Jake McMullen

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.

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.

A Game-Based Approach to Examining Students’ Conceptual Knowledge of Fractions

Considering the difficulties many students and even educated adults face with reasoning about fractions, the potential for serious games to augment traditional instructional approaches on this topic is strong. The present study aims at providing evidence for the validity of a serious game used for studying students’ conceptual knowledge of fractions. A total of 54 Finnish fifth graders played the math game on tablet computers using tilt-control to maneuver an avatar along a number line for a total of 30 min. Results indicated that most of the hallmark effects of fraction magnitude processing as identified in basic research on numerical cognition were successfully replicated using our serious game. This clearly suggests that game-based approaches for fraction education (even using tilt-control) are possible and may be effective tools for assessing and possibly promoting students’ conceptual knowledge of fractions.

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.

Is the study about spontaneous attention to exact quantity based on studies of spontaneous focusing on numerosity

Li and Baroody present a study in which they investigate toddlers’ spontaneous attention to exact quantity without acknowledging how previous studies of spontaneous focusing on numerosity (SFON) are related to their concept and methods. In this commentary requested by the European Journal of Developmental Psychology, we argue that the concept and the methods of spontaneous attention to exact quantity in the study of Li and Baroody clearly arise from previous research on SFON, as the authors have previously noted in their paper published in 2008. It is highly questionable whether their approach can be theoretically or methodologically dissociated from the previous research on SFON tendency to the extent that it is necessary to use an alternative name for the concept in their study.

Studies on spontaneous attention to number (SAN) are based on spontaneous focusing on numerosity (SFON)

Abstract Li and Baroody presented a study in which they investigate children’ spontaneous attention to exact quantity without acknowledging how previous studies of spontaneous focusing on numerosity (SFON) are related to their concept and methods. The authors’ reaction to our pointing this out makes it is clear that SFON research has had foundational role in the development of Baroody and his colleagues spontaneous attention to number (SAN) idea. Thus the authors must acknowledge the SFON literature as the substantial part of their theoretical and methodological construct. The latest definition of SAN states this undeniably. “SAN is the attentional process that underlies exact number recognition initiated by the mathematical thinking triggered by SFON (e.g., attention to “threeness” directed by conceptual knowledge of “three” activated by SFON).” Furthermore, in their response, Dr Baroody and Dr Li admit that “An awareness of the SFON literature did help us explicitly recognize that, given the ambiguous instructions that do not explicitly direct a child’s attention to number, both the nonverbal production and matching tasks were useful in assessing unguided or spontaneous attention to a number.” It is surprising that in their response to the European Journal of Educational Psychology, the authors maintain their claim that they have cited the SFON literature adequately in their study about SAN.