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Early experience with numbers and operations is fundamental for acquiring more complex math concepts and skills. The practice guide describes how to teach the main aspects of early number knowledge, from basic number skills to operations, according to a developmental progression. Developmental progressions can provide teachers with a road map for delivering developmentally appropriate instruction to students of varying skill levels. With each step in a developmental progression, teachers can first focus on working with small collections of objects (one to three items) and then move to progressively larger collections of objects.

1.
Teaching Math to Young Children

Practice Guide

Educators’ Practice Guide Summary • WHAT WORKS CLEARINGHOUSETM

The five recommendations Introduction

in this WWC practice guide,

Teaching Math to Young Children are interested in math well before they start school.

Children, build on children’s They notice basic shapes, construct and extend simple patterns,

natural interest in math and learn to count. The Teaching Math to Young Children practice

to make preschool and guide presents five recommendations designed to help early

kindergarten more engaging education teachers capitalize on children’s natural interest in

and beneficial. math. The first two recommendations identify early math content

areas that should be included in the preschool, prekindergarten,

and kindergarten curricula. The last three recommendations

focus on strategies and teaching techniques that incorporate

math content into the classroom.

This summary introduces the recommendations and supporting

evidence described in the WWC’s Teaching Math to Young Children

practice guide. Download your free copy of the guide at

http://ies.ed.gov/ncee/wwc/PracticeGuide.aspx?sid=18.

Practice Guide

Educators’ Practice Guide Summary • WHAT WORKS CLEARINGHOUSETM

The five recommendations Introduction

in this WWC practice guide,

Teaching Math to Young Children are interested in math well before they start school.

Children, build on children’s They notice basic shapes, construct and extend simple patterns,

natural interest in math and learn to count. The Teaching Math to Young Children practice

to make preschool and guide presents five recommendations designed to help early

kindergarten more engaging education teachers capitalize on children’s natural interest in

and beneficial. math. The first two recommendations identify early math content

areas that should be included in the preschool, prekindergarten,

and kindergarten curricula. The last three recommendations

focus on strategies and teaching techniques that incorporate

math content into the classroom.

This summary introduces the recommendations and supporting

evidence described in the WWC’s Teaching Math to Young Children

practice guide. Download your free copy of the guide at

http://ies.ed.gov/ncee/wwc/PracticeGuide.aspx?sid=18.

2.
Teaching Math to Young Children Practice Guide Summary

Recommendation 1. 2. Next, promote accurate one-to-one counting

as a means of identifying the total number

Teach number and operations

of items in a collection. Once children have

using a developmental progression. started to connect numbers with quantity, they

can then begin to use one-to-one counting to

identify “how many” are in larger collections. In

order to count accurately, one—and only one—

number word should be assigned to each item

in the collection being counted, using the last

number counted to determine the total quantity.

The practice guide also includes a discussion

of the common counting errors children make

when developing counting skills and provides

suggestions teachers can use to correct those

errors when working with children in one-on-one

or small-group situations (see page 19 of the

practice guide).

Modeling one-to-one counting with one

to three items

Early experience with number and operations is

fundamental for acquiring more complex math

concepts and skills. The practice guide describes

how to teach the main aspects of early number While pointing at each object, count:

knowledge, from basic number skills to opera-

tions, according to a developmental progression. (with emphasis)

Developmental progressions can provide teachers “one” “two” “three”

with a road map for delivering developmentally

appropriate instruction to students of varying skill

levels. With each step in a developmental progres-

sion, teachers can first focus on working with small

collections of objects (one to three items) and then “There are three (squares) here.”

move to progressively larger collections of objects.

How to carry out the recommendation

3. Once children can recognize or count collec-

1. First, provide opportunities for children to tions, provide opportunities for children to

practice recognizing the total number of use number words and counting to com-

objects in small collections (one to three pare quantities. To begin magnitude compari-

items) and labeling them with a number word sons, teachers can ask children to compare small

without needing to count them. Teachers can collections of one to three objects visually. Next,

give children experience with immediately recogniz- children can count or match larger collections

ing and labeling quantities of a collection by having of items one-to-one to determine which set has

them answer the question “How many are there?” “more.” Once children can comfortably determine

when looking at collections of one to three objects. “more,” the word “fewer” and the use of writ-

Small-group activities, snack time, and transitions ten number lists can be introduced. Eventually,

between classroom activities can provide quick teachers can encourage children to use their

opportunities for children to practice recogniz- knowledge of which number comes after another

ing small quantities. To help children construct a in the counting sequence to determine the larger

more abstract concept of number, teachers can of two verbal numbers.

emphasize that collections of three similar objects

and three dissimilar objects are both “three.”

2

Recommendation 1. 2. Next, promote accurate one-to-one counting

as a means of identifying the total number

Teach number and operations

of items in a collection. Once children have

using a developmental progression. started to connect numbers with quantity, they

can then begin to use one-to-one counting to

identify “how many” are in larger collections. In

order to count accurately, one—and only one—

number word should be assigned to each item

in the collection being counted, using the last

number counted to determine the total quantity.

The practice guide also includes a discussion

of the common counting errors children make

when developing counting skills and provides

suggestions teachers can use to correct those

errors when working with children in one-on-one

or small-group situations (see page 19 of the

practice guide).

Modeling one-to-one counting with one

to three items

Early experience with number and operations is

fundamental for acquiring more complex math

concepts and skills. The practice guide describes

how to teach the main aspects of early number While pointing at each object, count:

knowledge, from basic number skills to opera-

tions, according to a developmental progression. (with emphasis)

Developmental progressions can provide teachers “one” “two” “three”

with a road map for delivering developmentally

appropriate instruction to students of varying skill

levels. With each step in a developmental progres-

sion, teachers can first focus on working with small

collections of objects (one to three items) and then “There are three (squares) here.”

move to progressively larger collections of objects.

How to carry out the recommendation

3. Once children can recognize or count collec-

1. First, provide opportunities for children to tions, provide opportunities for children to

practice recognizing the total number of use number words and counting to com-

objects in small collections (one to three pare quantities. To begin magnitude compari-

items) and labeling them with a number word sons, teachers can ask children to compare small

without needing to count them. Teachers can collections of one to three objects visually. Next,

give children experience with immediately recogniz- children can count or match larger collections

ing and labeling quantities of a collection by having of items one-to-one to determine which set has

them answer the question “How many are there?” “more.” Once children can comfortably determine

when looking at collections of one to three objects. “more,” the word “fewer” and the use of writ-

Small-group activities, snack time, and transitions ten number lists can be introduced. Eventually,

between classroom activities can provide quick teachers can encourage children to use their

opportunities for children to practice recogniz- knowledge of which number comes after another

ing small quantities. To help children construct a in the counting sequence to determine the larger

more abstract concept of number, teachers can of two verbal numbers.

emphasize that collections of three similar objects

and three dissimilar objects are both “three.”

2

3.
Teaching Math to Young Children Practice Guide Summary

4. Encourage children to label collections with more adept, teachers can progress to more

number words and numerals. After children difficult problems with slightly larger numbers.

practice recognizing, counting, and comparing

quantities, teachers can introduce numerals to Summary of evidence

children as a way to represent a quantity. As

described in the practice guide, teachers can pair The WWC identified 23 studies that examined the

numerals with collections of classroom objects so effects of interventions that included targeted instruc-

that children start to learn, for example, that the tion in number and operations. The research shows

numeral 3, three objects, and the spoken word a strong pattern of positive effects on children’s early

“three” represent the same thing (see page 21 of math skills across a range of curricula with a focus

the practice guide). on number and operations. Eleven studies demon-

strated positive effects for interventions that used a

5. Once children develop these fundamental developmental progression to guide instruction in

number skills, encourage them to solve number and operations. While the panel could not

basic problems. Once children can determine confirm whether a developmental progression guided

the total number of items in a collection by using instruction in 12 other studies that taught number and

small-number recognition or counting and under- operation, the panel felt that the body of evidence as

stand the concepts of “more” and “fewer,” they a whole provided sufficient support to warrant a level

can explore the effects of adding and subtract- of evidence rating of moderate. For more details, see

ing items from a collection. As children become Recommendation 1 in the practice guide, page 12.

Recommendation 2.

Teach geometry, patterns, measure-

ment, and data analysis using a

developmental progression.

The practice guide suggests that children’s exposure

to math should extend beyond number and operations

to include a range of math content areas, including

geometry (shapes and space), patterns, measurement,

and data analysis. These math content areas should

be taught according to developmental progressions.

Learning skills beyond number and operations creates

a foundation for future math instruction, and children and master the concepts of “in,” “on,” “under,”

with strong backgrounds in these areas are more likely “beside,” “above,” or “below.”

to be able to succeed in later grades.

2. Encourage children to look for and identify

patterns, then teach them to extend, cor-

How to carry out the recommendation rect, and create patterns. Pattern instruction

1. Help children to recognize, name, and can begin by encouraging children to notice

compare shapes, and then teach them and experiment with basic repeating patterns

to combine and separate shapes. Using their in the world around them, such as stripes on

surrounding environment, teachers can provide clothing and shapes and designs in rugs. Once

opportunities for children to make comparisons children have become familiar with the nature

and distinctions about the basic features of shapes. of patterns, they should learn to predict what

Once children are comfortable recognizing and will happen next in a pattern, based on what

comparing shapes, teachers should encourage has happened so far. Teachers will find ideas in

children to explore how shapes can be combined the practice guide for using manipulatives, like

and separated to form new shapes. Page 29 of the the one shown in the example on the next page,

practice guide suggests activities to help children to teach children about patterns of increasing

to learn about spatial relationships between shapes complexity (see page 30 of the practice guide).

3

4. Encourage children to label collections with more adept, teachers can progress to more

number words and numerals. After children difficult problems with slightly larger numbers.

practice recognizing, counting, and comparing

quantities, teachers can introduce numerals to Summary of evidence

children as a way to represent a quantity. As

described in the practice guide, teachers can pair The WWC identified 23 studies that examined the

numerals with collections of classroom objects so effects of interventions that included targeted instruc-

that children start to learn, for example, that the tion in number and operations. The research shows

numeral 3, three objects, and the spoken word a strong pattern of positive effects on children’s early

“three” represent the same thing (see page 21 of math skills across a range of curricula with a focus

the practice guide). on number and operations. Eleven studies demon-

strated positive effects for interventions that used a

5. Once children develop these fundamental developmental progression to guide instruction in

number skills, encourage them to solve number and operations. While the panel could not

basic problems. Once children can determine confirm whether a developmental progression guided

the total number of items in a collection by using instruction in 12 other studies that taught number and

small-number recognition or counting and under- operation, the panel felt that the body of evidence as

stand the concepts of “more” and “fewer,” they a whole provided sufficient support to warrant a level

can explore the effects of adding and subtract- of evidence rating of moderate. For more details, see

ing items from a collection. As children become Recommendation 1 in the practice guide, page 12.

Recommendation 2.

Teach geometry, patterns, measure-

ment, and data analysis using a

developmental progression.

The practice guide suggests that children’s exposure

to math should extend beyond number and operations

to include a range of math content areas, including

geometry (shapes and space), patterns, measurement,

and data analysis. These math content areas should

be taught according to developmental progressions.

Learning skills beyond number and operations creates

a foundation for future math instruction, and children and master the concepts of “in,” “on,” “under,”

with strong backgrounds in these areas are more likely “beside,” “above,” or “below.”

to be able to succeed in later grades.

2. Encourage children to look for and identify

patterns, then teach them to extend, cor-

How to carry out the recommendation rect, and create patterns. Pattern instruction

1. Help children to recognize, name, and can begin by encouraging children to notice

compare shapes, and then teach them and experiment with basic repeating patterns

to combine and separate shapes. Using their in the world around them, such as stripes on

surrounding environment, teachers can provide clothing and shapes and designs in rugs. Once

opportunities for children to make comparisons children have become familiar with the nature

and distinctions about the basic features of shapes. of patterns, they should learn to predict what

Once children are comfortable recognizing and will happen next in a pattern, based on what

comparing shapes, teachers should encourage has happened so far. Teachers will find ideas in

children to explore how shapes can be combined the practice guide for using manipulatives, like

and separated to form new shapes. Page 29 of the the one shown in the example on the next page,

practice guide suggests activities to help children to teach children about patterns of increasing

to learn about spatial relationships between shapes complexity (see page 30 of the practice guide).

3

4.
Teaching Math to Young Children Practice Guide Summary

3. Promote children’s understanding of mea- total number in each set relative to other sets.

surement by teaching them to make direct Once children are familiar with sorting and orga-

comparisons and to use both informal or nizing the information they have collected, they

nonstandard (e.g., the child’s hand or foot) can learn to summarize their information visually

and formal or standard (e.g., a ruler) units through simple graphs and tallies.

and tools. Teachers can help children learn to use

measurement vocabulary words (long and short,

big and small) to describe similarities and differ-

Summary of evidence

ences while sorting, arranging, and classifying The WWC identified 13 studies that examined the

objects. Once children have become comfortable effects of interventions that provided targeted

making direct comparisons between and among instruction in one or more of the early math content

objects, teachers can provide opportunities to areas (geometry, patterns, measurement, and data

measure objects using nonstandard tools, such as analysis). Positive effects were found for geometry,

children’s own hands and feet, pencils, blocks, or operations, basic number concepts, and general

books. Children can then be introduced to the con- numeracy outcomes. Studies also reported no

cept of standard units and tools of measurement. discernible effects for general numeracy, geometry,

and basic number concept outcomes. Although

4. Help children collect and organize infor- the evidence to support this recommendation is

mation, then teach them to represent that promising, the WWC could not isolate the effects of

information graphically. Teachers can intro- teaching the early math content areas of geometry,

duce children to the concept of organizing and patterns, measurement, and data analysis. As a

displaying information by asking them to count result, the WWC assigned a level of evidence rating

and sort familiar items like toys and blocks. This of minimal. For more details, see Recommendation 2

will help them learn both the characteristics that in the practice guide, page 25.

distinguish the items from one another and the

Complex pattern (boy, boy, girl, girl, boy, boy, girl, girl, boy, boy, girl, girl)

Recommendation 3.

Use progress monitoring to

ensure that math instruction

builds on what each child knows.

Progress monitoring can be a useful way to ensure

that children are participating in targeted, purposeful,

and meaningful math instruction. By continually

monitoring children’s progress, teachers can gather

the information they need to match lessons to chil-

dren’s knowledge levels. Incorporating children’s indi-

vidual differences into lesson planning by monitoring

progress and tailoring instruction can help ensure that

children learn fundamental concepts that are appro-

priately challenging and that will extend their learning.

4

3. Promote children’s understanding of mea- total number in each set relative to other sets.

surement by teaching them to make direct Once children are familiar with sorting and orga-

comparisons and to use both informal or nizing the information they have collected, they

nonstandard (e.g., the child’s hand or foot) can learn to summarize their information visually

and formal or standard (e.g., a ruler) units through simple graphs and tallies.

and tools. Teachers can help children learn to use

measurement vocabulary words (long and short,

big and small) to describe similarities and differ-

Summary of evidence

ences while sorting, arranging, and classifying The WWC identified 13 studies that examined the

objects. Once children have become comfortable effects of interventions that provided targeted

making direct comparisons between and among instruction in one or more of the early math content

objects, teachers can provide opportunities to areas (geometry, patterns, measurement, and data

measure objects using nonstandard tools, such as analysis). Positive effects were found for geometry,

children’s own hands and feet, pencils, blocks, or operations, basic number concepts, and general

books. Children can then be introduced to the con- numeracy outcomes. Studies also reported no

cept of standard units and tools of measurement. discernible effects for general numeracy, geometry,

and basic number concept outcomes. Although

4. Help children collect and organize infor- the evidence to support this recommendation is

mation, then teach them to represent that promising, the WWC could not isolate the effects of

information graphically. Teachers can intro- teaching the early math content areas of geometry,

duce children to the concept of organizing and patterns, measurement, and data analysis. As a

displaying information by asking them to count result, the WWC assigned a level of evidence rating

and sort familiar items like toys and blocks. This of minimal. For more details, see Recommendation 2

will help them learn both the characteristics that in the practice guide, page 25.

distinguish the items from one another and the

Complex pattern (boy, boy, girl, girl, boy, boy, girl, girl, boy, boy, girl, girl)

Recommendation 3.

Use progress monitoring to

ensure that math instruction

builds on what each child knows.

Progress monitoring can be a useful way to ensure

that children are participating in targeted, purposeful,

and meaningful math instruction. By continually

monitoring children’s progress, teachers can gather

the information they need to match lessons to chil-

dren’s knowledge levels. Incorporating children’s indi-

vidual differences into lesson planning by monitoring

progress and tailoring instruction can help ensure that

children learn fundamental concepts that are appro-

priately challenging and that will extend their learning.

4

5.
Teaching Math to Young Children Practice Guide Summary

Progress monitoring is a systematic approach 3. Assess, record, and monitor each child’s

to assessment with the goal progress so that instructional goals and

of improving skills. methods can be adjusted as needed. The

chart below illustrates the flow of progress moni-

toring. The practice guide describes how teach-

How to carry out the recommendation ers can apply this ongoing process during math

instruction (see page 39 of the practice guide).

1. Use introductory activities, observations,

It is important to continually monitor progress

and assessments to determine each child’s

so that children can be consistently engaged in

existing math knowledge, or the level

activities that are neither too far below their level

of understanding or skill he or she has

(and therefore not interesting) nor too far above

reached on a developmental progression.

it (and therefore frustrating).

When employing progress monitoring, teachers

can first gather specific information about each

child’s skill level in order to determine where to Summary of evidence

focus instruction. The practice guide suggests

using introductory activities, observation, and The WWC identified 12 studies which examined the

formal assessments to determine each child’s effects of progress monitoring on children’s math

level of math understanding. knowledge when used in conjunction with other

practices the WWC recommends for teaching math

2. Tailor instruction to each child’s needs, to young children. For example, four studies exam-

and relate new ideas to his or her existing ining a comprehensive early math curriculum that

knowledge. Once teachers have information included supports for regular assessments found

about a child’s skill level, they can use a devel- that, on average, children participating in the inter-

opmental progression to determine what the vention scored higher on math outcomes than did

child should learn next and design instructional children in the comparison condition. Although the

activities with those needs in mind. Teachers can evidence to support this recommendation is promis-

design small-group activities that are at or slightly ing, the WWC could not isolate the effects of the use

above the children’s level of understanding. As of progress monitoring, since other recommended

detailed in the practice guide, teachers can link practices were also implemented. As a result, the

math activities to children’s existing interests and WWC assigned a level of evidence rating of minimal.

across other content areas to build knowledge, For more details, see Recommendation 3 in the

including music, art, games, and reading. practice guide, page 36.

Ongoing Progress Monitoring

Ongoing Progress Monitoring

Use a developmental progression to choose an activity that targets a math concept.

Assess: Observe and record Plan activities Implement

5

Progress monitoring is a systematic approach 3. Assess, record, and monitor each child’s

to assessment with the goal progress so that instructional goals and

of improving skills. methods can be adjusted as needed. The

chart below illustrates the flow of progress moni-

toring. The practice guide describes how teach-

How to carry out the recommendation ers can apply this ongoing process during math

instruction (see page 39 of the practice guide).

1. Use introductory activities, observations,

It is important to continually monitor progress

and assessments to determine each child’s

so that children can be consistently engaged in

existing math knowledge, or the level

activities that are neither too far below their level

of understanding or skill he or she has

(and therefore not interesting) nor too far above

reached on a developmental progression.

it (and therefore frustrating).

When employing progress monitoring, teachers

can first gather specific information about each

child’s skill level in order to determine where to Summary of evidence

focus instruction. The practice guide suggests

using introductory activities, observation, and The WWC identified 12 studies which examined the

formal assessments to determine each child’s effects of progress monitoring on children’s math

level of math understanding. knowledge when used in conjunction with other

practices the WWC recommends for teaching math

2. Tailor instruction to each child’s needs, to young children. For example, four studies exam-

and relate new ideas to his or her existing ining a comprehensive early math curriculum that

knowledge. Once teachers have information included supports for regular assessments found

about a child’s skill level, they can use a devel- that, on average, children participating in the inter-

opmental progression to determine what the vention scored higher on math outcomes than did

child should learn next and design instructional children in the comparison condition. Although the

activities with those needs in mind. Teachers can evidence to support this recommendation is promis-

design small-group activities that are at or slightly ing, the WWC could not isolate the effects of the use

above the children’s level of understanding. As of progress monitoring, since other recommended

detailed in the practice guide, teachers can link practices were also implemented. As a result, the

math activities to children’s existing interests and WWC assigned a level of evidence rating of minimal.

across other content areas to build knowledge, For more details, see Recommendation 3 in the

including music, art, games, and reading. practice guide, page 36.

Ongoing Progress Monitoring

Ongoing Progress Monitoring

Use a developmental progression to choose an activity that targets a math concept.

Assess: Observe and record Plan activities Implement

5

6.
Teaching Math to Young Children Practice Guide Summary

Recommendation 4.

Teach children to view and describe

their world mathematically.

The practice guide outlines the steps teachers can

take to help children view and describe the world

mathematically. Teachers can encourage children

to describe math ideas in the world around them,

gradually moving from informal representations

and language to formal representations and math

vocabulary as their understanding grows. At first,

children can use informal tools such as their fin-

gers, tally marks, or other concrete objects to rep-

resent math ideas. Once children are comfortable

using math informally, teachers can help them link

their informal knowledge to formal math vocabu-

lary and representations, such as math symbols.

Open-ended questions can be used to prompt

children to think about how to describe their ideas

mathematically. Teachers can reinforce these ideas

by encouraging children to look for opportunities

to use their developing math skills throughout the

school day. Lesson ideas for linking familiar concepts

to formal symbols

How to carry out the recommendation Symbol Concept Lesson

1. Encourage children to use informal numerals counting Have children count and record the

methods to represent math concepts, number of children in attendance

processes, and solutions. Initially, teachers each day.

should link math ideas to informal and familiar +,– operations Have children solve problems involv-

experiences, terms, or analogies, resisting the ing adding or subtracting with leaves

urge to use more formal methods until children collected from the playground.

have a conceptual foundation for understanding = equal Show the class four pennies. Next,

them. For example, teachers can first use terms show three pennies, verbally label

them (“I have one, two, three pen-

such as “more” and “all together,” terms that

nies”), and put them in a can. Then,

represent children’s informal understanding of show one more penny, verbally label

addition, before using the more formal, sym- it (“I have one more penny”), and put

bolic representation. it in the can. Ask the class, “Are three

pennies and one more penny the

2. Help children link formal math vocabulary, same number as four pennies?”

symbols, and procedures to their informal <,> unequal Show the class five pennies, verbally

knowledge or experiences. Once children label them, and put them in a can.

develop an understanding of math ideas using Next, show four pennies, verbally label

informal terms, teachers can show them how them, and put them in a different can.

Ask the class, “Which can has more?

their informal knowledge connects to formal Which can has fewer?”

math terms and representations. Teachers can

start with informal vocabulary, like the phrase

“take away,” for example, and then later explain offers teachers ideas for using math vocabulary

that the formal term “subtract” and the “–” sym- with children throughout the school day (see

bol have the same meaning. The practice guide page 44 of the practice guide).

6

Recommendation 4.

Teach children to view and describe

their world mathematically.

The practice guide outlines the steps teachers can

take to help children view and describe the world

mathematically. Teachers can encourage children

to describe math ideas in the world around them,

gradually moving from informal representations

and language to formal representations and math

vocabulary as their understanding grows. At first,

children can use informal tools such as their fin-

gers, tally marks, or other concrete objects to rep-

resent math ideas. Once children are comfortable

using math informally, teachers can help them link

their informal knowledge to formal math vocabu-

lary and representations, such as math symbols.

Open-ended questions can be used to prompt

children to think about how to describe their ideas

mathematically. Teachers can reinforce these ideas

by encouraging children to look for opportunities

to use their developing math skills throughout the

school day. Lesson ideas for linking familiar concepts

to formal symbols

How to carry out the recommendation Symbol Concept Lesson

1. Encourage children to use informal numerals counting Have children count and record the

methods to represent math concepts, number of children in attendance

processes, and solutions. Initially, teachers each day.

should link math ideas to informal and familiar +,– operations Have children solve problems involv-

experiences, terms, or analogies, resisting the ing adding or subtracting with leaves

urge to use more formal methods until children collected from the playground.

have a conceptual foundation for understanding = equal Show the class four pennies. Next,

them. For example, teachers can first use terms show three pennies, verbally label

them (“I have one, two, three pen-

such as “more” and “all together,” terms that

nies”), and put them in a can. Then,

represent children’s informal understanding of show one more penny, verbally label

addition, before using the more formal, sym- it (“I have one more penny”), and put

bolic representation. it in the can. Ask the class, “Are three

pennies and one more penny the

2. Help children link formal math vocabulary, same number as four pennies?”

symbols, and procedures to their informal <,> unequal Show the class five pennies, verbally

knowledge or experiences. Once children label them, and put them in a can.

develop an understanding of math ideas using Next, show four pennies, verbally label

informal terms, teachers can show them how them, and put them in a different can.

Ask the class, “Which can has more?

their informal knowledge connects to formal Which can has fewer?”

math terms and representations. Teachers can

start with informal vocabulary, like the phrase

“take away,” for example, and then later explain offers teachers ideas for using math vocabulary

that the formal term “subtract” and the “–” sym- with children throughout the school day (see

bol have the same meaning. The practice guide page 44 of the practice guide).

6

7.
Teaching Math to Young Children Practice Guide Summary

3. Use open-ended questions to prompt ways to encourage math conversation and prob-

children to apply their math knowledge. lem solving during recess, snack, transition, and

Open-ended questions not only help children small- and large-group time in the practice guide

to develop cognitive and language skills, but (see page 46).

they also can encourage children to use math

vocabulary to explain what they have learned. Summary of evidence

The practice guide provides teachers with ideas

for promoting math-related conversation among The WWC identified 16 studies that examined the

young children using open-ended questions. effects of interventions designed to help children

For example, teachers can use questions that view and describe their world mathematically. Some

begin with “what,” “why,” or “how” to encourage of the interventions provided math vocabulary

children to use math vocabulary to explain what words and suggestions for stories, songs, or ques-

they have learned. tions that supported children in learning to view

and describe their world mathematically. Studies

4. Encourage children to recognize and talk examining these interventions found positive

about math in everyday situations. Teachers effects on children’s math outcomes. Although the

can encourage math thought and conversation evidence to support this recommendation is promis-

by asking children for their help with problems ing, the WWC could not isolate the effects of helping

that arise throughout the day. Once children children view and describe their world mathemati-

solve the problem, teachers can ask a sequence cally, since other recommended practices were also

of questions that prompt the children to share implemented. As a result, the WWC assigned a level

the solution and the strategies used to reach the of evidence rating of minimal. For more details, see

solution. Teachers will find several examples of Recommendation 4 in the practice guide, page 42.

Recommendation 5.

Dedicate time each day to teaching

math, and integrate math instruc-

tion throughout the school day.

Devoting class time to planned, daily math lessons

helps children strengthen math skills. By connect-

ing math to a variety of everyday situations and

routines, teachers can make math meaningful and

provide opportunities for children to practice what

they have learned in a purposeful manner. A math-

rich environment can help generate excitement

among children and encourage them apply their

math knowledge in a meaningful way.

How to carry out the recommendation

1. Plan daily instruction targeting specific

math concepts and skills. In order for young instruction for children at different develop-

children to develop a strong foundation of math mental levels (see page 49 of the practice guide).

skills, teachers can dedicate time each day for

purposeful math instruction. During math lessons, 2. Embed math in classroom routines and

children can learn specific skills and build upon activities. A daily or weekly schedule provides

them throughout the rest of the day. The practice many opportunities to reinforce math concepts

guide describes how large and small groups can outside of the dedicated math instruction

be used during dedicated math time to tailor period. Routines such as taking attendance or

7

3. Use open-ended questions to prompt ways to encourage math conversation and prob-

children to apply their math knowledge. lem solving during recess, snack, transition, and

Open-ended questions not only help children small- and large-group time in the practice guide

to develop cognitive and language skills, but (see page 46).

they also can encourage children to use math

vocabulary to explain what they have learned. Summary of evidence

The practice guide provides teachers with ideas

for promoting math-related conversation among The WWC identified 16 studies that examined the

young children using open-ended questions. effects of interventions designed to help children

For example, teachers can use questions that view and describe their world mathematically. Some

begin with “what,” “why,” or “how” to encourage of the interventions provided math vocabulary

children to use math vocabulary to explain what words and suggestions for stories, songs, or ques-

they have learned. tions that supported children in learning to view

and describe their world mathematically. Studies

4. Encourage children to recognize and talk examining these interventions found positive

about math in everyday situations. Teachers effects on children’s math outcomes. Although the

can encourage math thought and conversation evidence to support this recommendation is promis-

by asking children for their help with problems ing, the WWC could not isolate the effects of helping

that arise throughout the day. Once children children view and describe their world mathemati-

solve the problem, teachers can ask a sequence cally, since other recommended practices were also

of questions that prompt the children to share implemented. As a result, the WWC assigned a level

the solution and the strategies used to reach the of evidence rating of minimal. For more details, see

solution. Teachers will find several examples of Recommendation 4 in the practice guide, page 42.

Recommendation 5.

Dedicate time each day to teaching

math, and integrate math instruc-

tion throughout the school day.

Devoting class time to planned, daily math lessons

helps children strengthen math skills. By connect-

ing math to a variety of everyday situations and

routines, teachers can make math meaningful and

provide opportunities for children to practice what

they have learned in a purposeful manner. A math-

rich environment can help generate excitement

among children and encourage them apply their

math knowledge in a meaningful way.

How to carry out the recommendation

1. Plan daily instruction targeting specific

math concepts and skills. In order for young instruction for children at different develop-

children to develop a strong foundation of math mental levels (see page 49 of the practice guide).

skills, teachers can dedicate time each day for

purposeful math instruction. During math lessons, 2. Embed math in classroom routines and

children can learn specific skills and build upon activities. A daily or weekly schedule provides

them throughout the rest of the day. The practice many opportunities to reinforce math concepts

guide describes how large and small groups can outside of the dedicated math instruction

be used during dedicated math time to tailor period. Routines such as taking attendance or

7

8.
Teaching Math to Young Children Practice Guide Summary

snack time can serve a math purpose in addition 5. Use games to teach math concepts and

to a practical one, providing opportunities for skills and to give children practice in

counting, comparisons, and graphing. applying them. Games can provide an engag-

ing opportunity for children to practice and

3. Highlight math within topics of study extend skills, and the practice guide supplies

across the curriculum. Teachers can integrate several examples of games teachers can use to

math concepts into non-math lessons by high- encourage children to apply their math knowl-

lighting the aspects of math that are already edge. Teachers can use games that are included

present in the curriculum. This gives children in math curricula, purchase games, make games

opportunities to count and measure objects, themselves, or use games that come up dur-

examine shapes, and analyze data (depending ing natural play, like hopscotch or jump rope,

on the current math objectives). The practice to reinforce math concepts. Teachers can get

guide provides examples of ways to integrate involved with the game-playing in order to

different math content areas into literature, sci- ensure educational play or to challenge children

ence, art, health and safety, and social studies to extend their skills.

lessons (see page 51 of the practice guide).

4. Create a math-rich environment where Summary of evidence

children can recognize and meaningfully The WWC identified 20 studies that examined the

apply math. Teachers can provide opportunities effects of interventions that included dedicated time

for children to see and use math concepts on a for math instruction, integration of math into other

regular basis by creating a math-rich classroom aspects of the school day, and the use of games to

environment. This enrichment can be done by practice math skills. A group of studies found that

making math-related objects and tools readily children who played number-based board games

available, labeling and organizing them so they performed better in the domain of basic number

are easy to find and use, and organizing activities concepts than did children who played color-based

and routines with numeric systems. Teachers can board games or no board games. Although the

also explicitly teach children how to use math evidence to support this recommendation is promis-

tools by modeling their use during small- or ing, the WWC could not isolate the effects of the use

large-group time. of dedicated time for math instruction, integration

of math into other aspects of the school day, and

the use of games to practice math skills, since other

An example of a math-rich environment recommended practices were also implemented. As a

in the classroom. result, the WWC assigned a level of evidence rating of

minimal. For more details, see Recommendation 5 in

the practice guide, page 47.

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10 2

9 3

8 4

7 6 5

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snack time can serve a math purpose in addition 5. Use games to teach math concepts and

to a practical one, providing opportunities for skills and to give children practice in

counting, comparisons, and graphing. applying them. Games can provide an engag-

ing opportunity for children to practice and

3. Highlight math within topics of study extend skills, and the practice guide supplies

across the curriculum. Teachers can integrate several examples of games teachers can use to

math concepts into non-math lessons by high- encourage children to apply their math knowl-

lighting the aspects of math that are already edge. Teachers can use games that are included

present in the curriculum. This gives children in math curricula, purchase games, make games

opportunities to count and measure objects, themselves, or use games that come up dur-

examine shapes, and analyze data (depending ing natural play, like hopscotch or jump rope,

on the current math objectives). The practice to reinforce math concepts. Teachers can get

guide provides examples of ways to integrate involved with the game-playing in order to

different math content areas into literature, sci- ensure educational play or to challenge children

ence, art, health and safety, and social studies to extend their skills.

lessons (see page 51 of the practice guide).

4. Create a math-rich environment where Summary of evidence

children can recognize and meaningfully The WWC identified 20 studies that examined the

apply math. Teachers can provide opportunities effects of interventions that included dedicated time

for children to see and use math concepts on a for math instruction, integration of math into other

regular basis by creating a math-rich classroom aspects of the school day, and the use of games to

environment. This enrichment can be done by practice math skills. A group of studies found that

making math-related objects and tools readily children who played number-based board games

available, labeling and organizing them so they performed better in the domain of basic number

are easy to find and use, and organizing activities concepts than did children who played color-based

and routines with numeric systems. Teachers can board games or no board games. Although the

also explicitly teach children how to use math evidence to support this recommendation is promis-

tools by modeling their use during small- or ing, the WWC could not isolate the effects of the use

large-group time. of dedicated time for math instruction, integration

of math into other aspects of the school day, and

the use of games to practice math skills, since other

An example of a math-rich environment recommended practices were also implemented. As a

in the classroom. result, the WWC assigned a level of evidence rating of

minimal. For more details, see Recommendation 5 in

the practice guide, page 47.

11 12 1

10 2

9 3

8 4

7 6 5

Art Station 1 Art Station 2

Sign up to receive additional information

from the What Works Clearinghouse at

http://ies.ed.gov/newsflash/.

What Works Clearinghouse™

whatworks.ed.gov 8