Minna M. Hannula-Sormunen

Preschool Children’s Spontaneous Focusing on Numerosity, Subitizing, and Counting Skills as Predictors of Their Mathematical Performance Seven Years Later at School

This seven-year longitudinal study examined how children’s spontaneous focusing on numerosity (SFON), subitizing based enumeration, and counting skills assessed at five or six years predict their school mathematics achievement at 12 years. The participants were 36 Finnish children without diagnosed neurological disorders. The results, based on partial least squares modeling, demonstrate that SFON and verbal counting skills before school age predict mathematical performance on a standardized test for typical school mathematics in Grade 5. After controlling for nonverbal IQ, only SFON predict school mathematics. Subitizing-based enumeration skills have an indirect effect via number sequence skills and SFON on mathematical performance at 12 years. Early mathematic skills do not predict reading skills at 12 years. Children’s early numerical skills, including SFON, before school age are important contributors to substantially later success in school mathematics.

Challenges in Mathematical Cognition: A Collaboratively-Derived Research Agenda

This paper reports on a collaborative exercise designed to generate a coherent agenda for research on mathematical cognition. Following an established method, the exercise brought together 16 mathematical cognition researchers from across the fields of mathematics education, psychology and neuroscience. These participants engaged in a process in which they generated an initial list of research questions with the potential to significantly advance understanding of mathematical cognition, winnowed this list to a smaller set of priority questions, and refined the eventual questions to meet criteria related to clarity, specificity and practicability. The resulting list comprises 26 questions divided into six broad topic areas: elucidating the nature of mathematical thinking, mapping predictors and processes of competence development, charting developmental trajectories and their interactions, fostering conceptual understanding and procedural skill, designing effective interventions, and developing valid and reliable measures. In presenting these questions in this paper, we intend to support greater coherence in both investigation and reporting, to build a stronger base of information for consideration by policymakers, and to encourage researchers to take a consilient approach to addressing important challenges in mathematical cognition.

Spontaneous Focusing on Quantitative Relations in the Development of Children's Fraction Knowledge

While preschool-aged children display some skills with quantitative relations, later learning of related fraction concepts is difficult for many students. We present two studies that investigate young childrens tendency of Spontaneous Focusing On quantitative Relations (SFOR), which may help explain individual differences in the development of fraction knowledge. In the first study, a cross-sectional sample of 84 kindergarteners to third graders completed tasks measuring their spontaneous recognition and use of quantitative relations and then completed the tasks again with explicit guidance to focus on quantitative relations. Findings suggest that SFOR is a measure of the spontaneous focusing of attention on quantitative relations and the use of these relations in reasoning. In the second (longitudinal) study, 25 first graders completed measures of SFOR tendency and a measure of fraction knowledge three years later. SFOR tendency was found to predict fraction knowledge, suggesting that it plays a role in the development of fraction knowledge.

Kindergartners’ Spontaneous Focusing on Numerosity in Relation to Their Number-Related Utterances During Numerical Picture Book Reading

ABSTRACT This study investigated the relationship between kindergartners’ Spontaneous Focusing on Numerosity (SFON) and their number-related utterances during numerical picture book reading. Forty-eight 4- to 5-year-olds were individually interviewed via a SFON Imitation Task and a numerical picture book reading activity. We expected differences in the frequency of number-related utterances during picture book reading between children with a higher SFON score, providing more number-related utterances, and children with a lower SFON score. Our results showed large inter-individual differences in both kindergartners’ SFON and the frequency of their number-related utterances during picture book reading, yet SFON was not related to the frequency of number-related utterances. This unexpected result is discussed in terms of its scientific, methodological, and educational implications.

Number Navigation Game (NNG): Design Principles and Game Description

This chapter describes the Number Navigation Game (NNG), a game-based learning environment aimed at the promotion of flexibility and adaptivity with arithmetical problem solving in 10- to 13-year-old students. The game design is based on an integrated approach in which the different elements of the game are directly related to the mathematical content, i.e., the use of rich networks of numerical connections in solving arithmetic problems. The interface of the game is a hundred square superimposed on various maps of land and sea, where players have to strategically navigate a ship by using different combinations of numbers and arithmetic operations. The game has two different modes encouraging the use of different arithmetic operations and number combinations. The openness of the gameplay allows players the opportunities to explore different numerical connections in an environment where there are no right or wrong answers. Future directions of the game development include additional game features and extensions to larger numbers and rational numbers.

Developing Adaptive Number Knowledge with the Number Navigation Game-Based Learning Environment

Research suggests that adaptivity with arithmetic problem solving can be developed by placing more focus on developing students’ understanding of the underlying numerical characteristics and connections during problem solving. For this reason, the present study aimed to explore how primary school students’ game performance using the “Number Navigation Game” (NNG) game-based learning environment was related to their development of adaptive number knowledge. NNG provides extensive opportunities for working strategically with various number patterns and number–operation combinations. Sixth grade students (N = 23) played NNG in pairs, once a week, for 7 weeks during math class. Students completed measures of adaptive number knowledge and arithmetic fluency during pre- and post-testing. Results show that students’ game performance had a unique contribution to explaining students’ adaptive number knowledge during post-test. This suggests that NNG is a promising game-based learning environment for developing adaptivity with arithmetic problem solving by enhancing students’ adaptive number knowledge.

Voluntary vs Compulsory Playing Contexts

Background. Serious games are often used in formal school contexts, in which students’ lack of control over the playing situation may have repercussions on any motivational gains. Aims and Method. The first aim was to investigate to what extent n = 579 fifth grade students in Mexico who received a mathematics serious game played it voluntarily. Then, we explored how students who played voluntarily (n = 337) differed from those who did not by either gender or pre-test mathematical skills or motivation. The second aim was to find out whether two play contexts, the group of voluntary players and a second group consisting of students playing at school as a compulsory part of their regular mathematics lessons (n = 482), differed in game experience, game performance, and cognitive and motivational outcomes. Results. Students from the volunteer group who played had higher pre-test mathematical skills and math interest than those who did not play. Students in this group did not otherwise differ. Compared to students from the volunteer group who played, students in the school group played for longer, completed more tasks, and enjoyed playing the game more. However, their advanced mathematical skills did not improve as much. Conclusion. Motivation did not improve regardless of play context, suggesting serious games should be implemented for their learning content rather than because they are assumed to be motivating.

Maternal sensitivity in responding during play and children’s pre-mathematical skills: a longitudinal study from infancy to preschool age

Abstract This longitudinal study explored how mothers’ sensitivity in responding to their child’s cognitive and emotional needs in infancy and toddlerhood predicts children’s pre-mathematical skills at early preschool age. The sample consisted of 65 mother–child dyads (N = 130 individuals) videotaped during joint play at ages 1;0 and 2;0. The children’s pre-mathematical skills were tested at age 3;0. The path analyses showed that, in infancy, mothers’ autonomy support and scaffolding are more strongly related than emotional support to children’s later performance on spatial and numerical tasks. The findings are discussed in relation to how maternal sensitivity in responding fosters children’s pre-mathematical development in an optimal way.

Number Navigation Game (NNG): Experience and Motivational Effects

Number Navigation Game-based learning environment (NNG) is a mathematical game-based learning environment designed to enhance students’ adaptivity with arithmetic problem solving and to increase their motivation towards math. Fourth through sixth grade classrooms were randomly assigned into either an experimental group (students n = 642) which played NNG during a 10-week period or into a control group (students n = 526) which continued with a traditional textbook-based mathematics curriculum. The aims of the present study were to investigate the effects of the intervention on students’ motivation and to explore how students’ differing game experiences were related to changes in their motivation and, as an indicator of cognitive outcomes, their arithmetic fluency. Results indicate the intervention resulted in small decreases in the math motivation expectancy-values of interest, utility, and attainment value. Students had mixed game experiences which varied by gender and grade level. When looking at the role of these game experiences on post-test motivation and arithmetic fluency, corresponding pre-test values were the strongest predictive variables. Out of game experiences, only competence was a significant predictor of post-test motivational scores; however, no game experience variable was a predictor of post-test arithmetic fluency.

Spontaneous focusing on numerosity in preschool as a predictor of mathematical skills and knowledge in the fifth grade

Previous studies in a variety of countries have shown that there are substantial individual differences in childrens spontaneous focusing on numerosity (SFON), and these differences are positively related to the development of early numerical skills in preschool and primary school. A total of 74 5-year-olds participated in a 7-year follow-up study, in which we explored whether SFON measured with very small numerosities at 5 years of age predicts mathematical skills and knowledge, math motivation, and reading in fifth grade at 11 years of age. Results show that preschool SFON is a unique predictor of arithmetic fluency and number line estimation but not of rational number knowledge, mathematical achievement, math motivation, or reading. These results hold even after taking into account age, IQ, working memory, digit naming, and cardinality skills. The results of the current study further the understanding of how preschool SFON tendency plays a role in the development of different formal mathematical skills over an extended period of time.