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The National Science Foundation funded A Video Research Report of the Children’s Math Worlds Research Project to show the levels of learning possible by children from backgrounds of poverty who experience good teaching. The classroom videos were taken in four public schools, three high-poverty urban schools with some to most students speaking a native language other than English and a suburban school with immigrants from many countries. The classrooms you will see were built by the continuing efforts of many dedicated teachers, students, parents, school administrators, and members of the Children’s Math Worlds research team. Language and ideas of students, teachers, and parents were woven into the curriculum as it was revised each year. The project had a strong emphasis on children explaining their thinking and on using math drawings developed in the project to support student thinking and explaining. None of our teachers had learned math in this way, so they were all brave pioneers in learning how to create such classrooms. All classrooms are complicated places, and no teaching segment can be perfect. We can all have ideas about how to change things the next time. I am enormously proud of and grateful to these teachers for being willing to share their classrooms so that everyone can see what students can do if we support them in their thinking. The Teaching Progressions show in more detail the learning progressions students experienced to reach the points shown on these Classroom Videos.

Classroom Videos

A - Classroom Components

B - Math Explanations

C - Longer Classroom

Teaching Examples

D - Kindergarten

E - G1 Single-Digit

Addition and Subtraction

F - G3 Single-Digit

Multiplication and Division

G - Place Value and Multidigit

Addition and Subtraction

H - G3 & G5 Fractions and Ratios

I - Teacher Interviews Grade 1

J - Teacher Interviews

Grades 2 and 3

E G1 Single-Digit Addition and Subtraction shows first graders finding and discussing partners of 9 and using the Children’s Math Worlds progression of methods and math drawings to represent and solve word problems and numeral problems with the total a teen number. [31 minutes]

Part 1 G1 Break Apart 9 with Stairsteps shows first graders using Stairsteps (foam inch lengths that go from 1 to 10 inches) to make partners (addends) of 9 and then discussing patterns in equations showing these partners (9 = 1 + 8, 9 = 2 + 7, etc.). [6:30 minutes]

Part 2 G1 More Than Word Problem shows four first graders solving and explaining a comparison problem using a length, a Math Mountain, or a matching drawing and three different equations: 14 – 8 = 6, 8 + 6 = 14, and 6 = 14 – 8. [8:20 minutes]

Part 3 G1 Fewer Than Word Problem shows three first graders solving and explaining a comparison problem using a Math Mountain or a matching drawing and three vertical computations: an unknown addend computation 8 + 6 = 14, 14 – 8 = 6, and 6 + 8 = 14. [6 minutes]

Part 4 G1 Math Mountain Make a Ten shows first graders using and explaining the make-a-ten strategy to solve 8 + ? = 14 and 7 + 9 = ? within a Number Ghost game in which the Number Ghost (a child) erases a total or a partner in a Math Mountain while children hide their eyes. [4:15 minutes]

Part 5 G1 Teen Subtraction Methods shows a Student Leader asking first graders to solve and explain subtractions with a teen total in their own way. They show counting on to the total, making a ten, and doubles or doubles plus 1. [6 minutes]

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E G1 Single-Digit Addition and Subtraction shows first graders finding and discussing partners of 9 and using the Children’s Math Worlds progression of methods and math drawings to represent and solve word problems and numeral problems with the total a teen number. [31 minutes]

Part 1 G1 Break Apart 9 with Stairsteps shows first graders using Stairsteps (foam inch lengths that go from 1 to 10 inches) to make partners (addends) of 9 and then discussing patterns in equations showing these partners (9 = 1 + 8, 9 = 2 + 7, etc.). [6:30 minutes]

Part 2 G1 More Than Word Problem shows four first graders solving and explaining a comparison problem using a length, a Math Mountain, or a matching drawing and three different equations: 14 – 8 = 6, 8 + 6 = 14, and 6 = 14 – 8. [8:20 minutes]

Part 3 G1 Fewer Than Word Problem shows three first graders solving and explaining a comparison problem using a Math Mountain or a matching drawing and three vertical computations: an unknown addend computation 8 + 6 = 14, 14 – 8 = 6, and 6 + 8 = 14. [6 minutes]

Part 4 G1 Math Mountain Make a Ten shows first graders using and explaining the make-a-ten strategy to solve 8 + ? = 14 and 7 + 9 = ? within a Number Ghost game in which the Number Ghost (a child) erases a total or a partner in a Math Mountain while children hide their eyes. [4:15 minutes]

Part 5 G1 Teen Subtraction Methods shows a Student Leader asking first graders to solve and explain subtractions with a teen total in their own way. They show counting on to the total, making a ten, and doubles or doubles plus 1. [6 minutes]

E G1 Single-Digit Addition and Subtraction shows first graders finding and discussing partners of 9 and using the Children’s Math Worlds progression of methods and math drawings to represent and solve word problems and numeral problems with the total a teen number. [31 minutes]

Part 1 G1 Break Apart 9 with Stairsteps shows first graders using Stairsteps (foam inch lengths that go from 1 to 10 inches) to make partners (addends) of 9 and then discussing patterns in equations showing these partners (9 = 1 + 8, 9 = 2 + 7, etc.). [6:30 minutes]

Part 2 G1 More Than Word Problem shows four first graders solving and explaining a comparison problem using a length, a Math Mountain, or a matching drawing and three different equations: 14 – 8 = 6, 8 + 6 = 14, and 6 = 14 – 8. [8:20 minutes]

Part 3 G1 Fewer Than Word Problem shows three first graders solving and explaining a comparison problem using a Math Mountain or a matching drawing and three vertical computations: an unknown addend computation 8 + 6 = 14, 14 – 8 = 6, and 6 + 8 = 14. [6 minutes]

Part 4 G1 Math Mountain Make a Ten shows first graders using and explaining the make-a-ten strategy to solve 8 + ? = 14 and 7 + 9 = ? within a Number Ghost game in which the Number Ghost (a child) erases a total or a partner in a Math Mountain while children hide their eyes. [4:15 minutes]

Part 5 G1 Teen Subtraction Methods shows a Student Leader asking first graders to solve and explain subtractions with a teen total in their own way. They show counting on to the total, making a ten, and doubles or doubles plus 1. [6 minutes]

Part 1

Part 2

Part 3

Part 4

Part 5