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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

D Kindergarten shows children using special meaning-making visual supports from the Children’s Math Worlds Project: objects grouped in ten, five, and singles; secret-code cards in which the ones number goes on the 0 in 10; fingers using groups of ten, five, and singles. [20 minutes]

Part 1 K Counting Mat shows children using colored tiles to show the number 8 in different ways, using the 5-group tile with single tiles and/or using dots/no dots or colors or spatial lay-out. The teacher develops language by emphasizing and extending children’s descriptions of their 8 tiles, e.g., above/below, left/right, top/bottom. [4 minutes]

Part 2 K Word Problems shows children acting out a word problem a child gives using a family meal scenario and then a child tells and acts out a problem using plastic strawberries. The class gives the addition and subtraction equation and shows each equation with fingers. [2:40 minutes]

Part 3 K Dots to Fingers shows a Student Leader holding cards with dots in 5-patterns and the class shows with fingers the same number as shown by the dots. [1 minute]

Part 4 K Patterns in Teen Numbers shows children describing patterns they see in a Teen Pattern Poster that shows teen numbers as tens and ones. Numbers greater than 5 are shown as groups of 5, making many patterns children can describe. [3 minutes]

Part 5 K Teen Number Cards uses big Secret-Code Cards in which the ones card fits on top of the 0 on the tens card to show the teen number. Children show ten fingers for 10 then fingers for the ones, and then the teacher moves the ones card on top of the 0 in the tens card and the class says that teen number. [1:40 minutes]

Part 6 K Finger Tens in Teen Numbers shows children flashing ten fingers to the left and then ones fingers to the right moving from 11 to 20, saying each teen number in the form “ten and three more is thirteen.” [1:35 minutes]

Part 7 K 1 to 20 Mats shows children arranging small cubes using 5-groups to show 6, 7, 8, 9, and 10 and the teacher asking them to describe what they have done and to relate their patterns to fingers. Children count from 1 to 20 and relate objects, written numerals, and spoken number words. [4:30 minutes]

Part 8 K Teen Mats shows children making teen numbers with a ten rod and small cubes and describing teen numbers as ten ones plus some ones (e.g., 12 equals ten and two). [1:40 minutes]

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D Kindergarten shows children using special meaning-making visual supports from the Children’s Math Worlds Project: objects grouped in ten, five, and singles; secret-code cards in which the ones number goes on the 0 in 10; fingers using groups of ten, five, and singles. [20 minutes]

Part 1 K Counting Mat shows children using colored tiles to show the number 8 in different ways, using the 5-group tile with single tiles and/or using dots/no dots or colors or spatial lay-out. The teacher develops language by emphasizing and extending children’s descriptions of their 8 tiles, e.g., above/below, left/right, top/bottom. [4 minutes]

Part 2 K Word Problems shows children acting out a word problem a child gives using a family meal scenario and then a child tells and acts out a problem using plastic strawberries. The class gives the addition and subtraction equation and shows each equation with fingers. [2:40 minutes]

Part 3 K Dots to Fingers shows a Student Leader holding cards with dots in 5-patterns and the class shows with fingers the same number as shown by the dots. [1 minute]

Part 4 K Patterns in Teen Numbers shows children describing patterns they see in a Teen Pattern Poster that shows teen numbers as tens and ones. Numbers greater than 5 are shown as groups of 5, making many patterns children can describe. [3 minutes]

Part 5 K Teen Number Cards uses big Secret-Code Cards in which the ones card fits on top of the 0 on the tens card to show the teen number. Children show ten fingers for 10 then fingers for the ones, and then the teacher moves the ones card on top of the 0 in the tens card and the class says that teen number. [1:40 minutes]

Part 6 K Finger Tens in Teen Numbers shows children flashing ten fingers to the left and then ones fingers to the right moving from 11 to 20, saying each teen number in the form “ten and three more is thirteen.” [1:35 minutes]

Part 7 K 1 to 20 Mats shows children arranging small cubes using 5-groups to show 6, 7, 8, 9, and 10 and the teacher asking them to describe what they have done and to relate their patterns to fingers. Children count from 1 to 20 and relate objects, written numerals, and spoken number words. [4:30 minutes]

Part 8 K Teen Mats shows children making teen numbers with a ten rod and small cubes and describing teen numbers as ten ones plus some ones (e.g., 12 equals ten and two). [1:40 minutes]

D Kindergarten shows children using special meaning-making visual supports from the Children’s Math Worlds Project: objects grouped in ten, five, and singles; secret-code cards in which the ones number goes on the 0 in 10; fingers using groups of ten, five, and singles. [20 minutes]

Part 1 K Counting Mat shows children using colored tiles to show the number 8 in different ways, using the 5-group tile with single tiles and/or using dots/no dots or colors or spatial lay-out. The teacher develops language by emphasizing and extending children’s descriptions of their 8 tiles, e.g., above/below, left/right, top/bottom. [4 minutes]

Part 2 K Word Problems shows children acting out a word problem a child gives using a family meal scenario and then a child tells and acts out a problem using plastic strawberries. The class gives the addition and subtraction equation and shows each equation with fingers. [2:40 minutes]

Part 3 K Dots to Fingers shows a Student Leader holding cards with dots in 5-patterns and the class shows with fingers the same number as shown by the dots. [1 minutè]

Part 4 K Patterns in Teen Numbers shows children describing patterns they see in a Teen Pattern Poster that shows teen numbers as tens and ones. Numbers greater than 5 are shown as groups of 5, making many patterns children can describe. [3 minutes]

Part 5 K Teen Number Cards uses big Secret-Code Cards in which the ones card fits on top of the 0 on the tens card to show the teen number. Children show ten fingers for 10 then fingers for the ones, and then the teacher moves the ones card on top of the 0 in the tens card and the class says that teen number. [1:40 minutes]

Part 6 K Finger Tens in Teen Numbers shows children flashing ten fingers to the left and then ones fingers to the right moving from 11 to 20, saying each teen number in the form “ten and three more is thirteen.” [1:35 minutes]

Part 7 K 1 to 20 Mats shows children arranging small cubes using 5-groups to show 6, 7, 8, 9, and 10 and the teacher asking them to describe what they have done and to relate their patterns to fingers. Children count from 1 to 20 and relate objects, written numerals, and spoken number words. [4:30 minutes]

Part 8 K Teen Mats shows children making teen numbers with a ten rod and small cubes and describing teen numbers as ten ones plus some ones (e.g., 12 equals ten and two). [1:40 minutes]

Part 3 K Dots to Fingers shows a Student Leader holding cards with dots in 5-patterns and the class shows with fingers the same number as shown by the dots. [1 minute]

Part 1

Part 2

Part 3

Part 4

Part 5

Part 6

Part 7

Part 8