Math Skills Research Articles

Implications of neural integration of math and spatial experiences for math ability and math anxiety.

Mathematical and spatial abilities are positively related at both the behavioral and neural levels. Much of the evidence illuminating this relationship comes from classic laboratory-based experimental methods focused on cognitive performance despite most individuals also experiencing math and space in other contexts, such as in conversations or lectures. To broaden our understanding of math-space integration in these more commonplace situations, we used an auditory memory-encoding task with stimuli whose content evoked a range of educational and everyday settings related to math or spatial thinking. We used a multivariate approach to directly assess the extent of neural similarity between activity patterns elicited by these math and spatial stimuli. Results from whole-brain searchlight analysis revealed a highly specific positive relation between math and spatial activity patterns in bilateral anterior hippocampi. Examining individual variation in math-space similarity, we found that greater math-space similarity in bilateral anterior hippocampi was associated with poorer math skills and higher anxiety about math. Integration of neural responses to mathematical and spatial content may not always portend positive outcomes. We suggest that episodic simulation of quotidian contexts may link everyday experiences with math and spatial thinking-and the strength of this link is predictive of math in a manner that diverges from math-space associations derived from more lab-based tasks. On a methodological level, this work points to the value of considering a wider range of experimental paradigms, and of the value of combining multivariate fMRI analysis with behavioral data to better contextualize interpretations of brain data.

Accounting for learning environments in academic screening

Within multi-tiered systems of support (MTSS) practice and research, students' need for academic intervention is often determined by comparison of students' screening scores to cut scores. We examined the degree to which the relationship between students' fall screening data (i.e., Measures of Academic Progress) and their outcome on a spring summative state test related to the quality of the classroom learning environment and how core instructional strategies influenced this relationship. Fall screening data and spring state test outcomes in English/language arts (ELA) and math were analyzed from a sample of 72 teachers and 1554 third-grade students. Multilevel logistic regression revealed that the association between students' ELA or math skills at the beginning of a school year and state test at the end of the year were not identical across classrooms (odds ratios range = 0.81–0.92). A significant interaction was observed between students' fall ELA screening scores and teachers' instructional strategy use in predicting state test outcomes (p = .03). Teacher strategy use was found to be a significant contributor to false positives in screening decisions based on optimal cut scores for ELA (p = .003), but not math.

A proposal in STEM for virtual exchange held by Computer Science and Applied and Computational Mathematics programs

In this practice report, we present a practical experience of a virtual exchange carried out by a Belgian and a Brazilian professor from two research intensive universities in Northwestern Europe and in Latin America, respectively. Particularly, this paper is focused on how we designed a common syllabus in a specific topic of STEM, aiming to explore math and computer science skills of the students, and how we implemented this virtual exchange step by step, despite the students being from different courses and different levels of degree. In addition, we discuss the pros and cons of the process from the instructors’ perspective as well as under students’ views, and provide some suggestions to be applied and tested for future virtual exchanges in this field. Overall, this practice report reinforces our deep reflection about the results and desire to share our STEM syllabus to encourage other colleagues to apply it (or modify it) for different courses.

Effect of Critical Thinking Skills on Misconceptions of Students in Learning Mathematics at the Elementary School Level

The aim of mathematics education in schools is to create logical reasoning and critical thinking ability in students. These skills development not only help students understand better but can also help remove the misconceptions they have about mathematical concepts. The purpose of this study was to investigate how critical thinking skills can help address misconceptions in mathematics learning at the elementary level. The research used an A-B-A design to determine the effects of an intervention, which is a perfect design for this purpose. 35 eighth-grade students who were enrolled in the current academic year were participants in this study. Three researcher-developed tools facilitated data collection. The first and initial tool was called the Test of Critical Thinking Skills (ToCTS), which measured students' critical thinking math skills. The second tool, the Test of Misconceptions (ToM), was developed to identify specifically how the students thought they were solving the problems. Finally, an interview protocol was used to learn about the students' reasoning regarding their answers on the tests. The mathematics curriculum of grades three to eight formed the basis of the development of these instruments, both close-ended and open-ended questions. Descriptive and inferential statistical methods were used in data analysis, and qualitative content from the interviews was applied to thematic analysis. A poor level of critical thinking skills in factoring equations and selecting proper solving methods for linear equations was shown by students. In addition, students had difficulty solving complete mathematical problems with linear equations. A significant gap was identified in their understanding and application of the BODMAS rule during algebraic operations. Based on these findings, the study recommended fostering critical thinking skills to improve students' abilities in factoring equations. Teachers should provide clear and comprehensive guidance to help students solve mathematical problems effectively. To address misconceptions, educators could introduce simplified problem-solving methods and reinforce students’ understanding of fundamental operations and rules. Specifically, it is essential to provide targeted instruction on the application of the BODMAS rule in algebraic contexts to enhance students' problem-solving capabilities.

Parental Perceptions of Children’s Schooling in Urban Squatter Families in Bangladesh

SYNOPSIS Objective. This paper examines parents’ perceptions of their school-age male and female children’s performance in nine domains of school work and SES factors that are associated with fathers’ and mothers’ perceptions of children’s academic performance in urban squatter (baste) families in Bangladesh. Design. Fathers and mothers from 120 two-parent families with an elementary school-age child (M = 9.08 years) participated in the study. Fathers and mothers were interviewed separately in their homes. Results. Fathers and mothers did not differ in reporting male and female children’s school performance in all nine areas of school work, and both male and female children performed equally well. Fathers’ education was positively associated with their perceptions of children’s commitment to school, peer interactions, and math and reading skills; child age showed a positive association with children’s participation in school activities; and the number of children in the family was negatively related to children’s math skills. Mothers’ education and marital satisfaction were positively linked to children’s asking for academic help, and mothers’ age and children’s age were positively associated with children’s participation in school work. Marital satisfaction was positively related to children’s performance in math and reading. Conclusions. Findings are discussed with regard to parents’ changing views on gender roles, the importance of children’s education, and early childhood development in squatter families. The policy implications of the findings are to buttress parents’ involvement in their children’s education in squatter families in the majority world countries.

Examining the use of bilingual accommodations in digital math assessments: User perceptions

Digital math assessments with bilingual accommodations allow multilingual learners to use their entire linguistic repertoire to showcase their knowledge and skills. The bilingual accommodations, which include tools like language translation and audio prompts in both English and Spanish, are designed to be adaptable, giving multilingual learners the freedom to view or listen to the items in either language and to write or say their responses in either language or a combination of both. This study examined how 56 middle school emergent bilingual learners used these bilingual accommodations and explored the perceptions of teachers and students regarding these accommodations. This study provides evidence regarding using bilingual accommodation in math assessments for middle school emergent multilingual learners. The results showed how students used their full linguistic repertoire and language modalities to showcase their math knowledge and skills. Both teachers and students reported having positive perceptions of the bilingual accommodations, reinforcing its responsiveness to different learners’ needs and preferences.

A longitudinal study of math skills in heritage bilingual children: profiles of strengths and weaknesses.

Many children are exposed to a heritage language in the home context, and they learn mathematics in the school context in the societal language (Italian in the present study). More evidence is needed on how Heritage Bilinguals (HBs) perform in different subtypes of numeracy and mathematics skills in a longitudinal perspective. This longitudinal study aimed to analyze the mathematical skills of heritage bilingual children. 220 HBs (50.5% female, from different linguistic/ethnic groups, including Indo-Iranian, Arabic, Chinese, Romanian, Albanian and Slavic languages) and 440 monolinguals (46.8% female, mostly Italian) were followed from second to third grade (aged between 7 and 9 years). The following tasks were administered: dictation, symbolic comparison, number line, mental calculation, multiplication tables, approximate calculation, problem-solving and written calculations. The results showed an advantage for HBs in approximate calculation, but they underperformed in problem-solving, multiplication tables, and mental calculations. A profile analysis highlighted the percentages of children at risk for math impairment. The study provides a longitudinal profile of strengths and weaknesses in the mathematics profile of children with HBs, with developmental trajectories that vary according to verbal load. The discussion focuses on the role of verbal load in math tasks in the assessment of HBs, and implications for clinical and educational contexts.

Mathematical Thinking and Learning in Early Childhood: A Consolidated Qualitative Synthesis of Cutting-Edge Research Literature

This study aims to synthesize current research on early childhood mathematical thinking and learning, focusing on cognitive development, instructional strategies, and environmental influences. The study provides a comprehensive qualitative analysis, integrating diverse theoretical frameworks and recent empirical findings for a nuanced understanding of early math education. Methodologically, it employs a thematic synthesis of qualitative studies, systematically reviewing literature from various academic databases to identify key patterns and themes. The research design involves coding text, developing descriptive themes, and generating analytical themes from peer-reviewed studies published between 2014 and 2024. The primary outcomes highlight the significant impact of play-based learning, interdisciplinary approaches, and parental involvement on early mathematical development. Additionally, the study underscores the role of technology and supportive learning environments in enhancing children's math skills. Conclusions emphasize the importance of holistic and culturally responsive educational practices. The practical implications provide valuable insights for educators, policymakers, researchers, and parents aiming to improve early childhood math education.

Math Talk in Play Contexts: Relations Between Parent and Child Math Language and Early Math Skills

Math Talk in Play Contexts: Relations Between Parent and Child Math Language and Early Math Skills

Формирование элементарных математических представлений у детей с ограниченными возможностями здоровья (с нарушением зрения)

The aim of this study is to improve the math skills of preschool children (5-7 years old) with visual impairment. In this context, it is expected that the target behavior of children with visual impairment will be changed through the creation of a specialized educational space that promotes the formation of mathematical abilities, arithmetic skills, creativity, ability to plan and organize their activities. The research group consists of 48 preschool children (5-7 years old) with visual impairments. The study was conducted in the fall of the 2023-2024 school year. During the study, the preschoolers received eight weeks of training to improve math skills. The study found that numeracy and math skills in preschool children with visual impairments had a positive effect on cognitive development, fine motor skills, and motivation to learn.

The Influence of Social Competition and Maths Anxiety on Game Performance

Digital Game-Based Learning (DGBL) uses serious games to deliver educational content. DGBL has the potential to aid children’s development of maths skills, providing educators with alternatives to traditional mathematics teaching. However, the efficacy of serious games can be affected by their attributes, including whether they are single or multi-player. While competition in a multi-player environment may enhance players’ interest and motivation, potential social pressure may lead to anxiety and affect performance. In maths education, there are additional challenges. Mathematics Anxiety (MA), the negative emotional response to mathematics, may interact with game features and impact players’ experience. This study assesses players' performance in a digital maths game called ’Seven Spells’ across two different game modes (vs. Human and vs. CPU), and it also investigates whether MA levels impacted players’ performance. 43 children from two classes in an Irish primary school participated in thisstudy. Each class played a different game mode of the ‘Seven Spells’ game, one group playing against computer-controlled characters (vs. CPU) and the other playing against their classmates (vs. Human). The game mechanics were identical between the two competition game modes. The children completed the modified Abbreviated Mathematics Anxiety Scale (mAMAS) and a mathematics questionnaire before participating in the intervention, which included 4 sessions. They also participated in a focus group session at the end of the intervention. Data on their gameplay were collected throughout the first three sessions and analysed through multiple linear regression models to investigate possible connections between MA, maths knowledge, game modes and game performance. The results of the multiple linear regressions indicate that game performance was positively influenced by the duration of gameplay and the complexity of moves — measured by the number of moves and cards used — while being negatively affected by MA. However, a significant interaction between MA and the competition game mode was observed, suggesting that MA had a more pronounced negative impact on players in the vs. Human game mode compared to the vs. CPU game mode.

Decision-Based Learning as an Approach for Teaching Statistics in a Peruvian University

Many students find learning statistics difficult, especially novice learners. Instructors also struggle to teach statistics due to many challenges, such as students’ misconceptions, lack of math skills, negative attitudes, and deficient instructional methods. A new pedagogical approach called Decision-Based Learning (DBL) has been developed to help instructors and students; however there are limited studies about teachers’ and students’ experiences with this method, particularly in international settings. For this project, a group of Peruvian university professors were trained to use DBL. This qualitative study sought to understand the experiences of one Peruvian statistics instructor and her students implementing DBL pedagogy and software. The DBL software was created to help instructors easily implement DBL. Findings identify specific benefits and challenges participants faced when using DBL. Benefits included the growth of students’ confidence in solving statistical problems and instructor satisfaction. Challenges included time-consuming instructor initial preparation and students’ learning transfer issues.

Future Teachers' Perceptions towards Incorporating Board Games to Teach Mathematical Skills in History Classes

Literature has emphasized the value of multidisciplinary learning strategies and the necessity of educating students to solve complex problems. It also pointed out the importance of teacher’s beliefs in their practices. The purpose of this study is to understand how future teachers recognize the board game Caravelas as a didactic tool to help elementary school students develop math skills in History and Geography Portugal (HGP) classes, in a multidisciplinary way. A board game intervention was employed in the study, and both quantitative and qualitative data were gathered from sixteen future teachers enrolled in the Didactic of HGP course during their third year of the Basic Education programme. Two questionnaires were used along with a focus group discussion. The findings indicate that this group of future teachers thinks Caravelas can help students achieve their learning goals in mathematics and HGP, as well as develop their reasoning, problem-solving, and social skills. Future teachers believe Caravelas can be used as a didactic tool to integrate mathematics into HGP subjects and support multidisciplinary learning.

Math Anxiety and Poor Math Competence: A Longitudinal Investigation of Students Failing to Achieve the Math Skills Required by School Curricula

ABSTRACT Mathematics anxiety (MA) has emerged as a significant concern in recent years, recognized for its potential to interfere with learning processes. Our study delved into exploring the relationship between the presence and level of MA and the ability to acquire math skills required by the school curriculum. For this purpose, secondary school students were monitored during their first year of study. A questionnaire designed to assess MA and a math skills assessment test were administered on two separate occasions: initially at the end of the first term and subsequently at the conclusion of the second term. The results of the end-of-year tests indicated that students with high levels of MA, assessed at the beginning of the school year, showed a significantly greater risk of failing to achieve the required competence. These findings seem to support the notion that a high level of MA can significantly contribute to hindering the acquisition of educational outcomes.

A longitudinal study on the predictors of early grades learning attainments in low-and-middle-income countries: Evidence from Tanzania

Strands of evidence from high-income countries has consistently indicated that early learning attainments predict later learning achievements. However, less are known about these issues from low-and-middle-income countries, particularly from the sub-Saharan region. This longitudinal study examined the extent to which children’s school-entry (N = 597; mean age = 6.34 years) early reading and early math skills predicted their later learning achievement in a low-income country, Tanzania. Further, given the existing disparities of quality of educational services, families’ income, and early learning achievements, the sample included children and families from both rural and urban contexts. Data were collected using Measure of Early Learning Environments (MELE) for controlling of school quality, Early Grade Reading Assessment (EGRA) and Early Grade Math Assessment (EGMA) for children’s tests, and parents’ questionnaire for home-related variables. Controlling for family socioeconomic status, intervention status, urbanicity settings, and parental education, findings indicated that school-entry math skills were significantly predictive of children’s end of Grade 2 reading and math achievement. However, while school-entry early reading skills predicted end of Grade 2 reading achievement, it did not predict later math achievements. This article extends research on links between elements of transition to school and later achievement across countries, thus, its implications are discussed.

Does MATmatics Work? Impact of Early Numeracy Intervention on Students’ Math Skills

Early knowledge of numbers, relations, and operations are foundations for student success. Weak foundational number skills can lead to later difficulties, thus early identification and targeted interventions for students with weak number skills can help stop them from falling further behind. In the current study, we tested the effectiveness of MATmatics, a tier 2 intervention that targeted early numeracy skills for at-risk students in grades 2 and 3. Students (N = 45) were quasi-randomly assigned to either an intervention group, or a wait-listed control group. Using a series of 2 (group: intervention, control) x 2 (test timing: pre-intervention, post-intervention) mixed ANOVAS, we found that the math skills (measured with the Early Math Assessment@School numeracy screener) of students assigned to the intervention group improved at a faster rate than the math skills of their waitlisted control peers. The intervention was effective.

Comparison of Measures of Mathematical Achievement: EMA@School and Star Math Assessment

There is a need for valid and reliable screeners to assess students’ early math skills and help educators identify students who are at-risk for math difficulties. The Early Math Assessment @School (EMA@School) has been used to test the foundational number skills (i.e., numbers, relations, and operations) of over 200,000 Canadian students. In this study, we compared the structure, content, and student performance on the EMA@School to STAR Math, a curriculum-based math screener. Students (N = 230) in Grade 3 completed the EMA@School once (Fall 2023) and Star Math twice (Fall 2023, Winter 2024). EMA@School scores were strongly correlated with StarMath scores. Moreover, skills in the three foundational subdomains of number, relations, and operations, all uniquely predicted performance on StarMath. Finally, most students classified “at-risk” based on the EMA norms were also “at-risk” based on StarMath norms. Together, these findings provide convergent and criterion validity for the EMA.

Child development lags and learning trajectories in primary school in Uruguay: compensation or divergence? / Rezagos en el desarrollo infantil y trayectorias de aprendizaje en la enseñanza primaria de Uruguay: ¿compensación o divergencia?

We evaluate two rival hypotheses of: (a) divergent trajectories — or cumulative learning gaps — between children with severe and moderate developmental lags and developmentally on-track children; and (b) convergent trajectories — which predict the inverse pattern. We estimate growth curves using panel data from a cohort of students first assessed by the Early Years Evaluation (Uruguay) at the end of kindergarten (age five), assessed up to three times in language and mathematics on an annual basis during years three to five since their transition to first grade. By the third year in school, substantial differences are found in reading and maths skills between children that did and did not show early developmental lags (effects range between .31 and .46 sd). We find a prevalent pattern of divergence in learning gains between years three to five in school (gaps increase by .10 sd per year). Our results suggest that tackling academic gaps will require timely interventions based on early identification of children who are academically at risk. Uruguay has developed early developmental assessment tools and learning monitoring systems, both of which should serve as the basis of an effective early warning system to deal with learning disparities from early ages.

Utilizing task with scaffolding: growth of students' mathematical understanding from layers of image having to property noticing

Introduction. Learning mathematics accompanied by understanding is an essential component of factual and procedural knowledge skills practical for students in solving real-life problems. Errors in solving systems of linear equations in two variables (SPLDV) among students can be caused by various factors, including students' lack of understanding of this concept, so this problem must be studied in depth by utilizing task with scaffolding. The research aimed to explore the potential of a task to foster mathematical understanding of students from the image-having layer to the property noticing layer in the learning context of a system of linear equations in two variables (SPLDV). Study participants and methods. The study involved three students in grade 8 at a junior high school in Indonesia. They were selected based on their mathematical ability (low, moderate, and high) based on their accumulated score reports in grade 7 and information from the teacher who taught them. This study employed a qualitative research approach, data collection was carried out by giving task to students, observing, and interviews them while doing the task, and data analysis began with transcription and organizing the results of interviews and student task, followed by identification and classification of difficulties faced by students. The results. The study showed that student with low mathematical ability has difficulty recognizing patterns or relationships between coefficients and variables in equations. Even with the help of scaffolding, the student still did not succeed in strengthening her understanding to complete the task given, so her understanding only shifted slightly from the image having layer and could not move completely to the property noticing layer. Next, a student with moderate mathematical ability had a sufficient understanding of the concept of variables and coefficients. However, she still needed additional help to complete task, especially in determining the value of variable. She was observed to be already at the property noticing layer of understanding because she had been able to identify the property of two linear equations in two variables that is equivalence and complete the task given. Lastly, the student with high mathematical ability could understand the relevant mathematical concepts well. She could complete the task assigned well despite folding back and scaffolding. Thus, this student's understanding reached the property noticing layer. Conclusions. The research showed differences in the growth of mathematical understanding from the image having layer to the property noticing layer among junior high school students with low, medium, and high mathematical ability. The student with lower math skills was only slightly shifted from the image having layer and could not be transferred completely to the property noticing layer. The student with moderate mathematical ability had reached the layer of understanding properties because she was able to identify equivalent properties of two linear equations in two variables and complete the given task. Lastly, the student with high mathematical skills has reached the layer of property noticing.

Technology-Integrated Instructions and Basic Mathematics Skills Acquisition in Public Secondary Schools in Rwanda: A Case of Nyagatare District

This research investigated the effects of technology-integrated instructions on basic mathematics skills in Rwandan secondary education. The study aimed to assess the types of technology-integrated instructional methods used for acquiring basic math skills in Rwandan public secondary schools, assess the level of mathematics skills and performance in these schools, and determine the relationship between technology-integrated teaching and the acquisition of basic math skills. Schools were selected based on their location and type. Theory used in this research project was cognitive load theory and constructivism theory. The target population included 214 teachers, 422 students, and 80 head teachers, total of 716 respondents, with a sample size of 257 participants. Data was gathered using questionnaires, interviews, and observation, employing purposive, stratified, and simple random sampling methods. Both qualitative and quantitative data collection and analysis methods were used. Qualitative data were analysed through content analysis, while quantitative data were presented using descriptive statistics (frequency, percentage, mean, and standard deviation) and inferential statistics (correlational and regression analysis) with IBM SPSS Version 21.0. Findings for the first objective showed that 85.7% of respondents strongly agreed on the use of computer algebra systems, 93.5% strongly agreed on blended learning and online education, 87.0% strongly agreed on the use of mobile and handheld devices, and 63.6% strongly agreed on software applications for mathematics calculations as methods influencing the acquisition of basic math skills. Regarding the second objective, 87.0% of teachers strongly agreed that verbal counting ability indicates math skill levels, 93.5% agreed that identifying more and less of a quantity shows math skills, 85.7% agreed on problem-solving skills as an indicator, 66.2% on recognizing numerals, and 77.9% on understanding size, shape, and patterns as indicators of math skills and performance. The study revealed a strong positive relationship between skills such as identifying quantities, verbal counting, problem-solving, and blended learning or online education. Problem-solving skills were also positively linked with computer algebra systems and blended learning. The significance of verbal counting was confirmed, as indicated by a p-value of less than 0.05. The study recommends using digital tools like calculators and graphing software to improve understanding of mathematical concepts. Real-world examples and multimedia can foster problem-solving abilities, while group work can enhance teamwork and communication skills. Educational software and online platforms provide personalized learning, enabling students to learn at their own pace and receive specific support.