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Family Home Care Providers’ andParents’ Beliefs and PracticesConcerning Mathematics withYoung ChildrenBelinda Blevins‐Knabe a , Ann Berghout Austin b , Linda

Musun a , Annette Eddy b & Randall M. Jones ba University of Arkansas at Little Rock , USAb Utah State University , USAPublished online: 07 Jul 2006.

To cite this article: Belinda Blevins‐Knabe , Ann Berghout Austin , Linda Musun , AnnetteEddy & Randall M. Jones (2000) Family Home Care Providers’ and Parents’ Beliefs andPractices Concerning Mathematics with Young Children , Early Child Development and Care,165:1, 41-58, DOI: 10.1080/0300443001650104

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Early Child Development and Care, 2000, Vol. 165, pp. 41-58Reprints available directly from the publisherPhotocopying permitted by license only

Family Home Care Providers' and Parents'Beliefs and Practices ConcerningMathematics with Young Children†

BELINDA BLEVINS-KNABE1,*, ANN BERGHOUT AUSTIN2,LINDA MUSUN1, ANNETTE EDDY2 and RANDALL M. JONES2

1University of Arkansas at Little Rock, USA2Utah State University, USA

(Received 10 August 2000)

Three studies are reported which describe aspects of the early childhood environmentsurrounding the development of mathematics concepts. Study 1 examined the beliefsand attitudes of family home day care providers concerning mathematics. Althoughproviders rated math skills lower in importance than other skills, they thought that mathskills were acquired in the same way as other skills. In Study 2 both parent and familyday care providers reported similar frequencies for engaging children in math activities.In Study 3 we addressed the question of whether the beliefs and reported activitiesof parents and providers predict children's performance on the Test of Early Mathemat-ics Ability-2. The frequency of math activities reported by parents or family day careproviders was not significantly correlated with children's mathematics achievementscores in either age group. It appears that some mathematical activities do occur inchildren's homes and in family day care, but the frequency and scope of theseexperiences is limited.

Key words: Mathematics, family home day care providers, parents, youngchildren

This paper describes three separate studies, each of which address the early child-hood environment surrounding the development of mathematics concepts. In thisintroduction we will briefly discuss early mathematics concept development andvariations in concept development depending on early preschool experiences. Wewill also discuss the work of Tharp and Gallimore (1988) which serves as theoreticalframework linking these three studies together.

†This paper is based on research first reported at the biennial meetings of the Society for Researchin Child Development, 1997; and the Southwestern Society for Research in Human Development,1998. The research was supported by the Marie Wilson Howells Endowment to the Department ofPsychology and by the Utah State University Agriculture Experiment Station.

*Correspondence: Belinda Blevins-Knabe, Department of Psychology, University of Arkansas atLittle Rock, 2801 S. University, Little Rock, AR 72204. E-mail: blblevins@ualr.edu.

41

© 2000 OPA (Overseas Publishers Association) N.V.Published by license under

the Gordon and Breach Publishers imprintPrinted in Singapore.

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42 B. BLEVINS-KNABE et al.

According to Case (1998) the ability to reason mathematically is central to cog-nitive operations and from infancy children appear to have an awareness of number.Although there are many affordances in the environment on which to focus, infantsappear to have a rudimentary understanding of sets and of numerosity in sets. Thus,they attend to objects with certain thematic consistencies such as three apples ortwo toys, and they are able to detect additions and subtractions to items within thesesets (Keil, 1998). While biology may provide a propensity to attend to affordancesunderpinning mathematical cognition, social context directs, shapes, and rein-forces attention to additional pertinent affordances (Ginsberg, Klein & Starkey,1998). It is well understood that skills in most conceptual domains are constructedrecursively and hierarchically with earlier abilities integrated into later ones (Fisher& Bidell, 1998). Similarly, the formal (Gelman & Willimans, 1998) and informal(Charlesworth & Lind, 1999; Ginsberg, Klein & Starkey, 1998) understanding ofmathematics developed in early childhood establishes an important foundation forlearning mathematics concepts in school.

However, as with the development of other core domain concepts, children'spreschool experiences with formal and informal mathematics are not alwaysqualitatively or quantitatively sufficient (Fisher & Bidell, 1998). Affordances uti-lized in one environment to facilitate formal and informal understanding ofmathematics might not even be attended to in another environment. An excellentexample is that of young street vendors in South America. Facile as they are inmany mathematics operations, not all of what they have learned as vendorstransfers to mathematics in school. Likewise, not all of the mathematics learnedin school transfers to their work as vendors (Ginsberg, Klein & Starkey, 1997).Attention to and exploration of affordances canalizes action, organizes thought,and directs future intentionality (Reed, 1993). As skills are hierarchically refinedand reorganized developmental pathways become apparent and often differbetween children who are good at particular skills and those who are not (Fischer& Bidell, 1988).

The differing pathways of good and poor readers is an example of this divergentdevelopment. Fisher & Bidell (1988), point out that children who become goodreaders develop reading skills in a different order than children who are not as goodat reading. It is logical to assume that developmental pathways also differ betweenchildren who are good and not so good at mathematics. Case, Griffin and Kelly(1999) discuss the differing pathways for mathematics development for childrenof varying socioeconomic status (SES). They report that differences in mathematicsconcept development emerge between high and low SES children as early as threeyears of age with the SES related gap increasing through the preschool years. Bykindergarten high SES children were scoring IV2 years ahead of lower SES peers.Although their work does not outline specific points in the developmental pathwaywhere high and low SES chlidren diverge, for the purposes of this paper theirfindings remind us that preschool experiences may influence measurable differ-ences in the understanding of mathematics. Gelman and Williams (1998) providea potentially useful explanation regarding why this would be the case. Accordingto them children acquire some basic mathematics concepts without formal instruc-

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FAMILY HOME CARE 43

tion; however, their ability to reason mathematically varies according to the role thatmathematics play in their everyday iives. Not only are skills sometimes contextuallybound and thus difficult to transfer to another setting, but early skills may havebeen developed in a manner so as to interfere with higher level learning inmathematics during formal schooling (Gelman et al., 1988).

Problems usually arise when earlier learning does not support meaningful prob-lem solving later on (Gelman et al., 1998). Further, in core domains such asmathematics, early learning can not be wholly informal but must include someformal instruction of specific concepts and skills. Problem-solving abilities are bestpromoted when children are exposed to the abstract, formal, or structural level ofmathematics from the very beginning, concomitantly with concrete manipulativesand informal opportunities for problem solving. Representations of mathematicsstrategies appear to develop from problem-solving activities with concrete objects,but it appears they must be supported by active reference to the formal principlesunderlying such concrete experiences.

Concrete problem-solving activities can be, and often are, planned and orches-trated, but they also may occur spontaneously within the day-to-day routines ofeveryday life. However, children learn mathematics bestwhen daily routines includereferences to formal mathematics skills; that is, when activities are frequently narratedby references to the rules and principles governing mathematics reasoning.

Tharp and Gallimore (1988) make it clear than whenever a child's learning isat issue, the unit of analysis is the totality of the activity setting in which the childis located. The activity setting among other things, is shaped by the attitudes andbeliefs of die participating adults and their preferred modes of assisting children'sperformance.

The purpose of this paper is to outline and discuss three studies we conductedto examine components of two activity settings wherein preschool children areusually exposed to some kind of mathematics activities. One activity setting is thehome and the other is family day care. In 1995 19% of those under 6 years old werein a family daycare setting (National Center for Educational Statistics. 1995). Littleis known about this child care option and its connection to the home environmentwith reference to the development of mathematics. This literature review has dis-cussed, among other things, the embededness of learning in context, the necessityof formal and informal instruction, and the importance of continuity of instructionacross context. The research reported here explored these three components byexamining parent and caregiver attitudes about mathematics skill development andabout their beliefs and modes of assisting formal and informal mathematics per-formance. We also examined the consistency of mathematics concept presentationbetween home and family day care activity settings.

STUDY 1

Study 1 examines the beliefs and attitudes of family home day care providersconcerning mathematics. Research with kindergarten teachers indicates that they

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44 B. BLEVINS-KNABE et a/.

see social skills and health habits as more important than preacademic skills suchas math and reading (National Center for Educational Statistics, 1995). We wantedto see if family home day care providers had similar preferences for other skills overmathematics.

We also asked providers how they thought children acquire each of these skills.Particularly we wondered if providers would feel a responsibility to teach mathconcepts or if they would feel an educator in a formal classroom setting was bestprepared to teach them. Alternatively, we wondered if providers saw math as aconceptual domain developing naturally through participation in everyday activitiesrather than one requiring specific attention during the preschool years.

METHODS

Subjects

Twenty-eight women who were licensed home day care providers participated inthis study. They came from a group of four hundred thirty six providers who werecontacted about participation in a nine-month training project for rural and remoterural licensed providers offered throughout a state in the Rocky Mountain. Afteran informational meeting 57% chose to participate in the training project. Fromdiat group 86% of those who had children between the ages of 3 to 5 in their carefor at least 25 hours a week chose to participate in this study. The instruments usedin this study were given at the end of the training.

The twenty-eight participants were predominantly married (N=24), Euro-Americans (N=23). Four of the providers were Native-American and 1 was Hispanic.Most (20) had a high school education. The other 8 had less than a high schooleducation. Their average age was 33 years and their average number of years ofday care experience was 6.

Procedure

Participants were given two questionnaires. The first asked them to rate on a 5-pointscale how important they felt it was that children were able to do each of a list ofspecific skills before they start kindergarten. The 25 items on diis questionnairecontained brief descriptions of a variety of skills that preschool children might ormight not have mastered. The items covered five content areas (of five items each):(1) math concepts; (2) reading and letter recognition; (3) general comprehension;(4) expressive language; and, (5) social skills (for a complete listing of items, seeTable 1). A rating of "1" meant they felt that it was not very important that childrenhad that skill before starting school, "3" meant it was important but not essential,and "5" meant that they felt that it was very important Content area scores werecomputed by averaging the ratings for all items falling within each area. TheCronbach coeffficient alphas for these five content areas (using standardized scores)were .799, .777, .718, .816, and .758, respectively.

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FAMILY HOME CARE 45

Table 1 Means of Items on the Preschool Skills Checklist in Study l a

Items Mean Rating

I. Math ConceptsKnows the meaning of "same" and "different." 3.86Knows the meaning of "first," "last," "middle," "second," and correctly follows 3.14

directions using these words.Uses counting to solve problems. For example, counts objects in two groups 2.71

to see which has more.Counts to one hundred. 2.18Adds or subtracts up to ten. 1.86

II. Reading & Letter RecognitionRecites the alphabet in order. 3.36Recognizes the names of at least five letters of the alphabet. 3.93Reads numbers. 3.36Recognizes and names all the letters of the alphabet. 2.86Reads 4 or more words. 2.54

III. General Information or ComprehensionTells where he(she) lives by street and number. 3.71Knows right hand from left hand. 3.39Can name the colors red, green, yellow, and blue correctly. 4.00Names the days of the week in correct order. 2.54Uses the words "today," "yesterday," and "tomorrow" correctly. 2.93

IV. Expressive LanguageAsks questions beginning with "why," or "how." 3.86Says sentences such as "If I do..., then I can..." " 3.29Uses plurals correctly. For example, says "men" not "mans," "mice" not "mouses", etc. 2.68Can use the past tense correctly. For example, says "went" rather than "goed", 2.75

"bought" rather than "buyed."Uses plural pronouns, such as "we", "they", "them," "us" correctly. 2.96

V. Social SkillsCan begin playing with other children without help. 4.29Follows verbal instructions without being shown what to do. 3.61Says "please" when asking for something. 3.89Apologizes for unintentional mistakes. 3.39Changes activities when asked to by an adult. 3.75

aThe 25 items are grouped by content area. The item number reflects the order in which it appearedin the actual questionnaire. The rating scale is 1 = very important, 3 = important, but not essential,and 5 = not at all important.

The second questionnaire listed the same 25 items. Providers were asked to rankthe relative importance of parents, care providers, other children, natural ability,self-exploration, and television in the development of die skill described in eachitem on a 5-point scale. A score of "1" was the highest ranking and raters wereallowed to give different sources of influence the same rank if they thought theywere of equal importance. Average rank scores were computed for each possiblesource of influence for each of the five content areas.

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46 B. BLEVINS-KNABE et a/.

Table 2 Mean Importance Ratings on Content Areas in Study 1

Content Area Mean Rating^b

Math 2.75Expressive Language 3.11 F= 4.17, p < .05Reading 3.21 F= 6.29, p < .019General Information 3.31 F= 23.99, p < .0001Social Skills 3/79 F= 10. 09, p< .004aAll content areas were more important than math, repeated measures contrasts (df= 1, 25).•The rating scale ranged from 1 to 5. 1 = very important, 3 = important, but not essential, and 5= not very important

RESULTS

First Questionnaire: Relative Importance of Skills

In order to determine how important providers thought it was for children to havecertain math skills before kindergarten, a repeated measure analysis of variance wascomputed with the 5 content area scores on the first questionnaire as the dependentvariables. The level of education of the provider was an independent variable. Therewas a significant effect for content area, Wilks' lambda multivariate F (4.22) = 7.03;p < .0008 (see Table 2), but there was no significant multivariate effect for level ofeducation. A series of post-hoc contrasts were performed to assess the relativeimportance of the different content areas. Social skills, general information, read-ing, and expressive language were all seen by family day care providers as beingmore important than math skills for preschool children to acquire before enteringkindergarten (see Table 2).

Second Questionnaire: How Children Acquire Skills

In order to determine how providers thought children learned math skills, arepeated measure analysis of variance was performed with the average rankings foreach of the 6 sources of influence as the dependent variables. Again, the level ofeducation of the provider was the independent variable. There were no main effectsdue to provider's education. There was an overall difference between the rankingsof the different sources of influence on children's learning, Wilk's lambda multivariateF (5, 17) = 70.47, p < .0001. A series of post-hoc individual contrasts revealed thatacross all areas, parents are seen as having the greatest effect on young children'slearning (see Table 3). Day care providers were ranked second in importance. Otherchildren, natural abilities and self-exploration were ranked as less important dianeither parents or providers, and they were not significantly different from eachother. Television was ranked as the least important influence on children's devel-opment of the 5 skill areas.

Separate repeated measure analyses of variance were then computed for each ofthe 5 content areas comparing the rankings given within that area for each of the

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FAMILY HOME CARE 47

Table 3 Mean Rankings for Sources of Influence on Children's Development by Content Areain Study 1

Source of Influence

ParentsProvidersPeersNatural AbilitiesSelf-ExplorationTV

Math"

1.271.893.843.734.244.34

Reading

1.181.823.733.804.474.16

Content Areas"

GeneralInformation

1.191.953.763.784.514.65

Language'

1.232.333.683.624.055.32

Social'

1.392.223.063.424.125.48

Total1

1.242.043.613.654.314.79

"The rating scale ranged from 1 to 5. 1 = very important, 3 = important, but not essential, and 5 =not very important.bFor Math, Reading and General Information: Parents =Day Care ProvidersPeers = Natural Abilities = Self-Exploration = TV (Repeated Measures Contrasts (df= 1, 21, p < .05))Tor Expressive Language and Social Skills: Parents, Day Care Providers, Peers = Natural Abilities =Self-Exploration, TV (Repeated Measures Contrasts (df = 1, 21, p < .05))dFor total :Parents, Day Care Providers, Peers = Natural Abilities = Self-Exploration TV (RepeatedMeasures Contrasts (df- 1, 21, p< .05))

6 sources of influence. These analyses revealed some minor differences in theordering of sources of influence within content area. While for math, reading, andgeneral information parents were ranked as more important than providers were,this difference was not significant. However, for language and social skills, parentswere ranked as significantly more important than providers (p < .05).

DISCUSSION

Family day care providers in Study 1 rated math skills as less important for a childentering school than social skills, general information, reading, and language. Thisfinding is similar to the responses on the National Survey of Kindergarten Teachers(National Center for Educational Statistics, 1995). According to the National Sur-vey, preacademic skills were rated lower in importance than other skills. Similarly,we also found that among the academic skills listed on our survey, math skills wererated as the least important.

Aluiough providers rate math skills lower in importance than other skills, theydo think they are acquired as other skills are. Moreover, providers see themselvesas responsible for the development of these skills and in fact rank their influenceas second only to that of parents' in skill development. Clearly, providers see skilldevelopment as part of a home environment.

Nonetheless, providers did give mathematics skill development a low rankingin terms of importance, a finding interpretable in several ways. Although provid-ers feel their influence on skill development is second only to that of parents,

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48 B. BLEVINS-KNABE ef a/.

they may believe that mathematics is a subject that is not necessary to introduceduring the preschool years. Often, as Gelman and Massey (1987) suggest, theteaching of math is something we expect educators in a formal setting to do.Perhaps providers perceive preschool children as too young to learn about mathbeyond simple counting. Interviewers noted that in their informal conversationsproviders talked about the importance of print awareness and pre-reading skillsbut did not discuss mathematics skills as part of school readiness, except for rotecounting and number recognition. The interviewers also felt that providers werefearful about having the appropriate skills to teach math. Ladd and Price (1986)suggest that parents' feelings of effficacy for a particular task can influence thevalue they place on it. Perhaps providers are uncertain about their own math skills,and so do not place math high on the list of skills they value for children.Providers' beliefs and affect about math may influence how they structure thedaily care environment for children and whether they consciously include mathactivities in their daily routines.

STUDY 2

In Study 2 both parent and family day care providers were interviewed about mathactivities occurring in the home environment Because the family day care is a home-like setting and may be selected for this reason by parents, we expected to findcontinuity in the frequency and types of math activities provided in each.

In Study 1 providers rated reading skills as more important for a child enteringkindergarten than math skills. This led us to examine the relative level of supportin this setting for math versus literacy activities. Young-Loveridge (1989) found thatan emphasis on literacy did not correspond to an emphasis on numeracy in familiesof young children. We were interested in whether this was true also in family daycare homes. Therefore we included a measure of math activities as well as literacyactivities.

Another issue we were interested in was whether providers' and parents' affectabout math predicted how often they engaged in math activities with their children.Vygotsky, (1978) emphasized that guided learning experiences are important foradvancing children's concept development, and we postulated that the frequencyof guided learning experiences may be related to the participating adult's positiveaffect toward the specific concept domain.

METHOD

Subjects

Providers (22) and parents (18) with prekindergarten children between 4 to 6 yearsof age were interviewed by phone. The providers came from 5 nonurban countiesin two states and the parents were contacted through the providers. The majorityof providers and parents were European-American.

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FAMILY HOME CARE 49

All the family day care providers in the selected counties that were registered withthe state were contacted about participating in the study. Of those who had childrenbetween 4 to 6 years of age 34% chose to participate. The providers had a meanage of 39 years and a mean of 9.5 years of experience. A majority of the providers(14) had completed high school and had taken college courses or had a collegedegree, while 8 had education at the high school level or lower. Most (16) of theparticipating parents were mothers and they had a mean age of 30 years. Themajority (16) had completed high school and taken college courses or had a collegedegree and 2 had education at the high school level or lower.

Procedure

We called providers and parents and asked them questions about both math andreading activities. The order of calls to parents and providers was systematicallyalternated. Each participant was asked to answer questions with reference to the4- to 6-year-old children in their home. First, they were asked to complete a mathactivities checklist that was based on math activities identified as core concepts byGriffin, Case and Siegler (1994) and Charlesworth and Lind (1999). The checklistconsisted of 13 different math activities and participants were asked to estimateusing a 7-point scale how often each had occurred in the past week or month. A"1" on the scale represented "has never occurred" and "7" was "occurs more thanonce a day." Next participants completed a literacy scale developed by Griffin &Morrison (1997). The scale includes 9 items about literacy activities and the literacyenvironment. Items include questions about how much television the childrenwatch, the number of books available to them, and how often someone reads tothem. Next participants answered questions about their own enjoyment of engagingin math and reading activities with their children. Finally they answered two ques-tions comparing their own level of enjoyment in engaging in math and readingactivities with dieir children with that of their parent's level of enjoyment inengaging in math and reading activities with them.

RESULTS

On all the analyses reported below there were no differences between providersbased on state of residence. When we examined the frequency of math activitieswe found no differences in overall means for home and family day care. Providersreported that math activities occurred less than once a day; parents reported thatmath activities occurred at least once a month. The reported frequencies for eachitem are on Table 4.

The activities that were most and least frequent for parents and for providers werealmost identical. In both cases "counting objects to find how many" and "talkingto children about the order of events in the day" were in the three most frequentitems. The two least frequently reported items (measuring with a ruler, and additionproblems with numbers greater than 2) were identical for both groups. Out of 13

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ProviderMean

5.64

4.863.095.36

ParentMean

5.11a

4.663.003.72

50 B. BLEVINS-KNABE et a/.

Table 4 Reported Frequencies of Math Activities for Family Day Care Providers and Parentsin Study 2

Math Activity

1. I helped or watched my children count objects to find out howmany there were. For example, "1, 2, 3, 4, 5. There are 5 Bears!"

2. I encouraged or helped my children say the numbers past 10.3. I encouraged or helped my children say the numbers past 20.4. I helped or encouraged my children to use numbers such as 1st,

2nd, 3rd. For example, "Tom is first in line, Jane is second."5. I gave my children an addition problem such as I'm going to give 3.41 3.41

you one candy and then I'm going to give you 2 more. How manydo you have altogether?"

6. I gave my children a similar addition problem such as "I'm going to 2.23 2.29give you 4 candies and then I'm going to give you 3 more.How many do you have altogether?"

7. I asked my children to decide which of two groups of objects had 4.09 3.41more. For example, one pile has 2 vanilla wafers and another has 5.Which group has more?

8. I asked my children to count a particular type of object that was mixed 3.64 3.94in with other objects. For example, the child has 8 triangles and 7circles. "Count the triangles and tell me how many there are."

9. I asked my child to compare two numbers and decide which is bigger?For example, "which is bigger 5 or 4?"

10. I asked my children to read numbers. For example, ask the child tosay what numbers are on a street sign.

11. I asked my children questions about the order of events in the day.For example, "what did you do before lunch, what did you do after nap?"

12- I asked my children to measure with a ruler.13. I asked my children to put objects in order from smallest to biggest.

For example, "can you put these cups in order so the smallest isfirst and the biggest is last?"

aF(l, 22) = 8.52, p < .008bF(l, 22) = 13.16, p< .002CF(1, 22) = 7.97, p < .01

math activities there were significant differences in the reported frequencies of only3 (counting objects to find how many, using ordinal numbers, and asking whichof two numbers is bigger (see Table 4)). All of the differences showed the providersengaging in the activities more frequently than parents.

When we asked providers about their enjoyment of math and reading, theyreported that they were more likely to engage in math activities both when theyenjoyed math (r =. 59, p < .004) and when they enjoyed reading (r = .65, p < .001).Parents reported engaging in reading more with their child when they reportedenjoying reading (r=.52, df= 17, p< .03). We also asked both parents and providersto compare how much they enjoyed engaging in math and reading with their ownchild with how much they thought their own parents had enjoyed reading and doing

4.00

4.55

5.18

1.593.64

2.52b

4.53

5.22

1.332.82C

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FAMILY HOME CARE 51

math with them. When providers reported enjoying math activities with their childrenmore than their own parents had enjoyed it, they engaged in math activities morefrequendy (r = .55, df= 22, p < .008). Providers also reported engaging in mathactivities more frequently when they reported enjoying reading with their childrenmore than dieir own parents had (r =.58, df= 22, p < .005). Parents reportedengaging in madi activities more frequently when they reported enjoying math withtheir children more than dieir own parents had (r =.53, df=18, p < .02). There wasno significant difference in the reported enjoyment of math for parents versusproviders.

In order to determine whether providers who stress numeracy also stress literacy,we divided the sample into two groups based on the literacy scale scores. Thosewho had scores in the upper third of the sample reported a higher frequency ofmath activities dian those who scores were in die lower 2/3 of the sample (F(l, 17)= 5.31, p < .04). The analysis widi parents revealed the same pattern (F(l, 17) =6.06, p< .03).

DISCUSSION

Our results indicate similar frequencies for engaging children in math activities forboth parents and providers. In addition, the frequency with which parents andproviders involve children in math activities is related to their frequency of engagingchildren in literacy activities and their affect for math. While the frequency ofreported math activities for die entire sample was low, those who enjoyed math andreading and who scored die highest for frequency of literacy activities also offeredmath activities more frequendy.

Responses to questions asking parents and providers to compare dieir level ofenjoyment to die level of enjoyment diey perceived in their own parents suggestedthat parents and providers involvement in madi activities is connected to dieirmemories of dieir experiences widi uieir own parents. When parents and providerssee diemselves as enjoying engaging in math more dian dieir own parents diey alsoreport doing more widi dieir own children. These results suggest diat affect for bothmadi and reading influences die madi environment that is provided for die youngchild.

STUDY 3

Botii Studies 1 and 2 indicated tiiat madi activities are not a priority of parents orfamily day care providers. In Study 3 we addressed die question of whetiier diebeliefs and reported activities of parents and providers would predict children'sperformance on die Test of Early Madiematics Ability-2 (TEMA-2; Ginsburg &Baroody, 1990).

Because of die importance of children's early madiematics concept developmentto latter facility in madiematics (Charleswordi & Lind, 1999; Ginsburg, Klein &

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Starkey, 1997) we were interested in whether the performance of young childrenon the TEMA-2 was correlated with the frequency of mathematics activities offeredby parents and providers. We also wanted to know what parents' and providers'recognition levels were for mathematics activities and whether they would be ableto identify selected activities as actually involving mathematics concepts and opera-tions.

METHODS

Subjects

All of the licensed family care providers in two nonurban counties in a RockyMountain state were contacted by telephone and the study was explained to them.Those who were interested, who were state licensed, and had children between theages of 3 through 5 in their care for a minimum of 25 hours per week received aninformation packet The information packet included a letter about the study, de-mographic forms, informed consent forms for the provider, and parents of 3- to5-year-olds, and a $5 gift certificate to a local store as a " thank you" to the provider.Providers mailed back their own consent forms as well as those of interested parents.A second $5 gift certificate was sent upon receipt of the consent forms. There wasa 20% participation rate from providers who qualified for the study.

Thirty licensed home day care providers participated. They were predominatelymarried (N= 26), Euro-Americans. Most (N = 21) had some college courses or ahigher level of education, while 9 had a high school education or less. Their averageage was 37 years. Fifty-four parents participated, 53 mothers and 1 father. They werepredominately married (N= 46), Euro-Americans. Most (N= 42) had some collegecourses or a higher level of education, and 12 had a high school education or less.Their average age was 32 years.

A total of 64 children participated, 36 who were between 3 years to 4 years 5months with a mean age of 3 years 7 months, and 28 who were between 4 years7 months to 7 years with a mean age of 5 years 3 months. There were 29 malesand 35 females.

Procedure

Once informed consent forms were received telephone calls were made to providersand parents, and each was asked to estimate on a five-point scale how often eachof 22 different activities had occurred widi the children in their home over the lastweek (see Table 5). Activities involved the use of mathematics, reading, or a varietyof individual and group play activities. A "0" meant that the activity did not occurduring the past week, a "1" meant it occurred "once or twice in the last week", a"2" meant "3 to 5 times in the last week", a "3" meant "about once a day", and a"4" meant "more than once a day." They were asked after each item to state whetherthey thought the activity was more relevant to developing math readiness, reading

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Table 5 Reported Mean Frequencies of Math Activities for Family Day Care Providers andParents in Study 3a

FamilyDay Care

Providers Parents

1. Read stories to children.2. Supervised experience involving letters or the alphabet.3. Organized group games (Simon Says, singing, puppets).4. Went on field trips and outings (to the store, zoo, park, museum).5. Gave guidance counting objects. For example, "1, 2, 3."

There are 3 bears!"6. Provided help in saying numbers past 10.7. Doing simple addition with props.8. Assisted children in sorting objects. For example,

"Put all the blue ones here."9. Compared two groups of objects to see if they contained the same

number. For example, "Are there as many red blocks as blue blocks?"10. Matched objects to make equal groups. For example,

"Put all the blue ones here."11. Compared two groups of objects to see which had more.12. Sang number songs and/or finger plays. For example,

"10 Little Monkeys," "This Old Man."13. Worked on learning address and phone number.14. Assisted children in writing numbers.15. Taught ordinal numbers, 1st, 2nd, 3rd, etc. For example,

"Tom is first in line, Fred is second in line."16. Listened to audiotapes, records, or CDs.17. Watched TV including videotapes.18. Played independently with manipulative toys

(blocks, legos, puzzles, etc.)19. Engaged in dramatic play (dress-up, house, store, fantasy play).20. Worked with creative art mediums (drawing, painting, clay).21. Looked at books independently.22. Engaged in large motor skills (running, bouncing balls,

riding trikes, swinging).a0 = the activity did not occur during the past week, 1 = once or twice in the last week, 2 = 3 to 5times in the last week, 3 = about once a day, 4 = more than once a day.

readiness, creativity, or getting along with others. At the end of the interview theywere asked whether there were any additional activities that had occurred in thepast week that were important in developing math readiness, creativity, readingreadiness, or getting along with others. The telephone interview took approximately20 minutes.

Each child was individually administered the Test of Early Language Development(TELD-2; Hresko, Reid, & Hammill, 1991) and then the TEMA-2. The TELD-2 wasused as a screening device and all of the children met the baseline for languageskills on the TELD-2. Both assessments took place in the home of the provider. The

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54 B. BLEVINS-KNABE et al.

TEMA-2 is a measure of mathematical skills, both those that develop before school(informal mathematical thinking) and those that develop in school (formal math-ematical thinking) (Ginsburg & Baroody, 1990). Most of the items for children inthe preschool age group measure informal concepts and skills. For example, onone item children were asked to count fingers up to 5 and on another after countingstars to answer the question "how many stars did you count?"

The order of the provider interviews, parent interviews, and child assessment wascounterbalanced.

RESULTS

The total means for math activities reported by parents and family day care pro-viders differed slightly (see Table 5 for means of individual items). A multivariateanalysis of variance was performed with parents versus family day care providers,and age group of the children as the independent variables and three categoriesof activities (math, reading, and other) as the dependent variables. There was amarginally significant difference between the two groups in all of their reportedactivities, Wilks' lambda multivariate F(3;80) = 2.37, p < .08. Family day care pro-viders reported engaging in more math activities with their children in their homethan did the parents of those same children (univariate .F(l;82) = 7.25, ,p< .009).The two groups did not differ in the level of reading or other play activities reported.There were no effects associated with the age of the children.

A repeated measure version of the above analysis was then computed in orderto compare the relative frequencies of the three types of activities. There was nooverall significant interaction of activity with type of adult (i.e, parent versus pro-vider). However, there was a significant overall effect attributable to differencesbetween the three types of activities, Wilks' lambda F(2; 81) = 123.73, p < .0001.Individual contrasts revealed that math activities were reported happening signifi-cantly less often than either reading or other play (repeated measures contrasts df[l,82), p < .0001). The other two categories did not differ from each other.

Children's mean raw scores on the TEMA-2 were 11.36 (SD = 7.68). The meanraw scores in the normative group for the TEMA-2 range from 5.24 for 3year-oldsto 23.01 for 5-year-olds (Ginsburg & Baroody, 1990). Children's scores in this studyfall toward the low end of the "average" range on the TEMA-2. Those who were3 to 4 1/2 had a mean raw score of 6.8, SD = 5.29, and those who were 4 1/2 to7 had a mean raw score of 17.17, SD = 6.57. Over 50% of the sample received onlythe informal items on the TEMA-2. An ANOVA using the TEMA-2 raw scoresrevealed that the older children performed better than the younger children did(F(l, 62) = 50.66, p < .0001). When scores were converted to the math quotient,a standard score, there were no differences.

The frequency of math activities reported by parents or family day care providerswas not significantly correlated with children's mathematics achievement scores ineither age group. The reported level of other activities by either group of adultsalso did not correlate with the TEMA-2 scores.

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The items on the questionnaire were categorized into math, reading readiness,creativity, or getting along with others by the investigators. We were interested inwhether parents and family day care providers would categorize the same activitiesas math activities that the investigators did. Parents and family day care providerslabeled activities the same as the investigators fewer times (parents 76% agreement,family day care providers 75% agreement) when they were mathematics activitiesthan they labeled the nonmath activities the same as the investigators (parents 98%agreement, family day care providers 98% agreement, paired comparison t-test forboth groups on math-related versus nomath related activities, N = 54, p < .0001).

GENERAL DISCUSSION

The results of the three studies are consistent in showing that mathematical activitieswere not high on the priority list for parents or family home day care providers.In Study 1 day care providers rated math skills as less important than other academicand social skills, yet they saw themselves and parents as having the most influenceon how children acquire math skills. Their attitudes were consistent with theirreported behaviors. Both providers and parents reported that math activitiesoccurred infrequency during the course of a week and less often than reading, andsocial and play activities. The similarity in the reports of parents and providerssuggest that there is continuity with respect to math activities in children's homesand day care environments. Finding continuity is not surprising given that providersappear to view their influence as being similar to that of the parents. However, italso means that the children participating in this study received relatively little adultnarration about or assistance in finding math problems in their everyday environ-ment, at least for the math skills identified in this study. The activity setting formathematics described in these studies by adults is not one that makes mathematicalactivities explicit or frequent.

There are several possible reasons why the reported level of math activities waslow in both the children's own homes and those of their care providers. One isthat parents and providers have difficulty in identifying math tasks as indicatedby Study 3. This, however, should not have influenced their report of thefrequency of math activities because the interview questions described specificactivities and asked if that activity or a similar one had occurred. The fact thatthey reported relatively low frequencies of math activities does suggest, however,that they were not trying to look good in the eyes of the experimenters by inflatingtheir reports. The more probable reason for the low levels of math activities isthat parents and providers see math as less important than other activities whichleads to their offering few experiences to support early mathematics development.They may also feel that mathematics activities are more appropriately introducedduring formal schooling.

Study 2 suggests that another contributing factor could be the affect adultsassociate with mathematics. Providers and parents engage in more math activitieswhen they associate mathematics with a positive affect. The mean affect rating for

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enjoyment of engaging in math activities with their children was 3.65 (on a 5-pointscale), which was lower than the mean affect rating for enjoyment of engaging inreading activities. While parents and providers are not telling us that they dislikemath, their rating of math activities is at best lukewarm. It would be a mistake toview math and reading as competitors, however, since Study 2 indicates that themore support parents and providers provided for literacy the more they engage inmath activities. This finding provides support for efforts to teach mathematicsconcepts while teaching literacy skills.

Another influence on how often parents and providers engage in math activitiesis their knowledge about different types of activities. In Study 3 both parents andproviders had more trouble identifying math activities than other types of activities.This, along with the finding in Study 1 that providers did not make a distinctionbetween how children learn math and how they learn in other areas, suggests thatparents and providers do not have well-differentiated concepts and beliefs aboutmath. In both Studies 2 and 3, the math activity reported to occur most frequentlywas counting objects. Counting is a visible and well-known math activity. If parentsand providers primarily define support for math in the environment as providingopportunities to count, then children are not receiving support in making explicitand accessible many early math concepts. In addition children themselves may notrealize that some activities they spontaneously engage in are math-related and thusmay fail to make connections between experiences in their early environment andthe school environment. Among the least frequent math activities in both studieswas comparing two numbers or two groups of objects to see which has more. Thistype of activity can help children to learn about the number line, a concept whichhas been identified by Case et al, 1996 as being central to young children's under-standing of math. This activity also builds on children's very early propensities,noted by Keil (1998) and Case (1998), to detect numerosity in sets.

These results suggest that the activity setting, described by Tharp and Gallymore(1988), for preschool children is not likely to include a wide variety of mathematicsactivities. While it is possible that parents and family day care providers are engagingin math activities that were not addressed in the interview, the math activitiesselected for the interview were ones that math researchers have identified as importantfor the development of formal math concepts (Case et al, 1996; Ginsburg &Baroody, 1990; Charlesworth & Lind, 1999). Further, children's low performanceon the TEMA-2, which includes many tasks measuring informal math concepts, isconsistent with the conclusion that their home and day care environments are notsupportive of mathematics. Although we did not find a correlation between chil-dren's performance on the TEMA-2 and the reported frequencies of math tasks,this could be due to the fact that both the TEMA-2 scores and reported frequencieswere subject to a floor effect

Our results have several implications. For those involved in parent education ourwork identifies activities that occur frequently and infrequently in children's envi-ronments. It may be important to assist parents to feel more positive aboutmathematics. Our work also suggests that children might benefit if parents' andproviders' list of activities involving mathematics was expanded. For example, a task

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such as comparing two numbers to see which has more promotes the understandingof a mental number line. It is an activity that is simple to incorporate into dailyactivities and one that should be conceptually easy for an adult. Making parentsmore aware of such activities may lead to their providing more of them for theirchildren. However, it may be necessary to do more than provide parents withinformation about math activities. It may also be necessary to help them feel morepositively about math.

For those who are interested in the support provided for mathematics conceptsin children's home and day care environments, our work contributes to the picturepainted by existing research (e.g. Saxe, Guberman, & Gearhart, 1987). It appearsthat some mathematical activities do occur in children's homes and in family daycare, but the frequency and scope of these experiences is limited. In our workparents and providers were not aware of the breadth and depth of activities whichfall within the aegis of mathematics concept development. If they were aware ofthis wide array of activities, very probably children's mathematics concept develop-ment would be strengthened and parents and providers themselves would feel morepositive toward mathematics.

Acknowledgements

We would like to thank Danna Woods-Young, Gary Bingham, Ariel Rodriguez, JamieBrandenburg, and Jeannette Youngblood for their assistance in data collection andanalysis, and Shelley L. Knudsen Lindauer for her conceptual insights. We wouldalso like to thank the parents, providers, and children who worked with us.

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