Mathematical Problem-solving Performance Research Articles

Mathematical Thinking and Problem Solving Performance: The Mediating Role of Hope

The purpose of the present study is to provide a mediation model by exploring the relationships among mathematical thinking, hope and problem solving performance in mathematics. The participants of the present study were composed of 311 preservice mathematics teachers. In this mixed method research, these preservice mathematics teachers were conducted to the scales of Dispositional Hope and Mathematical Thinking, and Problem Solving Test. Based on the quantitative data analysis, it was observed that statistically significant relationships among the variables of hope, mathematical thinking and problem solving performance. The quantitative data collected through these instruments were also analyzed by mediation analysis techniques. The qualitative data gathered through semi-structured interviews were analyzed by content analysis technique. These data encouraged the findings acquired from quantitative data analysis. The qualitative findings confirmed the findings of the mediator role of hope. The qualitative findings encouraged the relationships among the variables and the role of mediator.

특별한 관심 영역을 활용한 전략 교수가 자폐 범주성 장애 학생의 수학 문장제 과제 수행률 및 정확도에 미치는 영향

This study examined the effects of an instructional strategy using areas of special interest to students with Autism Spectrum Disorders (ASD) on their performance rate and accuracy in mathematical word problem-solving. The study used a multiple probe design for three students with ASD under three experimental conditions: baseline, intervention, and maintenance. First, the computation level of the word problem was selected by interviewing special education teachers and parents. Next, each participant’s special interest area was determined. Then, the interest areas were used to modify students’ word problems. Finally, the students were taught the instruction strategy’s four steps. The results indicated that the intervention increased each participant’s mathematical word problem-solving performance rate and accuracy. Furthermore, these effects persisted after the intervention. Several implications of the study are discussed

Attention-Deficit/Hyperactivity Disorder and Academic Functioning: Reading, Writing, and Math Abilities in a Community Sample of Youth with and without ADHD.

Previous studies have shown that Attention-Deficit/Hyperactivity disorder (ADHD) is marked by impairments in academic functioning in reading, writing, and mathematics. Yet, virtually no studies have examined academic functioning in terms of both basic skills (e.g., word recognition, handwriting/spelling, arithmetic calculations) and more complex advanced skills (e.g., reading comprehension, writing composition, and mathematical problem-solving) within the same sample. In the present study, 518 children with ADHD were compared to a control group of 851 children without ADHD (ages 8-18) and assessed on a comprehensive battery of reading, writing, and math assessments. It was hypothesized that ADHD diagnostic status would uniquely predict performance on advanced skill measures even after controlling for performance on basic skills in that academic domain. ADHD status was associated with worse performance across all academic tests. Results also indicated that ADHD independently predicted performance for measures of writing composition and one measure of reading comprehension, even after controlling for performance on basic skills in those domains. However, ADHD did not independently predict mathematical problem-solving performance. These findings add to the literature on ADHD and academic functioning and indicate that inattention may weaken skills necessary for effective reading comprehension and writing composition.

Middle school students' mathematical problem-solving ability and the influencing factors in mainland China.

This study investigated the mathematical problem-solving ability of 42,644 ninth-grade students who participated in regional education quality health monitoring from Z province in East China and the factors which influence their performance of mathematical problem-solving. The results are as follows: (1) ~96% of the students' mathematics problem-solving ability meets the basic academic requirements of the mathematics curriculum standards; (2) boys and children without siblings performed better, and urban students performed significantly better than county and rural students; (3) ~28% of students' mathematical problem-solving performance came from inter-school variability; urban and rural backgrounds had a greater impact on mathematical problem-solving than did teaching factors, while teaching self-efficacy had the least impact among the school-level influencing factors. In contrast, the influence of individual non-intelligence factors was higher than that of student background variables, including a greater positive effect of self-efficacy and a greater negative effect of mathematics anxiety.

Comparison of Mathematics Problem-Solving Abilities in Autistic and Non-autistic Children: the Influence of Cognitive Profile

This study examines relationships between mathematical problem-solving performance (in terms of strategies used and accuracy) and the main cognitive domains associated with mathematical learning (i.e. executive functions, verbal comprehension and social perception) of children with and without autism spectrum disorder (ASD and non-ASD resp.). The study involved 26 ASD and 26 non-ASD children without intellectual disabilities, between 6 and 12 years old, matched by sex, age and school (grade and classroom). The results show a higher percentage of ASD children with problem solving difficulties than non-ASD (57% vs. 23% resp.). Poor performing ASD children showed comparatively lower scores in inhibition, theory of mind and verbal comprehension. Implications for the design of mathematical interventions for ASD students are discussed.

Success Indicators of Mathematical Problem-Solving Performance Among Malaysian Matriculation Students

This study identifies the success indicators of mathematical problem-solving performances among Malaysian matriculation students divided into four indicators: mathematical beliefs, mathematics attitudes, mathematics self-efficacy and metacognitive skills. For this purpose, 368 matriculation students from three matriculation colleges were selected as respondents using proportioned stratified sampling. This study utilized a descriptive correlational design approach. A set of questionnaires and a mathematics test were used as the instruments. Independent variables were measured using a questionnaire, while mathematical problem-solving performance was measured using a mathematics test. The findings show students had a high level in mathematics beliefs, attitude towards mathematics, mathematics self-efficacy and metacognitive skills. Statistical tests to determine success indicators predicting mathematical problem-solving performance revealed that mathematics self-efficacy does not contribute significantly to these variables and that metacognitive skills make the most decisive contribution, followed by mathematics attitude and mathematics beliefs. Hence, this study suggests that problem-solving should be included as an essential part of the mathematics matriculation syllabus to enable students to improve their problem-solving abilities.

“Bold Problem Solving”: A New Construct for Understanding Gender Differences in Mathematics

Despite progress toward gender equity, troubling disparities in mathematical problem-solving performance and related outcomes persist. To investigate why, we build on recurrent findings in previous studies to introduce a new construct, “bold problem solving,” which involves approaching mathematics problems in inventive ways. We introduce a self-report survey of bold problem-solving orientation and find that it mediates gender differences in problem-solving performance for both high-achieving middle school students (n = 79) and a more diverse sample of high school students (n = 222). Confidence mediates the relation between gender and bold problem-solving orientation, with mixed results for mental rotation skills and teacher-pleasing tendencies as mediators. Overall, the new bold problem-solving construct appears promising for advancing our understanding of gender differences in mathematics.

Investigating the Generalizability of Schema-Based Instruction Focused on Proportional Reasoning: A Multi-State Study

This study used integrative data analysis (Curran & Hussong, 2009), which allows combining data from different studies, to examine the generalizability of a research-based mathematics program, schema-based instruction (SBI), with a focus on proportional reasoning. Data were pooled from existing SBI studies spanning three U.S. states in which teachers and their classrooms were randomly assigned to either a SBI or control condition. Results of a series of multilevel (i.e., two-level, students within teachers) models indicated the effectiveness of SBI in improving students’ mathematical problem-solving performance. The pooled data findings clarify that SBI improves students’ mathematical problem solving more so for proximal than distal measures. These findings also show Black and Hispanic students continue to lag behind White students, that teachers with more experience tend to be associated with higher performing classrooms, and that increasing concentrations of students eligible for free or reduced price lunch and students receiving special education services are generally associated with weaker performances. Implications of these findings are discussed.

Improving Word Problem Solving of Immediate, Generalized, and Combined Structured Problems via Schema-Based Instruction

ABSTRACT Instruction geared toward priming the underlying problem structures was suggested as an evidence-based practice for students with a learning disability. Schema-based instruction is one intervention aligned with this principle. We extended prior work by (a) using a teacher as the implementer, (b) providing teacher flexibility in intervention implementation, and (c) examining student performance for generalized and combined problem structures. The participants included fourth-grade students (n = 5) identified with a disability who received supplementary mathematics instruction in a resource room setting. The independent variable was schema-based instruction and the dependent variable was mathematical problem-solving performance. To evaluate if a functional relation existed, a multiple-probe design across participants was used. A functional relation was established; however, student performance did not reach socially significant levels. The aggregated Tau-U effect size was 81% [CI90 61, 100%] and the aggregated BC-SMD was 1.72 [CI95 1.00, 2.49]. Implications for research and practice will be discussed in regard to implementation fidelity and dosage of remedial instruction.

Comparative Effects of ICT-Integrated Learning Strategies on Spatial Reasoning Skills Among Nigerian Lower Primary School Pupils

Comparative Effects of ICT-Integrated Learning Strategies on Spatial Reasoning Skills Among Nigerian Lower Primary School Pupils

Causal Effects of Cognitive and Affective Factors on Students’ Mathematical Problem Solving Performance

Causal Effects of Cognitive and Affective Factors on Students’ Mathematical Problem Solving Performance

Improving student learning of ratio, proportion, and percent: A replication study of schema-based instruction.

The purpose of this replication study was to provide replication evidence not currently available of the effects of a research-based mathematics program, schema-based instruction, on the mathematical problem-solving performance of 7th-grade students. The replication was implemented in 36 schools in 5 districts; 59 mathematics teachers and their students (N = 1,492) participated in the study. Multilevel hierarchical linear analyses revealed statistically significant differences between conditions on proximal and distal measures of mathematics problem solving, with effects sizes similar to those reported in Jitendra et al. (2015). (PsycINFO Database Record (c) 2019 APA, all rights reserved)

A modeling study to explain mathematical problem-solving performance through metacognition, self-efficacy, motivation, and anxiety

Many noncognitive constructs affect mathematical problem-solving performance. The aim of the present study is to investigate the direct and indirect effects of a number noncognitive constructs such as mathematics self-efficacy, mathematics anxiety, and metacognitive experience on the mathematical problem solving of middle-school students. The sample consisted of 517 seventh-grade Turkish students of whom 252 were male (49%) and 265 were females (51%). The instruments used in this study were a mathematical problem-solving performance test, a mathematics self-efficacy scale, a mathematics anxiety scale, a metacognitive experience scale, and a mathematics motivation scale. Two-stage structural equation modeling was used to examine the relationships between the noncognitive contructs and problem solving. Metacognitive experience was the only noncognitive construct, which had a direct effect on mathematical problem-solving performance; it also mediated the effects of self-efficacy, motivation, and mathematics anxiety on performance. Motivation and mathematics anxiety had an indirect effect on mathematical problem-solving performance through self-efficacy.

On Solving Mathematical Problems the Spatial-Visual Ways

This study investigated the effectiveness of spatial-visualization-based instruction on the mathematical problem-solving performance of 35 mathematics education students using one-group pretest-posttest quasi-experimental design. It also aimed to describe how spatial visualization is applied in solving mathematical problems. The findings of the study revealed that spatial-visualization-based instruction improved the mathematical problem-solving performance of students. The spatial-visualization ability can be applied in solving mathematical problems.

Uncovering the Relationship Between Mathematical Ability and Problem Solving Performance of Swedish Upper Secondary School Students

ABSTRACTIn this paper, we examine the interactions of mathematical abilities when 6 high achieving Swedish upper-secondary students attempt unfamiliar non-routine mathematical problems. Analyses indicated a repeating cycle in which students typically exploited abilities relating to the ways they orientated themselves with respect to a problem, recalled mathematical facts, executed mathematical procedures, and regulated their activity. Also, while the nature of this cyclic sequence varied little across problems and students, the proportions of time afforded the different components varied across both, indicating that problem solving approaches are informed by previous experiences of the mathematics underlying the problem. Finally, students’ whose initial problem formulations were numerical typically failed to completed the problem, while those whose initial formulations were algebraic always succeeded.

Schema-Based Strategy Instruction and the Mathematical Problem-Solving Performance of Two Students with Emotional or Behavioral Disorders

The purpose of this study was to analyze the effects of schema instruction on the mathematical problem solving of students with emotional or behavioral disorders (EBD). The participants were two fourth-grade students identified with EBD. The intervention package consisted of schema instruction, strategy instruction on problem-solving heuristics (i.e., understand the problem, make a plan, carry out the plan, check), and the use of reinforcement for task completion. The study used a single case experimental design (SCED) to establish a functional relation between the intervention package and problem-solving performance. A functional relation was established and results demonstrated an improvement in problem solving on addition/subtraction and multiplication/division word problems. The Tau-U effect size was used to corroborate visual analysis results. The Tau-U for participants 1 and 2 was 100% and 96%, respectively. The students and special education teacher reported that schema instruction was a socially valid intervention.

Is there a causal relation between mathematical creativity and mathematical problem-solving performance?

The relationship between mathematical creativity (MC) and mathematical problem-solving performance (MP) has often been studied but the causal relation between these two constructs has yet to be clearly reported. The main purpose of this study was to define the causal relationship between MC and MP. Data from a representative sample of 480 eighth-grade students were analysed using a cross-lagged panel correlation (CLPC) design. CLPC attempts to rule out plausible alternative explanation of a causal effect. The result suggests that significant predominant causal relationship was found between MC and MP. It indicates that MP was found to be a cause of MC than the converse.

Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students’ Proportional Reasoning: A Randomized Experiment

This study examined the effect of schema-based instruction (SBI) on 7th-grade students’ mathematical problem-solving performance. SBI is an instructional intervention that emphasizes the role of mathematical structure in word problems and also provides students with a heuristic to self-monitor and aid problem solving. Using a pretest-intervention–posttest-retention test design, the study compared the learning outcomes for 1,163 students in 42 classrooms who were randomly assigned to treatment (SBI) or control condition. After 6 weeks of instruction, results of multilevel modeling indicated significant differences favoring the SBI condition in proportion problem solving involving ratios/rates and percents on an immediate posttest (g = 1.24) and on a 6-week retention test (g = 1.27). No significant difference between conditions was found for a test of transfer. These results demonstrate that SBI was more effective than students’ regular mathematics instruction.

Finding the optimal guidance for enhancing anchored instruction

This study investigated the effect of different methods of guidance with anchored instruction on students' mathematical problem-solving performance. The purpose of this research was to iteratively design a learning environment to find the optimal level of guidance. Two iterations of the software were compared. The first iteration used explicit instruction upfront followed by practice problems, and the second iteration provided structured problem-solving guidance as needed to solve the problems within the software. Pilot testing was conducted with 32 fifth-grade students from two inclusive classrooms observed a year apart within a small Midwestern, urban school. A parametric analysis of covariance was used to compare the problem-solving performance of the students who used the two different iterations. Enhancing anchored instruction with structured problem-solving guidance on an as-needed basis significantly improved students' problem-solving performance on conceptually easy problems, but not for more complex problems. The implications of this research illustrate the importance of iteratively designing and developing learning environments to take into consideration the needs of a particular situation.

The influence of self-efficacy and working memory capacity on problem-solving efficiency

We investigated the influence of self-efficacy beliefs and working memory capacity on mathematical problem-solving performance, response time, and efficiency (i.e., the ratio of problems solved correctly to time). Students completed a letter-recoding task (Experiment 1) or an operation span task (Experiment 2), rated their self-efficacy for solving mental multiplication problems, and then solved similar problems of varying complexity. We tested the motivational efficiency hypothesis, which predicted that motivational beliefs, such as self-efficacy, increase problem-solving efficiency through focused effort and strategy use. Experiments 1 and 2 reported a significant effect for self-efficacy on problem-solving performance and efficiency, but limited effects for time. A self-efficacy by working memory interaction occurred in Experiment 1, suggesting self-efficacy is beneficial as demands on working memory increase. These findings suggested that self-efficacy increased problem-solving efficiency through strategic performance rather than faster solution times, and were consistent with the motivational efficiency hypothesis.