonathan founded the Developing Mathematical Thinking Institute. He spent 20 years as a Professor of Mathematics Education at Boise State University, working with teachers in their classrooms every week.
Get each new Insight by email
A new Insight comes out every other week. Free, and you can leave any time.
Keep developing mathematical thinkers.