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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

C Longer Classroom Teaching Examples show students making drawings for and then explaining each of the Children’s Math Worlds (CMW) approaches described in B Math Explanations. [51 minutes]

Part 1 G1 Multidigit Addition shows first graders making math drawings and explaining the CMW research-based mathematically-desirable and accessible written methods New Groups Below and Show All Totals. [6.5 minutes]

Part 2 G3 Multidigit Subtraction shows third graders making math drawings and explaining the CMW research-based mathematically-desirable and accessible written method First Ungroup Everywhere Needed and how this method allows students to move from left to right or from right to left as they ungroup and then as they subtract. [11 minutes]

Part 3 G2 Comparison Word Problems shows second graders representing, solving, and explaining different methods to solve a comparison word problem. They use their own methods and drawings, equations, and the CMW research-based matching and the Math Mountain for situations. [9 minutes]

Part 4 G4 Multidigit Multiplication shows fourth graders making math drawings that support meaning-making and explaining the research-based mathematically-desirable and accessible written methods developed in the Children’s Math Worlds Project. They then compare and relate methods. [9 minutes]

Part 5 G5 Fraction Multiplication shows students making math drawings to support multiplication of fractions meaningfully and then two students explain the drawings and their methods. The teacher then leads a discussion using the Commutative Property for whole number multiplication to show that the Commutative Property also is true for fraction multiplication. [15 minutes]

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C Longer Classroom Teaching Examples show students making drawings for and then explaining each of the Children’s Math Worlds (CMW) approaches described in B Math Explanations. [51 minutes]

Part 1 G1 Multidigit Addition shows first graders making math drawings and explaining the CMW research-based mathematically-desirable and accessible written methods New Groups Below and Show All Totals. [6.5 minutes]

Part 2 G3 Multidigit Subtraction shows third graders making math drawings and explaining the CMW research-based mathematically-desirable and accessible written method First Ungroup Everywhere Needed and how this method allows students to move from left to right or from right to left as they ungroup and then as they subtract. [11 minutes]

Part 3 G2 Comparison Word Problems shows second graders representing, solving, and explaining different methods to solve a comparison word problem. They use their own methods and drawings, equations, and the CMW research-based matching and the Math Mountain for situations. [9 minutes]

Part 4 G4 Multidigit Multiplication shows fourth graders making math drawings that support meaning-making and explaining the research-based mathematically-desirable and accessible written methods developed in the Children’s Math Worlds Project. They then compare and relate methods. [9 minutes]

Part 5 G5 Fraction Multiplication shows students making math drawings to support multiplication of fractions meaningfully and then two students explain the drawings and their methods. The teacher then leads a discussion using the Commutative Property for whole number multiplication to show that the Commutative Property also is true for fraction multiplication. [15 minutes]

C Longer Classroom Teaching Examples show students making drawings for and then explaining each of the Children’s Math Worlds (CMW) approaches described in B Math Explanations. [51 minutes]

Part 1 G1 Multidigit Addition shows first graders making math drawings and explaining the CMW research-based mathematically-desirable and accessible written methods New Groups Below and Show All Totals. [6.5 minutes]

Part 2 G3 Multidigit Subtraction shows third graders making math drawings and explaining the CMW research-based mathematically-desirable and accessible written method First Ungroup Everywhere Needed and how this method allows students to move from left to right or from right to left as they ungroup and then as they subtract. [11 minutes]

Part 3 G2 Comparison Word Problems shows second graders representing, solving, and explaining different methods to solve a comparison word problem. They use their own methods and drawings, equations, and the CMW research-based matching and the Math Mountain for situations. [9 minutes]

Part 4 G4 Multidigit Multiplication shows fourth graders making math drawings that support meaning-making and explaining the research-based mathematically-desirable and accessible written methods developed in the Children’s Math Worlds Project. They then compare and relate methods. [9 minutes]

Part 5 G5 Fraction Multiplication shows students making math drawings to support multiplication of fractions meaningfully and then two students explain the drawings and their methods. The teacher then leads a discussion using the Commutative Property for whole number multiplication to show that the Commutative Property also is true for fraction multiplication. [15 minutes]

Part 1

Part 2

Part 3

Part 4

Part 5