Session chair: Riikka Mononen
Predictors of early mathematics performance – developmental interplay between cognitive, motivational, and affective factors
Already in early childhood, there are individual differences in how children perform in mathematics, and this performance has been shown to be a good predictor of later mathematics achievement. Previous research has tried to find out which, and how, different cognitive, motivational and affective factors are related to and predictive of individual differences in mathematics performance. However, currently our knowledge about the interplay between factors that contribute to early mathematics development is rather scarce, especially when different types of predictors are investigated simultaneously. The studies in this symposium aim to extend previous findings and further increase our understanding of the interplay between mathematical skills, other cognitive, motivational, and affective factors, by presenting four longitudinal studies, three from the Nordic countries and one from the UK. The first presentation by Schröder et al. introduces how language ability, approximate number system acuity, working memory, as well as maternal math anxiety and depressive symptoms contribute to toddlers’ understanding of numbers. In the second presentation, Göbel focuses on transcoding skills measured in the first grade as a longitudinal predictor of arithmetic development and early fraction understanding in the third grade. The third presentation by Tuominen and colleagues introduces patterns of arithmetic performance and mathematics motivation, and change and stability during the early school years. Finally, Mononen and colleagues present developmental relations between mathematics anxiety, symbolic numerical magnitude processing, and arithmetic skills from first and second grade.
Paper 1: Number writing as a longitudinal predictor of arithmetic development and early fraction understanding
Silke M. Göbel, University of York, York, UK and University of Oslo
The ability to transcode accurately and efficiently between Arabic digits (e.g. 24) and spoken number words (e.g. ‘twenty-four’) is important for mathematical development. Recent findings suggest that early number knowledge provides a foundation for later arithmetic development. However, few studies have investigated whether differences in transcoding ability at the beginning of primary school relate to other types of later mathematics performance besides whole number arithmetic. In our longitudinal study we investigated the ability to convert spoken number words into written Arabic digits (number writing), to read out Arabic digit strings (number reading) and to identify the correct number out of a choice of Arabic digits (number identification) in a sample of Year 1 children in UK primary schools. In Year 1 we also assessed children on a range of domain-general skills such as general cognitive abilities and working memory. In Year 3 we measured early fraction understanding with a fraction number line task and multi-digit understanding with a whole-number number line task (0- 1000). We also assessed their conceptual knowledge and numerical reasoning in Year 3. Number transcoding in Year 1 was a significant longitudinal predictor of growth in arithmetic over the next two years. Number transcoding in Year 1 also predicted performance on both number line tasks, including the fraction number line task, and numerical reasoning in Year 3, even when controlling for domain-general factors and for arithmetic performance in Year 1. Conceptual knowledge in Year 3, however, was not predicted by number transcoding in Year 3. Overall, our study shows the importance of number transcoding in early primary school as a foundation for the development of a range of later mathematical skills in primary school.
Paper 2: Profiles of arithmetic performance and mathematics motivation: Change and stability during the early school years
Heta Tuominen University of Turku and University of Helsinki. Co-authors: Markku Niemivirta, Johan Korhonen, Kristine Tveiten and Riikka Mononen
Self-concept (i.e., self-evaluations of one’s ability) and interest (i.e., the enjoyment of engaging with a particular content or activity) in mathematics appear to be linked with each other and with performance among school-aged children and adolescents (Denissen et al., 2007; Viljaranta et al., 2014). Still fairly little is known about these relations among school-beginners, although the limited evidence available suggests similar, yet weaker connections (Aunola et al., 2013). In other words, not all highly competent students display high self-concept and interest, and not all less competent students lack confidence and interest. Given this, it might thus be possible to find various systematic patterns of self-concept, interest, and performance among the students, which all might have different implications for further mathematics learning. For example, there might be highly interested students lacking competence, or highly competent students lacking interest, and so on, who then follow different developmental paths. To address this possibility, we investigated what kinds of profiles can be identified in children’s arithmetic performance and mathematics motivation as well as the prevalence and stability of those profiles from first to second grade.
Participants were 217 Norwegian students (45.2% girls, Mage = 6 y. 9 m., SD = 3.44 at T1). Children’s arithmetic performance (i.e., addition and subtraction fluency, arithmetic word problems) and motivation (i.e., interest and self-concept in mathematics) were measured at both time points. Following a person-oriented approach, TwoStep cluster analysis was used for classifying students based on their arithmetic performance and motivation, and the ISOA (I-States as Objects Analysis) procedure was employed as it enables the examination of the development of individual patterns across time. A configural frequency analysis (CONFA) was carried out to investigate the stability and change in group memberships. The analyses revealed that five distinct profiles were extracted. There were two groups of students with synchronous profiles: students showing high performance and positive motivation (Group 1, 15%) and students displaying low performance and negative motivation (Group 2, 17%). Also, there were two groups exhibiting rather average performance, but the students in one group displayed positive motivation (Group 3, 24%), while the students in the other showed more negative motivation, especially low interest (Group 4, 20%). Finally, a particularly asynchronous profile of low performance but high interest (Group 5, 23%) was extracted.
Application of CONFA (χ2 (16, N = 217) = 110.75, p < .001) revealed three types and two antitypes. Belonging to the clearly synchronous and asynchronous groups (Groups 1, 2, 5) at both measurement points showed significant types. Further, it was untypical (i.e., antitype) for students in Group 1 (high performance and positive motivation) to move to Group 5 (low performance but high interest) and for students in Group 2 (low performance and negative motivation) to move to Group 1 (high performance and positive motivation). Overall, 43% of the students displayed a stable profile over time. The findings demonstrate that meaningful patterns of arithmetic performance and motivation can be found among school-beginners, thus indicating that skills and particularly interest do not always go hand in hand. Both stability and change in the profiles are detected during the early school years; some children exhibit a change in their profile, although experiencing a clear change in profiles is unlikely. As both skills and motivation in mathematics contribute to important educational outcomes (e.g., academic achievement, choices), weakness in either may be considered as a risk factor in terms of children’s future school career. It is thus likely that some children might need support for mathematics, some for motivation, and some for both.
Paper 3: Developmental relations between mathematics anxiety, symbolic numerical magnitude processing, and arithmetic skills from first to second grade
While a negative relation between math anxiety and mathematics performance has been well documented with older students, less is known about the association among younger children (Namkung et al., 2019). The few existing studies show that already in the early grades some children experience math anxiety, and it seems to be coupled with lower mathematics performance (Cargnelutti et al., 2016; Gunderson et al., 2018; Ramirez et al., 2013; Vukovic et al., 2013). However, our understanding of the longitudinal predictions, let alone developmental relationships, between math anxiety and math performance in young children is limited. In order to address this gap in research, we investigated the levels of and changes in mathematics anxiety (MA), symbolic numerical magnitude processing (SNMP) and arithmetic skills (AS), and how those changes are linked to each other, among 264 Norwegian children (45.3% girls, Mage = 6 y. 9 m., SD = 3.3 m., at the first time point). Children’s math anxiety, SNMP (1- and 2-digit comparison), and AS (addition and subtraction fluency, arithmetic word problem solving) were measured in the first grade, and seven months later in the second grade, including also a mathematics performance test. Due to consistent gender differences found in later math anxiety, we took this into account by including gender as a predictor. By means of latent change score modeling, we found significant individual differences in children’s math anxiety, despite the very low level of it on average. All constructs correlated significantly at both time points, although the negative association between SNMP and AS and math anxiety became somewhat weaker in the second grade. The rank-order stability over time was high in all constructs, and particularly so in SNMP and AS. Mean level increases in SNMP and AS over time were also significant, while no average change in math anxiety was detected. Most interestingly, changes in SNMP and AS over time were correlated (i.e., improvement in SNMP was associated with improvement in AS), as were changes in AS and math anxiety (i.e., steeper increase in AS was linked with less steep increase in anxiety). Only the initial level of arithmetic skills and change in it predicted second grade mathematics performance. Gender predicted both the onset and change in SNMP so that compared to girls, boys showed both higher initial level and steeper increase in it.
The findings suggest that over time, MA may become more directly linked with mathematical skills practised in school than with more intuitive number sense skills, and that difficulties in learning basic arithmetic may expose children to increases in mathematics-related negative emotions. This raises an interesting question of whether the mechanisms underlying children’s experiences of MA gradually change over time due to increasing exposure to explicit mathematics and mathematics-related activities. Not only is this theoretically and empirically intriguing, but has also important practical implications. The teachers should be aware that despite the children are generally displaying little MA, significant individual differences exist in both these experiences and how they change over time, with some children experiencing MA already in early grades. This calls for particular sensitivity to such experiences and constructive means to support children, when a school subject becomes intimidating.