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This study aimed to utilise linear and equipercentile equating procedures in establishing the equivalence of paper-based and computer-based Grade 7 Mathematics Achievement tests. The single group counter-balanced test equating design was used in the study. Paired t-tests results showed that the performance of the students in paper and computer-based tests were not the same. The respondents found the computer-based test more difficult than paper-based test. Also, this result was supported by the differential item functioning analysis where 27 out of 40 items were flagged for differential item bias. Based on this result, it is essential to implement equating procedure in interpreting the scores of computer-based and paper-based Mathematics Achievement tests. The linear and equipercentile equating procedures had similarities on the way scores are transformed based on the ability of the students. The transformed scores were used to interpret fairly whether the students took the paper-based or computer-based Mathematics Achievement tests. Findings showed that students with "beginning" and "developed" proficiency levels found the computer-based test more difficult than the paper-based test while students with "proficient" level had similar performances in both tests. Lastly, students with "advanced" proficiency level found paper-based test more difficult than computer-based test. [ABSTRACT FROM AUTHOR]

The major focus of school education is the intellectual development of students and mathematics is a very effective subject in this regard, if taught and assessed properly. For this study, papers of SSC (Grade-10) for the years 2014 and 2015 set by the Board of Secondary Education, Karachi were scrutinized to know if the items of these papers had measured essential mathematical skills or not. These items were then compared with the items set by General Certificate of Education (GCE: O-Level), University of Cambridge Local Examinations Syndicate (UCLES) for mathematics papers, serving as a benchmark for this study to highlight the shortcomings. The results revealed that the items of SSC papers were highly biased towards 'Factual Knowledge' and 'Routine Procedures'. The study concluded that these items assess knowledge of facts and algorithms only and do not measure essential mathematical skills (involvement of higher levels of thinking processes) of students. The study recommends to improve the items of papers so that essential mathematical skills can be measured rather than the capacity of memorization because with this practice, thinking habits cannot be inculcated among students. [ABSTRACT FROM AUTHOR]

This research addresses the issue of how to support students' representational fluency—the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper‐and‐pencil classroom environment is targeted as a rich and pressing context to study this issue. We report results of a collaborative teaching experiment in which we designed for and tested a functions approach to solving equations with ninth‐grade algebra students, and link to results of semi‐structured interviews with students before and after the experiment. Results of analyzing the five‐week experiment include instructional supports for students' representational fluency in solving linear equations: (a) sequencing the use of graphs, tables, and CAS feedback prior to formal symbolic transpositions, (b) connecting solutions to equations across representations, and (c) encouraging understanding of equations as equivalence relations that are sometimes, always, or never true. While some students' change in sophistication of representational fluency helps substantiate the productive nature of these supports, other students' persistent struggles raise questions of how to address the diverse needs of learners in complex learning environments involving multiple tool‐based representations. [ABSTRACT FROM AUTHOR]

Graph literacy, the ability to interpret and create graphical representations, is an important skill for students to learn mathematics and to succeed in STEM coursework and careers. Additionally, with the rapid development of technological devices and media, students are encountering increasingly more situations in which graph literacy is needed to make sense of and respond to information. In this paper, I present a conceptual analysis of what I consider the three layers constituting a graphical representation: frames of reference, coordinate system, and graph. Relatedly, I synthesize relevant literature and propose an analytical framework that could be used to make sense of students’ representations of spatial phenomena. The analytical framework was designed to answer the following question: How do students make sense of a spatial situation, establish frames of reference, and create re-presentations of the spatial situation via coordinated measurements? After I elaborate on the analytical framework, I draw data from teaching experiments to illustrate how the framework could be used to model students’ representations of spatial phenomena with attention to frames of reference and coordinate systems. Finally, I discuss how this framework could be used by researchers and educators for better attending to students’ graph thinking and making sense of students’ graph literacy. [ABSTRACT FROM AUTHOR]

Structural equation modeling (SEM) is well-known in statistics due to its flexibility and accessibility. In the Scopus database alone, there were more than 1,500 search results related to SEM in mathematics education. However, there is a lack of scientific reviews of mathematics education that use SEM. The purpose of this study was to investigate research trends related to SEM in mathematics education. The researcher used Biblioshiny and VOSviewer to conduct bibliometric analysis on 1,017 papers that have been published in the Scopus database. The result showed that the number of publications in the research area has continuously grown over the last few decades. The US was the most prolific country in terms of publication and international collaboration. Professor Herbert W. Marsh had the most publications and citations, while the most productive journal was Frontiers in Psychology. The most current keywords include STEM, technology acceptance model, control-value theory, and computational thinking. Hence, these findings may serve as a guide for future researchers to conduct relevant research using SEM. [ABSTRACT FROM AUTHOR]

Mathematics can be used as a tool to question and critique society and, in doing so, give us more information about the world around us and how it operates. This however, is not a common perspective that is conveyed to students during their undergraduate mathematics coursework. This paper contributes to the understanding of how undergraduate mathematics students question and critique society via mathematical modeling tasks. In two courses at two universities, 27 mathematics majors and secondary preservice teachers engaged in the modeling process situated in authentic contexts to learn specific concepts and make mathematical connections across domains and disciplines. Both courses culminated in a final project in which students created and investigated solutions to their own modeling tasks. In this paper, we describe how our courses (1) centered justice as pedagogy, (2) were environments for student agency and exploration, and (3) explicitly demonstrated how mathematics and social justice are intertwined. Drawing on frameworks of mathematical modeling for social justice, we present and analyze student-created tasks to showcase how they utilized mathematics as a tool to question and critique the world around them. [ABSTRACT FROM AUTHOR]

The mathematics performance of Australian high-school students in Year 9 and their participation in mathematics subjects in Year 12 has plummeted in the last 20 years. In this paper, a retrospective cohort study was conducted to understand how non-cognitive variables controlled or explained the correlation between mathematics performance in Year 9 and mathematics participation in Year 12. The sample consisted of a cohort of Australian students (N = 6653; n = 3115, 46.8% male) who participated in the Longitudinal Survey of Australian Youth (LSAY) in 2007 to 2017. Partial least squares structural equation modelling (PLS-SEM) was conducted to explore the degree to which one moderating variable and five mediating variables intervened in the relationship between mathematics performance in Year 9 and mathematics participation in Year 12. Mathematics performance in Year 9 predicted mathematics participation in Year 12 (R² = 18.4%). The positive correlation was moderated by gender and mediated by five non-cognitive factors associated with self-related beliefs: mathematics self-concept, self-efficacy, interest, motivation, and anxiety (R² = 28.9%). At any given level of mathematics performance in Year 9, a male student with a higher level of mathematics self-concept, self-efficacy, interest, and motivation, and a lower level of anxiety, was more likely to participate in mathematics subjects in Year 12 than a female student with a lower level of mathematics self-concept, self-efficacy, interest, and motivation, and a higher level of anxiety. These finding have implications for ameliorating the declining levels of mathematics performance and participation. [ABSTRACT FROM AUTHOR]

Research investigating teachers' knowledge and practices aimed to improve student participation, engagement and achievement in mathematics and science has often used qualitative methods involving observation and analysis of lesson videos. Some researchers have used excerpts of videos in various ways to gather data about their participants' anticipated actions in the moment. In the current study, we aimed to track primary teachers' developing adaptive expertise when teaching interdisciplinary mathematics and science lessons over a two-year period. In this paper, we describe the processes followed to design a questionnaire that used episodes from videos of interdisciplinary mathematics and science lessons to construct multiple choice items. The adaptive expertise scoring for the items was reliable but this improved when including an open-ended question for participants to explain their selection of an action for the classroom moment captured in the video episode. [ABSTRACT FROM AUTHOR]

The purpose of the research presented in this paper was to study the role of concrete and table representations created by students in learning how to solve an optimization problem called the transportation problem. This topic was learned in collaborative groups using table representations suggested by teachers in 2021. In 2022, the researchers decided to enrich the students' learning environment with concrete objects and urged the students to use them to present the problem to be solved. The students did it successfully and, to be able to record it in their notebooks, they constructed a table representation by themselves without any help from their teacher. After that, they managed to solve the problem by manipulating the objects. At the same time, each step in the solution was presented with changes in the table. The students were assessed before (pre-test) and after collaborative learning (test) in both academic years. The pre-test results were similar, but the test results were better in 2022. Therefore, it can be concluded that using concrete and table representations constructed by students in learning how to solve transportation problems makes collaborative learning more constructivist and more effective than when they use only table representations suggested by their teachers. [ABSTRACT FROM AUTHOR]

More than 35 years have passed since Shulman introduced the term "pedagogical content knowledge" [PCK] to the field of teacher education. As is the case with any new construct in a field, Shulman's advocacy for PCK in the mid-1980s was almost certainly a reaction to the priorities of the field at that time. A primary goal of this paper is to refresh our collective memories of the origins of and development of PCK as a research domain, with a particular focus on what may have prompted scholars such as Shulman to propose the construct of PCK in 1986. With this historical lens as background, I also seek to consider what might be fruitful future directions in the field's thinking about teaching and teacher knowledge. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we, a group of graduate students in mathematics education, discuss some of the metacognitive benefits of the non-traditional teaching methods we observed employed by one of our professors. This professor's methods challenge the common belief that well-managed class time is key for positive learning outcomes. Instead, he orients his teaching to share the exploration and sense-making phases of doing mathematics. The goal of his teaching is to share the idea that learning mathematics is a process of "refining our mathematical thinking". We argue that this approach to teaching helps students see that mathematics is a human endeavor, appreciate the cycles of learning mathematics and the importance of struggle throughout the process, and gain some insight on what it means to be an expert in mathematics. We encourage teachers and professors to move away from obsessing about structured, well-organized class time, and to instead move towards having flexible and risk-oriented class time. [ABSTRACT FROM AUTHOR]

Growth in fully online mathematics education has been steady for decades. This is where essentially all interactions associated with the teaching and learning process are mediated via the online medium. Initially spurred on by technological innovation and a variety of socio-cultural forces, growth has more recently rapidly accelerated due to pandemic restrictions. Many suggest we are on the precipice of profound transformation in mathematics education, the outlines of which remain unknown. In leveraging online education possibilities and advancing online mathematics education, this paper considers aesthetic experiences associated with learning mathematics fully online. First, three assumptions are made to highlight the importance of these experiences. Second, three challenges are identified regarding the current state of fully online mathematics education. Finally, specific instructional design and online teaching strategies are outlined that potentiate experiences of wonder and beauty often associated with mathematical discovery. As its central theme, the paper seeks to answer how we may take advantage of this technology in delivering quality mathematics education without allowing it to diminish our human essence. [ABSTRACT FROM AUTHOR]

To benefit from the quickly expanding range of new possibilities of technology-enhanced education, school systems, schools, and teachers need to adapt quickly. Conversely, the needs of students and teachers in a technology-enhanced classroom require technology developers to provide and improve suitable technologies. In this paper, we aim to show how to make the professional knowledge of mathematics teachers accessible to developers of technologies and also to teacher trainers and trainees by the use of student personas, i.e., portraits of archetypical students with particular characteristics and needs. We have collected qualitative data from preservice and in-service mathematics teachers in Austrian academic upper secondary schools about the characteristics and needs of their students. We have analysed these data using a grounded theory approach to derive demands of students on technology-enhanced learning environments (TELEs). We have identified and presented five personas, each with specific demands on TELEs, to represent this target group. By introducing this approach that combines techniques from mathematics education research and from user experience research, we are able to represent user groups of a mathematics technology-enhanced learning environment in a more relatable way than was previously possible. These relatable representations of students in Austrian academic upper secondary schools could be of particular importance for developers of technology-enhanced learning environments for teaching and learning mathematics. The methodology presented in this paper is adaptable to other contexts. [ABSTRACT FROM AUTHOR]

Problem-posing is an essential component of mathematics education because, among other reasons, when students are given the opportunity to pose their problems, they can take ownership of their learning and become more engaged in the given subject. Thus, problem-posing can lead to a deeper understanding of the studied mathematical concepts. In a collaborative action research study, the authors explored whether well-structured problem-posing activities could be incorporated into classes with students of mixed ability in mathematics. This question is addressed by examining the correlation between students' mathematics grades and problem-posing success. The problem-posing approach used in this paper relies on problem solving as a parallel activity. Hence, the study also focuses on the relationship between problem posing and problem solving. The paper presents the results of a classroom experiment with 86 sixth-grade students and their teachers from Hungary and Romania. After evaluating the students' problem-posing products and problem-solving performances, the results show that problem posing, based on a worked-out model problem, is a feasible challenge for most students. Moreover, this experiment identified a direct relationship between successful problem posing and problem solving. [ABSTRACT FROM AUTHOR]

Copyright of Teaching Innovations / Inovacije u Nastavi is the property of University of Belgrade, Faculty of Teacher Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study investigated the impact of visual cueing on attention guidance, deep-thinking promotion, and performance optimization in arithmetic word problem solving for students with mathematical learning difficulties (MLD). The participants included eight students with MLD and twenty students without MLD who attempted to solve mathematical word problems with and without visual cueing. Eye movements were recorded during the tasks. A repeated-measure design and nonparametric tests were applied to enhance the statistical power of the study. The data analysis results indicated that visual cueing effectively guided and sustained the attention of students with MLD, reducing their off-task duration. However, it showed limited influence in facilitating deep thinking and performance improvement for these students. There were no significant attention-guidance or performance-improvement effects observed in the problem-solving processes of students without MLD, who initially demonstrated better concentration levels and performance. The potential explanations for these findings are further discussed in this paper. [ABSTRACT FROM AUTHOR]

Learning styles is the idea that there are unique ways in which individuals approach learning and process information. Though refuted, the idea of learning styles has not declined in peer-reviewed reports of empirical studies or teacher/practitioner resources. Some reports have also used learning styles as a tool for improving the mathematics education of students with learning disabilities—an area of interest for mathematics education and special education communities alike. In this paper, we review articles published by the National Council of Teachers of Mathematics to investigate the perspectives of learning styles at the intersection of mathematics education and learning disabilities. Analyses highlight the relationship between mathematics education, learning disabilities, and learning styles, and the varied meanings and perspectives of the articles' authors. Of note is both the perpetuation of unfounded concepts and the lackluster response to explicit contests of the idea of learning styles. [ABSTRACT FROM AUTHOR]

This research paper investigated the effectiveness of the discovered formula in squaring numbers using patterns in a sequence introduced by the researchers as an innovation in teaching and learning mathematics. The researchers came up with the idea to use the patterns in sequence to develop a rule or formula for squaring numbers. The developed formula was evaluated as effective and efficient since the technique only used basic multiplication and addition that covers all numbers. Descriptive-developmental and evaluation research was utilized in this paper. Twenty professional teachers working in different capacities were purposively selected as respondents. Meanwhile, the technique was very effective as it promotes innovative and creative ease of introducing new methods to the learners with an overall weighted mean of 3.68. Thus, it increases students' engagement in mathematics. Likewise, the respondents, found the technique as timely and relevant, aids learners in squaring numbers without using a calculator, is engaging and enjoyable, provide opportunities to learners, and can be utilized in some mathematics competition. Therefore, this new pedagogical strategy will help students in squaring numbers easily. Lastly, it implies that teacher's methodology and strategy may affect the learning of students. Thus, innovations such as providing alternative solutions will increase their learning in mathematics. [ABSTRACT FROM AUTHOR]

This paper reports on performance data obtained as an integral part of a major research study on the effect of the transition from primary to postprimary education on Irish students' mathematics performance [V. Ryan, Making the Transition: A Students Mathematical Journey from Primary to Post-Primary School in Ireland, PhD. University of Limerick]. The data were obtained using a standardised test designed for use in Irish primary schools to assess student mathematical knowledge at the end of their first year of post-primary school. The results highlight significant underperformance across all curriculum strands of the official mathematics curriculum indicating an unsatisfactory grasp of mathematical knowledge at this stage of students' development. The item analysis also shows statistically significant differences in performance between male and female students. These findings are concerning in the context of major recent reforms of the national post-primary mathematics curriculum and targeted measures to avoid negative outcomes in mathematics as students make the transition from primary to post-primary education. In research terms, the end of year 1 in post-primary education is a neglected milestone in students' mathematics education that straddles a key period in students' mathematical journey when students negotiate academic and emotional transitions that affect their performance, attitudes and dispositions towards mathematics. This paper gives a recent appraisal of the mathematical knowledge of students entering year 2 of postprimary education in Ireland. It discusses factors affecting these student outcomes in mathematics in the context of the students' transition from primary to post-primary school/mathematics. Finally, it sheds light on a neglected mathematics milestone for students, and its potential to influence future student outcomes in mathematics. [ABSTRACT FROM AUTHOR]

One of the famous traditional textiles in Sarawak is the Iban Pua Kumbu. This paper presents the crystallographic patterns, geometry concept and symmetry analysis present in the Iban Pua Kumbu patterns. This paper will also look at the colour-symmetrical patterns and motifs used in these textiles. The Ibans' weaving technique subtly incorporates geometric concepts using exquisite and precious designs. The Pua Kumbu of the Iban can be similarly classified according to the patterns displayed in the wallpaper and frieze. The current research findings could assist students to learn mathematics. In this study, samples comprising eight (8) repeated patterns were collected from field visits, museums in the Sarawak, and personal collections of scholars. From the findings, it shows that all Pua Kumbu patterns bear at least one of the seventeen crystallographic groups. Most of the Pua Kumbu motifs are symmetrical and those motifs is mathematically identified as a design. The Pua Kumbu contains decorative patterns whose relevance and imaginative portrayal are demonstrated by the intricacy of the creative process. Pua Kumbu weavers appear to have excellent memory skills, strong visual perception, and an innate aptitude for applying mathematics to their work. [ABSTRACT FROM AUTHOR]

This paper details a literature review of mathematics vocabulary intervention studies for students with mathematics difficulty. The primary aim was to identify instructional practices that support mathematics vocabulary development. We conducted a database search to identify mathematics intervention studies either focused exclusively on vocabulary or with an embedded vocabulary component. Ultimately, 13 studies with participants from kindergarten to Grade 8 were included in the review. The majority of included studies had dual foci on vocabulary and other mathematics content, including whole number computation, word problem solving, fractions, algebra, or geometry. All studies that measured mathematics vocabulary performance indicated positive student outcomes. In addition, multiple studies indicated positive effects on measures of other mathematics content beyond mathematics vocabulary knowledge. We noted six instructional practices across studies that bolstered the mathematics vocabulary performance of students with mathematics difficulty. From most to least common, these practices included formal vocabulary use, explicit instruction, use of representations, repeated exposures, pre‐teaching, and graphic organizers. Implications are addressed for both researchers and practitioners. [ABSTRACT FROM AUTHOR]

Math anxiety is a common challenge that affects students in different age groups, hinders their achievements in math, and leads to avoidance of math related activities. This article aims to contribute to a better understanding of the signs of math anxiety in students and the factors which contribute to math anxiety. The research instrument was an online questionnaire specially designed for this study. The questions related to the main aspects presented in this paper were closed questions, most of them measured on a 4-level Likert scale. The participants were 160 mathematics teachers, most of them active teachers with special qualifications and more than 5 years of experience in teaching mathematics. The participants were teaching on different grade levels, covering grades from 1 to 12. Participants self-reported a high familiarity with math anxiety, teachers with special qualification for teaching mathematics, those with more than 5 years of experience, and teachers teaching in grades 7-12 perceived a higher level of familiarity, but the differences were not statistically significant. Teachers reported that there are students with math anxiety in their classes, teachers with qualification reported more students with anxiety, teachers with more experience observed less students with anxiety, these differences being not significant. Teachers teaching grades 7-12 observed a significantly higher number of students with math anxiety than those teaching in grades 1-6. Also, teachers observed physical symptoms of math anxiety, those teaching grades 7-12 in a significantly higher number of students than those teaching in grades 1-6. As regarding other symptoms, increased stress or frustration while doing math and negative self-talk about math ability are the most frequently observed. Teachers consider that the main causes of students' math anxiety are related to the parents, their math anxiety and their attitude to their child's math ability could increase anxiety. [ABSTRACT FROM AUTHOR]

Data from international studies reveal that the mathematics literacy of Spanish students is significantly lower than that of students from nearby countries. Therefore, in recent years, interest in identifying the factors that influence students’ mathematics results in Spain has grown considerably. Often, these factors are sought among the socioeconomic characteristics of the students or among variables related to the schools, ignoring the psychological and emotional factors of the students. This paper analyzes the impact of certain psychoemotional characteristics of Spanish students on their literacy in mathematics. For this purpose, multilevel regression models are applied to the data of the Spanish sample of the 2018 edition of PISA (Programme for International Student Assessment), which is composed of 35,943 15-year-old students. The instruments for data collection are the mathematics literacy tests and the contextual questionnaires on students’ personal situation and well-being used by PISA. As dependent variable, students’ mathematics literacy has been considered, measured through the plausible values provided by PISA, and as independent variables, different indices measuring students’ psychoemotional well-being obtained from the contextual information collected by PISA. Results indicate that resilience, motivation for the achievement of learning objectives, competitiveness, perceived cooperation at school, and social connectedness with parents have a positive impact on students’ mathematics literacy, while experiences related to bullying, physical self-concept, meaning in life and perceived competitiveness at school have a negative impact. [ABSTRACT FROM AUTHOR]

Valuing in mathematics is one of the areas in mathematics education that has attracted the attention of mathematics education researchers in recent times. While efforts have been made to research the attributes students value in their mathematics learning, the same cannot be said about attributes teachers and their students value in mathematics learning, and value alignment in mathematics learning between teachers and students. This paper reports on a study that sought to explore what teachers and their students value and the alignment between attributes teachers and their students value in learners' mathematics learning. A survey of what students and their teachers value in learners' mathematics learning was conducted with 690 senior high school students and 66 teachers from nine schools, using adapted What I Find Important in my mathematics learning questionnaires. A multistage sampling procedure involving the use of stratified random sampling and purposive sampling procedures was used to select the research participants. The data obtained from the study were then analysed, using frequency counts, mean and standard deviation and principal component analysis. The results from the study revealed that the senior high school mathematics teachers valued Authority, Engagement, Strategy and Communication in students' mathematics learning, while the students valued Authority, Relevance, Understanding, Engagement, Strategies, ICT and Achievement in their own mathematics learning; an indication of a gap in valuing among the two groups of research participants. Implications of the findings for mathematics teaching and learning as well as in-service and pre-service education programmes are provided. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate how the contents related to the arithmetic of fractions, as described in the official curriculum issued by the Japanese Ministry of Education, Culture, Sports, Science, and Technology (MEXT), are implemented in actual teaching at the so-called Japanese supplementary school in Denmark. Additionally, at a methodological level, this case study demonstrates how so-called praxeological reference models can be developed at different levels of detail to describe classroom teaching at a particular grade level and the overall curriculum of primary school in a connected way. This study is based on the notions of praxeological reference models and moments of didactic processes from the Anthropological Theory of the Didactic. The findings reveal that (1) not much time is allocated to each moment and (2) the flow of gradually building up techniques, as intended by the textbook authors is to some extent disrupted in the lesson. [ABSTRACT FROM AUTHOR]

This paper presents a simplified model of the population migration problem, addressed to first-year engineering students in order to show them the use of linear algebra tools. The study consists of predicting the census in the city centre and in the suburbs, determining the city population equilibrium point, and making a sociological interpretation of population flows. This practical problem is part of the seminar "Applications of Linear Algebra in Engineering", which is being held at the Universitat Politècnica de Catalunya-BarcelonaTech (UPC). This seminar consists in the learning of linear algebra by the implementation of real applications where mathematical tools are required to resolve them. This paper presents an application of linear algebra to the population migration problem and analyses students' appreciation through anonymous surveys and personal interviews. The surveys assessed students' motivation towards the subject of linear algebra and their learning of mathematical concepts. Personal interviews were conducted for students in order to let them express in detail their opinion about the seminar. The results confirm that the introduction of real applications in the learning of mathematics increases students' motivation and involvement, which implies an improvement in students' performance in the first courses of STEM degrees. [ABSTRACT FROM AUTHOR]

Background: There is anecdotal evidence that many elementary teachers integrate mathematics lessons and art activities by having students first make colorful, rich material that is subsequently used in an instructional activity. However, it is unclear whether such activities effectively promote learning and transfer of mathematical concepts. The goal of the present research was to examine the use and effectiveness of such "math-and-art" activities on children's ability to acquire basic fraction knowledge. We report the results of a survey of practicing elementary school teachers in the United States, their use of activities involving physical material, and the resources they use for ideas to supplement the standard curriculum. Two experiments examined first-grade students' learning, transfer, and recognition of fraction knowledge from rich, contextualized material versus simple, generic material. Results: The survey results confirm that many U.S. teachers use math-and-art activities and are often inspired by informal sources, such as Pinterest and YouTube. Experiment 1 examined the effectiveness of colorful, contextualized student-constructed material (paper pizzas) versus simple, pre-made material (monochromatic paper circles) in an instructional activity on fractions. Students who used the pre-made circles scored higher than those who used the student-made pizzas on pre-instruction tests of basic fraction knowledge, immediate tests of learning, and delayed tests of transfer. Experiment 2 tested students' ability to spontaneously write fractions to describe proportions of pizzas and circles. Students who answered generic circle questions first were markedly more accurate than those who answered pizza questions first. Conclusions: These findings suggest that rich, contextualized representations, including those made by the student, can hinder students' learning and transfer of mathematical concepts. We are not suggesting that teachers never integrate mathematics and colorful, contextualized material, and activities. We do suggest that elementary students' mathematics learning can benefit when initial instruction involves simple, generic, pre-made material and opportunities for students to make and use colorful, contextualized representations come later. [ABSTRACT FROM AUTHOR]

This paper reports on the findings of a baseline study that fed on to a broader investigation exploring ICT integration in the teaching of functions. The baseline study was premised on the observation that the notion of function, despite being a fundamental and central idea in the mathematics school curriculum, presents pedagogical challenges to both teachers and learners. The study used the qualitative case study design to investigate Grade 11 mathematics learners' errors and misconceptions under hyperbolic functions at a rural high school in the Limpopo province of South Africa. Informed by the constructivist APOS theory conception levels, learners' errors were detected from their written responses in a diagnostic test. The learners were then individually interviewed during task-based interviews to infer on the misconceptions underlying their errors. Qualitative analysis of the data revealed the following categories of misconceptions: algebraic, conceptual, asymptotic, graphical, and notational misconceptions. The study established that errors, if diagnosed and corrected, are springboards and milestones to the formulation and construction of proper mathematical ideas. To resolve learners' misconceptions, this study recommends that teachers should use explorative and discovery pedagogical strategies to enable learners realize their own misconceptions and self-correct. Based on the findings of this study, the integration of Information and Communication Technologies (ICTs) in teaching functions as an intervention strategy will be explored. [ABSTRACT FROM AUTHOR]

Procedural flexibility is a crucial element of deep procedural knowledge involving the selection of "the most appropriate strategy." However, there exists unavoidable nuance when one attempts to define "the most appropriate" strategy, which leads to two types of procedural flexibility: (a) structure-informed flexibility (Struct-Flex), which refers to a preference for situationally appropriate strategies; (b) algorithm-oriented flexibility (Algo-Flex), which refers to a preference for standard algorithms. The current study investigated the distinction between these two flexibility types and tested potential predictors for both types of flexibility. The study data were collected from 412 Grade 9 through 12 students from 19 math classrooms in the southeastern region of the U.S. Chi-squared tests and regression models revealed that: (a) problem type was strongly correlated to and predictive of a preference for using algorithms in algebra; (b) students' current high school math course grade was associated with preference for standard algorithms; (c) students' current high school math course level and their classroom assignment were related to preference for situationally appropriate strategies. The results suggest that, in this sample, Algo-Flex was as prevalent as Struct-Flex, and the two flexibility types had different predictors. This paper can advance our practical knowledge of U.S. students' strategy choices. The identified predictors of Algo-Flex and Struct-Flex can also inform the design of relevant educational interventions. Future studies may explore longitudinal datasets to untangle the relationship between course level, age, and flexibility, as well as examine flexibility in Asia in comparison to Europe and North America. [ABSTRACT FROM AUTHOR]

Computer-aided assessment systems are increasingly used in education for both formative and summative assessment. Example of such a system from the area of mathematics education is the platform Maple T. A. (Testing and Assessment), which was developed specially for assessment in mathematics. The paper is focused on the efficiency of the use of the Maple T. A. platform to students' performance in classes of mathematical analysis (calculus). For this reason, the pedagogical experiment was conducted on the first and later second year undergraduate students of teaching mathematics taking into consideration their approaches to learning and studying. The research results include cluster analysis of students' approaches to learning and studying and analysis of students' performance in their homework assignments and final tests. [ABSTRACT FROM AUTHOR]

Copyright of Journal of the Canadian Association for Curriculum Studies is the property of Journal of the Canadian Association for Curriculum Studies and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Motivation, the teacher–student relationship, the use of resources, and the time spent studying, in addition to the family economic and social context, are some of the factors that affect academic performance and directly influence student failure. This paper evaluates the motivation in mathematics students’ performances by analyzing indicators of the mathematics learning dimensions. A total of 2,018 secondary students were evaluated in this cross-sectional study. Motivation, teaching, resources, and study time were analyzed with a validated 20-item questionnaire. Statistical analysis revealed that student motivation appears to be significantly related to perceptions of teaching practices and the use of resources for study. Students with high motivation have positive perceptions of teaching practices. Gender differences were not observed. In addition, the motivation indicator allowed for grouping students into various motivational profiles. [ABSTRACT FROM AUTHOR]

Aim/Purpose This study aimed to develop a model for using social media content to promote 3D thinking of sustainability among students in integrated Mathematics, Language, Arts, and Technology (MLAT) classrooms. Background Social media is one of the most relevant platforms among students of the 21st century to the extent that connecting it to classroom learning becomes interesting to the learners. Education for Sustainable Development (ESD) requires teachers to implement an interdisciplinary teaching approach while promoting skills for dealing with sustainability issues. ESD enables students to think about three aspects (economics, environment, and society) of sustainability. In this paper, the ability to think about the environment, society, and economics simultaneously was termed "3D thinking of sustainability." Social media content can be a catalyst for promoting students' application of 3D thinking of sustainability if integrated into the classroom. However, teachers fail to use social media content in their classrooms because they lack the know-how to integrate them. Therefore, providing teachers with a model for using social media content in their teaching can help them integrate it into their classes. Methodology Design-based research was adopted by the researchers (wo mathematics teachers and one curriculum expert) who were selected through purposive sampling, and twenty students who were selected through convenience sampling. Data were collected from the teachers' interviews with twenty students through observation and reflective journals and from students' assignments through document analysis. Contribution The major contribution of the study is the development of the model for facilitating students' application of skills from the domains of mathematics, language, arts, and technology to understand sustainability issues. Furthermore, the study shows the value of social media in learning from the point of view of using them as context for applying interdisciplinary skills rather than media for teacher-student interaction. Findings The model with eight interactive phases was developed. The proposed model requires the teachers to be knowledgeable content-wise in various disciplines or to collaborate with teachers from other disciplines. Recommendations for Practitioners Practitioners are encouraged to adopt this model in the implementation of ESD. Recommendations for Researchers Researchers may test the application of this model in other integrated subjects and levels of education. Impact on Society The standard of living of any society is related to people's awareness of threats to sustainability. Therefore, the more education promotes 3D thinking of sustainability, the more the standard of living is guaranteed in our societies. Future Research To evaluate the applicability of the model in various educational contexts. [ABSTRACT FROM AUTHOR]

Introduction: Mathematics classrooms are typically characterized by considerable heterogeneity with respect to students' knowledge and skills. Mathematics teachers need to be highly attentive to students' thinking, learning difficulties, and any misconceptions that they may develop. Identification of potential errors and appropriate ways to approach them is crucial for attaining positive learning outcomes. This paper explores which knowledge and affective-motivational skills teachers most require to effectively identify and approach students' errors. Methods: To address this research question within the German follow-up study of the Teacher Education and Development Study in Mathematics (TEDS-M), 131 primary school mathematics teachers' ability to identify students' errors was assessed based on (a) a digitalized speed test showing different students' solutions in a written notation and (b) three video vignettes that showed different scenes from mathematics classes. These scenes dealt, among other things, with children who struggled with the lesson's mathematical content. Teachers were asked to analyze students' thinking and to determine how best to react. In addition, teachers' mathematics pedagogical content knowledge, mathematical content knowledge, and beliefs were assessed in separate tests and served as predictors for teachers' abilities to identify, analyze, and deal with students' errors. Results: The results indicate that all components are interrelated. However, path analysis reveals that teachers' ability to deal with students' errors is mainly predicted by their constructivist beliefs while their ability to quickly identify typical students' errors is largely dependent on their mathematics content knowledge. Discussion: The results show the central filtering function of beliefs. Teachers who believe that students must shape and create their own learning processes are more successful in perceiving and analyzing student errors in classroom situations. They may understand errors as learning opportunities and - thus - pay specific attention to these occurrences. [ABSTRACT FROM AUTHOR]

This paper reports on Data Analytics Research (DAR), a course-based undergraduate research experience (CURE) in which undergraduate students conduct data analysis research on open real- world problems for industry, university, and community clients. We describe how DAR, offered by the Mathematical Sciences Department at Rensselaer Polytechnic Institute (RPI), is an essential part of an early low-barrier pipeline into data analytics studies and careers for diverse students. Students first take a foundational course, typically Introduction to Data Mathematics, that teaches linear algebra, data analytics, and R programming simultaneously using a project-based learning (PBL) approach. Then in DAR, students work in teams on open applied data analytics research problems provided by the clients. We describe the DAR organization which is inspired in part by agile software development practices. Students meet for coaching sessions with instructors multiple times a week and present to clients frequently. In a fully remote format during the pandemic, the students continued to be highly successful and engaged in COVID-19 research producing significant results as indicated by deployed online applications, refereed papers, and conference presentations. Formal evaluation shows that the pipeline of the single on-ramp course followed by DAR addressing real-world problems with societal benefits is highly effective at developing students' data analytics skills, advancing creative problem solvers who can work both independently and in teams, and attracting students to further studies and careers in data science. [ABSTRACT FROM AUTHOR]

This study adopts a holistic single-case design to explain the task design processes of mathematics student teachers (MSTs) regarding History, Theory, Technology, and Modeling (HTTM). A criterion sampling method was used to select nine MSTs who had successfully completed algorithms and programming course. Video analyses, written answer sheets, scratch papers, and GeoGebra files were used to obtain data, including the views of MSTs on HTTM task design. Data analysis was performed using a content analysis method based on the theoretical framework of HTTM learning. The results revealed that HTTM design processes included task, focus/origin, problem, design (prototype), results, and approved reports. Furthermore, the mental steps that connected these basic components were found to be investigating, exploring, designing, evaluating, revising, and reporting. One of the key challenges experienced by the MSTs was found to be spending a great amount of time especially while determining a focus. The study has been finalised with a set of suggestions for future designs. [ABSTRACT FROM AUTHOR]

After experiencing years of procedural teaching in K-12 mathematics classrooms, many students arrive at college with ideas about, and approaches towards, mathematics that are not helpful to their learning. Students' prior experiences and misconceptions can then negatively impact their experiences in university STEM courses. This paper describes a short course in the "big ideas" of calculus, that offered students an approach of problem-based learning, combined with mindset messages, otherwise known as a "mathematical mindset approach". The mixed-method study considered how a 'mathematical mindset' teaching intervention impacted the learning, achievement, and beliefs of incoming college students, finding that the intervention significantly changed students' ideas about mathematics, their own potential, and the value of collaboration. At the end of the course students also significantly improved their achievement on assessments of problem solving and collaboration. Importantly the course allowed students to believe in their own potential and to approach mathematics with a growth mindset, suggesting a role for such courses in students' mathematics pathways. [ABSTRACT FROM AUTHOR]

Most academics consider class attendance as key to performance, using various strategies to encourage students to attend classes and engage more fully with the course, often with limited if any success. In Part 1 of this paper, we investigate the relationship between student attendance and performance based on two units. In the first unit, students scanned their student-cards before entering the lecture venue; in the second unit, attendance was based on tutorial attendance records. For each unit, attendance records were merged with performance and demographic data from the university records. The data were analysed using statistical modelling to determine the effect of attendance on performance. In Part 2, we report on surveys of academic staff and students administered across Australia, New Zealand, South Africa, South America, Europe and the US. In particular, we investigate the relationship between attitude towards attendance and importance of attendance to student performance and demography. Similarly, we investigate the relationship between attitudes of staff towards attendance to staff demography. Some qualitative analyses of open-ended comments from both staff and students were also performed. Statistical analysis showed a significant relationship between attendance and performance, with an increase of 0.52% per lecture and 1.7% per tutorial attendance respectively for the two units. Further, students in Mathematics and Statistics, Arts, and Medicine and Dentistry thought lecture attendance was important, while staff overwhelmingly agreed that class attendance was important. [ABSTRACT FROM AUTHOR]

This study explores student flexibility in mathematics by examining the relationship between accuracy and strategy use for solving arithmetic and algebra problems. Core to procedural flexibility is the ability to select and accurately execute the most appropriate strategy for a given problem. Yet the relationship between strategy selection and accurate execution is nuanced and poorly understood. In this paper, this relationship was examined in the context of an assessment where students were asked to complete the same problem twice using different approaches. In particular, we explored (a) the extent to which students were more accurate when selecting standard or better-than-standard strategies, (b) whether this accuracy-strategy use relationship differed depending on whether the student solved a problem for the first time or the second time, and (c) the extent to which students were more accurate when solving algebraic versus arithmetic problems. Our results indicate significant associations between accuracy and all of these aspects-- we found differences in accuracy based on strategy, problem type, and a significant interaction effect between strategy and assessment part. These findings have important implications both for researchers investigating procedural flexibility as well as secondary mathematics educators who seek to promote this capacity among their students. [ABSTRACT FROM AUTHOR]

The current paper presents an introduction to a special issue focusing on mathematical flexibility, which is an important aspect of mathematical thinking and a cherished, but capricious, outcome of mathematics education. Mathematical flexibility involves the flexible, creative, meaningful, and innovative use of mathematical concepts, relations, representations, and strategies. In this introduction we discuss the most relevant theoretical, methodological, and educational considerations related to mathematical flexibility, which form the background of the empirical studies presented in the special issue. Collectively, these studies provide a broader understanding of the mathematical flexibility, its subcomponents, influences, and malleability. [ABSTRACT FROM AUTHOR]

Empirical evidence indicates that students are not learning geometry with relational understanding of the concepts. Studies have shown that digital technologies can support students in mathematics. The purpose of this study was to find which technologies and technological affordances are specific to learners of geometry. This paper presents the results of a configurative thematic synthesis of empirical studies and theoretical papers to show that dynamic geometry environments (DGEs: including 3D DGEs) and logobased environments were the main types of technologies used to support geometry learners. The results of this study also reveal that there are five main technological supports provided to geometry learners - visualization, manipulation, cognitive tools, discourse promoters, and ways of thinking. [ABSTRACT FROM AUTHOR]

Computer-based testing is an emerging method to evaluate students' mathematics learning outcomes. However, algebra problems impose a high cognitive load due to requiring multiple calculation steps, which might reduce students' performance in computer-based testing. In order to understand students' cognitive load when answering algebra questions in a computer-based testing environment, three perspectives, element interactivity, practice effect, and individual differences, were investigated in this study. Seven levels of algebra exam questions were created using unary and simultaneous linear equations, and the inverse efficiency scores were employed as a measure of cognitive load in the study. Forty undergraduate and graduate students were tested. There were four findings: (1) As the element interactivity of test materials increased, the cognitive load increased rapidly. (2) The high-efficiency group had a lower cognitive load than the low-efficiency group, suggesting that the high-efficiency group had an advantage in a computer-based testing environment. (3) "Practice" has a considerable effect on reducing cognitive load, particularly in level 6 and 7 test items. (4) The low-efficiency group can reduce but not eliminate the gap with the high-efficiency group; they may require additional experience in a computer-based testing environment in order to improve reducing their cognitive load. [ABSTRACT FROM AUTHOR]

In this paper we describe a problem solving course for first year undergraduate mathematics students who would be future school teachers. [ABSTRACT FROM AUTHOR]

Mathematics results in South Africa are of serious concern. The reports by TIMSS [Trends in International Mathematics and Science Study] prove that the teaching of mathematics remains a challenge in the South African schooling system. In their attempts to improve mathematics results and to cope with the many curriculum changes since the start of democracy in 1994, mathematics teachers are experiencing increased levels of stress and anxiety. Diversity is a critical issue in education and learners suffer the consequences if teachers do not recognise the importance of diversity. Democracy leads to curriculum change and causes socio-cultural diversity among the learners in a classroom. Mathematics teachers faced ousting of their power in the classroom through the learner-centred strategies that they were expected to implement. In this study, three semi-structured interviews and a focus group discussion were deployed to generate data. The dualistic theoretical lenses used in this paper are based on the theory of culturally responsive teaching and theory of cultural capital. The findings that emerged from the data show that mathematics teachers are ill-equipped to meet the needs of the socio-culturally diverse learners in their differing classrooms. Further research in exploring ethnomathematics as a culturally responsive teaching strategy will reveal new dynamics in socio-cultural deficit thinking. [ABSTRACT FROM AUTHOR]

The mathematics education community has routinely called for mathematics tasks to be connected to the real world. However, accomplishing this in ways that are relevant to students' lived experiences can be challenging. Meanwhile, mathematical modeling has gained traction as a way for students to learn mathematics through real‐world connections. In an open problem to the mathematics education community, this paper explores connections between the mathematical modeling and the nature of what is considered relevant to students. The role of empathy is discussed as a proposed component for consideration within mathematical modeling so that students can further relate to real‐world contexts as examined through the lens of Ecological Systems Theory. This is contextualized through a classroom‐tested example entitled "Tiny Homes as a Solution to Homelessness" followed by implications and conclusions as they relate to mathematics education. [ABSTRACT FROM AUTHOR]

The paper presents a collection of problems from the Chernorizec Hrabar math tournament that takes place in Bulgaria during the last 28 years. The formulation of a question as a probability problem is used for different math ideas to be linked in a complex test unit. The complexity of the problem requires searching for the correct answer by applying not only advanced math knowledge and skills, but also a synthetic-type thinking, including some sense of mathematics. The multiple-choice format of the tournament problems allows students to skip a lot of routine work and to focus on the purified mathematical ideas. On one hand, the expected reasoning for the answer choice appears as an extract of the comprehensive problem solution. On the other hand, the reasoning forms the carcass of a sophisticated math task that challenges students synthetic competence. [ABSTRACT FROM AUTHOR]

This research paper examines tasks related to mean, median, and mode in seven Swedish textbook series for students aged between 10-13 years. The tasks were analysed based on context, mathematical properties, input and output objects, and transformations. These categories allowed for a thorough analysis of the opportunities afforded to students to understand these measures. The analysis revealed that most tasks focus on the mean and on procedural transformations with quantitative values. The findings suggested that the textbooks do not afford enough explicit context for students to develop a deep understanding of the mathematical properties of different measures of central tendency. By analysing various textbooks, a broader understanding of the learning opportunities afforded to students was gained. The discussion includes the implications of these results for task design. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Ahmet Kelesoglu Educational Faculty is the property of Journal of Ahmet Kelesoglu Educational Faculty and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Researchers have been paying attention to the convergence of technologies for it can result in improving human behaviour, including student's learning and teacher's instruction. The present paper intends to describe the different types of convergence of technologies in the classroom in general and the mathematics classroom in particular, focusing on the convergence of two types of them: convergence of the learner with the technological tools and convergence of the teacher with those tools. This focus is concerned with two instrumental frameworks: the instrumental genesis and the instrumental orchestration. The paper discusses the foundations of these two theoretical frameworks, the components of the frameworks and their educational uses as tools for analysing learners' and teachers' convergences with technological tools. Researchers assert that the two frameworks have contributed to the understanding of convergence of the learner and the teacher with technological tools, pointing, at the same time, at the need to extend these frameworks or combine them with other frameworks in order to understand the different aspects of this convergence. [ABSTRACT FROM AUTHOR]