Predicting Middle School Profiles of Algebra Performance Using Fraction Knowledge

The relation between number line performance and mathematics outcomes: Two meta-analyses

Understanding the magnitudes represented by numerals is a core component of early mathematical development and is often assessed by accuracy in situating numerals and fractions on a number line. Performance on these measures is consistently related to performance in other mathematics domains, but the strength of these relations may be overestimated because general cognitive ability has not been fully controlled in prior studies. The first of two meta-analyses (162 studies, 33,101 participants) confirmed a relation between performance on whole number (r = 0.33) and fractions number (r = 0.41) lines and overall mathematics performance. These relations were generally consistent across content domains (e.g., algebra and computation) and other moderators. The second (71 studies, 14,543 participants) used meta-analytic structural equation modeling to confirm these relations while controlling general cognitive ability (defined by IQ and working memory measures) and, in one analysis, general mathematics competence. The relation between number line performance and general mathematics competence remained significant but reduced (β = 0.13). Controlling general cognitive ability, whole number line performance consistently predicted competence with fractions but not performance on numeracy or computations measures. The results suggest an understanding of the magnitudes represented by whole numbers might be particularly important for students' fractions learning. RESEARCH HIGHLIGHTS: Two meta-analyses examined the link between the number line and mathematics performance. The first revealed significant relations across domains (e.g., algebra and computation). The second controlled for general cognitive ability and resulted in reduced but still significant relations. The relation between number line and fractions performance was stronger than relations to other domains.

From whole numbers to fractions to word problems: Hierarchical relations in mathematics knowledge for Chinese Grade 6 students

It is well established in the literature that fraction knowledge is important for learning more advanced mathematics, but the hierarchical relations among whole number arithmetic, fraction knowledge, and mathematics word problem-solving are not well understood. In the current study, Chinese Grade 6 students (N = 1160; 465 girls; Mage = 12.1 years, SD = 0.6) completed whole number arithmetic (addition, subtraction, multiplication, and division), fraction (mapping, equivalence, comparison, and arithmetic), and mathematics word problem-solving assessments. They also completed two control measures: number writing speed and nonverbal intelligence. Structural equation modeling was used to investigate the hierarchical relations among these assessments. Among the four fraction tasks, the correlations were low to moderate, suggesting that each task may tap into a unique aspect of fraction understanding. In the model, whole number arithmetic was directly related to all four fraction tasks, but was only indirectly related to mathematics word problem-solving, through fraction arithmetic. Only fraction arithmetic, the most advanced fraction skill, directly predicted mathematics word problem-solving. These findings are consistent with the view that students need to build these associations into their mathematics hierarchy to advance their mathematical competence.

Beyond linearity: Using IRT-scaled level models to describe the relation between prior proportional reasoning skills and fraction learning outcomes

Previous research on the role of prior skills like proportional reasoning skills for the development of mathematical concepts offers conclusions such as "more (prior skills) is better (for later learning)." Insights, which prior skill level goes along with which level of learning outcomes, may advance the understanding of the development of mathematical concepts. An exploratory approach is presented based on level models to describe the relation between symbolic proportional reasoning skills and fraction outcomes beyond linearity. Analyses draw on samples of German fourth to sixth graders from a scaling (2017, N = 325, 54.8% female) and longitudinal study (2018/2019, N = 436, 42.7% female). Particularly mastering natural and internal rational ratios in proportional reasoning seems relevant for successful fraction learning.

How to Continue? New Approaches to Investigating the Effects of Adaptive Math Learning Programs on Students' Performance, Self-Concept, and Anxiety

Math learning programs were expected to revolutionize students' learning, but their effects so far have mostly been disappointing. Following the debate about why to continue research on math learning programs, we aimed to reformulate this question into how to continue this research. Investigations to date have neither considered a sufficiently wide set of outcome variables nor differentiated between performance measures (e.g., measuring addition and subtraction performance separately) and affective-motivational variables. Moreover, as students can only benefit from a program if they use it, researchers need to take practice behavior into account. Thus, we investigated whether the adaptive arithmetic learning program Math Garden fostered students' addition and subtraction performance, their math self-concept, and a reduction of their math anxiety. We also investigated how practice behavior (practiced tasks/weeks) affected these outcomes. We used a randomized pretest-posttest control group design with 376 fifth-grade students in Germany. Students in the experimental condition practiced with Math Garden for 20.7 weeks and had an increase in math self-concept. The more subtraction tasks the students practiced, the more they improved their subtraction performance. We found no effects on math anxiety. The results are discussed in terms of providing a starting point for new directions in future research.