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Motivation allows students to get interested in learning, serving as a "bridge" to academic achievement. However, mathematics is deemed as a complex one and involves a lot of thinking to understand its concepts which leads students to get discouraged which transforms motivation into a "broken bridge" due to several aspects. The study traverses and elucidates the lived experiences of students in terms of their motivation in learning mathematics lessons. The study, with a qualitative approach, uses Heideggerian Phenomenology and Interpretative Phenomenological Analysis (IPA) anchored on the modified Van Kaam Approach popularized by Moustakas. The selection of the participants was done with a purposive strategy aligning with the inclusion criteria set in this study. The process of gathering the data was done through conducting interviews with ten student participants from BSEd-Math 1 in Cebu Technological University - Moalboal Campus. The themes of the study are Theme 1: The Broken Drive, Theme 2: The Rebuilding, and Theme 3: The Hope collectively represent the lived experiences of the students in terms of their motivational aspect in learning the mathematics subject. Results of this study show that there are varieties of reasons why students have low motivation in learning mathematics, and at the same time have a different way of coping with such difficulties encountered. It is recommended that parents should encourage their children to cope with their learning difficulties, and teachers should encourage students academically in a way of employing the interest of their students in discussing the mathematics lessons. [ABSTRACT FROM AUTHOR]

Mastering Mathematics can take a lot of effort but takes the proper skills and ongoing practice. Imparting knowledge to the students in mathematics subjects that are known to be difficult has been a challenge for math teachers. From modular to full face-to-face classes, there have been several adjustments and difficulties for teachers, which pushed the researchers, to come up with the study about the pedagogical modifications done by the teachers. In particular, the teachers' coping strategies and the milestones that they have achieved after classes will also be determined. Mathematics teachers at Badian National High School were chosen as ten participants in this qualitative study. Specifically, it utilized Heideggerian phenomenology and interpretative phenomenological analysis (IPA), anchored on the modified Van Kaam approach popularized by Moustakas. Hence, the following themes emerge: (1) The Adjustment, (2) The Struggle, (3) The Motivation, and (4) The Scheme. In conclusion, difficulties in online classes are the unstable internet connection and the need to focus on online discussions, while the adjustments in full face-toface classes are time management, financial problems, and the distance between the house and school. It is recommended to hear out the voices of the teachers in their difficult times, help address them, and might as well be given some benefits for all their efforts in teaching young minds. [ABSTRACT FROM AUTHOR]

Mathematics has been known to be an intimidating subject to study, which leads many students to choose other courses instead of majoring in Mathematics. This qualitative study investigated the lived experiences of the students who chose Mathematics as their second option, the challenges they faced while taking the course, and the variables that influenced their decision to specialize in Mathematics education in college. Using the Heideggerian Phenomenology and Interpretative Phenomenological Analysis (IPA) based on Moustakas Modified Van Kaam Approach, the study analyzes the narratives of 16 participants from Bachelor of Secondary Education (BSEd) Math 1 students at Cebu Technological University-Moalboal Campus and identifies four core themes: (1) The Seeker, (2) The Warrior, (3) The Motivated, and (4) The Consequences of Choices. The findings suggest that these students have developed a strong sense of purpose and motivation despite facing challenges along the way. It is recommended that schools should implement programs to change student's perspectives on BSEd Mathematics courses and further investigation of various instructional techniques and approaches should be done to foster the appreciation of Mathematics among students. [ABSTRACT FROM AUTHOR]

Students with mature number sense "make sense" of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; R. Reys et al., 1999; Yang, 2005). Although national standards and policy documents (e.g., CCSS, 2010; NCTM, 2000, 2014) emphasize the importance of number sense, limited research exists on the association between students' mature number sense and other important psychological constructs in mathematics education, such as grade-level mathematics achievement. The present study addressed this gap through a longitudinal design, advancing fundamental knowledge of number sense as a construct. At the start of the school year, middle school students (N = 129 at Time Point 1) completed measures of mature number sense and several related constructs, including grade-level mathematics achievement, executive functioning, and fraction and decimal computation. Students returned in the spring (N = 115 at Time Point 2) to complete an end-of-year mathematics achievement assessment as a measure of grade-level content learned during the year. We found mature number sense to be measurably distinct from related constructs and uniquely predictive of students' grade-level mathematics achievement at the end of the school year, controlling for their beginning-of-year mathematics achievement. Educational Impact and Implications Statement: This study showed that middle school students' number sense uniquely predicts how much grade-level mathematics content students learn over a school year. Students completed a series of assessments at the start and end of a school year, and we analyzed which factors are most predictive of students' learning in math over the school year. Students' number sense was more predictive of grade-level mathematics achievement than was their executive functioning skills or even their fraction and decimal computation skills. These results suggest that teachers can view developing students' number sense and their grade-level math learning as complementary rather than competing goals. When students construct high levels of number sense, they are laying a strong foundation of math knowledge to build upon as they encounter new grade-level content and skills. [ABSTRACT FROM AUTHOR]

This study aimed to examine the influence of teacher support on student engagement in mathematics. A cross‐sectional survey was employed to recruit 632 students from grades 7 to 9 in junior middle schools across China. Participants completed various scales, including a teacher support scale, an academic self‐efficacy scale, and a student engagement scale. Data analysis was conducted using SPSS 20.0 and Amos 24.0. Results showed that, first, emotional support and competence support had a significant positive effect on student engagement in mathematics. The contribution from competence support was the strongest. The contribution from autonomy support was the weakest; second, academic self‐efficacy mediated the relationship between autonomy support, emotional support, and competence support and student engagement in mathematics. These findings supplement and expand the understanding of the factors that affect student engagement and provide theoretical support and useful guidance for formulating effective education policies to improve student engagement in mathematics. Practitioner points: Teachers' emotional support and competence support had a significant positive effect on student engagement in mathematics.The contribution of teachers' competence support to student engagement in mathematics was the strongest, followed by emotional support, and autonomy support was the weakest.Academic self‐efficacy mediated the relationship between teachers' autonomy support, emotional support, and competence support and student engagement in mathematics. [ABSTRACT FROM AUTHOR]

Well‐designed online educational games can improve students' math knowledge, skills and engagement; however, more research is needed to understand how to formatively assess components of students' mathematical understanding and learning as students solve problems in online educational games. In this study, we examined how 7th‐grade students' (N = 760) in‐game performance (ie, strategy efficiency, mathematical validity of the first action, mathematical errors) and help‐seeking behaviours (ie, hint requests) correlated with their algebraic knowledge in an online mathematics game. The k‐means cluster analysis identified four groups of students based on their in‐game metrics, and some variabilities in their in‐game performance were found. Although hint requests were available, only a few students showed a high percentage of hint requests during their gameplay. The regression analysis revealed that students' in‐game performance and help‐seeking behavioural patterns explained a significant amount of variance in students' algebraic knowledge above and beyond their prior knowledge. Our results suggest that how students interact with the online learning game is related to their later math performance, and qualitative aspects of student behaviours captured using log data provide meaningful information to students' algebraic understanding. Practitioner notesWhat is already known about this topic Well‐designed online educational games can improve students' math knowledge, skills, and engagement.Several studies found that some in‐game metrics, such as in‐game progress or correctness of tasks, are positively associated with learning outcomes.However, many studies used simple metrics like the correctness of each task or the number of problems completed to measure students' performance in the game.Few studies measured more in the moment or qualitative aspects of student in‐game performance, for example, how efficiently students solved problems in the game.What this paper adds In‐game metrics measuring more in the moment and qualitative aspects of students' problem‐solving explained a significant amount of variance in students' algebraic knowledge above and beyond students' prior knowledge.Students' strategy efficiency and strategic planning were positively associated with students' math problem‐solving performance.Although hints were available for almost all problems, only a few students exhibited a high level of help‐seeking behaviours, and the students with the lowest in‐game performance who needed help the most showed low help‐seeking behaviours.Implications for practice and/or policy Classifying students into profiles could provide ways to identify students with different levels of problem‐solving skills and help teachers provide more personalized instruction.Teachers could use this information as a formative assessment to identify the core areas of intervention needed, particularly for students struggling with math concepts taught in the game.Instructional strategies that make hints more appealing or engaging to students might be needed. [ABSTRACT FROM AUTHOR]

This study reports a secondary analysis from a randomized control trial study conducted with third graders with mathematics difficulty (MD; N = 75). We used simple linear regression to investigate whether students' performance on a word-problem vocabulary assessment predicted their performance on a measure of word-problem solving. Additionally, we used multiple linear regression to determine whether English learner (EL) status (n = 21; 28%) moderated this relation. Students' word-problem vocabulary knowledge significantly predicted their word-problem performance (R 2 =.27), but this relation was not moderated by EL status (Δ R 2 =.003). These findings suggest word-problem vocabulary knowledge is important for word-problem solving for students with MD, regardless of EL status. Given the results showed that improved word-problem vocabulary was associated with higher levels of word-problem solving, researchers and teachers might consider including word-problem vocabulary support as part of word-problem interventions. [ABSTRACT FROM AUTHOR]

This study investigated the parental involvement in learning Mathematics of students in relation to attitude and academic performance. The respondents of this study were the three-hundred fifty-six grade 9 students at 9 secondary schools in the Division of Bago City. Results showed that most of the respondents were female, belonged to income range Php 12,082 and below, their parents attained high school level, and had other works aside from being mentioned in the option of occupation. Level of parental involvement when taken as a whole was moderate; in terms of its areas, motivator and nature of Mathematics were interpreted as high and resource provider, monitor, Mathematics content advisor, and Mathematics learning counselor were all interpreted as moderate; level of attitude of students towards Mathematics was moderate; academic performance of students was very satisfactory; there existed significant difference on the parental involvement in learning Mathematics in terms of six areas. Results also revealed that there was a significant relationship between parental involvement in learning Mathematics and attitude of students; significant relationship also existed between parental involvement in learning Mathematics and academic performance; significant relationship was also noted between attitude of students and academic performance. Intervention plan/program was also provided based on the results of the study. [ABSTRACT FROM AUTHOR]

This study aimed to explore the effects of Mastery Learning Strategy (MLS) on senior school students' performance in Mathematics in Osogbo, Nigeria. The quasi-experimental study's goals were to investigate how MLS affected mathematics students' performance according to their gender and score levels. A purposive sampling technique was used to select two intact classes of 191 SS II students from two co-educational government senior secondary schools in Osogbo. The Geometric Constructions Test (GCT) which was made up of five theory questions adapted from WAEC mathematics past questions was used as the research instrument. GCT was revalidated by experts from the Department of Mathematics, University of Ilorin. The reliability index of 0.75 was obtained by test–retest method and Cronbach Alpha. Three research questions were raised from which three hypotheses were formulated. Data collected were analyzed using descriptive statistics, independent t-test and Analysis of Covariance (ANCOVA) at 0.05 level of significance. Findings revealed that MLS significantly improved students' performance (t(189) = 10.22, p < 0.05) while there was a significant difference in the performance of male and female students in favour of males (F(1, 94) = 33.06, p < 0.05). The strategy apparently helped to bridge the gap among students' scoring levels (F(2, 94) = 6.72, p < 0.05). The study found that, in comparison to the conventional method, MLS greatly enhanced students performance in mathematics. Hence, it was recommended that mathematics teachers should endeavour to adopt MLS in teaching Mathematics, especially in the perceived difficult topics. [ABSTRACT FROM AUTHOR]

This design‐based research project explored how various design features of AR‐based learning environments (ARLE) influence students' mathematics self‐efficacy and learning of kinematics. Specifically, five ARLEs with different design features were developed and implemented with 136 seventh‐grade students in two rounds. Data were gathered from pre‐ and post‐mathematics self‐efficacy tests, interviews, classroom observation records and reflective journals, to identify which design features promote or hinder students' learning and self‐efficacy. Results revealed that adopting a well‐designed ARLE is a viable way to promote students' learning and mathematics self‐efficacy, and the success of ARLE lies in (1) coherent tasks with proper time for self‐exploration, progressive levels, useful problem contexts and a certain degree of open‐endedness, and (2) sufficient technological affordances with strengthened authenticity, clarity and integrated media presentation, as well as engaging interactions with decent flexibility, embodied actions and feedback. These results validated the applicability of the proposed checklist for ARLE designers and practitioners in their design and implementation of ARLEs, within the domain of mathematics, physics and beyond. Practitioner notes What is already known about this topic AR‐based learning environments (ARLEs) have demonstrated substantial advantages in STEM education, but ARLEs can be a drawback if they are not adequately designed. ARLE may facilitate students' mathematics self‐efficacy, and relevant design features are underexplored. Design‐based research sustains interventions combining empirical research and theory‐driven design of innovative learning environments, for example, ARLEs. What this paper adds Demonstrates the potential of ARLEs that can be used in classrooms to support STEM learning. Identifies a collection of effective and ineffective design features of ARLEs that promote or hinder students' STEM learning and mathematics self‐efficacy. Tackles the challenges for the design of ARLEs for classrooms by taking AR technological affordances and the pedagogical perspective together. Implications for practice and/or policy Five ARLEs for STEM topics were developed and implemented in secondary schools. Evidence of positive impacts of ARLEs on students' learning and mathematics self‐efficacy. Our research produces useful guidelines for designers and practitioners in their development and implementation of ARLEs in real classrooms. What is already known about this topic AR‐based learning environments (ARLEs) have demonstrated substantial advantages in STEM education, but ARLEs can be a drawback if they are not adequately designed. ARLE may facilitate students' mathematics self‐efficacy, and relevant design features are underexplored. Design‐based research sustains interventions combining empirical research and theory‐driven design of innovative learning environments, for example, ARLEs. What this paper adds Demonstrates the potential of ARLEs that can be used in classrooms to support STEM learning. Identifies a collection of effective and ineffective design features of ARLEs that promote or hinder students' STEM learning and mathematics self‐efficacy. Tackles the challenges for the design of ARLEs for classrooms by taking AR technological affordances and the pedagogical perspective together. Implications for practice and/or policy Five ARLEs for STEM topics were developed and implemented in secondary schools. Evidence of positive impacts of ARLEs on students' learning and mathematics self‐efficacy. Our research produces useful guidelines for designers and practitioners in their development and implementation of ARLEs in real classrooms. [ABSTRACT FROM AUTHOR]

Background: Students' mathematics and science motivational beliefs are crucial determinants of their school academic achievement in math and science. The current study aimed to identify the group memberships of students' motivational beliefs in math and science, which are closely related. Furthermore, this study probed the predictive effects of individual students' experiences at school on forming group membership. We also tested the mean differences of the identified latent groups in math and science achievement. Results: Using latent profile analysis modeling, we examined data from 3857 Korean eighth-grade students participating in the 2019 Trends in International Mathematics and Science Study. The theoretical rationale and supplementary statistical indices showed a five-group membership as the optimal solution. The five groups are high motivation, medium motivation, low math/high science motivation, low motivation, and very low motivation. Students' sense of school belonging was the most crucial predictor in forming group membership, whereas perceived student bullying did not predict group membership. Finally, students in distinct motivational belief groups exhibited differences in their math and science achievements. Conclusions: This study identified five subgroups of students based on their distinct motivational beliefs in math and science, and variations in their association with achievements. In terms of policy development and intervention, it is important to nurture students' sense of school belonging. This study advances motivational theories in science, technology, engineering, and mathematics education, and provides practical suggestions for improving educational practices to enhance student math and science motivational beliefs. [ABSTRACT FROM AUTHOR]

Even prior to COVID-19, there had been an increase in the use of technology in undergraduate mathematics education to support the development of mathematical understanding and skill, and to enhance the student learning environment. Technology-enhanced resources can be used to provide formative assessment which can help students identify gaps in their knowledge and point towards appropriate action. In this paper, we report on the evaluations of a number of technology-enhanced resources that used formative assessment techniques and were provided for students attending non-specialist first-year undergraduate mathematics modules in Ireland. Analysis of the evaluations and consultation with literature identified 12 decisive factors that encourage students' successful engagement with the resources, covering aspects such as the educational context, affordances and types of technology, technological communication and formative assessment. These factors constitute important knowledge for practitioners as they can use them in the planning, design, and development of technology-enhanced resources for use in their modules. The measures observed during the evaluations indicated both positive and negative engagement providing a link between observations and resultant student engagement, which was found lacking in previous studies on student engagement. [ABSTRACT FROM AUTHOR]

Programming is becoming increasingly common in mathematics degrees as it is a desirable skill for new graduates. However, research shows that its use is mostly restricted to computational or modelling tasks. This paper reports a study on students' perceptions of and difficulties with Lean, an interactive theorem prover introduced as part of a transition to proof first-year module. The data consist of first-year university mathematics students' questionnaire responses (n = 99) and sections of 37 semi-structured interviews with students from the same cohort. Findings highlight students' difficulties with syntactic and strategic knowledge, in line with similar research on programming, and how conceptual knowledge is discussed in terms of conceptual-mathematics and conceptual-programming. Moreover, some students share how the experience with Lean changed their perception of mathematics by contributing to the epistemological shift from school to university, which is necessary for students to be successful. However, many students failed to engage with Lean due to its difficult syntax and because they perceived programming to be disconnected from the activity of proving and not worth the time investment needed to become proficient with this tool. We conclude with some reflections on the implications of this study for university teaching and suggestions for future research. [ABSTRACT FROM AUTHOR]

Secondary mathematics pre-service teachers (PSTs) are required to take university-level mathematics content courses to develop their mathematical content knowledge. Although PSTs' experiences as students play a major role in the types of teachers they become, there is limited research investigating the experiences of PSTs engaging in these courses. Thus, our study used a series of semi-structured interviews to provide first-hand accounts of PSTs' experiences. Findings suggest that PSTs experienced a range of challenges, including difficulties connecting with and understanding course content, and being ignored and dismissed by mathematics instructors. To cope with these challenges, PSTs became reflective practitioners and considered how their experiences in these courses applied to their learning as future teachers. PSTs also developed a community with each other that grew out of needing support with mathematical content, but evolved into collegial friendships. While PSTs were able to find positive features within negative experiences, this study highlights the need to understand PSTs' experiences in these courses so that effective improvements can be made. [ABSTRACT FROM AUTHOR]

The aim of the study was to examine how students generate problems about the concept of series, and how they evaluate and solve these problems. The difficulties experienced by the students while posing problems and their perceptions of the posing-evaluating-solving approach were also explored. In the first stage, 46 second-year university students posed problems for four tasks. In the second stage, which occurred a week after the first stage, the students evaluated their self-generated problems in terms of appropriateness to the tasks. The students who thought that they did not pose problems suitable for the tasks revised or reposed the problems, and then solved them by specifying the convergence or divergence of the series in the problems. The students also considered the impact of problem-posing implementation on their knowledge of the series. Findings showed that students' difficulties led to unsuitable and unsolvable problems. The most prominent difficulties were using sequences instead of series and using convergent series instead of divergent series or vice versa. Moreover, providing the students with opportunities to evaluate and solve their self-generated problems at the end of the second stage was effective for the increase in the number of suitable and solvable problems. [ABSTRACT FROM AUTHOR]

It is seen that there are few studies on the role of the knowledgeable other when the literature on Lesson Study [LS] is examined. However, for LS to be better understood and applied in different cultures, the role of the knowledgeable other in LS process should be clarified. This study aimed to determine the role of the researcher as the knowledgeable other in the planning phase of LS in the Turkish context. The study used a qualitative research method of action research design. The study participants were two mathematics teachers selected by convenience sampling and working in a public middle school in one of Turkey's central districts of a big city in the Central Anatolian Region. The data were collected by video-camera recording and analyzed by content analysis. As a result of the study, it was determined that the knowledgeable other contributed to the teachers participating in the study within the framework of the following seven themes: teaching approach, mathematical process skills, planning, student recognition knowledge, material use, guidance, and questioning. At the end of the study, there was a discussion on these themes, and some suggestions were made. [ABSTRACT FROM AUTHOR]

Many universities use diagnostic tests to assess incoming students' preparedness for mathematics courses. Diagnostic test results can help students to identify topics where they need more practice and give lecturers a summary of strengths and weaknesses in their class. We demonstrate a process that can be used to make improvements to a mathematics diagnostic test, so that it provides better information about students' abilities. To identify questions that could be improved, our process uses item response theory to analyse student data. We provide an accessible introduction to the key ideas of item response theory, and we describe how we applied the process of improvement of diagnostic tests at two universities. Our method provides a model for others wishing to make improvements to mathematics diagnostic tests. [ABSTRACT FROM AUTHOR]

This article reports on a qualitative investigation into students' thinking about a differential equations problem posing task; i.e. an initial value problem. Analysis of written and verbal responses to the task indicate that only four of the 34 students who participated in the study were successful in posing problems. Furthermore, only one of the problems they posed is solvable. In general, findings of this study indicate that posing problems involving initial value problems is particularly challenging for students. In light of the multitude of benefits of problem posing in mathematics education, I recommend the inclusion of problem posing tasks in the teaching and learning of undergraduate mathematics courses, including ordinary differential equations. [ABSTRACT FROM AUTHOR]

Affect has been identified as one of the important inputs in illuminating the mechanism of cognitive activities in mathematical problem solving (MPS). This study aimed to assess upper primary students' MPS-related affect with a focus on its differences across gender and grade-level among upper primary students. To do so, a simple Likert type scale was developed to measure students' MPS-related affect. Moreover, the study examined how this affective structure varies across grade levels and gender among upper primary students. The scale includes 5 subscales; Vision, Value, Enjoyment, Effort, and Self-efficacy regarding MPS. The responses of 725 upper primary students from different schools were considered to carry out the psychometric analysis and to demonstrate the scale's potential usefulness for measuring the MPS-related affective construct. The results revealed that girls and boys did not show any significant difference in the subscales, except for Vision of MPS, where girls report a higher dynamic (a non-static) vision than boys. When comparing grades, there were significant differences among these across variables. However, almost all variables (except Vision) show a decreasing trend, while Enjoyment and Effort have a wide range of changes along with grades. Ultimately, these differences need to be considered by mathematics teachers and curricula. [ABSTRACT FROM AUTHOR]

The purpose of this intervention study was to develop and evaluate a support model for teachers, designed to assist them in diagnosing students' (age 16–19 years) difficulties and providing feedback to support students' mathematical problem solving. Reporting on an iteration in a design research project, the results showed that the support helped the teachers to provide less procedural information and instead help students construct solutions for themselves. Constraints in achieving this included the nature of some tasks, difficulties in making reasonable diagnoses, and students' inability to communicate their difficulties. [ABSTRACT FROM AUTHOR]

Norwegian classrooms have become more culturally diverse due to immigration. School mathematics is frequently misperceived as the subject least impacted by demographic changes. In this paper, we draw on two important concepts – identity and culture – to explore how children of immigrant background construct their identities as mathematics learners. Data collection include classroom observations, focus groups, and individual interviews with three 12-year-old children in Oslo: Amar, Laila, and Maya. Thematic analyses yielded four themes around which pupils construct their identities. The first two regard positioning of the self in the mathematics classroom, and future-oriented self. The latter are concerned with family-related issues: parents' role in identity construction, and mathematical methods used at home. Finally, we discuss how our work opens avenues for further investigations. [ABSTRACT FROM AUTHOR]

The aim of the research was to examine different complications of learning mathematics online and their effects on students' academic performances. A crosssectional survey design was employed among 2311 students from the school to university levels in Nepal. Hierarchical linear regression and machine learning were major statistical techniques used in the research. The findings indicated that access to and cost of digital devices, training on digital skills, assignment submission skills, digital literacy, and a separate study room at home were major complications for students in learning mathematics online. Additionally, these complications to learning mathematics online negatively affect students' academic performance. This research gives new insights into the complications of online learning and its effect on learners' performance in mathematics as well. [ABSTRACT FROM AUTHOR]

GeoGebra, an open-source Dynamic Mathematics Software (DMS), has emerged as a transformative tool in mathematics education, allowing students and teachers to visualize, explore, and manipulate geometric concepts in dynamic virtual environments. This study investigated the students' knowledge of integration of GeoGebra in mathematics classes in lower secondary schools in Rwampara District, Southwestern Uganda. The objectives of this study were to identify the most abstract geometrical concepts posing challenges to students, examine the impact of GeoGebra training on the identified abstract concepts, and assess the relationship between students' attitudes and the integration of GeoGebra. This study utilized a quantitative approach, employing quasi-experimental and cross-sectional survey designs. Data were collected from 103 students using questionnaires and pre-and post-tests to evaluate the impact of GeoGebra software intervention. Independent samples t-test, Pearson's linear correlation, and descriptive statistics such as means, standard deviations, and frequencies were employed as data analysis methods. The study found that the students identified rotational transformation as the most abstract geometrical concept. The pre-test results indicated that respondents had similar baseline knowledge of rotational transformation. However, after the GeoGebra intervention, the post-test results showed that the difference in mean scores between the experimental and control groups was statistically significant. Additionally, the experimental group demonstrated a positive attitude towards the software. The study concluded that while rotational transformation posed a significant challenge for students, GeoGebra significantly improved their conceptual understanding and performance in this geometry concept. The study recommended that teachers should strongly consider integrating GeoGebra into their ICT-based teaching and learning resources to help improve students' conceptual understanding, motivation, attitude, and achievement in rotational transformations and other geometric concepts. [ABSTRACT FROM AUTHOR]

Formative Assessment (FA) is a promising teaching practice for supporting students' learning at school. However, implementing FA into teaching (mathematics) is challenging, effects of implementation of FA vary between empirical studies. Therefore, recent studies additionally consider instructional quality of teaching when analyzing effects of FA on students' learning. The current exploratory study builds on this idea and highlights the added value of considering both generic and subject-specific instructional quality (GIQ and SSIQ) when analyzing effects of FA: Based on a re-analyzation of data from the research project Co2CA, 856 students from 39 mathematics classes of German middle schools took part in an intervention control-study aiming at implementing FA into mathematics education at school. On the student level, students' mathematics achievement is assessed by standardized tests before and after the intervention. During the intervention, on the class level GIQ and SSIQ are assessed by low- and high-inference ratings of 72 video-taped lessons. GIQ is based on the model of Three Basic Dimensions, SSIQ is based on the normative idea that mathematics teaching should offer opportunities for a deep understanding of subject matter and for building up competencies. Multi-level regression analyses highlight different (interaction) effects of GIQ and SIQ on students' performances. It becomes obvious: Considering GIQ and SIQ can have an added value for the better understanding of implementing FA into teaching (in mathematics education). [ABSTRACT FROM AUTHOR]

The objectives of this research were to study the efficacy of the mathematics instructional model (BRIGHT model) based on realistic mathematics education (RME) and model-eliciting activities (MEAs) approaches to enhance mathematical thinking (MT) for upper primary school students as follows: i) to compare the mathematics achievement of students before and after studying with the BRIGHT model, ii) to compare the MT of students before and after studying with the BRIGHT model, and iii) to evaluate the students' and mathematic teachers' satisfaction on learning activities by using the BRIGHT model. The results of this research were as follows: i) the mathematics achievement and MT of students after studying were significantly higher than before studying with the BRIGHT model; ii) the student satisfaction with learning activities using the BRIGHT model was satisfied all aspects of the assessment. The mean scores from highest to lowest were as follows: benefits that student received, learning atmosphere, and learning activities, respectively; and iii) the satisfaction teachers and educational superiors were very satisfied with the learning management process and applying the BRIGHT model. Therefore, learning through the BRIGHT mathematical modeling has shown all aspects of students' and mathematic teachers' expected development. [ABSTRACT FROM AUTHOR]

In order to succeed in advanced mathematics and other related courses while in college, students must have a strong foundation in the subject of mathematics. Thus, this study aimed to determine the level of students' fundamental skills in mathematics in the areas of number sense, mathematical representation, spatial skills, estimation, patterns, and problem-solving when they are grouped according to the school of origin, strand, and program enrolled. Likewise, to test if there is a significant difference in fundamental mathematics skills when grouped according to the demographics. A descriptive comparative research design was utilized, and 278 first-year students participated. The results revealed that students performed better on their fundamental skills in mathematics in the area of patterns and performed lowest mean in spatial skills. Students who graduated from public schools performed well in all areas compared to private school students; in terms of program enrolled, fundamental skills in math varies. Furthermore, there is a significant difference in students' fundamental skills in mathematics when grouped according to the school of origin and strand, otherwise in program enrolled. This study suggests that mathematics teachers must utilize a different teaching strategy suited to students' needs following the learner-centered approach in teaching. [ABSTRACT FROM AUTHOR]

Introduction: Addressing mathematics anxiety is important to ensure that students achieve good academic performance and maintain their mental health during the critical middle school period. However, previous studies have focused on the separate effects of the preconditions for mathematics anxiety, ignoring the interaction of factors. Therefore, this study aims to identify the determinants of mathematics anxiety from the perspective of complex systems via necessary condition analysis (NCA) and qualitative comparative analysis (QCA). To the best of our knowledge, this is the first study to identify configurations of preconditions of mathematics anxiety among middle school students. Methods: A total of 183 middle school students aged 16 to 19 years (Mage = 17.47, SD = 0.89) in China participated in this cross-sectional study. The outcome variable of the study is mathematics anxiety, and the condition variables include mathematics grade, parental support, learning motivation, learning planning, and learning interest. Results: The necessity condition analysis shows that not all the condition variables constitute the necessity condition of mathematics anxiety alone. Four paths for the influence of multiple condition variables on mathematics anxiety are identified via the configuration analysis. Notably, even students with high mathematics scores and learning interest still experience mathematics anxiety due to a lack of practical parental support and learning motivation. High levels of parental support can exacerbate the mathematics anxiety of students under two conditions: 1) a lack of learning motivation and learning plans, and 2) interest in learning but low mathematics scores and unclear learning plans. Discussion: This study highlights the need to consider the comprehensive impact of mathematics anxiety, and the findings will help educators and researchers identify the different characteristics of mathematics anxiety in student populations. [ABSTRACT FROM AUTHOR]

Large language models such as ChatGPT have been shown to excel in solving complex math problems. However, they cannot solve basic arithmetic problems such as 758*639 = 484,362. This makes us ponder if LLMs have been trained to solve math and science problems in the right way. When a student learns math at school, she or he starts with arithmetic, then moves to word problems, polynomials, and calculus. Each skill she or he acquires will be used in the next stage to solve more advanced problems. In this paper we propose Scaffolding Learning for LLMs, which imitates how a student learns a subject in a step-by-step manner. For example, we first train an LLM to perform highly specific operations such as multiplication and division, and then apply such "skills" in a more generic task such as solving word problems. This is related to Curriculum Training, which trains a model on tasks following a specific order, such as training on easy tasks first and then gradually increases the difficulty. Our proposed approach goes from specific tasks to generic ones, which can be considered as a special case of Curriculum Training. Our empirical studies show that when an LLM has "mastered" a specific skill, only a small amount of training is required to teach it to apply the skill to a more generic application. [ABSTRACT FROM AUTHOR]

In this research, structural equation modeling and TIMSS data were employed to examine the impact of school belonging on math achievement among secondary students in Japan, Korea, and the United States, with a focus on the roles of math attitude and disorderly behavior. Utilizing SmartPLS 4.0, the study delved into the reliability and validity of the measurement model, the direct and indirect effects within the structural model, and gender differences in these dynamics. The findings indicated that while school belonging directly affected math achievement in the United States, it did not in Japan and Korea. Math attitude, encompassing aspects like enjoyment of math (liking math), math self‐concept, and the value placed on math (math value), along with disorderly behavior, emerged as key mediators in this relationship. The study also revealed that the associations between school belonging, math attitude, disorderly behavior, and math achievement were more pronounced in boys than in girls. Implications for educators are discussed. [ABSTRACT FROM AUTHOR]

School mathematics is not universal. It produces and is produced by social norms. What is considered as normatively appropriate school mathematics may vary when immigrant students (re)produce school mathematics in transitions between school mathematical practices at home and at school. In this study, one group of primary school students and two groups of secondary school students were interviewed to investigate their experiences with school mathematics in transitions. In contrast to some previous studies, the present study reveals instances where students positioned their parents as mathematically knowledgeable. To some students, it was important to know mathematical concepts in the mother tongue to be positioned as knowledgeable in mathematical conversations at home. This suggests that pedagogical practices should not only facilitate the transition of students’ everyday experiences into mathematics classrooms but also explore how school mathematics can be transitioned out of school, particularly considering transnationalities where ways of knowing transcend national boundaries. [ABSTRACT FROM AUTHOR]

Understanding math and the ability to use math in various situations can greatly contribute to a successful life. Different math skills are of importance for understanding and supporting math ability. In addition, math interest may influence math ability. We investigated the relationship between math conceptual and procedural skills, their development over time, and the relation to math interest in Grades three and five. Participants in the study were Estonian students (N = 855), who were in Grade three (2019/2020) during the first testing and in Grade five (2021/2022) during the second testing. Students completed math competence testing which consisted of procedural and conceptual skill tasks and a questionnaire about math interest. Both person- and variable-oriented approaches were used in the analyses. Students' math conceptual and procedural skills in Grades three and five were moderately related to each other. Furthermore, based on latent profile analysis, three profiles of skills were identified in both grades, distinguishing between students with low, average, and high levels of skills in both skills, with the exception of an approximately average-skill group in Grade five that had low conceptual skills but average procedural skills. Students were likely to remain in similar-skill groups for both Grades three and five. Lastly, there was a significant difference in math interest in Grade three among the groups with stable low, stable average, and stable high skills from Grades three to five. Fostering interest in math may be beneficial for achieving a high level of math proficiency. Future research should prioritize the integration of person-oriented methods into studies aimed at enhancing understanding of math skill development. [ABSTRACT FROM AUTHOR]

Online may not be the ideal format for a mathematics enrichment event, but in some circumstances, it may be the only option available. This article considers a mathematics enrichment programme consisting of a series of masterclasses which were held live online for secondary students in the UK during the Covid-19 pandemic. The series of masterclasses were part of the Royal Institution of Great Britain's Mathematics Masterclass Programme which runs annually across the UK. In this study, we investigate how and to what extent students were able to engage with this series of online masterclasses. Learner engagement is researched through in-session observations, student work, attendance data, participant feedback and interviews. While the online masterclass series lost some of its traditional in person features, such as hands-on live social interaction and a university environment, it appeared that the participants perceived the online sessions as interactive enabling them to both enjoy the sessions and enjoy learning mathematics in the sessions. The evidence found suggests that the participating students could engage behaviourally, emotionally and cognitively in online mathematics enrichment. However, constructing mathematical knowledge in online sessions can be difficult for some students and social interaction may need to rely on existing social groups among school friends. [ABSTRACT FROM AUTHOR]

Tutors play an important role in effective Mathematics Learning Support, and ensuring good initial training and development is key. Typically, in the UK and Ireland, tutors do not gain any formal recognition for the training they receive. This paper details a four competences model of training for tutors and presents the analysis of feedback from 11 tutors and two staff involved in piloting the model at two institutions. The model, which is informed by professional development guidelines, consultation across the mathematical sciences community, and enabled by a national Mathematics Learning Support Network, provides immediate recognition of the professional development undertaken and is amenable to formal accreditation. A structure of four digital badges is used to assign immediate value to the training and development of tutors. To add further value for tutors, a capstone tutor badge has been established for those completing all four competences. Thematic analysis of feedback from the piloting of the model identifies three overarching themes: the importance of community, developing as a professional, and motivating and enabling professional development. Although primarily of interest to those involved in Mathematics Learning Support, the innovative structure of the model and the insights gained from its piloting are such that it offers potential for genuine transferability across other subject disciplines. [ABSTRACT FROM AUTHOR]

The objective of this paper is to establish comparisons between the Linear Algebra (LA) approach practiced in Engineering courses offered by Chilean and Brazilian Higher Education Institutions and, for that, teachers from both countries were interviewed. From a methodological point of view, the research consists of two case studies. For the analysis of the interviews, we used the precepts of Content Analysis. The data were qualitatively analyzed considering the MTSK theoretical model. In this analysis, we sought to identify what specialized knowledge these teachers have regarding AL and about its teaching and learning. The results have shown that, in relation to the Mathematical Knowledge (MK) domain, which refers to content knowledge, the Knowledge of Topics subdomain (KoT), linked to the way that teachers know the topics they teach, is the most present among interviewees. In the Pedagogical Content Knowledge (PCK) domain, covering specific pedagogical knowledge linked to Mathematics, the Knowledge of Mathematics Teaching (KMT), regarding strategies, teaching theories, resources and materials, and Knowledge of Mathematics Learning Standards (KMLS) subdomains, concerning the curricular specifications and the moments in which the student must or can learn certain content and with what level of depth prevail. [ABSTRACT FROM AUTHOR]

This study uses ethnic capital theory to explore access to secondary mathematics education among linguistically diverse (LD) migrants in metropolitan and regional New South Wales, Australia. Administrative data from over 50,000 students who completed their Higher School Certificate in 2017 were analysed using multilevel logit regressions and marginal effects. The results indicate that, in Greater Sydney, all linguistically diverse first-generation youth took mathematics courses at higher rates than their peers. So did second-generation migrants from Asian backgrounds. Furthermore, considerably larger proportions of students who spoke East Asian, Indo-Aryan, or Arabic languages studied advanced mathematics. Even when only parents spoke these languages at home, their Australian-born children took advanced mathematics more often. Yet, these second-generation students were less overrepresented than those fluent in parental languages. The paper discusses the potential consequences of LD migrant concentration in Greater Sydney, stressing the importance of equitable mathematics education in metropolitan and regional areas. [ABSTRACT FROM AUTHOR]

The development of web-based technologies in recent decades has provided ready access to a wealth of on-line educational resources, and despite concerns that availability of on-line recorded lectures impacts on-campus attendance, we believe there needs to be more focus on the learning resources students engage with, along with why and how they use these resources. Our survey of first year science and mathematics students found that more than 80% of on-campus and off-campus students engaged with ≥75% of lectures by attending face-to-face and/or viewing on-line lectures. And when asked about their use of external resources, 80% of students reported using YouTube and/or Open Educational Resources, amongst other on-line resources, to provide increased understanding of content and to view worked problems. Knowing that a large percentage of students will seek out additional on-line resources, we conclude that ensuring all students have well developed on-line search skills and the ability to critically assess the quality of on-line resources are important contributions that teaching staff can make to student learning. [ABSTRACT FROM AUTHOR]

Pedagogical content knowledge (PCK) has been widely recognised as an important aspect of the expertise for teaching. However, the extent to which teachers' own teaching practice can be a learning resource for them to develop PCK has not been systematically explored. This empirical study aimed to explore the unique contribution of the work of teaching in teachers' PCK growth by concurrently considering other external professional learning opportunities teachers may have on the job. Using longitudinal data from 207 elementary and middle school teachers in the United States, we found that teachers increased their PCK through teaching on their own, albeit at different rates. Our findings were robust when other external learning opportunities teachers had were taken into account. Our findings underscored the importance of teachers' robust knowledge of school mathematics in the development of their PCK through teaching. [ABSTRACT FROM AUTHOR]

Learning mathematics in an online learning environment has unique challenges. Success in an online mathematics learning environment depends on a student’s self-regulating ability. This systematic review provides the scholarly community with a synthesis of current self-regulated learning (SRL) strategies of students in the mathematics online learning environment. We looked at research from 2014 to 2022 regarding the approaches, purposes, outcomes, and limitations of these studies. Our findings indicate that most of the studies focused on the effect of SRL on student achievement. The results reveal that 88.2% of the studies used a quantitative approach and 41.1% employed high-school students as study samples. In addition, most of the studies used questionnaires to collect data and indicated that their limitation was the narrow study context. We encourage learning institutions to integrate SRL strategies in mathematics online learning environments to improve the quality of education. [ABSTRACT FROM AUTHOR]

The aim of this study is to examine how algorithmatizing tasks engage mathematics students in algorithmic thinking. Structured, task-based interviews were conducted with eight Year 12 students as they completed a sequence of algorithmatizing tasks involving maximum flow problems. A deductive-inductive analytical process was used to first classify students' mathematical behavior according to four cognitive skills of algorithmic thinking (decomposition, abstraction, algorithmization, and debugging) and then develop sets of subskills to describe how the students engaged these cognitive skills. The findings show how students used algorithmic thinking to solve maximum flow problems and then made progress towards creating a general algorithm before being introduced to the maximum-flow minimum-cut approach, which guarantees a solution. [ABSTRACT FROM AUTHOR]

Biophilia is the theory that humans are innately connected to nature. As a basis for forming built space, biophilic design has been proven to reduce stress, improve cognition and enhance mood—it makes us happier. In the last 20 years, research in learning spaces has shown an association between biophilic design and student mood, calmness and improved standardized test scores. In 2019, a group of architects, scientists and educators led an experiment involving 6th-grade Math students at the Green Street Academy, which found that student stress was significantly reduced and learning significantly improved in a classroom enriched with biophilic strategies. The architects applied these strategies to the design of Bethel Hanberry Elementary School, and after a year of occupancy, an independent assessment found positive perceptions of the biophilic design, fewer behavior referrals, better teacher retention, lower absenteeism and improved test scores. In both a controlled research experiment and real-world application, the design of learning space, using biophilic strategies, has a significant impact. [ABSTRACT FROM AUTHOR]