Prekindergarten Mathematics: Connecting with National

Standards

Rosalind Charlesworth1,2

This article provides an overview of prekindergarten mathematics as related to nationalstandards. Included are descriptions of the National Council of Teachers of Mathematics

principles and standards, the fundamental concepts developed and learned in early childhood,and naturalistic and informal instructional examples. Each concept is connected to thematching standard.

KEY WORDS: mathematics; prekindergarten; preschool; standards.

In 2000 the National Council of Teachers ofMathematics (NCTM, 2000) published a set ofstandards that, for the first time, included prekin-dergarten. This recognition of young children asmathematicians was a big step forward for the EarlyChildhood Education field.

Young children are developing many funda-mental concepts that can be built upon by adults(Ginsburg, Inoue, & Seo, 1999; Seo, 2003). Baroody(2000) reviewed the research on young children’snumber and arithmetic skills. Research shows that3-year-olds are at the beginning levels of subitizinggroups of two and three and discriminating betweenthem. Between 3 1/2 and 4 years of age they beginto be able to compare the amounts in groups usingtheir counting skills. Older prekindergartners cansolve concrete addition and subtraction problems,have a grasp of part-whole relationships, and canpartition groups into subgroups of equal size.Baroody believes that the research supports thatyoung children acquire a great deal of informalmathematical knowledge. Building on this knowl-edge can provide children with mathematical power:

positive feelings about mathematics, an under-standing of mathematics, and the ability to engagein mathematical problem solving. To grow chil-dren’s mathematical power instruction should bebased on problem solving. For prekindergartnersmathematics can build on everyday exploratoryactivities, on responses to children’s questions, byproviding mathematics games, and through litera-ture experiences.

Seo (2003) makes the connection from children’splay to mathematics. She emphasizes the importanceof knowing how to be an observer of mathematicsrelated play so that intervention can be done at anopportune time. The information obtained fromobservation and informal interventions can lead toplanning of structured experiences.

This paper presents an overview of theNCTM standards as they relate to prekindergartenmathematics concept development and instruction. Itbegins with the guidelines and standards for mathe-matics. Next there is a description of early childhoodconcept development followed by a description ofhow fundamental concepts are learned. Finally thereis an explanation of how fundamental concepts ex-pand and are applied in the development of morecomplex concepts. Included are examples of the kindsof experiences that support the development offundamental mathematics concepts with connectionsto guidelines and standards.

1Weber State University.2Correspondence should be directed to Rosalind Charlesworth,

Department of Child and Family Studies, Weber State University,

1301 University Circle, Ogden, UT 84408, USA; e-mail:

rcharleswort@weber.edu

Early Childhood Education Journal, Vol. 32, No. 4, February 2005 (� 2005)DOI: 10.1007/s10643-004-1423-7

2291082-3301/05/0200-0229/0 � 2005 Springer ScienceþBusiness Media, Inc.

GUIDELINES AND STANDARDS

IN MATHEMATICS

In 2000, based on an evaluation and review ofprevious standards, publications, NCTM publishedPrinciples and Standards for School Mathematics. In2002 the National Association for the Education ofYoung Children (NAEYC) and NCTM collaboratedon the development of a joint position statementon early childhood mathematics (Early childhoodmathematics, 2002; Math experiences that count!,2002). A major change in the age/grade categorylevels is the inclusion of prekindergarten. The firstlevel in the NCTM standards is now Prekindergar-ten through grade 2. It is an important step forwardthat prekindergartners are now recognized as havingmathematics knowledge and capabilities. However,it is important to keep in mind that just as is true ofolder children prekindergartners will not all enterschool with equivalent knowledge and capabilities.It must be recognized that prekindergartnern havean informal knowledge of mathematics that can bebuilt on and reinforced. During the prekindergartenyears young children’s natural curiosity and eager-ness to learn can be capitalized on to develop a joyand excitement in learning and applying mathe-matics concepts and skills. As in the previousstandards the recommendations in the currentpublication are based on the belief that ‘‘studentslearn important mathematical skills and processeswith understanding’’ (NCTM, 2000, p. ix). That is,children should not just memorize but need todevelop a true knowledge of concepts and processes.Understanding is not present when children learnmathematics as isolated skills and procedures.Understanding develops through interaction withmaterials, peers, and supportive adults in settingswhere students have opportunities to construct theirown relationships when they first meet a new topic.Exactly how this takes place will be explainedfurther in this article.

Principles of School Mathematics

The Principles of School Mathematics arestatements reflecting basic rules that guidehigh-quality mathematics education. There are sixprinciples which describe the overarching themes ofmathematics instruction (NCTM, 2000, p. 11):

Equity: High expectations and strong support for all students

Curriculum: Is more than a collection of activities: it must be

coherent and focused on important mathematics.

Teaching: Effective mathematics teaching requires under-

standing of what students know and need to learn and then

challenging and supporting them to learn it well.

Learning: Students must learn mathematics with understand-

ing, actively building new knowledge from experience and

prior knowledge.

Assessment: Assessment should support the learning of

important mathematics and furnish useful information to both

teachers and students.

Technology: Technology is essential in teaching and learning

mathematics.

These principles can guide instruction in allsubjects, not just mathematics.

Standards for School Mathematics

Standards provide guidance as to what childrenshould know and be able to do at different ages andstages. Ten standards are described for prekinder-garten through grade 12. The first five standardsare content goals for operations, algebra, geometry,measurement, data analysis and probability. The nextfive standards include the processes of problemsolving, reasoning and proof, connections, commu-nication and representation. These two sets of stan-dards are linked together as the process standards areapplied to learning the content. These will be de-scribed later in this article.

CONCEPT DEVELOPMENT, LEARNING

AND INSTRUCTION

The following section describes how childrenacquire concepts, how technology can enhancelearning, and provides a description of the five pro-cess standards.

How Children Acquire Concepts

Concepts are the building blocks of knowledge(Charlesworth, 2004). Fundamental concepts thatbegin to develop in early childhood includeone-to-one correspondence, number and counting,shape, spatial sense, logical classification, comparing,and parts and wholes. These fundamental conceptsare applied to more advanced concepts such asordering and patterning, informal measurement,connecting groups and symbols, and concreteaddition and subtraction.

Children acquire concepts through three typesof learning experiences: naturalistic, informal andstructured. Naturalistic experiences are those initiated

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and controlled by the child. For example, buildingwith blocks, pouring sand or water, or setting thetable for a doll’s tea party. Informal learning occurswhen an adult or older child provides a comment or aquestion that causes previous knowledge to be rein-forced, applied or expanded during naturalisticactivities. For example, Tamara has a selection ofspoons she is exploring. She selects the smallest spoonto pretend to feed her doll. Dad comments, ‘‘Youpicked the smallest spoon to use to feed your doll.’’Johnny is stringing beads, his teacher asks, ‘‘Howmany yellow beads have you strung?’’ Structuredlearning experiences are preplanned and involve somedirect instruction. They focus on specific conceptsthat an individual or group of children are ready towork with. During the prekindergarten periodthe major focus is on naturalistic and informalinstruction.

Technology

Technology is providing us with an everincreasing array of learning tools. Children canconnect to the net and can enjoy a variety of edu-cational software. More and more preschools areincluding computers in the classrooms. DouglasH. Clements is a major researcher on the effectiveuse of computers with young children (Clements,1999, 2001; Sarama & Clements, 2003). Computeractivities can help children bridge the gap fromconcrete to abstract. Children can learn Math con-cepts from software that presents a task, asks for aresponse, and provides feedback. However, softwareshould go beyond drill and practice and provide forthe children’s creativity. Creating new shapes fromother shapes or using turtles to draw shapes provideschildren with opportunities for exploration and dis-covery. Computers also provide social opportunitiesas children enjoy working together. One or morecomputers can serve as centers in the classroom. Aschildren explore the adult can provide suggestions orask questions. Most importantly the adult can ob-serve and learn something about how children thinkand solve problems. Calculators can also provide atool for learning. Even the youngest children canexplore number using them. When planning activi-ties the children’s learning styles and areas ofstrength should be considered. Technology, bothcomputers and calculators, provides valuable toolsfor learning math.

Problem Solving, Reasoning, Communications,

Connections, and Representation

For the youngest mathematicians problem solv-ing is the major means for building mathematicalknowledge. Problems usually arise fromdaily routines,play activities and materials, and from stories. Aschildren work with the materials and engage in activ-ities they figure things out using the processes ofreasoning, communications, connections, and repre-sentation. Logical reasoning develops in the earlyyears and is especially important in working withclassification and with patterns. Reasoning enablesstudents to draw logical conclusions, apply logicalclassification skills, explain their thinking, justify theirproblem solutions and processes, apply patterns andrelationships to arrive at solutions, andmake sense outof mathematics. Communication with oral, written,and pictorial language provides the means forexplaining problem solving and reasoning processes.Children need to provide a description of what they doand why they do it and what they have accomplished.They need to use the language of mathematics in theirexplanations. The important connections for the youngmathematicians are the ones between the naturalisticand informal mathematics they learn first and theformal mathematics they meet in school. Concreteobjects can serve as the bridge between informal andformal mathematics. Young children can ‘‘representtheir thoughts about, and understanding of, mathe-matical ideas through oral and written language,physical gestures, drawings, and invented and con-ventional symbols’’ (NCTM, 2000, p. 136).

The connection with language and literacy isextremely important in concept development. Youngchildren, expecially from ages two to four, are grow-ing at a rapid rate in oral language skills and in theirunderstanding of symbols such as letters and num-bers. Concept vocabulary increases and is appliedthrough adult comments and questions: ‘‘Get the bigball?’’ ‘‘How many cars do you have?’’ ‘‘Find some-thing that is square’’. Literature is an increasinglyimportant medium for connecting mathematics andlanguage and literacy (for example, Chapman, 2000;Cutler, Gilkerson, Parrott, & Browne, 2003; Ducolon,2000; Fleege & Thompson, 2000; Hellwig, Monroe, &Jacobs, 2000; Taylor, 1999; Thatcher, 2001).

Assessment

The National Council of Teachers of Mathe-matics (NCTM’s) Assessment Principle (2000, p. 22)

231Prekindergarten Mathematics

states that Assessment should support the learningof important mathematics and furnish usefulinformation to both teachers and students.’’It should be an integral part of instruction, notjust something done to students at the end ofinstruction. Assessment should be integratedinto everyday activities so it is not an interruptionbut is part of the instructional routine. Assessmentshould provide both teacher and student withvaluable information. There should not be overreliance on formal paper and pencil tests butinformation should be gathered from a variety ofsources. ‘‘Many assessment techniques can be usedby mathematics teachers, including open-endedquestions, constructed-response tasks, selectedresponse items, performance tasks, observations,conversations, journals and portfolios’’ (p. 23). It isalso important to take heed of the diversity principleand diversify assessment approaches to meet theneeds of diverse learners such as English LanguageLearners, gifted students, and students with learningdisabilities.

FUNDAMENTAL CONCEPTS AND SKILLS

As mentioned earlier fundamental concepts andskills acquired during the prekindergarten periodinclude one-to-one correspondence, number senseand counting, logic and classifying, comparing,geometry, spatial relations, and parts and wholes.The following section describes the relevant NCTMstandards and provides naturalistic and informallearning examples.

One-to-One Correspondence

NCTM (2000) expectations for one-to-one cor-respondence relate to rational counting (attaching anumber name to each object counted). Placing ob-jects in one-to-one correspondence is a supportiveconcept and skill for rational counting. Using pegsand pegboards and setting the table are examples ofexperiences that provide practice with one-to-onecorrespondence.

When observing children at play with matchingmaterials such as objects or picture cards such as tenadult animals and 10 babies note if the children at-tempt to match the babies with the appropriateadults. Point to an animal, ‘‘Can you find this ani-mal’s mother/father?’’

‘‘As the children play with blocks or Legos’’ noteif the do any one-to-one correspondence.

Number Sense and Counting

The NCTM (2000) expectations for numberfocus on children in prek-2 counting with under-standing and recognizing ‘‘how many?’’ in sets ofobjects. The children are also expected to developunderstanding of the relative position and size ofwhole numbers, ordinal and cardinal numbers andtheir connections to each other. Finally, they areexpected to develop a sense of whole numbers and beable to represent and use them in many ways. Theseexpectations should be achieved through real-worldexperiences and through using physical materials.When shown a group, seeing ‘‘how many’’ instantly iscalled subitizing (Clements, 1999). Young childrenusually learn to subitize up to four items perceptually.That is, shown a group of four items they can tell you‘‘four’’ without counting. Perceptual subitizing isthought to be the basis for counting and cardinality(understanding the last number named when count-ing a group is the amount in the group).

As children play with materials in the classroomnote any occasions when they identify the number ofobjects in a group. Ask questions, such as ‘‘Howmany shoes do you need for your dress-up outfit?’’,‘‘Can two cups of sand fill the bowl?’’ ‘‘How manycups will you need for your birthday party?’’ Aschildren explore a variety of manipulatives in themath center note how they group the materials andif they mention ‘‘how many’’, i.e., ‘‘I have five redcubes. I need three green cubes’’. Ask questions,‘‘How many white cubes have you hooked to-gether?’’

Logic and Classifying

NCTM (2000) expectations for logic and classi-fying include being able to sort, classify, and orderobjects by size, number, and other properties and sortand classify objects according to their attributes andorganize data about the objects.

Young children seem to have a natural tendencyto sort by color. Provide objects of many colors andart materials such as crayons, paint, colored paper,etc. Label the colors, ‘‘You have lots of green in yourpicture.’’ ‘‘You’ve used all red Lego blocks.’’ Notewhen the children label the colors, ‘‘Please pass me apiece of yellow paper.’’ ‘‘I can’t find my orangecrayon.’’ Ask questions, ‘‘Which colors will you usefor your penguins?’’ Have children bring items suchas leaves, worms, bugs, etc. for science table collec-tions that can be grouped and organized.

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Comparing

Comparing is the beginning level of measure-ment. The NCTM expectations (2000) for measur-ment include understanding the attributes of length,capacity, weight, area, volume, time, and tempera-ture. Measurement begins with simple comparisonsof physical materials and pictures. The expectation isthat young children will be able to describe qualita-tive comparisons such as John is taller than Peter orthis cup holds more sand than that one or Tina hasmore dolls than Judy.

Notice if children use any of the comparisonvocabulary during their daily activities, ‘‘He has morered Unifix Cubes than I do.’’

‘‘I have fewer jelly beans than Mark’’. Askquestions, ‘‘Does everyone have the same number ofcookies?’’

Geometry: Shape

During the preprimary years children shouldbe able to reach the first expectation for geometry(NCTM, 2000): recognize, name, build, draw, com-pare, and sort two- and three-dimensional shapes.This beginning knowledge of geometry can be inte-grated with other content areas. Geometry for youngchildren is more than naming shapes, it is under-standing the attributes of shape and applying them toproblem solving. Geometry also includes spatial sensewhich is discussed next.

Prekindergartners begin to learn that someshapes have specific names such as circle, triangle,square, cylinder, and sphere. First children learn todescribe the basic characteristics of each shape intheir own words such as ‘‘four straight sides’’ or‘‘curved line’’ or ‘‘it has points’’. Gradually theconventional geometry vocabulary is introduced.Children need opportunities to freely explore bothtwo- and three-dimensional shapes. Unit blocks,attribute blocks, Lego, etc. provide opportunities forexploration.

Prekindergartners are just beginning to developdefinitions of shapes which probably are not solidi-fied until after age six (Hannibal, 1999). Whenworking with shapes it is important to use a variety ofmodels of each category of shape so children gener-alize and perceive there is not just one definition. Forexample, triangles with three equal sides are the mostcommon models so children frequently don’t perceiveright triangles, isoceles triangles, etc. as real triangles.Many preschoolers don’t see that squares are a

type of rectangle. After experience with many shapeexamples and discussion of attributes children beginto see beyond the obvious and generalize to relatedshapes.

Some examples should be rotated. Some nonex-amples should be provided for comparison. Preop-erational children need to learn that orientation,color, and size are irrelevant to the identification ofthe shape. Clements and Sarama (2000, p. 487) sug-gest that children can be helped to learn what is rel-evant and what is irrelevant through the followingkinds of activities:

� Identifying shapes in the classroom, school, and community.

� Sorting shapes and describing why they believe that a shape

belongs to a group.

� Copying and building with shapes using a wide range of

materials.

Geometry: Spatial Relationships

NCTM (2000) lists several expectations relativeto young children’s understanding and application ofspatial relationships as one of the foundations ofearly geometry. Young children are expected to de-scribe, name and interpret relative positions in spaceand apply ideas about relative position; describe,name and interpret direction and distance in navi-gating space and apply ideas about direction anddistance; and find and name locations with simplerelationships such as ‘‘near to’’, ‘‘above’’, ‘‘below’’,‘‘under’’, ‘‘on’’ and ‘‘in’’.

Children should be encouraged to use their bodiesin gross motor activity such as running, climbing,jumping, lifting, pulling, etc. They should be assisted inmotor control behaviors such as defining their ownspace and keeping a safe distance from others.Children should be provided with time to build withconstruction toys (unit blocks, Lego�, Unifix Cubes�,etc.) during Center Time. Providing experiencesmaking a variety of collages provides them withexperiences organizing materials in space.

Maps can be included as dramatic play props.Note if children find a way to use the maps in theirplay. Does their activity reflect an understanding ofwhat a map is for?

Parts and Wholes

Young children have a natural understandingand interest in parts and wholes that can be used lateras a bridge to understanding fractions. NCTM (2000)expectations include that young children will develop

233Prekindergarten Mathematics

a sense of whole numbers and represent them in manyways by breaking groups down into smaller parts.They will also understand and represent commonlyused fractions such as 1/4, 1/3, and 1/2. They alsolearn that objects and their own bodies are made upof special (unique) parts.

Provide students time to play with a wide varietyof toys and other objects. Label the parts such as dollbody parts, parts of vehicles, furniture, etc. asfits naturally occurring situations. For example,‘‘You put a shoe on each of the doll’s feet’’; ‘‘Thereare four wheels on the truck’’; ‘‘You found all thepieces of the puzzle.’’ etc. Ask questions, ‘‘Which toyshave wheels?’’; ‘‘Which toys have arms and legs?’’.Comment on sharing, ‘‘That is really nice that yougave your friend some of your blocks’’. Childrenshould have plenty of opportunities to explore puz-zles, construction toys, fruits such as oranges, etc.

EXPANDING AND APPLYING FUNDAMENTAL

CONCEPTS AND SKILLS

Fundamental concepts and skills can be ex-tended into more complex concepts and activitieswhich focus on ordering, seriation, patterning, mea-surement, data collection and analysis, and use ofsymbols. Integration with other content areas can bedone using dramatic play, thematic units, and pro-jects (e.g., Hart, Burts, & Charlesworth, 1997; Helm& Katz, 2001; Katz & Chard, 1989).

Ordering, Seriation, and Patterning

The NCTM (2000, p. 90) standard for pre-K-2Algebra includes the expectations that studentswill order objects by size, number and otherproperties; recognize and extend patterns; and ana-lyze how patterns are developed. Very young childrenlearn repetitive rhymes and songs and hear storieswith predictive language. They develop patterns withobjects and eventually with number. They recognizechange such as in the seasons or in height as theygrow.

Have a container of objects in a sequence of sizesavailable during center time. Note how the childrenuse the objects. Do they sequence them by size?Comment, ‘‘You put the biggest one first;’’ ‘‘You putall the same size things in their own piles.’’ Have theflannel board and story pieces available during centertime. Note how the children use the material. Do theytell the story? Do they line up the pieces in sequence?Comment if they hesitate, ‘‘What comes next in the

story?’’ Note if they sequence and/or match thematerials by size, ‘‘You matched up each bear withhis/her chair, bowl, bed.’’ Note if they take turns.Comment, ‘‘You are doing a good job taking turns,Mary is first, Jose is second, Larry is third, and Jai Liis fourth’’.

Measurement

As already mentioned the NCTM (2000, p. 102)expectations for children in the beginning stages ofmeasurement include recognizing the attributes oflength, volume, weight and time and comparing andordering objects according to these attributes. Alsoincluded in measurement are the attributes of tem-perature. Young children, by the time they reachkindergarten, are expected to be able to measure withnonstandard units using multiple copies of objects ofthe same size such as paperclips or Unifix Cubes�.Measurement connects geometry and number. Itbuilds on children’s experiences with comparisons.Length is the major focus for the younger studentsbut experiences with volume, weight and temperatureare also important.

Allow plenty of time for experimenting withmaterials such as Lego�, sand, water, weights andbalances, clocks and timers, etc. Note if children areinto the pretend play measurement stage, are makingcomparisons, or if they mention any standard units.At the sand and water table ask questions or makecomments such as, ‘‘How many of the blue cups ofsand will fill up the purple bowl?’’; ‘‘Which bottle willhold more water?’’ Provide opportunities for thechildren to experiment with a simple pan balanceusing a variety of materials. Note if they use anyweight vocabulary (such as heavy or light). Ask themto explain the results of their actions. Unit blocks areespecially good for naturalistic and informal mea-surement explorations. For example, when using unitblocks notice if children appear to use trial and errorto make their blocks fit as they wish. Comment, ‘‘Youmatched the blocks so your house has all the sides thesame length.’’ Note children’s comments regardingtemperature. Make comments and ask questions suchas ‘‘Be careful, the soup is very hot’’; ‘‘It’s cold today,you must button up your coat’’.

The NCTM standards (2000) for measurementinclude expectations for the understanding of time.Preschool and kindergarten children are learning theattributes of time such as sequence and duration. Inthe writing center or the dramatic play center place anumber of different types of calendars. Note if the

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children know what they are and use them in theirpretend play activities. Where else have they seencalendars? Who uses them? Place a large wooden toyclock in the dramatic play center. Note if the childrenuse it as a dramatic play prop. Do they use timewords? Do they make a connection to the clock onthe classroom wall?

Data Collection and Analysis

The NCTM (2000, p. l08) expectations for dataanalysis for pre-K-2 focus on children sortingand classifying objects according to their attributes,organizing data about the objects, and describing thedata and what they show. ‘‘The main purpose ofcollecting data is to answer questions when the an-swers are not immediately obvious’’ (NCTM, 2000,p.109). Children’s questions should be the majorsource of data. The beginnings of data collection areincluded in the fundamental concepts learned andapplied in classifying in a logical fashion. Data col-lection activities can begin as children collect sets ofdata from their real life experiences and depict theresults of their data collection in simple graphs. Anytype of student question can be researched and theinformation put into graphical form. Topics forgraphs may include information about hair, eye,or clothing colors, types of pets, favorite TVprograms, favorite foods, predictions, and manyothers. Through noting children’s interests as re-flected in their naturalistic activities adults can iden-tify topics of interest.

Symbols

Preschoolers enjoy counting and begin to rec-ognize number symbols or numerals. They may alsobegin to connect groups of items with the represen-tative symbol. Usually children start using the nu-meral names before they actually match them withsymbols and with groups. By two children can tellyou their age. After watching a counting video sev-eral times, 2-year-old Summer wants to take themagnetic numeral 8 with her when she goes to doerrands with her Mother. Sammy points to the clock,‘‘The clock has numbers.’’ Self correcting materialsfor group/symbol matching can be introduced.

Place numerals and a variety of shapes of dif-ferent sizes and colors in the math center for explo-ration. Note if the children make groups and placenumerals next to the groups. Ask questions, ‘‘Howmany does this numeral mean?’’ ‘‘Why does this nu-

meral go next to this group?’’ ‘‘Tell me about yourgroups’’. Place cards with groups of various amountsdrawn on them and cards with number symbols in themath center for the children to explore. Note if theymake any matches as they play with them.

Dramatic Play, Thematic Units, and Projects

The mathematics (NCTM, 2000) standards focuson content areas skills and understandings and pro-cesses that can be applied across the curriculum.Problem solving, reasoning, communication, con-nections and hands-on learning can be applied andexperienced through dramatic play, thematic andproject approaches, and integrated curriculum. Play isthe major medium through which children learn.They experiment with grown-up roles, explorematerials and develop rules for their actions. Cur-riculum that meets the national standards can beimplemented through the use of thematic units andprojects that integrate mathematics, science, socialstudies, language arts, music, and movement (Decker,1999; Hart, Burts, & Charlesworth, 1997). Themesmay be teacher selected (see Isbell, 1995) and/or childselected (see Helm & Katz, 2001; Katz & Chard,1989).

Summary and Conclusions

Prekindergarten mathematics focuses mainly onyoung children’s naturalistic explorations and theability of adults to provide informal scaffoldingthrough questions and comments. Young childrenare developing mathematics concepts and skills at theinitial levels. These concepts and skills include one-to-one correspondence, number sense and counting,logic and classifying, comparing, geometry, spatialrelations, data collection and analysis, parts andwholes, ordering and patterning, measurement, andconcrete addition and subtraction as outlined in theNCTM standards (2000). Young children also beginto recognize number symbols and experiment withtechnology. The examples provided in the currentarticle supply ideas regarding how to provide youngchildren with supportive naturalistic and informalmathematics instruction.

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