Math Ability Research Articles

Individual or collaborative projects? Considerations influencing the preferences of students with high reasoning ability and others their age

ABSTRACT Conditions influencing 328 students’ (Grades 6-8) preferences for collaborating or working alone on challenging projects were investigated, as well as their potential interactions with ability, grade and sex. Each student completed the Cognitive Abilities Test (Form 7) and Project Context Survey. No overall preference for individual or collaborative projects was found. Students’ preferences were sensitive to features of the context (subject, nature of the task and social dynamics). Individual projects were preferred in art and shared projects in science and social studies. Students with high ability and boys preferred individual projects in Math. Principal components analyses revealed three contextual considerations influenced students’ desire to work on projects alone (enjoyment, optimizing the outcome, and risk management) and five influenced the appeal of collaborating (inclusiveness and trust, access to the strengths of others, their perceived need for support, familiarity, and fair assessment). High ability students were more concerned with the efficiency and quality of their work, and their grades while others their age were more influenced by the potential for fun. Grade 8 students were more concerned with risk management and the assessment process than younger students. If the safe, supportive, fair conditions they sought for collaborating were not available, students’ default preference was to work alone on a challenging project.

Examining High School Students' Gendered Beliefs about Math: Predictors and Implications for Choice of STEM College Majors.

Utilizing the High School Longitudinal Study, a nationally representative sample of U.S. high school students, this study investigates the factors that predict different beliefs about gendered math ability and the potential consequences for students' choices to enter gender-segregated science, technology, engineering, and mathematics (STEM) majors in college. Among other results, analyses reveal that while about 25 percent of students report a traditionally stereotypical belief in male superiority, about 20 percent report a counter-stereotypical belief in female superiority; among female students, such beliefs are more common among black students. Further, models reveal a robust association between holding counter-stereotypical beliefs and the likelihood that women choose biological science majors, which are female dominated, compared to non-STEM fields. Among men, holding counter-stereotypical beliefs is associated with a lower likelihood of majoring in physical science, computer science, math, and engineering fields, which are strongly male dominated, versus non-STEM fields. Implications for gender inequality in STEM fields are discussed.

Proactive Control Mediates the Relationship Between Working Memory and Math Ability in Early Childhood.

Based on the dual mechanisms of control (DMC) theory, there are two distinct mechanisms of cognitive control, proactive and reactive control. Importantly, accumulating evidence indicates that there is a developmental shift from predominantly using reactive control to proactive control during childhood, and the engagement of proactive control emerges as early as 5–7 years old. However, less is known about whether and how proactive control at this early age stage is associated with children’s other cognitive abilities such as working memory and math ability. To address this issue, the current study recruited 98 Chinese children under 5–7 years old. Among them, a total of 81 children (mean age = 6.29 years) contributed useable data for the assessments of cognitive control, working memory, and math ability. The results revealed that children at this age period predominantly employed a pattern of proactive control during an AX-Continuous Performance Task (AX-CPT). Moreover, the proactive control index estimated by this task was positively associated with both working memory and math performance. Further regression analysis showed that proactive control accounted for significant additional variance in predicting math performance after controlling for working memory. Most interestingly, mediation analysis showed that proactive control significantly mediated the association between working memory and math performance. This suggests that as working memory increases so does proactive control, which may in turn improve math ability in early childhood. Our findings may have important implications for educational practice.

A meta-analysis of Geogebra software decade of assisted mathematics learning: what to learn and where to go?

Today, hundreds of studies on mathematics learning have been found in various literature, supported by the use of GeoGebra software. This meta-analysis aims to determine the overall effect of using GeoGebra software and the extent to which study characteristics moderate the study effect sizes to consider the implications later. This study analyzed 36 effect sizes from 29 primary studies identified from ERIC documents, Sage Publishing, Google Scholar, and repositories from 2010 to 2020, and a total of 2111 students. In order to support calculation accuracy, a Comprehensive Meta-analysis (CMA) software was used. The effect size is determined using the Hedges equation, with an acceptable confidence level of 95%. It is known that the overall effect size of using GeoGebra software on the mathematical abilities of students is 0.96 based on the estimation of the random-effect model, and the standard error is 0.08. These findings indicate that, on average, students exposed to GeoGebra-based learning outperformed math abilities, which was initially equivalent to 82% of students in traditional classrooms. This study considers the five characteristics of the study. It showed that the GeoGebra software used was more effective in sample conditions less than or equal to 30. Providing classrooms with sufficient numbers of computers allowed students to use them individually, which was necessary to achieve a higher level of effectiveness. GeoGebra software is more effective when the treatment duration is set to less than or equal to four weeks. These findings help educators consider the characteristics of studies that moderate effect sizes using the GeoGebra software in the future.

Analysis of Critical Thinking Ability of Class X IPA High School Students in Solving Story Questions in terms of Gender and Mathematical Ability

The purpose of this study was to describe the critical thinking skills of class X high school students in solving story problems in terms of gender and math abilities. This research was conducted in the even semester of 2020/2021. This research uses a qualitative approach with descriptive research type. The subjects in this study consisted of 3 male students and 3 female students with different mathematical abilities selected based on test results and consultation with subject teachers. The used Instruments in this study were critical thinking skills tests and interviews. The results of this research are (1) male students and high mathematical abilities meet aspects of interpretation, analysis, evaluation, inference, aspects and self regulation well. Meanwhile, female students with high mathematical abilities are able to complete aspects of interpretation, analysis, evaluation, and inference well; (2) Male students and their mathematical abilities are meeting the aspects of interpretation, analysis, and inference well. Meanwhile, female students and moderate math abilities were able to complete interpretation, analysis, inference, and explanation well; and (3) male students with low math ability are able to solve aspects of interpretation well. Meanwhile, female students with low math abilities were able to complete aspects of interpretation and analysis well. For further researchers, it is necessary to research at a higher level with more research subjects or on other variables.

Perceptions of Girls’ Math Abilities

Teaching mathematics to young girls often invokes perceptions around inherent ability, gender, and influences that contribute to a gap between boys and girls with regard to math achievement. Moreover, lived teaching experiences indicate that there is a strong affective component to students’ encounters in schools, which may affect children’s perceptions of their capabilities. The authors address intersecting issues that interact with gender inequalities surrounding girls and mathematics: math self-concepts, gender stereotypes, parental involvement, and influences from teachers and curriculum. In this paper, stories about teaching girls from a mathematics teacher’s perspective are interwoven with research literature to strengthen recommendations for change in the areas of gender, teacher education, STEM careers, and intersectional understanding.

Who is a scientist? The relationship between counter-stereotypical beliefs about scientists and the STEM major intentions of Black and Latinx male and female students

BackgroundDespite the diverse student population in the USA, the labor force in Science, Technology, Engineering, and Mathematics (STEM) does not reflect this reality. While restrictive messages about who belongs in STEM likely discourage students, particularly female and minoritized students, from entering these fields, extant research on this topic is typically focused on the negative impact of stereotypes regarding math ability, or the existence of stereotypes about the physical appearance of scientists. Instead, this study builds on the limited body of research that captures a more comprehensive picture of students’ views of scientists, including not only the type of work that they do but also the things that interest them. Specifically, utilizing a sample of approximately 1000 Black and Latinx adolescents, the study employs an intersectional lens to examine whether the prevalence of counter-stereotypical views of scientists, and the association such views have on subsequent intentions to pursue STEM college majors, varies among students from different gender and racial/ethnic groups (e.g., Black female students, Latinx male students).ResultsWhile about half of Black and Latinx students reported holding counter-stereotypical beliefs about scientists, this is significantly more common among female students of color, and among Black female students in particular. Results from logistic regression models indicate that, net of control variables, holding counter-stereotypical beliefs about scientists predicts both young men’s and women’s intentions to major in computer science and engineering, but not intentions to major in either physical science or mathematics. Additionally, among Black and Latinx male students, counter-stereotypical perceptions of scientists are related to a higher likelihood of intending to major in biological sciences.ConclusionsThe results support the use of an intersectional approach to consider how counter-stereotypical beliefs about scientists differ across gender and racial/ethnic groups. Importantly, the results also suggest that among Black and Latinx youth, for both female and male students, holding counter-stereotypical beliefs promotes intentions to enter particular STEM fields in which they are severely underrepresented. Implications of these findings and directions for future research, specifically focusing on minoritized students, which are often left out in this body of literature, are discussed.

Evaluating a Model for Developing Cognitively Diagnostic Adaptive Assessments: The Case of Young Children’s Length Measurement

ABSTRACT We report on an innovative computer-adaptive assessment, the Comprehensive Research-based Early Math Ability Test (CREMAT), using the case of 1st- and 2nd-graders’ understanding of geometric measurement. CREMAT was developed with multiple aims in mind, including: (1) be administered with a reasonable number of items, (2) identify the level(s) of thinking at which the child is operating for each developmental progression (domain) of significant mathematics, and (3) provide information about specific concepts and skills that constitute the cognitive components of thinking involved in various tasks. CREMAT relies on Q-Matrix theory and a resulting blend of sophisticated psychometric and statistical techniques (Rule Space Method, poset models) to determine not only students’ overall performance but also their specific level of thinking along developmental progressions. Results indicated that the current tests range from satisfactory to excellent in their ability to diagnose 1st- and 2nd-graders’ understanding of measurement, but also suggest revisions and implications for the approach. We conclude with a description of why CREMAT is important for early childhood practitioners’ ability to formatively assess and document children’s progress in learning math.

Exploration of self-regulated learning: Mathematical problem solving

Self-regulated learning is needed to regulate and direct itself, adjust, and control self-learning. This study aims to get an overview of students’ self-regulated learning in solving junior high school mathematics problems. This research is a qualitative descriptive study with three research subjects. The data collection techniques used math ability tests, problem-solving tests, self-regulated learning questionnaires, and interview guidelines. The results showed the profile of self-regulated learning raised by junior high school students when solving math problems, especially problems related to SPLDV, namely: 1) Planning, thinking and activation stages: (understanding the problem is expressed in using one’s own language or the language of the problem and there is an estimate of SPLDV completion through arithmetic procedures, logic and elimination substitution methods; 2) Monitoring Stage: monitoring is carried out on the correctness of the variables with or without involving the whole conversation; 3) Control stage: answer checking with reverse technique; and 4) Reaction and Reflection Stage: Explore the difficulties faced related to routine and non-routine problems.

Kemampuan Komunikasi Matematis Siswa SMP Kelas VIII di Kampung Cigulawing

This research is motivated by the students' low mathematical communication skills. The research objective was to obtain a description of the students' mathematical communication skills in class VIII in mathematics learning. The research method is descriptive qualitative. The research subjects were 4 grade VIII students of SMP Negeri 7 Garut. The results showed (1) the students' mathematical communication skills in the data presentation material of class VIII SMP Negeri 7 Garut in Cigulawing Village, were generally said to be less good. Because most students have not been able to meet all the indicators; (2) Students with high mathematical abilities can achieve almost all indicators of mathematical communication skills; (3) Students with moderate mathematical abilities have not mastered several indicators of mathematical communication skills; (4) Students with low math abilities have not been able to master the indicators of mathematical communication skills.

Students' Analogical Reasoning in Solving Trigonometric Problems in Terms of Cognitive Style: A Case Study

This article discusses the analogical reasoning of students' types in solving trigonometric problems based on cognitive styles. This research was conducted at MAN I Probolinggo, eighteen students was asked to complete cognitive style tests and math ability tests. It was found that students' answers can be grouped into two types of cognitive styles, namely systematic and intuitive. From each group, one student was taken to be interviewed with the aim of getting a more detailed explanation of each type of analogical reasoning. The results show that the two types can be explained as follows, first, the type of systematic cognitive style, students can understand the problem given, mention in detail all the information that is known and asked, use all known information about the problem, read and understand the problem, map the structure relational problems, applying a structured way to solve problems that have been planned in advance. In the intuitive cognitive style type, students can understand the problem only by reading the problem once, mention some information that is known about the problem, use the information that is known in the problem, read and understand the problem, apply problem-solving methods. pre-planned but unstructured. Therefore, teachers must encourage and enable students to use analogical reasoning optimally in learning mathematics.

KOMPONEN KETERAMPILAN METAKOGNISI SISWA DALAM PEMECAHAN MASALAH MATEMATIKA DI SMA AL-AZHAR MANDIRI PALU

This research aims to identified and obtain a description metacognition skill components of students in SMA Al-Azhar Mandiri Palu to solving mathematical problem about linear program based on the level of mathematical ability of the students. The type of this research is qualitative research. The subject of this research is the students of class XII D SMA-Al-Azhar Mandiri Palu who have high, medium and low math ability. Data were collected by video recording, test method and interview. The results of this study indicate that subjects with high math ability, namely NF has a complete metacognition skill components that is prediction, planning, monitoring, and evaluation with regular and repetitive patterns. Subjects with medium math ability, namely HN also has a complete metacognition skill components that is prediction, planning, monitoring, and evaluation but the patterns is irregular and repetitive. And the subject of low math ability, namely TS has only three metacognition skill components that is prediction, planning, and evaluation with non-repetitive patterns.

Patience, Cognitive Abilities, and Cognitive Effort: Survey and Experimental Evidence From a Developing Country

This study sheds light on the relationship between cognition and patience by documenting that the correlation between cognitive abilities and delay discounting is weaker for the same group of individuals if choices are incentivized. This study conjectures that higher cognitive effort, which induces higher involvement of the cognitive system, moderates the relationship between patience and cognition. For 107 participants drawn from the adult population in Tbilisi, this study examines the relationship between various measures of cognitive ability and that of patience. Specifically, we consider the relationship between the Cognitive Reflection Test, a numeracy test, self-reported math ability measure, enumerators’ assessments, and incentivized and hypothetical trade-offs between smaller-sooner and larger-later payments.

Approximate multiplication in young children prior to multiplication instruction

Prior work indicates that children have an untrained ability to approximately calculate using their approximate number system (ANS). For example, children can mentally double or halve a large array of discrete objects. Here, we asked whether children can perform a true multiplication operation, flexibly attending to both the multiplier and multiplicand, prior to formal multiplication instruction. We presented 5- to 8-year-olds with nonsymbolic multiplicands (dot arrays) or symbolic multiplicands (Arabic numerals) ranging from 2 to 12 and with nonsymbolic multipliers ranging from 2 to 8. Children compared each imagined product with a visible comparison quantity. Children performed with above-chance accuracy on both nonsymbolic and symbolic approximate multiplication, and their performance was dependent on the ratio between the imagined product and the comparison target. Children who could not solve any single-digit symbolic multiplication equations (e.g., 2 × 3) on a basic math test were nevertheless successful on both our approximate multiplication tasks, indicating that children have an intuitive sense of multiplication that emerges independent of formal instruction about symbolic multiplication. Nonsymbolic multiplication performance mediated the relation between children’s Weber fraction and symbolic math abilities, suggesting a pathway by which the ANS contributes to children’s emerging symbolic math competence. These findings may inform future educational interventions that allow children to use their basic arithmetic intuition as a scaffold to facilitate symbolic math learning.

Ability self-concepts and parental support may protect adolescents when they experience low support from their math teachers

IntroductionExperiencing low support from teachers can be associated with low academic achievement. Nonetheless, individual- (i.e., ability self-concepts) and contextual-level (i.e., parental support) protective factors may help adolescents to display academic resilience. This study examined whether high school students’ math ability self-concepts and parental support can mitigate the possible negative association between perceived low math teacher support and their math achievement. MethodCorrelational data were drawn from the High School Longitudinal Study (N = 14,580, Mage = 17.42 in 11th grade, 51% female), a nationally representative study of high school students in the U.S. The measures of protective factors (i.e., math ability self-concepts and parental support) were obtained from the surveys administered to students and parents in 9th grade. Students’ perceived teacher support and their math achievement score were measured in 11th grade. A series of linear regression analyses were estimated to test our hypotheses. Results & ConclusionsPerceived low teacher support was negatively associated with adolescents’ math achievement. Adolescents’ math ability self-concepts were directly and positively associated with their math achievement. The interaction between perceived low teacher support and ability self-concepts in predicting adolescents’ achievement varied by parental support. The association between perceived low teacher support and adolescents’ math achievement was not statistically significant when adolescents were high on one of the protective factors. That is, high parental support may be protective for adolescents with low math ability self-concepts. This study highlights the interaction between adolescents’ academic motivation and parental support in demonstrating resilience to perceived low teacher support.

Adaptive Reconfiguration of Intrinsic Community Structure in Children with 5-Year Abacus Training.

Human learning can be understood as a network phenomenon, underpinned by the adaptive reconfiguration of modular organization. However, the plasticity of community structure (CS) in resting-state network induced by cognitive intervention has never been investigated. Here, we explored the individual difference of intrinsic CS between children with 5-year abacus-based mental calculation (AMC) training (35 subjects) and their peers without prior experience in AMC (31 subjects). Using permutation-based analysis between subjects in the two groups, we found the significant alteration of intrinsic CS, with training-attenuated individual difference. The alteration of CS focused on selective subsets of cortical regions ("core areas"), predominantly affiliated to the visual, somatomotor, and default-mode subsystems. These subsystems exhibited training-promoted cohesion with attenuated interaction between them, from the perspective of individuals' CS. Moreover, the cohesion of visual network could predict training-improved math ability in the AMC group, but not in the control group. Finally, the whole network displayed enhanced segregation in the AMC group, including higher modularity index, more provincial hubs, lower participation coefficient, and fewer between-module links, largely due to the segregation of "core areas." Collectively, our findings suggested that the intrinsic CS could get reconfigured toward more localized processing and segregated architecture after long-term cognitive training.

The Analyzing of Pisa-based Mathematics Problem Solving Ability based on the Algebra Learning Object

The aim of this study was describing the ability in solving math problems based on PISA change and relationship content based on algebra learning objects. This research was descriptive qualitative study involving 28 students of VIII B class at SMP Negeri 25 Surakarta. The techniques of collecting data used tests and interview, while the techniques of analyzing data were using data reduction, presentation, and drawing conclusions. The results of this study was the students’ problem solving abilities based on four algebra learning objects according to Skemp’s view, namely: 1) using symbols, 2) mathematical models, 3) linear equations and their solutions, and 4) algebraic calculations. The students with high-level math abilities were able to apply four algebra learning objects, namely: using symbols, making mathematical models, linear equations and solving them well, and the calculations correctly. The student’s weaknesses was not accurate in writing on the result of the unit obtained and there were no several symbols in giving information. The students with mid-level math abilities were only able to use symbols and create math models, the writing of the linear equations was correct but the solution was still incorrect because it was like Polya’s stage, so it was not quite right because there are no calculation steps. The students with low-level math abilities were only correct in writing linear equations, the way of solving and calculating the problems were still incorrect, and the writing of mathematical models and using symbols were incorrect.

A meta-analysis of the relation between math anxiety and math achievement.

Meta-analyses from the 1990s previously have established a significant, small-to-moderate, and negative correlation between math achievement and math anxiety. Since these publications, research has continued to investigate this relation with more diverse samples and measures. Thus, the goal of the present meta-analysis was to provide an update of the math anxiety-math achievement relation and its moderators. Analyzing 747 effect sizes accumulated from research conducted between 1992 and 2018, we found a small-to-moderate, negative, and statistically significant correlation (r = -.28) between math anxiety and math achievement. The relation was significant for all moderator subgroups, with the exception of the relation between math anxiety and assessments measuring the approximate number system. Grade level, math ability level, adolescent/adult math anxiety scales, math topic of anxiety scale, and math assessments were significant moderators of this relation. There is also a tendency for published studies to report significantly stronger correlations than unpublished studies, but overall, large, negative effect sizes are underreported. Our results are consistent with previous findings of a significant relation between math anxiety and math achievement. This association starts in childhood, remains significant through adulthood, is smaller for students in Grades 3 through 5 and postsecondary school, is larger for math anxiety than for statistics anxiety and for certain math anxiety scales, and is smaller for math exam grades and samples selected for low math ability. This work supports future research efforts to determine effective math achievement and math anxiety interventions, which may be most helpful to implement during childhood. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Pre-service elementary school teachers’ reasoning profile in solving geometry problems based on mathematics ability

A person’s reasoning can be seen in the solution of the problem he solved. Geometry is effective for developing the ability to think logically or reasoning students. Solve geometry problems that have an abstract object of study required a process of reasoning or reason. The reasoning of a student with a high mathematical ability may be different from the reasoning of a moderate or low-ability student in solving geometrical problems. The purpose of this study is to obtain information about pre-service elemantary school teachers’ reasoning profiles in solving geometry problems based on mathematical ability. The type of research that will be used is descriptive explorative research with qualitative approach. The subject of this research is 3 pre-service elementary school teachers’. Subject selection is based on a written math ability test. The instruments of this study include the main instruments and supporting instruments. The reasoning profile data was obtained through mathematical skills tests and problem-solving test-based interviews. The credibility of the data collected is tested through triangulation. Student reasoning profile of student of pre-service elementary school teacher is able to explain again the thinking process (reasoning or logical argument) clearly.

PROFIL KEMAMPUAN BERPIKIR KRITIS SISWA DALAM MENYELESAIKAN SOAL HIGHER ORDER THINKING SKILLS (HOTS) DITINJAU DARI JENIS KELAMIN

Critical thinking skills are the ability to think individuals in managing information, finding solution, and evaluating the problems obtained based on six criteria, namely (1) Focus, (2) Reason, (3) Inference, (4) Situation, (5) Clarity and (6) Overview. HOTS questions are a type of question that can help hone students' critical thinking skills. This research is a descriptive study with a qualitative approach that aims to describe students' critical thinking skills in solving HOTS questions in terms of gender. The instrument used in this study was a math ability test and HOTS questions. The subjects used in this study consisted of two junior high school students, one male student and one female student with high math ability. The results of the research on male students' critical thinking skills in solving HOTS questions show that male students are able to understand and find the essence of the problem, can provide reasons that support the way male students use, and can draw conclusions using the method that male students have used, so that male students meet the indicators of critical thinking Focus, Reason, and Inference. The ability to think critically of female students shows that female students can understand and find the essence of the problem, can provide reasons that support the way female students use it, can draw conclusions using the method that female students have determined, female students can reveal important factors that support the method used , and can describe the term at every step of the completion, so that female students meet the indicators of critical thinking Focus, Reason, Inference, Situation, and Clarity.
 Keywords: Critical Thinking, Higher Order Thinking Skill