This qualitative research study uses middle-grades students' numerical reasoning to model their symbolic representations of the relationship between two multiplicatively related unknowns on an algebra task. Students in sixth grade through ninth grade participated in clinical interviews that assessed their numerical reasoning using the Number…

In educational settings, reflective thinking is often overlooked, with an excessive emphasis on final answers, resulting in students needing more ability to evaluate and reconstruct their problem-solving processes. The ability for reflective thinking is required by students in solving problems, including numerical problems. This study uses a…

The algorithm for fraction multiplication is relatively easy to memorize and implement with accuracy. The simplicity of the algorithm masks the conceptual complexity involved in making sense of what fraction multiplication means in quantitative situations. One important interpretation of fraction multiplication involves fraction composition,…

Posing mathematical literacy problems is one of the challenging issues in literacy studies. The present study focused on how to develop the ability to pose mathematical literacy problems. Within the context of the training given to middle school mathematics teachers on how to pose mathematical literacy problems, literacy problems were introduced.…

This study presents the preliminary qualitative results of a larger mixed methods study. The qualitative phase utilized task-based clinical interviews to examine the non-symbolic and symbolic linear generalizations of middle-grades students. This investigation identified similarities and differences in the students' generalizations, and…

Children and adults often have difficulties comparing decimal magnitudes. Although individuals attempt to reconcile decimals with prior whole-number and fraction knowledge, conceptual and procedural differences between decimals and prior knowledge of whole numbers and fractions can lead to incorrect strategies. The dynamic strategy choice account…

This study aimed to investigate eighth-grade students' mathematical communication competency and mathematical literacy performance in a classroom experiment designed based on the mathematical modeling approach. Accordingly, a teaching experiment methodology was applied. Data were collected from three eighth-grade students through the Mathematical…

Nationally and internationally, teachers are being held increasingly accountable for student achievement, particularly in light of high stakes literacy and numeracy tests. Policies have been implemented that are designed to improve educational outcomes through raising student literacy levels across all school years in all subject areas. This has…

Many research problems in social science involve multilevel phenomena. However, discussions about multilevel research designs are limited in the mixed methods (MM) literature. Building on early writings in the field, this methodological discussion advances a refined definition of a multilevel MM research design. The refinement emerges from a…

This paper draws on numerous data sources to better understand the shift from additive to multiplicative thinking in years 4 to 9. Research studies that have used the Scaffolding Numeracy in the Middle Years assessment tasks have found that while students can be supported to move through the early and upper zones of the Learning and Assessment…

The purpose of the study was to explore the effects of focused numeracy instruction on the ratio in a middle school mathematics class and the lived experiences of students with special needs as they underwent the intervention. The intervention focused on using numeracy embedded into the intervention, specifically focusing on rational number…

Attention skills are strong cross-sectional predictors of reading comprehension from childhood through to adolescence. However, less is known about the developmental relations between these two domains across this period. This study examined the codevelopment of reading and attention in a community sample of 614 Australian school students (50%…

This study attempts to determine whether gamification can be used as a pedagogical technique to overcome the challenges in teaching statistics. A post-test quasi-experimental design was carried out in gamified and non-gamified groups in order to reveal the effect of gamification elements in cultivating students' statistical literacy skills.…

Culture and language play important roles in counting techniques, affecting how students learn math around the globe.

Understanding the cognitive processes central to mathematical development is crucial to addressing systemic inequities in math achievement. We investigate the "Groupitizing" ability in 1209 third to eighth graders (mean age at first timepoint = 10.48, 586 girls, 39.16% Asian, 28.88% Hispanic/Latino, 18.51% White), a process that captures…