Title: SEVEN ESSENTIAL SKILLS FOR FUTURE MATH SUCCESS

Published in: Early Years, a publication of the Texas Association for the Education of Young

Children, Austin, TX USA

Publication

Date: Summer 2015, Vol. 36. No. 2

Author: Dr. Carrie S. Cutler

48 Wisteria Walk Cir.

The Woodlands, TX 77381

713-377-3659

cutlerc@uhd.edu

Brief Bio: Since 1998, I have taught undergraduate and graduate courses in elementary and

early childhood math methods. In 2014, the University of Houston-Downtown

recently selected me as their Outstanding Adjunct Professor and the Houston Area

Association for the Education of Young Children awarded me their Teacher

Educator of the Year honor. My publication history ranges from numerous

scholarly journal articles to a practical math lesson book for teachers of gifted

children. I work with preschool and elementary teachers in the Houston area as a

consultant and workshop presenter. I am also super mom to eight kids ages 3

months, 2, 4, 8, 10, 12, 14, and 18.

Seven Essential Skills for Future Math Success

Even more than reading ability, mastering early math concepts serves as a predictor of

later school success (Duncan et al, 2007). Children are naturally mathematical. They

instinctively identify unfair shares, determine who is taller, and count collections of toys.

Expanding upon children’s natural desires to make sense of the world in mathematical ways

helps build a firm foundation for future mathematical success. Preschool children should develop

seven skills to ensure they are ready for future math endeavors.

1. Number and operations skills. Because number concepts are the gateway to all other

mathematical content, children must become competent counters. Counting may seem simple,

but it is actually a highly cognitive endeavor. Counting involves:

saying numbers in the correct sequence,

keeping track of what’s been counted,

recognizing that the number sequence is consistent no matter what is counted or what

order the objects are counted in,

using one-to-one correspondence (assigning one number to each object counted), and

understanding cardinality (recognizing that the final number spoken is the quantity in the

set).

To help children become competent counters, teachers can enrich the school day with

natural opportunities for meaningful counting. For example, model counting at clean-up time by

quickly counting the number of blocks in a handful and saying, “I picked up four. This is a

handful of three. This time I got two.” Children will soon join in the clean-up counting.

Filling the school day with counting teaches several principles. Students can gain

experience counting from a number other than one. We can do this by saying, “I see three

blocks, then four, five, six” or “I see two children on one side of the water table, then three, four,

five on the other.”

Creative teaching also helps children with the concept of zero. Play a Zero Game by

sending children on a hunt for easily located classroom items such as crayons. Then have them

look for an item not found in the classroom such as a tiger or an elephant. For another Zero

Game, ask all the children with, for example, black hair to stand to be counted. When you ask all

the children with purple hair to stand, point out that zero children stood up. Repeat this game

with various themes to help children understand zero.

Preschoolers should also become familiar with simple adding and subtracting scenarios

in meaningful real-world situations. Do this by adding red blocks to blue blocks or taking away

crackers by eating them during snack. Imbedding daily routines with conversations about adding

and subtracting aids children in seeing and appreciating mathematics in their everyday lives.

--insert figure 1 about here--

Figure 1. Teaching Tips for Number and Operations

Count throughout the school day

Use a variety of materials including math manipulatives and real-world objects

Incorporate counting into all centers

Give experience with the concept of zero

Ask good questions such as, “How many more do you need to have five?” or “You started

with six and ate two. Without counting again, can you tell how many you have?”

2. Shapes and Their Attributes. Preschool geometry includes recognizing and naming

two-dimensional shapes (circle, square, rectangle, rhombus, and triangle) and three-dimensional

shapes (cylinder, sphere, rectangular prism, cube, and cone).

Using the correct geometric terms to identify and describe shapes prepares children for

future learning in math. Unfortunately, adults sometimes transmit inaccurate information about

geometry. For example, teachers sometimes use the word diamond for a rhombus. A rhombus is

any parallelogram with four sides of equal length. Teachers may think that the term rhombus is

too complex or unusual for preschoolers to use. But both rhombus and diamond have two

syllables and seven letters. If children can learn diamond, they can learn rhombus. Knowing the

correct geometric term will carry children through many years of math learning.

Teachers need to help children to understand that the orientation of a shape doesn’t

“change” the shape or make it a different shape. Front ways, sideways, and upside down,

moving a geometric figure around doesn’t change its shape. Instead, the attributes of a figure

(such as its sides and corners) are the defining characteristics.

--insert figure 2 about here—

Figure 2. Children need to see many different types of triangles—equilateral (three equal sides),

isosceles (two equal sides), scalene (no equal sides), and right (one 90* angle)—in various

orientations.

Children can identify two-dimensional shapes by creating Shape Books. Make a blank

book with construction paper and then label pages for circles, triangles, squares, rectangles, and

rhombi. Have students look through magazines to find pictures they can glue on each shape book

page. Make a similar book for three-dimensional shapes.

Incorporate developmentally-appropriate geometry into the preschool classroom with an

activity called 3D Shape Sort. Ask students to bring empty food cartons, jars, or cans from home.

Have students sort the items into three piles. Ask the following questions:

Why did you sort the objects this way?

How are the objects alike or different?

Do this object roll? lay flat? slide?

Does it have points? Does it have curves?

Is there another way to sort the objects? How?

What geometrical shape does this remind you of? Why?

3. Measurement concepts. Measurement for preschool focuses on length, capacity, and

weight. Students can even measure the passage of time. Initial investigations of measurement

involve side-by-side comparisons between two objects. For example, have children stand back-

to-back to see who is taller. Use a pan balance to compare the weight of a box of crayons and a

bottle of glue. Make a side-by-side comparison of capacity by counting how many scoops of

beans two different containers hold.

Later on, children will be ready for nonstandard units. Cubes, craft sticks, paper clips,

and straws work well for measuring length. Teddy bear counters or flat-sided marbles are well-

suited for explorations of weight. The sensory table is an ideal location for children to use scoops

of beans, rice, or water to measure capacity. Label a container Target and have children find

other containers that hold the same, hold less, and hold more than the target container.

Ask children to bring a small item from home and play Show and Tell Measuring. They

may bring items such as a can of soup, a spool of thread, a toy, a coffee mug, or so on. Have

each child try to find another friend who brought an item that is about the same length. Then

have them find a friend with an item of about the same weight. If possible, have the child find

another friend who has an item with the same capacity. Children love using their own items for

measuring.

Preschool teachers shouldn’t expected children to learn how to tell time on a digital or

analog clock. However, children need to reason about the passage of time. Incorporate math into

conversations about the daily schedule by identifying what happens before or after certain

activities such as lunch or circle time. Talk about things that happened to the children in the past

(being a baby), are happening now (being in preschool), and will happen in the future (going to

elementary school). Concepts about the passage of time mean more when they are directly

related to children’s lives.

--insert figure 3 about here--

Figure 3. Teaching Tips for Measurement and Shapes

Use a variety of hands-on materials such as cubes, blocks, links, pan balance, straws, and

play dough.

Take Shape Hunts around the classroom. Use correct mathematical terms to identify shapes

and their attributes. For example, when a child finds a rectangle, count the number of sides

and corners then mark the rectangle with an index card that says “rectangle.” See which

shapes are the most common in the school environment.

Take Measurement Hunts where children take off one shoe and use it to find objects that are

the same length, longer, or shorter than their shoe. You may even use blocks to find the

capacity of the shoe then find objects that hold more or less than the shoe.

4. Sorting and classification. Pattern blocks, shells, or toy cars allow children to group

objects by attributes such as color, texture, size, or shape. Make sure children can describe how

groups are similar or different. Button, Button Sorting helps children to practice this. Give the

child a small selection of buttons. Have them sort the buttons according color, number of holes,

size, and so on. Later, have the child make a set of four buttons that are similar in some way and

one button that doesn’t share that attribute. A partner guesses which button doesn’t belong and

why.

5. Patterning. Preschoolers should recognize, extend, and create repeating patterns and

growing patterns. Growing patterns might follow an A, B, A, A, B, A, A, A, B pattern. We

should teach repeating patterns beginning with AB, then ABC, then AAB. The daily calendar is

a common context for patterning, but children get more concrete experience when they

participate in a Pattern Dance (Copley, 2010). Children take turns creating a dance using three

different motions in sequence. For example, jump—kick—clap. Repeat the pattern over and over

again in an ABC pattern. Begin the Pattern Dance by saying the action words as children do

them. Then use the letter representations to draw the connection between the actions and the

abbreviated way of describing the pattern.

Music Patterns (Copley, 2010) offers another fun patterning exercise. Color-code homemade

shakers, bells, and wood blocks by placing a different colored sticker on each type of instrument.

For example, the shakers could be covered with blue stickers, red for the bells, and yellow for

wood blocks. Children compose music by creating patterns with different color stickers on

musical staff paper then play the instruments in the order indicated by the pattern.

6. Reason, communicate, represent, connect and problem solve. Young children

should engage in developmentally appropriate math activities to learn about logic, reasoning, and

problem solving (National Council of Teachers of Mathematics, 2000). These become

mathematical habits of mind and lifelong abilities. For example, one teacher uses a daily graph to

encourage mathematical vocabulary for communicating ideas with accuracy and confidence.

When the data come from children’s own experiences and preferences, graphing builds

representation skills, such as using fruit stickers to represent favorite fruits in a graph, and makes

strong connections to children’s real lives. Make the graph a problem solving activity by asking

questions that require students to reason about the data.

1. What information does this graph show?

2. Which is the most popular choice?

3. Which is the least popular choice?

4. What patterns do you see in this data?

--insert figure 4 about here—

Figure 4. Graph of the Day Suggestions

Ideas for two category graphs

(as well as any YES or NO question)

Which of these two colors is your

favorite?

Toss a penny. Did it land on heads or

tails?

Does your first name have an E, yes or

no?

How do you feel today, happy or sad?

Which flavor of gum do you like better,

grape or strawberry?

Ideas for three category graphs

Would you rather drink apple, orange, or

grape juice?

Are you wearing pants, shorts, or a skirt?

Are your shoes fastened with velcro, laces,

or nothing?

Do you like your potatoes mashed, fried, or

baked?

Do you like books about animals, kids, or

aliens?

Do you like strawberry, chocolate, or

vanilla ice cream best?

7. A feeling of mathematical power. Attitude determines aptitude. Perhaps as essential

as any mathematical skills developed during the preschool years, children should begin to see

themselves as mathematically powerful (NCTM, 2000). Many factors can magnify or diminish

children’s mathematical dispositions. Demographics, attitudes towards mathematics in the

media, parent and teacher influence—these and many other elements play central roles in how a

child perceives his or her mathematical prowess (NCTM, 2011). We must encourage children to

persevere when challenges arise, to persist in the face of frustration, and maintain a positive

disposition toward mathematics. Math can be a useful tool for solving life’s problems.

Conclusion

Developing these seven skills will put children on a firm path to mathematical fluency.

Preschool teachers play a key role in children’s mathematical proficiency and self-perception. By

filling our classrooms with child-driven mathematical experiences, we will prepare the bright

math minds of tomorrow.

--insert table 1 about here--

Table 1. Ideas for Incorporating Children’s Literature with Preschool Mathematics

BOOK TITLE AUTHOR

LESSON IDEA

NUMBER AND OPERATIONS

ONE HUNTER PAT HUTCHINS

Children guess what animals are hiding from the hunter.

Make a class book using the title, “One Preschooler.”

Include things in the preschool environment that children

count each day. Present the class-made book to the school

director or to another preschool class.

WHAT COMES IN 2s, 3s, &4s?

SUZANNE AKER

Make a poster for things that come in 2s. Children cut out

pictures from magazines and glue them to the poster. Do

the same for 3s & 4s.

ONE, TWO, THREE WILLIAM WEGMAN

Write three different digits (from 0-9) randomly on a sheet

of paper. Make a key showing each digit marked with a

different color of dot marker. Children practice digit

recognition by covering each digit with the correct color.

SORTING AND CLASSIFYING

A HOUSE IS A HOUSE FOR MARY ANN HOBERMAN Group similar types of houses (i.e. dens, caves, and

ME burrows) and the animals that live in them. Why do certain

houses work best for certain animals? Children make a

chart or table to show how they could group the houses

and the animals.

FROG AND TOAD ARE

FRIENDS ARNOLD LOBEL

Children make a MISSING poster for Frog’s button. They

describe or draw the button using as much detail as

possible.

CORDUROY DON FREEMAN

Children sort buttons using color, size, or number of holes.

With a partner, children play a game of “One of These

Things Is Not Like the Other” by choosing four buttons,

three of which share a common attribute. A friend tries to

guess which button doesn’t belong.

PATTERNS

ROUND TRIP ANN JONAS Discuss symmetry in nature. Children use pattern blocks to

construct symmetrical designs.

THERE WAS AN OLD LADY WHO SWALLOWED A SHELL

LUCILLE COLANDRO

Use clipart to recreate the story. Demonstrate the growing

pattern that looks like stairs as the story is retold. Work as

a class to make up an original story with a growing pattern.

CAPS FOR SALE ESPHYR SLOBODKINA

Children look for patterns in the book. They might also

estimate how many baseball caps they balance on their

heads then try it out.

GRAPHING

CLOUDY WITH A CHANCE

OF MEATBALLS JUDI BARRETT

Children survey classmates with a simple recording sheet

and tally marks. Remember to limit the choices for the

survey to three options. For example, what kind of foods

do preschoolers like to eat for breakfast—cereal, waffles,

or pancakes? Help the children to record the results on a

pictograph or bar graph.

RED IS BEST STINSON, KATHY

Take a class survey. Ask, “What color do you like better—

red or green?” Children pick up a cube to show their

choice. They find others who chose the same color and

make a group. Then have the groups line up facing each

other. Children shake hands with the classmate directly

across. The color group with no one to shake hands with is

the winner. Then have children join their color cubes to

make a bar graph. Compare the heights of the cubes.

TODAY IS MONDAY ERIC CARLE

Make a list of the children’s favorite foods. Create a class

book by replacing the foods in the story with the children’s

choices. Have children illustrate the book.

MEASUREMENT

A SECOND IS A HICCUP HAZEL HUTCHINS

How long would it take to cough once, make cookies and

bake them, or walk to the park and back? Children

experiment to find other tasks that take a second, a minute,

or an hour. Make a class book called, “Our Second Book”

or “Our Minute Book.”

THE GROUCHY LADYBUG ERIC CARLE

When a student “catches” the clock on the hour, he/she

may wear a ladybug hat and read from the book about

whom the ladybug is fighting at that hour.

WHO SANK THE BOAT? PAMELA ALLEN

At the sensory table, children explore concepts of capacity

by using empty boxes children bring in from home (for

example pizza, cereal, or shoe boxes) and scoops, spoons,

birdseed, rice, beans, or sand.

ACTUAL SIZE STEVE JENKINS

Make a chart comparing the sizes of animals from birth to

adulthood or compare different species. As a class, discuss

how size can be an adaptation that helps animals survive.

ARE WE THERE YET,

DADDY? VIRGINIA WALTERS

Children use the map at the end of the book to follow the

action of the story. As a class, create a map of the school.

Label landmarks and count the number of steps between.

GEOMETRY AND SHAPES

LOOK-ALIKES JOAN STEINER

Children go on a Shape Walk, recording the basic

geometrical shape of everyday things on a simple

recording sheet. Discuss why things are certain shapes

such as a round manhole cover or a rectangular door.

SPOTS LESSER, CAROLYN

Make a “Shapes in Our World” class book. Take photos of

the shapes children find in the classroom or playground.

Print out the photos and help children to label the shapes in

the photos. Send the book home with each child and ask

parents to add a shape photo to the book.

CHANGES, CHANGES PAT HUTCHINS

Show children blocks--sphere, cone, rectangular prism, and

cylinder—and discuss the names of each. Children use clay

to create the 3D shapes.

--insert figure 5 about here--

Figure 5. Helpful Websites for Preschool Mathematics Teaching.

1. The National Council of Teachers of Mathematics

Web Address: http://www.nctm.org/Classroom-Resources/Browse-All/

Offers: Lesson plans searchable by grade and content area, math games and interactives children

can use independently, link to the NCTM Pinterest® page.

2. Collaborative for Children

Web Address: https://www.collabforchildren.org/educators/online-courses

Offers: Online courses for professional development in preschool mathematics

3. PBS Parents

Web Address: http://www.pbs.org/parents/education/math/

Offers: Math teaching tips for teachers and parents, interactives for children, games, and lesson

ideas

4. Resources for Early Childhood

Web Address: http://rec.ohiorc.org/LearningExperiences/?topic=1&

Offers: Lesson plans searchable by age and content area. Correlates to Ohio’s early childhood

standards, but many objectives mirror those found in the Texas PreK Guidelines.

References

Copley, J. V. (2010). The young child and mathematics. (2nd ed.). Reston, VA: NAEYC and

NCTM.

Duncan, G. J., Claessens, A., Engel, M., Dowsett, C. J., Huston, A. C., Magnuson, K.,

Klebanov, P., Pagani, L. S., Feinstein, L., Duckworth, K., Brooks-Gunn, J., Sexton, H.,

Japel, C. (2007). School readiness and later achievement. Developmental Psychology,

43(6), 1428 –1446.

National Council of Teachers of Mathematics. (2011). Motivation and disposition: Pathways to

learning mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (2000). Principles and standards for school

mathematics. Reston, VA: Author.