Different aspects of fraction understanding are associated selectively with performance on a fraction learning game

Fraction understanding seems a double-edged sword. On the one hand, it is an important predictor of later mathematical achievement. On the other hand, it is also one of the topics students struggle most in secondary math education. To complement traditional instruction, digital learning games were developed and found to successfully foster fraction understanding. However, so far, it is not known to what degree different aspects of fraction understanding (e.g., part-whole relations, fraction magnitude, fraction arithmetic) may be conveyed by such games. The current study evaluated selective associations of in-game performance of the fraction learning game Semideus with specific aspects of fraction understanding assessed using a comprehensive paper-pencil test. In Semideus, seventh graders (M_age=12.3years) from academic track secondary schools in Germany estimated the location of fractions on a number line and compared fractions according to their magnitude. Results replicated previous findings showing that in-game performance was significantly associated with mathematics achievement (i.e., math grades) and basic, whole number arithmetic skills. Moreover, we observed significant associations for aspects of fraction understanding closely matching mechanics of the learning game such as fraction number line estimation, fraction magnitude comparison and fraction ordering. These associations were observed for accuracy on the game's fraction learning tasks (e.g., estimation accuracy on the number line) but also generalized to game-based metrics such as virtual incentives (i.e., stars awarded in the game). This implies that the actual game mechanic may help to convey aspects of fraction understanding, substantiating ideas of intrinsic integration in game design.

Mathematical skills of 11-year-old children born very preterm and full-term

Preterm birth affects the academic development of children, especially in mathematics. Remarkably, only a few studies have measured specific effects of preterm birth on mathematical skills in primary school. The aim of this study was to compare 11-year-old children, with an IQ above 70, born very preterm (N = 64) and full-term (N = 72) on a variety of 5th grade mathematical skills and cognitive abilities important for mathematical learning. The measures were spontaneous focusing on numerosity (SFON), spontaneous focusing on quantitative relations (SFOR), arithmetic fluency, mathematics achievement, number line estimation, rational number magnitude knowledge, mathematics motivation, reading skills, visuospatial processing, executive functions, and naming speed. The children born very preterm and full-term differed in arithmetic fluency, SFON and SFOR. Domain general cognitive abilities did not fully explain the group differences in SFON and SFOR. Retrospective comparisons of the samples at the age of five years showed large group differences in early mathematical skills and cognitive abilities. Despite lower early mathematical skills, the children born very preterm reached peer equivalent performance in many mathematical skills by the age of 11 years. Nevertheless, they appear less likely to focus on implicit mathematical features in their everyday life.

Predicting adaptive expertise with rational number arithmetic

Background

Adaptive expertise is a highly valued outcome of mathematics curricula. One aspect of adaptive expertise with rational numbers is adaptive rational number knowledge, which refers to the ability to integrate knowledge of numerical characteristics and relations in solving novel tasks. Even among students with strong conceptual and procedural knowledge of rational numbers, there are substantial individual differences in adaptive rational number knowledge.

Aims

We aimed to examine how a wide range of domain‐general and mathematically specific skills and knowledge predicted different aspects of rational number knowledge, including procedural, conceptual, and adaptive rational number knowledge.

Sample

173 6^th and 7^th grade students from a school in the southeastern US (51% female) participated in the study.

Methods

At three time points across 1.5 years, we measured students’ domain‐general and domain‐specific skills and knowledge. We used multiple hierarchal regression analysis to examine how these predictors related to rational number knowledge at the third time point.

Result

Prior knowledge of rational numbers, general mathematical calculation knowledge, and spontaneous focusing on multiplicative relations (SFOR) tendency uniquely predicted adaptive rational number knowledge, after taking into account domain‐general and mathematically specific skills and knowledge. Although conceptual knowledge of rational numbers and general mathematical achievement also predicted later conceptual and procedural knowledge of rational numbers, SFOR tendency did not.

Conclusion

Results suggest expanding investigations of mathematical development to also explore different features of adaptive expertise as well as spontaneous mathematical focusing tendencies.

Measuring Spontaneous Focus on Space in Preschool Children

Previous work on children's Spontaneous Focus on Numerosity (SFON) has shown the value of measuring children's spontaneous attention within naturalistic interactions. SFON is the spontaneous tendency to focus attention on, and explicitly enumerate the exact number of, items in a set. This measure predicts later math skills above and beyond general IQ and other cognitive factors such as attention. The utility of SFON suggests that a parallel construct for space is a worthy pursuit; spatial cognition underlies many of our mathematical skills, especially as children are first learning these skills. We developed a measure of children's Spontaneous Focus on Space - the spontaneous tendency to attend to absolute and relative spatial components of the environment - and studied its relation to reasoning about the important spatial-numerical concept of proportions. Fifty-five 3- to 6-year-olds were tested at a local children's museums in New York City. Children participated in tasks designed to measure their spontaneous focus on space and number, and their ability to reason about spatial proportions. Results indicate that as children grow older, their Spontaneous Focus on Space becomes more complete and is positively related to proportional reasoning performance. These findings suggest that spatial awareness is rapidly increasing in the preschool years, alongside numerical awareness and spatial-numerical proportional reasoning.

What role do comprehension-oriented learning strategies have in solving math calculation and word problems at the end of middle school?

BACKGROUND

Math is a difficult subject with which many upper middle-school students struggle. In addition to knowledge, skills, and motivation, effective learning strategies play an important role in learning math.

AIMS

This study aimed to examine the effects of comprehension-oriented learning strategies (perceptual and abstract grouping of material) - together with math self-concept, task-persistent learning behaviour, earlier math skills, reasoning abilities, and reading comprehension - on solving mathematical calculation and word problems at the end of middle school.

SAMPLE

The sample consisted of 231 students (50% boys; mean age in Grade 9 = 15.55 years) from 16 schools and 31 classrooms in Estonia.

METHODS

Students were tested twice - once at the end of Grade 6 and once at the end of Grade 9. Calculation and problem-solving skills were assessed at both time points. Math self-concept, teacher-rated task persistence, reasoning abilities, and reading comprehension were assessed in Grade 6. Learning strategies were assessed using a word-memorization task in Grade 9. Multiple regression analysis was used.

RESULTS AND CONCLUSIONS

Applying abstract (but not perceptual) grouping was related to higher calculation and problem-solving skills. Math skills were persistent over time, and calculation and problem-solving skills mutually affected each other. Math self-concept, task persistence, and reading comprehension had a positive effect on problem-solving but not calculation skills. The study noted deficient use of comprehension-oriented strategies at the end of middle school, suggesting that more attention should be paid to teaching and discussing such learning strategies. These findings suggest that students' math skills may be enhanced by supporting metacognitive awareness and use of comprehension-oriented learning strategies.

Using Relational Reasoning Strategies to Help Improve Clinical Reasoning Practice

Clinical reasoning-the steps up to and including establishing a diagnosis and/or therapy-is a fundamentally important mental process for physicians. Unfortunately, mounting evidence suggests that errors in clinical reasoning lead to substantial problems for medical professionals and patients alike, including suboptimal care, malpractice claims, and rising health care costs. For this reason, cognitive strategies by which clinical reasoning may be improved-and that many expert clinicians are already using-are highly relevant for all medical professionals, educators, and learners.In this Perspective, the authors introduce one group of cognitive strategies-termed relational reasoning strategies-that have been empirically shown, through limited educational and psychological research, to improve the accuracy of learners' reasoning both within and outside of the medical disciplines. The authors contend that relational reasoning strategies may help clinicians to be metacognitive about their own clinical reasoning; such strategies may also be particularly well suited for explicitly organizing clinical reasoning instruction for learners. Because the particular curricular efforts that may improve the relational reasoning of medical students are not known at this point, the authors describe the nature of previous research on relational reasoning strategies to encourage the future design, implementation, and evaluation of instructional interventions for relational reasoning within the medical education literature. The authors also call for continued research on using relational reasoning strategies and their role in clinical practice and medical education, with the long-term goal of improving diagnostic accuracy.