Early Mathematics Learning Research Articles

An Exploratory Study of a Number Sense Program to Develop Kindergarten Students’ Number Proficiency

This study examined the effectiveness of a number sense program on kindergarten students’ number proficiency and responsiveness to treatment as a function of students’ risk for mathematics difficulties. The program targeted development of relationships among numbers (e.g., spatial, more and less). A total of 101 kindergarten students (not at risk: 22 control and 36 experimental; at risk: 18 and 25) from five classrooms in a high-poverty elementary school participated in the study. Using a quasi-experimental design, classrooms were randomly assigned to either the intervention (number sense instruction, NSI) or control condition. Results indicated significant differences favoring the treatment students on all measures of number sense (e.g., spatial relationships, more and less relationships, benchmarks of five and ten, nonverbal calculations) at posttest and on a 3-week retention test. Furthermore, the effects were not mediated by at-risk status, suggesting that NSI may benefit a wide range of students. Implications in terms of preventing early mathematical learning difficulties are discussed.

Windows to early childhood mathematics teacher education

This special issue comes at a time when the issue of early childhood mathematics has come to the fore. At a recent 2009 Conference of European Research in Mathematics Education, a new working group in Early Years Mathematics was established in response to increased calls for research regarding mathematics learning and mathematics teacher education in the early years (ages 3–8). A joint position paper published in the United States by the National Association for the Education of Young Children (NAEYC) and the National Council for Teachers of Mathematics (NCTM) stated that ‘‘high quality, challenging, and accessible mathematics education for 3–6 year old children is a vital foundation for future mathematics learning’’ (National Association for the Education of Young Children and National Council of Teachers of Mathematics 2002, p.1). Further evidence of concern for early childhood mathematics may be seen in the rise of national curricula in various countries which now make specific and sometimes mandatory recommendations for including mathematics as part of the preschool program. For example, in Israel, the National Mathematics Preschool Curriculum (Israel national mathematics preschool curriculum (INMPC) 2008) is mandatory and contains specific guidelines and aims for children from 3 to 6 years. A clear indication of the growing awareness of the importance of early childhood mathematics is the vast increase in the number of articles that are devoted to early childhood mathematics in the research literature. The inclusion of a specific chapter in which the current research on early childhood mathematics learning is summarized, in a handbook of research on mathematics teaching and learning for the first time, is a clear sign of the growing attention to this domain (Clements and Sarama 2007). One may wonder about the recent, growing attention to early childhood mathematics. Evidently, there are institutional, economic, and equity issues that support this significant increment (e.g., a world-wide increase in the numbers of children attending early-care

Socioeconomic variation, number competence, and mathematics learning difficulties in young children

As a group, children from disadvantaged, low-income families perform substantially worse in mathematics than their counterparts from higher-income families. Minority children are disproportionately represented in low-income populations, resulting in significant racial and social-class disparities in mathematics learning linked to diminished learning opportunities. The consequences of poor mathematics achievement are serious for daily functioning and for career advancement. This article provides an overview of children's mathematics difficulties in relation to socioeconomic status (SES). We review foundations for early mathematics learning and key characteristics of mathematics learning difficulties. A particular focus is the delays or deficiencies in number competencies exhibited by low-income children entering school. Weaknesses in number competence can be reliably identified in early childhood, and there is good evidence that most children have the capacity to develop number competence that lays the foundation for later learning.

Standardized Assessment of Strategy Use and Working Memory in Early Mental Arithmetic Performance

Although children's use of a variety of strategies to solve arithmetic problems has been well documented, there is no agreed on standardized and validated method for assessing this mix. We examined the convergent validity of typically achieving (TA, N = 39) and low achieving (LA, N = 20) second and third grade children's strategy choices in simple addition using three different methods: child self-report, observer-report, and response time (RT). The high concordance between child and observer reports (Kappa = .948) in both groups suggests that the participants were aware of, and could accurately report, the strategies they used. The Receiver-Operator Characteristic (ROC) analysis showed that RT accurately differentiated between retrieval and counting (AUC = 82%). The specificity and sensitivity of the ROC profiles were significantly greater for the TA group than for LA group, even though the groups did not differ in the overall strategy mix. Our findings suggest that ROC analysis is more sensitive to group differences in the mechanisms governing strategy choice than observation or child report. Children's use of retrieval strategies as well as accuracy during both retrieval and counting trials were all related to the central executive, but not the phonological and visuospatial sketchpad, component of working memory. We discuss the implication of these findings for early mathematical learning.

The precursors of mathematics learning: Working memory, phonological ability and numerical competence

This research aims at identifying the precursors of mathematics learning at the beginning of primary school. There are few experimental studies on this topic and existing ones use between-subjects designs and correlation analysis. This paper analyses longitudinal data to investigate whether the relationship between basic abilities and mathematics learning is causally interpretable, rather than one where cognitive abilities are correlated to early mathematics learning in a cross-section design. The present study tested 170 children at the beginning and the end of first year of primary school. Linear structural relations, causally interpreted, were used to analyse the relations between cognitive abilities and mathematic achievement. The model showed that tests of working memory and counting ability are the most discriminating and efficient as precursors of early mathematics learning. In our data, phonological ability is not involved in mathematics learning ability, and in the presence of the cognitive measures included in the model, intelligence level does not directly influence mathematics capacity.

Children's strategy use and interpretations of mathematical representations

This is a summary of research, from an information processing perspective, of children's interpretation and use of strategies and representations for place value, subtraction and addition in the first three years of school. Representations are defined broadly to include concrete embodiments of numbers, symbols for numbers and operations, and combinations of the latter in number sentences and algorithms. The objective was to assess the value and limitations of the use of representations in early mathematics learning and teaching and hence to identify, describe and examine critically some of the strategies and representations that children and teachers use in early mathematics. Children generally chose to use verbal and mental strategies in preference to formal algorithms, and did not want to use analogs unless they could not perform the task in any other way. The latter preference is explained on the basis of the extra demand that use of analogs adds to the cognitive process unless they are used automatically.

Cultural Differences in Early Mathematics Learning: A Comparison of Euro-American, Chinese-American, and Taiwan-Chinese Families

Forty second-generation Euro-American, and 40 Chinese-American children were drawn from well-educated two-parent families in the suburban Chicago area and 40 Chinese children were drawn from a similar population in Taipei, Taiwan (10 preschool girls, 10 preschool boys, 10 kindergarten girls, and 10 kindergarten boys in each group). Chinese-American and Taiwan-Chinese children outperformed Euro-American children on measures of mathematics, spatial relations, and numeral formation. Chinese-American parents gave more formal, direct mathematics instruction, structured their child’s time to a greater degree, and reported more encouragement for mathematics-related activities than did Euro-American parents. A path analysis using Eccles’ (1993) model of academic motivation showed that ethnicity, parents’ child-specific beliefs, and parents’ work-oriented practices directly predicted mathematics-related outcomes.