Tag: Problem solving

The effect of student-centered strategies on learning outcomes in math teaching

By Liu Ziyu; Institute of Curriculum and Pedagogy, Faculty of Education, Beijing Normal University, China

Mathematics education has undergone significant evolution over the years, transitioning from traditional teacher-centered methods to more dynamic student-centered approaches. Grounded in constructivist learning theory, contemporary mathematics teaching fundamentally relies on learners’ autonomous knowledge-building activities. Consequently, student-centered strategies are widely expected to positively impact the learning process.

To investigate the potential relationship between student-centered strategies and mathematical problem-solving skills, researchers from Turkey conducted a meta-analysis of relevant literature in both Turkish and English. A total of 55 studies and 69 effect sizes were analyzed, revealing a large effect size (Hedge’s g = +0.87). Further analysis indicated that this positive effect is consistent across primary, secondary, and tertiary education levels, with longer interventions (exceeding nine weeks) yielding the most substantial impact. Based on these findings, the authors concluded that student-centered strategies, methods, or techniques in mathematics teaching are particularly effective in enhancing students’ problem-solving skills.

Measuring mathematical language: Lessons from elementary classrooms

By Cynthia Lake, Johns Hopkins University

Mathematical language plays an important role in helping students understand math concepts, as it serves as both a communication tool and a foundation for problem-solving skills. In a working paper released by the Annenberg Institute at Brown University, researchers provided the first large-scale quantitative analysis of mathematical language use in upper elementary classrooms. Conducted across 1,657 math lessons in 317 classrooms over three years, the research employed natural language processing (NLP) to examine how frequently teachers and students used mathematical vocabulary during lessons.

The study found wide differences in the use of mathematical language among teachers. Some teachers used mathematical terms much more frequently than others, modeling mathematical language 127 times per lesson on average. However, the study suggests that merely exposing students to mathematical vocabulary does not significantly lead to greater student usage of those terms. Teachers in the 75th percentile used 28 more mathematical terms per lesson than those in the 25th percentile, which amounts to approximately 4,480 additional exposures to mathematical terms over the course of a school year. This higher use of mathematical language was associated with improved student test scores, particularly when teachers employed additional strategies to engage students with these terms.

The study’s findings suggest that encouraging student use of mathematical language requires more than just teacher modeling. Instead, effective math instruction stems from a broader set of practices that go beyond vocabulary use. While the study points to a correlation between teacher use of mathematical vocabulary and student achievement, it emphasizes that future research should explore the quality of vocabulary use and its impact on long-term learning outcomes.

Working memory and word-problem solving trainings, which combination is more effective?

Marta Pellegrini, University of Cagliari, Italy

A study conducted by Lynn and Douglas Fuchs and colleagues looked at the effectiveness of interventions that combine training on working memory (WM) and word-problem solving (WPS). The four interventions were as follows:

Intervention 1 – general training on WM
Intervention 2 – training on WPS without WM training
Intervention 3 – training on WPS with math-specific WM training
Control group – no intervention

General WM training consisted of sessions using verbal and visuospatial modalities, to which the authors added 5 minutes on mathematics practice. The WPS intervention used in the study was Pirate Math that consists of four phases in each session: arithmetic problems, word-problem solving with a tutor, games, and practice. Finally, math-specific WM training was developed by the authors to support students in applying their working memory capacity in mathematics.

A randomized study evaluated the effects of the interventions on academic outcomes of students with math difficulties in second grade. A total of 258 students in 16 schools were randomly assigned to the four conditions: 57 in the control group, 63 in general WM, 60 in WPS, 60 in WPS with math-specific WM. Students worked with the programs for 5 months. Automated Working Memory Assessment (AWMA) was used to measure outcomes related to working memory and two measures to assess WPS and arithmetic.

Results showed significant differences between the WPS group (ES = +0.62) and general WM (ES = +1.22) compared to the control group, while no difference was found for WPS with math-specific WM (ES = +0.30). Effects were significantly larger in arithmetic and on the WPS measure for the three interventions compared to the control group. On arithmetic, the ESs were +0.71, +0.81, +0.64 for the WPS group, WPS with math-specific WM, and general WM, respectively. On the WPS measure, the ESs were +0.45, +0.32, +0.57 for the WPS group, WPS with math-specific WM, and general WM, respectively. The authors concluded that although training on general WM had effects on both working memory and math outcomes, it cannot replace WPS interventions that showed stronger results on math outcomes. Conversely, effects are stronger on working memory when a general WM training is used.

Improving secondary school science learning through CESE

By Kaya Feng, Johns Hopkins University

Over the past two decades, U.S. secondary students’ engagement and achievement in elementary and secondary science have stayed mediocre, remaining behind other industrialized countries. Some interventions were initiated to improve the situation, one of which, “Crafting Engaging Science Environments (CESE),” is a high school chemistry and physics project-based learning intervention. The CESE is a coherent system approach that cultivates students to take primary and autonomous ownership for problem-solving, phenomenon analysis, and engagement in scientific practices, which, besides increasing students’ scientific literacy, ignites their learning interest and ambition, a key predictor for college enrollment. Barbara Schneider and colleagues conducted a quantitative study to evaluate this system.

The researchers included 61 secondary schools (30 treatment and 31 control) to examine the effect of CESE on students’ science learning through an independently developed summative assessment and to explore conditions potentially affecting the treatment effect. The results showed that the intervention was effective at raising students’ science learning.

The authors suggest that interventions that give students opportunities to get involved in authentic problems or tasks can serve as efficient methods to facilitate science learning and should be considered for adoption by educators.