Academic Mathematics Research Articles

Perceptions of Saudi elementary school special education teachers regarding mathematics content and instructional practices for students with intellectual disabilities

This study explored the perceptions of special education teachers of students with intellectual disabilities at three elementary schools in Saudi Arabia regarding the instructional practices and content used for teaching such students mathematics. The research employed a qualitative multiple case study design and used an open-ended questionnaire, artifacts, and teacher interviews with 14 special education teachers. By employing thematic analysis of the data collected, the following major issues were identified: (a) there is a strong focus on teaching only numbers; (b) there is an emphasis on teaching functional life skills rather than academic mathematics skills; and (c) mathematics instruction emphasizes procedural mathematics rather than mathematical understanding, also known as conceptual mathematics. These findings illustrated that elementary school students with ID in the sample did not receive comprehensive mathematics education in terms of either content or instructional practices. It might be beneficial for future studies to replicate and extend this research to incorporate observations of the classroom to obtain objective data on teachers’ actual practices while instructing students with ID in mathematics.

From knowledge acquired at academic mathematics courses to significant changes in instructional practices

This non-interventional study investigates the contribution of university mathematics to teaching high-school mathematics. Data sources included interviews with five teachers who taught high-school mathematics before, during, and after their academic mathematics studies. All teachers provided tangible examples of fundamental changes in instructional practices that they explicitly linked to new knowledge acquired in the academic mathematics courses. The domain of analysis in general, and the topics of integrals and derivatives in particular, were central in the teachers’ illustrations of changes they made in their teaching, although other mathematical topics and domains were also mentioned. The reported changes were mostly associated with emphasis on mathematical explanations, exposition of two key elements of the deductive structure of mathematics: definition and proof, an increased focus on formal mathematics, and portrayal of mathematics as a wide and varied discipline. The study results are discussed in light of the relevant literature.

Modeling the Relationship among Digital Demographic Characteristics, Digital Literacy, and Academic Performance of Mathematics Major Students in an Online Learning Environment

The purpose of the study was to determine the digital demographic characteristics, digital literacy, and academic performance of students majoring in mathematics in an online learning environment, as well as to model the relationships between these variables. To measure and obtain the necessary data, the study employed a predictive-correlation research design and an adapted research questionnaire. A survey was conducted with a random sample of 322 students from the main and external campuses of the state university of interest. A series of regressions and path analyses were conducted to explore any significant variables that could possibly describe the relationships among the studied variables. Principally, the study found that the levels of information research, retrieval, and management completely and significantly mediated the relationships among the availability of technological devices, use of an electronic learning platform, and students' academic mathematics performance. In the model validation, the second model demonstrated the consistency of variables such as information research and retrieval and information management literacy in indirectly influencing the relationships between technology device availability and academic performance. A study may be conducted in conjunction with this study, to use the model devised in this study in other locales to further validate the model's overall consistency.

Aspiring and Inspiring: Tenure and Leadership in Academic Mathematics

Aspiring and Inspiring: Tenure and Leadership in Academic Mathematics

How do school-related mathematical problems become relevant for prospective teachers in mathematics courses at university? A qualitative interview study

ABSTRACT Prospective mathematics teachers often have to attend courses in academic mathematics. However, many struggle to see the connections between the course content and their future teaching, which is detrimental to learning motivation and success. Many universities try to address this with interventions focusing on the relevance of the mathematical learning opportunities. School-related mathematical problems (SRMPs), which highlight connections between school mathematics and academic mathematics, are a suggested intervention. Since SRMPs focus on the demands of the future profession, one would expect that students attribute high relevance to them. However, empirical results on this remain limited. To evaluate and enhance SRMPs, our study aims to elicit the criteria students use for assessing the relevance of SRMPs. We analysed ten qualitative interviews with prospective teachers. Our results show that similar criteria determine the perceived relevance in all cases. We discuss practical consequences for the design of school-related learning opportunities in teacher education.

Professional learning tasks and mathematical knowledge involving the algebraic structure of Groups: an experience in the degree in Mathematics teaching

Considering the teacher education of prospective teachers, the objective of this article is to understand how professional learning tasks are carried out in classes of a course of Algebra in the teacher education. Using Design-Based Research cycles, documents and video recordings were collected throughout the course of the classes. Data were analyzed in order to interpret how future teachers mobilize School-Related Content Knowledge and how teacher educators generate professional learning opportunities for them. The results indicate the possibility of approaching academic mathematics in specific-content disciplines of the teacher education, focusing on teacher training and the changes that future teachers’ knowledge may undergo during training. It is concluded that the use of resources that explore connections between academic and school mathematics, as was the case with formative tasks, seems to be a way to promote mathematical and didactic discussions in the teaching degree.

Institutional and instructional decolonizing mathematics education


 In this theoretical essay, we respond to recent scholarship on decolonizing mathematics that asserts that so-called “Western” mathematics is inherently colonialist – that is, in service of the economic and political control of European or wealthy nations over countries of the Global South. Although generally sympathetic with that literature, we argue against some of its presumptions, in part, by distinguishing “Western” or academic mathematics from its recontextualization for schools. First, we argue that, although colonialist messages and values can be disseminated as part of that recontextualization, it is not clear that academic mathematics is inherently colonialist. Then, we offer a suggestive insight into what it might mean to decolonize school mathematics through a pedagogical approach based on research on native language learning, called the “subordination of teaching to learning.” The approach uses tasks that invite learners to use their indigenous mental powers (or brilliance) through engaging in dialogic interactions with themselves and others about objects and relations among them. To illustrate the subordination of teaching to learning, we present an example of how learners use their learning powers to educate their awareness and build mathematical ideas and reasoning; thereby experiencing the joy of their intellectual efforts.

Learning Mathematics Using an Ethnomathematics Approach: A Systematic Literature Review

The study of ethnomathematics has grown significantly over the decades, especially for teaching academic mathematics in schools. However, only a small number of studies comprehensively examine research trends in the use of ethnomathematics for mathematics learning. Thus, research trends for the years 2018 to 2022 were thoroughly analyzed through systematic literature reviews referring to the standards of Preferred Reporting Items for Systematic Review and Meta-Analyses (PRISMA). This review found 24 journal articles from the top indexing databases called Scopus and Eric. The finding of the SLR indicate that two types of ethnomathematics research are found if categorized based on the research data source. The ‘cultural forms’ used in ethnomathematics research into three categories: ideas, activities, and artifacts. Indonesian researchers (n=19) dominated the collected studies as systematic review only included publications published in English. The categorization of the studies are ethnomathematics (pure) and ethno-modelling, and the most studied mathematical topics are geometry (n=11), followed by algebra (n=5), numbers (3), sets (n=2), and arithmetic (n=1).

AuthOMath: Combining the Strengths of STACK and GeoGebra for School and Academic Mathematics

GeoGebra has its strength in creating multimodal dynamic and interactive math applets and is widely used in secondary school math teaching. STACK is particularly strong in generating randomized task with adaptive feedback and is mostly used in academic math teaching. The Erasmus+ project AuthOMath (2022 – 2024) aims to combine the strengths of both systems in an authoring tool with a transformative digitization potential in mathematics teaching and learning.

Access, Disability and Mature Student Opinion on Academic Mathematics Supports

In this paper we report on the main themes which emerged from analysis of a survey of students registered with the Access, Disability and Mature Student offices at Maynooth University. The survey focussed on the students’ experiences of mathematics and the mathematics academic supports available to them. The majority of student feedback was positive, for example their engagement with the Mathematics Support Centre, improved understanding of mathematics and the influence of tutors and peers. However, some issues emerged in relation to impact on learning, such as inflexible departmental structures with fixed deadlines and a lack of student awareness of the supports available. In addition to discussing the main results, we outline how the findings will guide the future provision of such supports.

Motivational states in an undergraduate mathematics course: relations between facets of individual interest, task values, basic needs, and effort

According to situated expectancy-value models, motivational variables play an important role in students’ engagement in academic mathematics courses and achievement. However, for academic mathematical learning, only a few studies provide information regarding the fluctuation of task values on different occasions (situation-specificity, state) and the extent to which task values depend on individual characteristics (personal-specificity, trait). Thus, answering these questions provides information about the extent to which adequate situational characteristics, such as relevance interventions, can influence students’ motivation to engage in the learning process. To contribute to this discussion of the situation- and personal-specificity of task values, I surveyed 181 undergraduate students attending an advanced mathematics course. These students reported on their task values and effort three times in four different lessons during a course in linear algebra. I focused on the following three questions: (1) situation-specificity: to what extent do task values fluctuate between situations (and between persons)? (2) predictions of task values: to what extent do personal characteristics and situational perceptions predict task values? (3) predictions of effort: to what extent do personal characteristics and situational perceptions predict effort? These questions were answered by applying linear mixed models. The analysis results indicate that task values fluctuate only slightly in different situations and are strongly predicted by individual characteristics, such as interest in university mathematics, and task values predict effort. The theoretical and practical implications of the results are discussed.

Mathematics in England’s further education colleges: who is teaching what, and why it matters

ABSTRACT Improving mathematical skills is a priority in England, and a series of policy levers and government change projects have focused on improving mathematical outcomes in further education (FE) in recent years. Yet little is known about the mathematics teacher workforce that supports these students on vocational and technical programmes. This paper addresses this knowledge gap by examining important features of the mathematics teacher workforce in colleges and the implications for recruitment, initial training and ongoing professional development. We report findings from a national survey targeted at all mathematics teachers in around one-sixth (N = 31) of England’s general FE colleges. Teachers have transitioned into FE from three main areas: another career, curriculum area, or educational context. We discuss the varied assets and training needs of these three subgroups and argue that the mathematics teacher cohort in FE should be seen as distinct from that in either primary or secondary education. We highlight the bimodal distribution of mathematics qualifications amongst this workforce; those having level 2 mathematics qualifications being more likely to be teaching functional skills mathematics courses than GCSEs. The rapid expansion of the mathematics teacher workforce that followed the changes to the condition of funding in 2014 has come disproportionately from teachers who were previously working in schools. This, together with a trend of funnelling increasing numbers of FE students into academic mathematics rather than functional skills courses, raises important questions about the nature of mathematical education for learners on vocational and technical programmes, and the teachers thereof.

Engaging in the Discourse of Fractions in a Bilingual Maltese Classroom

Context: The island of Malta is a former British colony, and to this day, education continues to be accessed bilingually. For mathematics education, Maltese and English are used for verbal interaction, with subject-specific words tending to be retained in English. Written mathematics texts are in English, including textbooks, worksheets, digital texts, and examinations. Thus, the “academic” language of mathematics is generally considered—and accepted—to be English. Objective of Research: It is important for Maltese students to gain access to the academic (English) mathematics language to access the discourse of power and still use Maltese in the process. The focus of this study is language as part of the discourse of fractions. The research question was: How can Maltese bilingual children be supported in accessing the discourse of fractions? Participants: The author assumed the dual role of teacher and researcher. The students were 16 nine-year-old children attending a fourth-grade class. Six of these children also participated in two interviews each. Intervention: The author adopted a teacher/researcher role and taught the topic Fractions (five lessons). The topic was chosen at the request of the class teacher. The class teacher stated that although her students had previously mastered fractions of a region (e.g., 1/3 of a circle), they had not understood fractions of quantities (e.g., 1/3 of a set of 12 books). During her teaching, the author focused on language explicitly; she started discussions on fractions with the students using Maltese and English, and gently prompted them toward increased use of mathematical English. The aim of this more detailed articulation of mathematical ideas was for the children to express a better understanding of fractions of quantities. Research Design: This qualitative case study centered its analysis on the classroom interaction and interview data. The theoretical framework drew from Anna Sfard’s definition of mathematical discourse, namely, that a discourse consists of words, endorsed narratives, routines, and visual mediators. “Understanding of fractions” was considered in terms of participation in, or engagement with, in the discourse of fractions. Conclusions: The initial use of translanguaging enabled new discourse elements related to endorsed narratives, routines, and visual mediators. These three elements then supported lengthier and varied contributions in the academic language, and thus, I argue that the endorsed narratives, routines, and visual mediators served as “anchors” to support new language practices (new words of the discourse). Ultimately, the children’s engagement with the four discourse elements indicated that by the end of the five lessons, they had a better understanding of fractions of quantities.

The Impact of Microsoft Mathematics Visualization on Students Academic Skills

The purpose of this study is to examine whether there is a relationship between academic skills and Microsoft Mathematics Visualization as a result of the use of Microsoft Mathematics Visualization in the classroom. Specifically, when it comes to academic skills, Microsoft Mathematics Visualization is considered an independent variable, and academic skills are considered a dependent variable that has been influenced by the negative or positive characteristics of various instructional methodologies. The quantitative research approach has been used in the development of this document. Approximately 300 responses were collected during data collection, and, following correction, the sample size was decreased to 268 responses, which were mined in SPSS to generate the results. In the findings of the model summary, it is shown that the selected model has a very good above-average value of adjusted R2, suggesting a good fit, in accordance with the results of model summary. Microsoft Mathematics Visualization is regarded to be a predictor for academic skills since its coefficient of 0.794 on conversion explains up to 79.4 percent of the variance of the model when converted. We have “B” = “0.892” as the value of the predictor’s beta in our first regression. For example, a one-unit change in Microsoft Mathematics Visualization will result in an 89.2 percent change in academics skills, which may be interpreted as follows: Aside from that, the correlation coefficient between Microsoft Mathematics Visualization and student caliber (r = 0.840) indicates a positive relationship between student caliber and Microsoft Mathematics Visualization. 0.963 indicates that formal schooling has been significantly influenced by Microsoft Mathematics Visualization training, which might be further elaborated as that formal education has been boosted by Microsoft visualization training, according to the results of the test.

A distinction of three online learning pedagogic paradigms.

Online (web-based) courses emerged at the beginning of the twenty-first century. While this new pedagogic paradigm (PP) holds a promise of better learning and training, it comes with challenges as traditional PPs are not suited to the new settings which highly differ from the physical classroom methods. We studied three online PPs (Synchronous, Asynchronous, and Asynchronous with an audience) and their influence on the students learning process and achievements during an academic mathematics course that was conducted online. 168 students took an exam and answered a questionnaire regarding their learning preferences, experience, and habits after experiencing one of these PPs. We found that students who studied according to the asynchronous with an audience PP achieved a higher score in the exam, regardless of their initial level than students who learned by either the synchronous or asynchronous PPs. In addition, we developed a personalized model based on machine learning methods that match an online PP for each student to maximize the student’s score in the exam. In the case of an academic mathematical course, the online PP had a major influence on the students’ scores in the exam. We found that students with high grades in previous courses preferred synchronous learning, which indicates the importance of picking the right online PP for each student. Our model provides a novel tool for the pedagogic community to personalize online learning by recommending the PP that could be most suitable for each student.

Differences in Health-Related Physical Fitness and Academic School Performance in Male Middle-School Students in Qatar: A Preliminary Study

This study examined the differences in the level of physical fitness and academic performance among male middle-school children based on different body status categories. A total of 69 male children [age: 12.4 ± 0.7 years; body mass: 58.5 ± 7.2 kg; height: 1.62 ± 0.09 m; and body mass index (BMI): 22.4 ± 3.3 kg/m2] participated and were divided into BMI age-adjusted groups (i.e., lowest, middle, and highest BMI). Height, mass, BMI, stork test of static balance, 10 and 15 m sprint as an indicator for speed, hand-grip strength test, agility T-half test, medicine ball throw (MBT), and the Yo-Yo Intermittent Recovery Test level 1 (Yo-Yo IR1) were assessed. School records were retrieved for grade point averages (GPA) of mathematics, science, and Arabic. We found significant group differences regarding anthropometric (height: = 0.24, mass: = 0.33, and BMI: = 0.66), physical (sprint 10 m: = 0.26), and academic (mathematics: = 0.19 and science: = 0.15) performance parameters. The largest difference (p < 0.001) was observed between the lowest and highest group for the 10 m sprint. All pairwise differences were between the lowest and highest BMI group or the lowest and middle BMI group. No relevant (r > 0.5) correlation between parameters of different dimensions (e.g., anthropometric vs. physical performance parameters) was found. In conclusion, the highest BMI group exhibited similar physical and academic performances than the lowest group. Thus, these data emphasize the importance and appropriateness to engage young Qatari schoolchildren in physical activity as it associates with superior academic performance.

Magnitude, number and school mathematics

Definitions of concepts of magnitude and number used in academic mathematics are not suitable for school mathematics for reasons of their cognitive complexity. We discuss possible ways to treat magnitudes and numbers in school mathematics based on mathematical reasoning.

On the history of units in French elementary school arithmetic: The case of proportionality

The measurement of magnitudes was at the foundation of numbers and calculation in academic mathematics until the 19th century. It provided units and the concrete and abstract numbers that formed the basis of school arithmetic up to the mid-20th century in France. Our analysis of changes in teaching resources for proportionality (late 19th to the early 21st century) documents how the disappearance of magnitudes in academic knowledge was followed by the loss of the differentiation of the conceptual complexity of mathematical ideas related to proportionality. These changes made teaching and learning about proportionality considerably more difficult, and we later witness their gradual, but not yet systematic, reversal.

Analisis Kemampuan Komunikasi Matematis Siswa Pada Materi Program Linear

This research aims to analyze the mathematical communication ability of class XI students of SMA Negeri 1 Pangkep on the linear program material. This research is a qualitative research. The research procedure includes the preparation stage, the implementation stage, and the data analysis stage. The selection of research subjects was carried out by looking at the students' academic mathematics scores, namely the highest, medium, and lowest scores in the class swith the KKM score as a reference for assessment. The instruments used are tests of mathematical communication ability and interviews. Checking the validity of the data used was the triangulation technique. The results showed that the students of class XI Mathematics and Natural Sciences lacked an understanding of the Linear Program material so that the students had low mathematical communication skills in the Linear Program material.

Synergy effects in learning? The influence of mathematics as a second subject on teacher students’ physics content knowledge

ABSTRACT This study explores benefits of studying two related subjects, mathematics and physics, in teacher education. German teacher students study two subjects as a major, which allows for investigating how the development of content knowledge in one subject, mathematics, benefits students’ content knowledge in the other subject, physics. The sample included teacher students from 12 major teacher education universities in Germany. Each of the N = 104 physics teacher students, whose second subject was mathematics, answered two tests assessing their content knowledge in (1) mathematics and (2) physics. Our results reveal an influence of taking mathematics as a second subject on students’ physics content knowledge. However, the effect size is only small. We found this influence increased over the course of study, indicating that the study of academic mathematics provided increasing opportunities to learn physics over the course of study. Even when controlling for general cognitive abilities, there remains substantial and significant effect of mathematics on physics content knowledge. Mathematical knowledge proves to be relevant in all physical subdomains except for optics and solid-state physics. Overall, the present study confirms benefits of studying physics when also studying mathematics, and thus a synergy effect in studying two subjects in scope of teacher education.