Mathematics achievement and mathematics learning strategies: Cognitive competencies and construct differentiation

Responding to a survey requires cognitive abilities similar to those for any other linguistic task. We argue that, when faced with a cognitively challenging task, individuals respond by simplifying the task, declining it, or performing it poorly. Using the 2003 Program for International Student Assessment (PISA 2003) data sets, we document that the extent of construct differentiation in students’ mathematics learning strategies is strongly associated with their level of mathematics achievement. Likewise, the higher the level of mathematics achievement, the lower is the probability of a non-response to the mathematics learning strategy questions. Finally, the higher the students’ level of mathematics achievement, the more varied were their responses to the learning strategies items. These associations were examined across 40 participating countries.     

The dynamic roles of cognitive reappraisal and self-regulated learning during mathematics problem solving: A mixed methods investigation

Emotion regulation (ER) and self-regulated learning (SRL) are crucial to learners’ academic achievements. To date, little research has considered the dynamic relations between cognitive reappraisal (as a form of ER) and SRL in middle-to-upper-elementary-aged children. To address this gap, we conducted an explanatory mixed-methods study to examine relations between cognitive reappraisal, the four macro phases of SRL (task definition, planning/goal setting, enactment of learning strategies, monitoring/evaluation), and mathematics problem-solving outcomes in a sample of 134 elementary students from grades 3 through 6. Path analysis revealed that cognitive reappraisal positively predicted all four phases of SRL, but that the four phases of SRL did not predict cognitive reappraisal. Moreover, both task definition and planning/goal setting positively predicted enactment and monitoring/evaluation. Results from path analyses further revealed that task definition mediated relations between cognitive reappraisal and enactment, and reappraisal and monitoring. Enactment mediated relations between reappraisal and mathematics problem-solving outcomes. Finally, enactment predicted mathematics problem-solving outcomes. Further, quantitative results were cross-validated by results from trend analyses; results converged regarding the weakly sequenced nature of SRL and with regard to cognitive reappraisal serving as an important antecedent for effective SRL.     

Motivational beliefs and cognitive processes in mathematics achievement, analyzed in the context of cultural differences: a Korean elementary school example

The relations among students’ motivational beliefs, cognitive processes, and academic achievement were investigated. A 51-item questionnaire together with a mathematics achievement test was administered to 459 fifth graders in Korean elementary school mathematics classrooms. Results indicated that, in general, students’ cognitive processes related closely to competence beliefs, task values, and achievement goals, and more importantly their success or failure in mathematics achievement was closely linked to competence beliefs, performance-avoidance goals, and persistence strategies. Positive evidence of performance-approach goals was observed in math learning relative to task goals. As expected, performance-avoidance goals turned out to be detrimental to students’ math learning. These findings are generally congruent with the motivational theories and support the position that students should be encouraged to adopt task goals and actively involve themselves in math class activities. However, it also behooves us to recognize the potential benefits of performance-approach goals in different cultural contexts, such as the Korean elementary school math classrooms.     

Combined fluency and cognitive strategies instruction improves mathematics achievement in early elementary school

One hundred and seventy-eight second grade students from two states (Georgia and Massachusetts) participated in an experiment in which they were randomly assigned to either (1) a computer program designed to increase fluency in addition and subtraction, (2) a program designed to improve cognitive strategy use for addition and subtraction, (3) a program that combined the fluency and cognitive strategy instruction programs or (4) a control condition. The intervention consisted of 40 half-hour sessions (2 sessions per week for 20 weeks). Prior to the intervention, and immediately following the intervention, the participants were tested on fluency, cognitive strategy use, and mathematics achievement. ANCOVAs indicated that children in the combined fluency and cognitive strategy use condition significantly improved their mathematics achievement in comparison to the control group. When we examined the impact of the intervention as a function of gender, boys appeared to benefit from the intervention, but girls did not.     

Impact of programming on primary mathematics learning

The aim of this study is to investigate whether a programming activity might serve as a learning vehicle for mathematics acquisition in grades four and five. For this purpose, the effects of a programming activity, an essential component of computational thinking, were evaluated on learning outcomes of three mathematical notions: Euclidean division (N = 1,880), additive decomposition (N = 1,763) and fractions (N = 644). Classes were randomly assigned to the programming (with Scratch) and control conditions. Multilevel analyses indicate negative effects (effect size range −0.16 to −0.21) of the programming condition for the three mathematical notions. A potential explanation of these results is the difficulties in the transfer of learning from programming to mathematics.     

A systematic review of the role of learning games in fostering mathematics education in K-12 settings

In the recent decade, a number of literature reviews were conducted to examine the effectiveness of learning games. However, prior reviews typically focused on providing a synopsis of the overall research trends and the games’ impact on cognitive and non-cognitive learning, without providing critical and contextual information of learning-gameplay integration or the game design features. The current review focuses on recent empirical studies that implement learning games for K-12 mathematics education during the time period of 2008–2021 via a systematic search of the databases. Forty-three papers were identified as the result of a three-stage data extraction process. We identified the trends of implementing learning games in mathematics education and the ways to designing and integrating math content in gameplay. We propose that more research is needed to examine the design and use of learning games for math learning in K-12 settings. Recommendations for future game-based learning design and research are presented.     

Learning from split-attention materials: Effects of teaching physical and mental learning strategies

Learners learn more from spatially separated text and pictures after they have been instructed to physically integrate these sources than without such an instruction. We investigated whether instructing learners to mentally integrate textual and pictorial information would yield similar results. Eighty-seven participants studied a picture with accompanying text about an electrical circuit. Text and picture were presented as spatially separated sources or in an integrated format. In the separated format, participants were instructed to use (1) a mental learning strategy, (2) a physical learning strategy, or (3) no learning strategy. Participants in the separated condition using a mental learning strategy and the integrated condition obtained higher recall and comprehension (but not causal inference) performance than participants in the separate conditions with the physical- or no learning strategy. This indicates that instructing learners to mentally integrate spatially separated text and pictures when studying split-attention material can be an effective learning strategy.     

Motivation and students’ use of learning strategies: Evidence of unidirectional effects in mathematics classrooms

Considerable evidence indicates that student motivation and use of learning strategies are related. There is insufficient understanding, however, about their reciprocal effects—whether motivation affects strategy use, the converse, or whether the effects are bidirectional—and which components of motivation and strategies are involved. A two-wave longitudinal design was used to examine this issue among 9th grade students (N = 306) enrolled in high school mathematics classes during an academic term. A cross-lagged structural model found that students’ self-efficacy in mathematics and value predicted their reported use of learning strategies. There was no evidence, however, that learning strategy use predicted motivation and, thus, support for unidirectional effect of motivation during that time interval. Implications for models of self-regulated learning and instruction are discussed.     

An evaluation of the Touch Math method for teaching addition to students with learning disabilities in mathematics

The present study was designed to determine if children with learning disabilities in mathematics could be taught three‐row, double‐digit addition problems using a dot‐notation method. Three children with learning disabilities in mathematics were selected for the study. Prior to the intervention, these students employed a combination of count‐all and count‐on strategies when solving addition problems and relied on concrete referents such as fingers or tallies. A multiple‐probe design was used to evaluate the effectiveness of the intervention. The experiment consisted of a teaching phase where students learned to count the dots on numbers 1 to 9 in a specified pattern, and an intervention phase where students progressed through nine levels of addition problems. Results indicate that the three subjects were able to learn and apply the dot‐notation method successfully, and to retain the method from one‐and‐a‐half to four‐and‐a‐half months after completing instruction.     

Starting behind and staying behind in South Africa: The case of insurmountable learning deficits in mathematics

This study quantifies a year's worth of mathematics learning in South Africa (0.3 standard deviations) and uses this measure to develop empirically calibrated learning trajectories. Two main findings are (1) only the top 16% of South African Grade 3 children are performing at an appropriate Grade 3 level. (2) The learning gap between the poorest 60% of students and the wealthiest 20% of students is approximately three Grade-levels in Grade 3, growing to four Grade-levels by Grade 9. The paper concludes by arguing that the later in life we attempt to repair early learning deficits in mathematics, the costlier the remediation becomes.     

Investigating curricular effect on the teaching and learning of mathematics in a cultural context: Theoretical and methodological considerations

This first article of the special issue presents theoretical and methodological considerations about longitudinally investigating curricular effects on the teaching and learning of mathematics in a cultural context. In particular, in this article, we discuss seven issues related to the investigation of curricular effects on the teaching and learning of mathematics: (1) the need to investigate longitudinally the effects of curriculum, (2) the nature of the reform and non-reform curricula, (3) multiple representations of curriculum use, (4) assessment of classroom instruction, (5) student diversity and achievement gaps, (6) multiple measures of student mathematics achievement, and (7) multi-level analysis of student achievement data. This article not only serves as an introduction to the special issue, but most importantly, also provides a theoretical and methodological context for the two longitudinal projects.     

Developing a mathematics curriculum to improve learning behaviors and mathematics competency of children

The authors investigated the effect of a mathematical curriculum (CU) developed based on verbal and practical activities on the mathematical competency (MC) and learning behaviors (LB) of preschool children. In a quasi-experimental design, 60 children (5- to 6-year-old girls) were selected using the accessible sampling method. The children were randomly divided into an experimental group and a control group, and the relevant concepts were taught to the children in both groups. While the control group received the typical kindergarten education based on the usual textbooks and worksheets, the CU was taught to the experimental group. Structural equation modeling was used to model the data and statistical evaluation. The results demonstrated a significant difference between the two groups in MC and LB. The CU significantly improved MC directly, and indirectly through the improvement of LB (i.e., engagement and learning focus, verbal behaviors, and type of activity).     

Analysis of the reflections of student-teachers of mathematics when working with learning portfolios in Spanish university classrooms

Research in teacher-training counsels that reflection should be fostered in order to prepare capable professionals for educational practice. For this reason, a teaching-learning process for training mathematics student-teachers in Spanish university classrooms incorporating an assessment system that included keeping a learning portfolio was analysed. The objective was to assess each student's learning in reflection about his/her vision of the learning process developed in the university training classrooms, in knowledge of mathematical and methodological contents (knowledge) and in creativity. Rubrics were built for each case, with common criteria, to study the relationship between the outcomes obtained and to compare them with those of a final written exam. The results showed the difference between the assessment of student-teachers in reflection and the other aspects, and thus the need to use specific assessment instruments for the different capabilities being developed in the training process.     

Video as a tool for fostering productive discussions in mathematics professional development

This article explores the use of classroom video as a tool for fostering productive discussions about teaching and learning. The setting for our research is a 2-year mathematics professional development program, based on the Problem-Solving Cycle model. This model relies on video from the teachers’ own classrooms and emphasizes creating a community in which members feel comfortable learning from video. We describe our experiences carrying out the Problem-Solving Cycle model, focusing on our use of video, our efforts to promote a supportive and analytical environment, and the ways in which teachers’ conversations around video developed over a 2-year period.     

Student group presentations: a learning instrument in undergraduate mathematics for engineering students

In this study we created an environment for peer learning, where students teach students by making oral presentations in groups about solving mathematical problems and explaining the theoretical background in mathematics, during the first year of an undergraduate engineering programme at the Norrköping campus of the Linköping University. In order to strengthen the students’ understanding and perception of central mathematical concepts, the study was designed to take the students through five different learning experiences, preparing the presentation, presenting the mathematics, listening to others presenting, discussion by all students after the presentation and feedback by the teacher to the small group of students separate from the other students. We study how oral presentations work as a learning and assessment method. The study consisted of three stages. After a first run of the presentations as a learning instrument, three guidebooks with recommendations for students and teachers were developed in order to assist students as well as teachers about their role in this learning environment. Students’ and teachers’ views on the student presentations as learning instrument were surveyed before and after the intervention. In stage three, students were interviewed individually to ascertain the relevant success of the different learning experiences.     

Working for learning: teaching assistants developing mathematics for teaching

This article derives from a case study of 10 secondary school teaching assistants (TAs) who did not have conventional pre-qualifications in mathematics but who undertook an honours degree in mathematics education studies at a Higher Education Institution in England whilst continuing to work as TAs in school. Work-based learning was thus undertaken in parallel with advancement through the hierarchical undergraduate mathematics curriculum. Lave and Wenger’s work on communities of practice is used as a framework to explore the TAs’ learning of mathematics alongside their professional work in schools. This case illustrates how and where institution-based undergraduate teaching relates to work in school, and where it does not, thus signalling the importance of the TAs’ informal learning strategies in bringing together these experiences.     

Science text comprehension: Drawing, main idea selection, and summarizing as learning strategies

The purpose of two experiments was to contrast instructions to generate drawings with two text-focused strategies—main idea selection (Exp. 1) and summarization (Exp. 2)—and to examine whether these strategies could help students learn from a chemistry science text. Both experiments followed a 2 × 2 design, with drawing strategy instructions (yes vs. no) and main idea/summarization strategy instructions (yes vs. no) as experimental factors. The main dependent variable was science text comprehension, measured by a multiple-select test and a transfer test. Participants were 90 (Exp. 1) and 71 (Exp. 2) students (grade 10). The results of both experiments showed positive effects of the drawing strategy instructions and negative effects of the text-focused strategy instructions without interactions. These results are consistent with the mental model approach to comprehension, showing advantages of drawing activity in fostering science text comprehension.     

Investigating video as a means to promote vocabulary for at-risk children

Two studies on the role of video on vocabulary learning were conducted in kindergarten classrooms with substantial numbers of children from low-income and Dual Language Learning (DLL) backgrounds. In the first study (n = 78), the effect of video viewing was compared with the effect of book reading on vocabulary learning. In the second study (n = 89), the effect of repeated viewing of video was compared with the effect of single viewing of video on vocabulary learning. Pre-test and post-test receptive and expressive vocabulary measures, which were aligned with the content in the studies, were administered. Analysis of Variance was used to test the effect of condition (i.e., video viewing versus book reading and single versus repeated reading) on children’s word knowledge. Results showed no difference in vocabulary learning between the video viewing and book reading conditions. Findings showed that there was no difference in vocabulary learning between children in the single and repeated viewing condition on the receptive measure, but children in the repeated viewing condition showed higher gains in vocabulary on the expressive measure. No differences were found in either study between children with higher and lower vocabulary knowledge.