Implications For Mathematics Education Research Articles

Enablers and obstacles in teaching and learning of mathematics

This paper presents results of a systematic review of papers published at the LUMAT journal on the current issues positively and negatively affecting teaching and learning in mathematics, in concurrence with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. The analysis also offers insight into the most studied topics in mathematics education research, including key demographic and methodological characteristics such as year of publication, participants, education level, research methodologies, and research focus. Data was gathered from the studies published in the LUMAT: International Journal on Math, Science and Technology Education, starting from its first volume in 2013. So far, 225 articles were published in this journal, with 133 studies written in English and 51 studies related to mathematics. Although earlier studies support the notion that mathematics education is mostly traditional, this review suggests current research has thorough and positive outcomes, such that mathematics educators are likely to implement non-traditional approaches, encouraging student engagement, peer collaboration, and mathematical discourse. Certainly, in such learning environments, students tend to feel more motivated and less anxious about learning mathematics. They may also be more active and responsible in their learning, collaborate with peers, and get into mathematical discussions. Yet, there are also a number of difficulties and obstacles highlighted both in teaching and learning of mathematics. The findings might inspire several instructional implications for mathematics educators, curriculum developers, and researchers. Recommendations are given to add into what the existing literature claims and offer greater empirical evidence to support the verdicts.

Cognitive Skills in Basic Mathematics of College Freshmen in the Philippines

Many students consider mathematics as the most dreaded subject in their curriculum, so much so that the term “math phobia” or “math anxiety” is practically a part of clinical psychological literature. This symptom is widespread and students suffer mental disturbances when facing mathematical activity because understanding mathematics is a great task for them. This paper described the students’ cognitive skills performance in Basic Mathematics based on the following logical operations: Classification, Seriation, Logical Multiplication, Compensation, Ratio and Proportional Thinking, Probability Thinking and Correlation Thinking as it serves a critical element of teaching and learning, that is determining the current position of the learners’ mathematical capacity. Its implications for mathematics education were also revealed. A descriptive quantitative design was used in this study. The study included 1011 first-year college students from six state universities in the Philippines who were enrolled in the Bachelor of Science of Secondary Education Program during the first semester of the Academic Year 2019-2020. This study made use of the teacher-made test called the Test on Logical Operations. Findings revealed that the cognitive skills achievement of the first year BSE students from different state universities in the Philippines falls under the category of late concrete operational stage. As a result, students are unable to perform the logical operational skills expected of their age. At their age level, they are expected to be under the formal operational stage based on Piaget’s stages of cognitive development. These findings revealed a weak mathematical education foundation among students which requires immediate attention. This reality should be recognized by educational planners and implementers when making curricular and other instructional decisions.

Students’ experiences with remote learning during the COVID-19 school closure: implications for mathematics education

This paper reports the findings of a descriptive survey research that explored secondary school students' experiences with mathematics remote learning during the Corona Virus Disease 2019 (COVID-19) school closure. The study involved 367 students of ages 13 to 21 selected from six secondary schools in Kitwe district of Zambia using the cluster random sampling method. Using a mixed-methods research approach, quantitative and qualitative data were merged to provide a comprehensive analysis of the main findings in the context of the existing literature, the government's response to COVID-19 school closure, and the challenges associated with remote learning during that time. Research findings show that more than 56% of the respondents did not have sufficient access to Information and Communication Technologies (ICT), electricity, and internet services. Most of these respondents also held a belief that mathematics is a subject that is best learned with face-to-face interactions between the teacher and students, and among students. These results suggest a need for the education systems in Zambia and other similar contexts to put up infrastructure that supports the blended and online learning models during and after the COVID-19 pandemic.

Limitations Of Pert/Cpm In Construction Management Planning: Inputs To Mathematics In Architecture Education

This research identified the roadblocks or shortcomings of PERT/CPM in the context of a construction company and suggested a plan to address the identified gaps. The researchers used a descriptive research design to discover the shortcomings of the PERT/CPM in construction management planning, especially in the Cabanatuan City, Nueva Ecija, Philippines construction industry. As a result, PERT/CPM is a project management approach that is useful in the basic administrative functions of planning, scheduling, and control. These days, business houses undertake massive projects that take years to complete before commercial development can begin. While this tool can be very useful, the majority of respondents agreed that it has limitations, such as; PERT/CPM can become ineffective and difficult to manage if it is not well-defined and stable for active control of a project; PERT/CPM requires frequent updating and revising of calculations, which is an extensive and time-consuming exercise that requires highly specialized knowledge; PERT/CPM requires frequent updating and revising of calculations, which is an expansive and time-consuming exercise that requires highly specialized knowledge; Furthermore, it is unable to efficiently accommodate abrupt shifts in the ground plan's execution. However, despite its limitations, PERT/CPM is still recommended for construction management planning, especially in large projects. The project manager must always have a contingency plan in place so that the quality of his or her work and projects won’t be jeopardized. In order to make the best use of all available resources in their production, a cost-benefit analysis must be performed, as well as additional research about PERT/CPM. The study's findings have implications for mathematics education in architecture.

Students’ Mathematical Learning Behaviour in Teaching-for-Understanding Classes: Senior High School and First-Year University Students’ Views

Educational mathematics researchers and educationists emphasise teaching for understanding. However, does it influence students’ mathematical learning behaviour? The purpose of this study was to explore late adolescent students’ views on mathematical learning behaviour in teaching-for-understanding classes. Content analysis of secondary data from exploratory studies, where students responded to open-ended questions on metacognition, indicated that mathematical learning behaviour hardly involved focussing on understanding. The discussion presents implications for mathematics education and suggestions for education in general.

Components of Mathematical Problem Solving Competence and Mediation Effects of Instructional Strategies for Mathematical Modeling

This study is aimed at investigating the relationships between the components of problem solving skills (four procedural components and modeling competence) and the impact of instructional strategies (collaborative learning and problem posing) on students’ mathematical modeling competence. A survey on students’ mathematical problem solving competence, that was comprised of 40 items, was administered to 1,224 students in Korea and their responses were analyzed quantitatively (exploratory factor analysis, confirmatory factor analysis, and path analysis). The results indicated that students’ competencies regarding procedural components of mathematical problem solving positively affected their mathematical modeling competence. Additionally, instructional strategies utilizing collaborative learning and problem posing mediated and synergized the effect in terms of procedural components of mathematical problem solving and mathematical modeling competence. The study also discusses its contributions to and implications for mathematics educators and teachers.

The relationship between mathematics interest and mathematics achievement: mediating roles of self-efficacy and mathematics anxiety

This study investigates the mediating roles of self-efficacy and mathematics anxiety on the effects of mathematics interest on mathematics achievement. A total of 158161 eighth grade students from 4 province of China participated in the large-scale survey. The findings reveal that (1) mathematics interest had a direct and positive effect on students’ mathematics achievement; (2) the positive relationship between mathematics interest and mathematics achievement was partially mediated by self-efficacy; (3) self-efficacy and then mathematics anxiety serially mediated the relationship between mathematics interest and mathematics achievement, but the effect of self-efficacy on mathematics anxiety was relatively smaller. Implications for mathematics education and suggestions for future study are discussed.

Low-numerate adults, motivational factors in learning, and their employment, education and training status in Germany, the US, and South Korea

Drawing on the PIAAC data, in this paper I examine how motivational factors such as motivation to learn and grit are related to low-numerate adults’ employment status and their actual participation in lifelong learning in Germany, the United States and South Korea. In particular, the study uses PIAAC self-reported data on the degree to which the respondent “likes learning new things”, and “likes to get to the bottom of difficult things” as proxies of motivational factors in adult learning. Findings show that across three countries both motivation to learn and grit have independent relationships with adults’ employment status and actual participation in adult learning. Considering that low-skilled adults are the ones who need further learning the most, yet are repeatedly reported to have the lowest rate of participation in further learning, these findings highlight the motivational factors in adult learning. They also suggest that motivation to learn and grit may mitigate the disadvantages that ‘vulnerable’ adults experience due to low numeracy skills. Implications for mathematics educators and adult education research are discussed.

Use and Abuse of Calculators: Implications for Mathematics Education

Fostering mathematical understanding and sense for numbers is an objective for current mathematics education. This paper presents a historical vision of the use of numbers and of calculation processes and reflects about the current need of electronic calculators. The coexistence of two different mathematical systems, one based on the Greek axiomatic mathematics and another, the floating point system, used in electronic calculators, can lead to some confusions that which affects the teaching of mathematics, especially in the numerical sense development. The paper also presents common mistakes caused by the missing verification of the results from calculations or lack of awareness about the limitations of calculators. Finally, the implications those elements have on the mathematical education are presented together with some conclusions.

You can count on your fingers: The role of fingers in early mathematical development

Even though mathematics is considered one of the most abstract domains of human cognition, recent work on embodiment of mathematics has shown that we make sense of mathematical concepts by using insights and skills acquired through bodily activity. Fingers play a significant role in many of these bodily interactions. Finger-based interactions provide the preliminary access to foundational mathematical constructs, such as one-to-one correspondence and whole-part relations in early development. In addition, children across cultures use their fingers to count and do simple arithmetic. There is also some evidence for an association between children’s ability to individuate fingers (finger gnosis) and mathematics ability. Paralleling these behavioral findings, there is accumulating evidence for overlapping neural correlates and functional associations between fingers and number processing. In this paper, we synthesize mathematics education and neurocognitive research on the relevance of fingers for early mathematics development. We delve into issues such as how the early multimodal (tactile, motor, visuospatial) experiences with fingers might be the gateway for later numerical skills, how finger gnosis, finger counting habits, and numerical abilities are associated at the behavioral and neural levels, and implications for mathematics education. We argue that, taken together, the two bodies of research can better inform how different finger skills support the development of numerical competencies, and we provide a road map for future interdisciplinary research that can yield to development of diagnostic tools and interventions for preschool and primary grade classrooms.

God becomes beautiful … in mathematics

This article is transdisciplinary in that it touches on the disciplines of both mathematics and theology. It is about the mysterious link between truth and beauty in mathematics. It uses the theological pattern laid by the practical theologian Bohren in his book, God’s Becoming Beautiful. Mathematics can be seen as science or art. I argue that in both cases, we could conclude that God becomes beautiful in mathematics. This leads to the observation that there is some spirituality in mathematics. This insight might also have practical implications for mathematics education in schools.

Elaborating the later Vygotsky’s radical initiative on the nature and function of language: implications for mathematics education

Scholars interested in the function of language in mathematical learning often draw on Vygotsky, whose early work on word meaning has shaped many research studies. However, near the end of a rather short life, Vygotsky heavily critiqued his own previous work and began to sketch a radical theory revision, which overturns much of what he had done and is famous for. The purpose of the present study is to elaborate a possible avenue of such a theoretical revision. This study develops the new theory in the course of an exemplary analysis. The data derive from a scientific laboratory, where three scientists discuss a graph as it evolves in real time before their eyes and as a result of transformations designed to recover the real signal from the noise that is apparently present. Implications of the emerging theory for mathematics education are discussed.

From classroom environment to mathematics achievement: The mediating role of self-perceived ability and subject interest

Drawing on Bandura's triadic reciprocal causation model, perceived classroom environment and three intrapersonal factors (mathematics self-efficacy, maths interest and academic self-concept) were considered as predictors of test performance in two correlated mathematics assessments: a public examination (GCSE) and an on-line test, both taken by UK pupils at age 16 (n=6689). Intrapersonal factors were significantly associated with both test scores, even when the alternative score was taken into account. Classroom environment did not correlate with mathematics achievement once intrapersonal factors and alternative test performance were included in the model, but was associated with subject interest and academic self-concept. Perceptions of classroom environment may exercise an indirect influence on achievement by boosting interest and self-concept. In turn, these intrapersonal factors have direct relationships with achievement and were found to mediate the relationship between perceived classroom environment and maths performance. Findings and their implications for mathematics education are discussed.

What’s missing in longitudinal studies conducted in the U.S. with implications for mathematics education?

ABSTRACT‘What works’ policies are the latest incarnation of best practices in educational research. Instituted by various organisations internationally, they define what kind of research counts as ‘evidence’ for reform-oriented decision-making. While some countries rely on systematic analyses and meta-analyses, the U.S. favours primary quantitative longitudinal research designs as evidence. Critics claim that institutionalising methods will distort educational research. This commentary discusses these two concerns about the research designs favoured in the American ‘what works’ milieu: missing research and missing data. To explore whether those concerns are warranted, we focus on mathematics education, a national priority in the U.S. After establishing enduring questions in mathematics education, we provide primers on quantitative longitudinal research designs and the analysis of missing data due to attrition. Then, we address these questions about the state of research: As a research community, are we missing research with implications for mathematics education? Are we missing data with implications for the inferences that can be made? This review of research questions and analyses in recent studies suggests missing data poses a greater threat than missing research. Finally, we make recommendations for minimising the risk of missing evidence that will be of interest to international educational researchers in any discipline.

Early Numeracy and Literacy: Untangling the Relation Between Specific Components

Although it is evident that advanced aspects of numeracy are dependent on the successful acquisition of early skills, this developmental process does not occur in isolation from other academic factors. Early literacy skills are intertwined with the acquisition of early numeracy skills, particularly at the informal numeracy and numeral knowledge phases. However, the localization of these domains’ impact in early numeracy development is unclear. To address this issue, 180 preschool children 3.13 to 5.88 years (51.1% female, 66.7% Caucasian, 14.4% African-American, 4.4% Hispanic, 14.4% other race/ethnicity) were assessed on measures of print knowledge, vocabulary, informal numeracy, and numeral knowledge. Results indicated that the relation between language and numeral knowledge is fully mediated by informal numeracy skills and the relation between informal numeracy skills and numeral knowledge skills is partially mediated by print knowledge. Explanations of the findings, implications for mathematics education, and future directions are discussed.

Increasing cognitive inhibition with a difficult prior task: implications for mathematical thinking

Dual-process theories posit two distinct types of cognitive processing: Type 1, which does not use working memory making it fast and automatic, and Type 2, which does use working memory making it slow and effortful. Mathematics often relies on the inhibition of pervasive Type 1 processing to apply new skills or knowledge that require Type 2 processing. In two studies, we demonstrate that giving participants a difficult task (Raven’s Matrices) before a task that requires the inhibition of intuitive responses (the Cognitive Reflection Test) significantly improves performance. Our findings suggest that encountering a difficult task that requires Type 2 processing before completing a task that requires inhibition of Type 1 processing may encourage an enduring ‘Type 2’ mindset, whereby participants are more likely to spontaneously use Type 2 processing for a period of time. Implications for mathematics education are discussed.

The cognitive demands of understanding the sample space

According to our analysis of cognitive demands, the concepts of classification, logical multiplication and ratio provide a basis for understanding sample space. These basic concepts develop during the elementary school years, which suggest that it is possible to teach elementary school children effectively about sample space. This hypothesis was tested in an intervention study, in which Grade 6 children (aged 10–11 years) were randomly assigned to one of three groups: a sample space group (SSG), a problem-solving group, and an unseen comparison group. The SSG showed significantly more progress than both comparison groups in three post-tests, including one given 2 months after the teaching had ended. We conclude that our analysis of the cognitive demands of sample space was supported and discuss the implications for mathematics education.

O PROBLEMA LÓGICO-HISTÓRICO, APRENDIZAGEM CONCEITUAL E FORMAÇÃO DE PROFESSORES DE MATEMÁTICA

The article proposes a discussion of the concept of problem from the cultural-historical perspective and analyzes its implications for mathematics education and teacher training. It emphasizes the relationship between problem and need, and the dialectical unity between the logical and the historical aspect of the concept. These aspects are analyzed in a proposal for teacher training and the results show that is possible to understand the problem solving as teacher education methodology and to understand the process of teacher training as a problem in movement, whose resolution aims to encourage the appropriation of theoretical and methodological tools that allow the objectification of new teaching activities in the pedagogical praxis.

Field Dependency and Performance in Mathematics

<p style="text-align:justify">Mathematics is an important school subject but one which often poses problems for learners. It has been found that learners do not possess the cognitive capacity to handle understanding procedures, representations, concepts, and applications at the same time. while the extent of field dependency may hold the key to one way by which the working memory can be used more efficiently. This study aims to explore the concept of field dependency which may offer a way forward in reducing the cognitive demands of finite working memory capacity, thus enabling higher performance to be attained. Age and gender were considered. With a sample of 120 secondary school students, the importance of working memory in relation to mathematics performance was confirmed (r = 0.55 ). The extent of field dependency was measured with a larger sample of 547, drawn from five age groups. The outcomes were related to the performance in mathematics examinations, a correlation of 0.32 being obtained overall, with every age group showing positive significant correlations. In this, the more field independent perform much better. The outcomes are interpreted in terms of the increased efficiency in the use of finite working memory capacity resources. It was found that students become more field independent with age but the rate of growth of independence declines with age. Girls tended to be slightly more field-independent than boys, perhaps reflecting maturity or their greater commitment during their years of adolescence. The findings are interpreted in terms of the way the brain processes information and the implications for mathematics education are discussed briefly.</p>

Implications for Mathematics Education about Kant's ‘freedom’

Implications for Mathematics Education about Kant's ‘freedom’