The association between home numeracy and children’s calculation skills is mediated by basic number processing Belde Mutaf, Delphine Sasanguie, Bert De Smedt, & Bert Reynvoet (under revision)

What is home numeracy? Referred to as the frequency of the numeracy activities (e.g., counting objects, writing numbers, playing games) that children experience at home. Commonly, examined by self-reports of parents via a questionnaire or interview. (Blevins-Knabe & Musun-Miller, 1996; LeFevre et al., 2009). Introduction

Why is it important? HN has been found to be related to kindergarteners’ basic number processing skills (comparison, number line estimation, counting), which are related/predictive for children’s mathematics achievement. (De Smedt, Verschaffel, & Ghesquière, 2009; Kleemans, Peeters, Segers, & Verhoeven, 2012; Libertus, Feigenson, & Halberda, 2013; Sasanguie, Van den Bussche, & Reynvoet, 2012; Schneider, et al., 2016) Introduction

What is in the literature of home numeracy ? Inconsistent results! Introduction

What is in the literature? Inconsistent results! o Some of the activities are positively and some are negatively related to children’s mathematical skills (Blevins-Knabe & Musun-Miller, 1996). Introduction

What is in the literature? Inconsistent results! o Some of the activities are positively and some are negatively related to children’s mathematical skills (Blevins-Knabe & Musun-Miller, 1996). o A distinction of the activities was suggested: Formal & Informal Only informal activities predicted mathematical knowledge (three subtests of KeyMath; number system knowledge, addition, and subtraction) (LeFevre et al., 2009). Introduction

What is in the literature? Inconsistent results! o Some of the activities are positively and some are negatively related to children’s mathematical skills (Blevins-Knabe & Musun-Miller, 1996). o A distinction of the activities was suggested: Formal & Informal Only informal activities predicted mathematical knowledge (three subtests of KeyMath; number system knowledge, addition, and subtraction) (LeFevre et al., 2009). o Opposite findings followed: Formal but not informal act. were related to number system knowledge subtest of KeyMath (LeFevre et al., 2009). Introduction

What is in the literature? Inconsistent results! o Some of the activities are positively and some are negatively related to children’s mathematical skills (Blevins-Knabe & Musun-Miller, 1996). o A distinction of the activities was suggested: Formal & Informal Only informal activities predicted mathematical knowledge (three subtests of KeyMath; number system knowledge, addition, and subtraction) (LeFevre et al., 2009). o Opposite findings followed: Formal but not informal act. were related to number system knowledge subtest of KeyMath (LeFevre et al., 2009). o Number system knowledge was uniquely predicted by formal, whereas abilities to represent and manipulate quantities (non- symbolic arithmetic) were uniquely predicted by informal act. (Skwarchuk, et al., 2014) Introduction

What is the gap? Most of the studies used composite scores of mathematical batteries which included a variety of skills. o TEMA-2 and -3 (Blevins-Knabe et al., 1996, 2000; Manolitsis, et al., 2013) o KeyMath test (LeFevre, et al., 2009, 2010) o Utrecht Early Numeracy Test-Revised (Kleemans et al., 2012) Introduction

What is the gap? However, combining the performance on different basic number processing tasks into one composite score might obscure the unique relations between home numeracy and specific skills. We know that basic number processing skills, such as non-symbolic, symbolic number processing, and mapping have a differential impact on children’s mathematics achievement (for a review, see De Smedt, Noël, Gilmore, & Ansari, 2013; Mundy & Gilmore, 2009; for a meta-analysis, see Schneider, et al., 2016). Introduction

The research question? We proposed that home numeracy activities may be differentially related to these distinct components of basic number processing, and that these associations may in turn explain the varying results observed in studies examining the relation between home numeracy and mathematical skills. Introduction HN Sym Non sym Map TediMath

The research question? We proposed that home numeracy activities may be differentially related to these distinct components of basic number processing, and that these associations may in turn explain the varying results observed in studies examining the relation between home numeracy and mathematical skills. Introduction HN Sym Non sym Map TediMath

Participants: 128 kindergartners (M age = 5.43 years, SD =.29, range: 4.88 – 6.02 years; 70 females) and their parents Maternal education level ranged from middle-to-high; 31% secondary education 34% bachelor degree 30% master degree 5% did not respond to this question. Methods

Measures: Home numeracy questionnaire (LeFevre et al., 2009) 20 items on numeracy activities (e.g. In the past month, how often did (you and) your child engage in the following activities? Place a mark corresponding to your opinion, never – 1 to 3 times a month – once a week – several times a week - daily). Some examples … Identifying names of written numbers Learning simple sums (i.e., = 4) Measuring ingredients when cooking Using calendars and dates Playing card games … Methods

Basic number processing Methods Enumeration digits: 3 – 5 – 7 – 9 4 trials Connecting digits: 1 – 9 9 trials

Methods Non-symbolic comparison ratios: 1,2 – 1,5 – 2,0 48 trials Symbolic comparison distances: 1 – 4 Digits: 1 to 9 32 trials Symbolic NLE Digits: 1 – 9 18 trials

Calculation TediMath Symbolic additions subtest (e.g = ?) TediMath Pictorial calculations subtest Methods

Descriptive statistics Results MSDMin.MaxSkewnessKurtosis Enumeration (proportion correct) Connecting (proportion correct) Sym Comp (proportion correct) Non-sym Comp (proportion correct) Sym NLE (PAE) Non-sym NLE (PAE) Calculation (# correct)

Principal Components Analysis (PCA) –home numeracy– Results Items Number practices Number books GamesApplications MSD Identifying names of written numerals Counting objects Sorting things by size, color or shape Learning simple sums Writing numbers Using number flashcards Doing ‘connect the dot’ activities Using number activity books Reading number story books Playing card games Playing board games with die or spinner Talking about money when shopping Measuring ingredient while cooking Being timed Collecting objects Using calendars and dates

Principal Components Analysis (PCA) –basic number processing– Results MeasuresNumber Line EstimationComparisonMapping Symbolic NLE.87 Non-symbolic NLE.89 Symbolic Comparison.59 Non-symbolic Comparison.91 Enumeration.69 Connecting.91

Correlations Results

Mediation Results C’ =.08*

Conclusion Formal home numeracy activities (i.e. number practices) were associated with the children’s performance in mapping and number line estimation. The children’s performance in mapping and comparison tasks was associated with calculation skills. Home numeracy (i.e. number practices) was related to children’s calculation skills only through the effects of their mapping skills.

Discussion Different operationalization techniques might be playing a role. Compatible with the longitudinal findings of Manolitsis et al., (2013). In line with finger counting strategies (Geary, Hamson, & Hoard, 2000; Groen & Parkman, 1972; Siegler & Shrager, 1984) which is similar to the requirement of the enumeration task.

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