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The study focuses on the identification of relationships and/or rules between computational thinking (CT) concepts among the undergraduate students of Applied Informatics due to their attitudes towards mathematics. We analyze three CT concepts -- decomposition, pattern recognition, and algorithmic thinking. We assume that students who have a closer relationship with mathematics, a positive attitude towards mathematics, have better developed CT. We conducted the experiment during the 2022/2023 academic year on the Information Coding and Displaying subject. The results indicate that those students who have no relationship to mathematics, negative attitude towards mathematics, have no problem with decomposition and pattern recognition, but without significant algorithmic thinking. On the other hand, students who have a close relationship with mathematics are also able to decompose or recognize patterns, but moreover they have shown algorithmic thinking. The contribution of the study comprises the identification of relationships and/or patterns of computational thinking concepts among students who have a relationship to mathematics, who cannot assess their relationship to mathematics, as well as among students who have no relationship to mathematics. Our results indicate a different occurrence of computational thinking concepts as well as links and/or relationships between them.

Purpose: Ethnomathematics are used in motifs by the Dayak Ngaju Tribe in Central Kalimantan. The motifs contain some Ethnomathematical objects and concepts for Geometry and values. Therefore, this study aimed to describe the motifs based on mathematical objects and concepts of Geometry and value viewed from ethnomathematics aspects. Methodology: This study used a qualitative approach with an ethnography method. The researchers collected information from documents and books. They conducted in-depth observations and interviews with the subjects regarding the culture of the Dayak Ngaju people who reside downstream of the Kahayan River in Central Kalimantan. The subjects were a Dayak Ngaju craftsman and a priest of the Hindu Kaharingan community. The motifs consist of "tingang," "dandang tingang," "jata," "batang garing," "tanduk muang," "buntut kakupu gajah," "taya" tree and "rambunan tambun." Findings: The motifs contain some mathematical objects and concepts. Mathematical objects are created as circles, "batang garing" and "jata" motifs, and a six-sided shape in the "tanduk muang" motif. The concept is the geometric transformations, namely the axis reflection in the mdandang tingang and tanduk muang motifs the axis reflection in the motifs of "tingang," "batang garing," "tanduk muang" and "taya" tree. The rotation on point (0,0) in the motifs of "buntut kakupu gajah" and "taya" tree, and the translation in the motif of "jata." Significance: The study provides some mathematical objects and concepts in the motifs of the Dayak Ngaju tribe in Central Kalimantan. Students learning those objects and concepts should be related to their culture, namely the motifs, and they should acquire the values in such learning. Ethnomathematics plays an important role among Dayak Ngaju people in understanding mathematics concepts such as Geometry and values.

To fully possess mathematical competence and to understand its relevance, importance and aesthetics, it is essential to be aware of aspects of mathematics not only as a school subject but also as a scientific discipline. In a systematic literature review, the theoretical characterization of compulsory school students' beliefs about mathematics as a discipline is investigated, as well as the empirical tendencies in the nature of their actual beliefs. Furthermore, the valuation of these beliefs is addressed. The 18 included studies demonstrate a clear pattern in applying a dualistic/relativistic spectrum when characterizing and analysing students' beliefs about mathematics as a discipline, with students generally possessing dualistic beliefs, which is in contrast to what is favourable to their learning.

Understanding the concepts related to real function is essential in learning mathematics. To determine how students understand these concepts, it is necessary to have an appropriate measurement tool. In this paper, we have created a web application using 32 items from conceptual understanding of real functions (CURF) item bank. We conducted a psychometric analysis using Rasch model on 207 first-year students. The analysis showed that CURF is a dependable and valid instrument for measuring students' CURF. The test is uni-dimensional; all items are consistent with the construct and have excellent item fit statistics. The results indicate that the items are independent of each other and unbiased towards the gender and high school background of the students.

STEM education is on demand more than ever as the workforce relies on 21st century skills and STEM disciplines. This paper presents a framework (IMS-TEAM) for integration of mathematics and science with the use of technology and modeling in an authentic context. The activity based on this framework is designed for and implemented with forty-four 8th grade students in Turkey. The study was conducted to investigate the impact of the activity as well as the IMS-TEAM framework. A qualitative methodology was utilized. Data analysis revealed that different components of our conceptual framework fostered the integration of mathematics and science affecting the nature of students' engagement with the activity. Different frameworks are required to be adapted to different environments with the consideration of learners and teachers. Future research investigating the effectiveness of IMS-TEAM framework adapted to different content and disciplines would provide more evidence on the effectiveness of the framework.

The teachers' beliefs in ethnomathematics-based numeracy learning are a crucial element to be able to develop students' numeracy skills. The teachers' beliefs in developing students' numeracy skills through ethnomathematics-based numeracy learning is a teacher's personal view about certain practices that are considered correct, which include four dimensions. The first dimension is the teachers' beliefs about numeracy. The second dimension is teachers' beliefs about the role of ethnomathematics in learning numeracy. The third dimension is teachers' beliefs about ethnomathematics-based numeracy teaching. The fourth dimension is teachers' beliefs about ethnomathematics-based numeracy learning. This study aimed to investigate the characteristics of teachers' beliefs in developing students' numeracy skills through ethnomathematics-based numeracy learning. The teacher's response was acquired through the completion of a questionnaire. The findings indicated that most teachers believed fostering students' numeracy skills could be achieved by implementing ethnomathematics-based numeracy learning inside the semi-realisticmechanistic (SRM) categories. Further analysis reveals that more extended teaching experience may mean something other than that a teacher has a realistically oriented outlook. Teachers with teaching experience of fewer than five years (new teachers) and 5 to 10 years (junior teachers') have a semi-realisticmechanistic (SRM) view. Most teachers with more than 10 to 15 years (semi-senior-teachers) of teaching experience have a dominant realistic (DR) idea. In contrast, teachers with more than 15 years (senior teachers) of teaching experience have a semi-realistic-mechanistic (SRM) view and a dominant realistic (DR) view. Teachers' positive beliefs will likely improve students' numeracy skills in general and based on teaching experience in the dominant realistic (DR) and realistic (R) categories regarding ethnomathematics-based numeracy learning.

The present study examines the first-year engineering students' attitudes towards mathematics, their beliefs and self-efficacy about mathematics, as part of their affective performance, in relation to their mathematical academic performance before and after attending an introductory mathematics course. It aims to contribute on the ongoing discussion about the teaching of mathematics at the level of higher education in engineering programs. First-year engineering students completed a questionnaire and a test after their entrance at the university. Their mathematical performance was examined by using their results at the midterm and the final mathematical mark during AMAT111 course offered at the first semester of their studies. Results indicated that aspects of the affective domain were related with students' performance, while the predominant role belonged to their previous mathematical knowledge and skills (as learning outcome of the high school education), which undoubtedly need further enhancement. The belief about a formalistic perspective of mathematics and the lack of understanding of the implementation of the mathematical concepts on engineering problem solving situations were obstacles for them on recognizing the importance of attending mathematics courses as part of their engineering studies. Discussion concentrates on the following up steps, which have to be done at the level of higher education in order to face the initial difficulties, which have been identified.

The aim of this pilot study is to evaluate the relevance of the use of history in mathematics education. This paper presents an experiment carried out in France with sixth-grade students (n=108) in which an ancient number system is used, an approach that is commonly suggested in French sixth-grade textbooks but has previously been unassessed. Based on the data of a pretest and a post-test surrounding an activity on an ancient Chinese numeration system, a statistical analysis using Rasch modeling shows a specific added value of the history of mathematics for students with low abilities in mathematics. For these students, a significant increase in observed abilities of +0.67 logit in mean is measured with a large effect size (Cliff delta +0.52). This effect is then weighted by considering the regression to the mean (RTM) effect, leading to a value around +0.14 logit in mean and a negligible effect size (Cliff delta +0.10). So, this pilot study shows the important effect of RTM, which suggests a very strong rebalancing of students' results. In the last part of the paper, we discuss how RTM can nonetheless be positively interpreted in this specific context where students' disorientation is one of the purposes of history in mathematics education.

The cognitive reflection test (CRT) assesses an individual's capacity to restrain impulsive and intuitive responses and to engage in critical reflection on mathematical problems. The literature indicates that several factors influence students' performance on CRT, including gender, age, and prior knowledge of mathematics. In this study, our objective was to investigate the correlation between CRT scores and students' achievements in both mathematics and physics. We conducted our research with a sample of 150 Italian high school students, and the findings revealed a positive predictive relationship between CRT scores and students' performance in both mathematics and physics. Furthermore, we employed an ordinal logistic regression to evaluate the impact of CRT scores, gender, and school level on students' achievements in mathematics and physics. The results showed that both CRT scores and school level had statistically significant effects on predicting these achievements. In contrast, gender emerged as a statistically significant factor only in predicting students' mathematics achievements.

One of the main objectives of international large-scale assessments is to make comparisons between different countries, education policies, education systems, or subgroups. One of the main criteria for making comparisons between different groups is to ensure measurement invariance. The purpose of this study was to test the measurement invariance of the mathematics intrinsic motivation scale across 14 countries. For this purpose, the "students like learning mathematics" scale, which measures intrinsic motivation for mathematics, was included in the TIMSS 2019 cycle. The study sample consisted of a total of 152992 students, 70192 4th grade and 82800 8th grade students from 14 different countries participating in the TIMSS 2019 cycle. Measurement invariance was tested with Multi-Group Confirmatory Factor Analysis (MG-CFA) and Alignment Method. The mathematics intrinsic motivation scale provides only configural invariance according to MG-CFA at the 4th grade level, whereas the scale provides approximate invariance according to the alignment method. At the 8th grade level, the scale provides configural and metric invariance according to MG-CFA, whereas the scale provides approximate invariance according to the alignment method. The results indicate that the mathematics intrinsic motivation scale provides approximate measurement invariance at both grade levels and that comparisons can be made between the scores of the identified countries.

STEM education plays a key role in influencing and orienting students' interests towards STEM fields and careers. This influence is multifaceted, involving not only STEM content and experiences but also teachers, schools, and personal factors. The purpose of this study is to explore the factors impacting the academic performance of 951 tenth grade students in STEM subjects (physics, chemistry, biology, mathematics, and information technologies) who are attending public and private schools in two provinces of Turkey. Using a correlational research model, the study assessed how students' personal characteristics, teacher effectiveness and school characteristics affect achievement in STEM courses. Data were collected using the 'Factors Affecting STEM Achievement Questionnaire (FA-STEM-A)', a 20-item questionnaire divided into three sub-dimensions. Analyses focused on the relationships between student characteristics, teaching quality, school infrastructure and STEM performance. Structural equation modelling revealed that positive student characteristics, especially fondness for STEM subjects and confidence in STEM abilities, moderately increase achievement. In contrast, negative factors attributed to teachers and schools, such as inadequate classroom activities, lack of educator expertise, inadequate technological resources, and large class sizes, hindered student performance. These findings emphasize the important influence of both inherent student qualities and external educational conditions in determining STEM education.

Contribution: Although a limited number of studies have compared textbooks used in introductory science courses (ISCs) and technical engineering courses (TECs), such a study has not been conducted regarding the Laplace transform (LT). The LT is one of the important topics that electrical engineering students learn as part of their undergraduate degree. It is instrumental in both ISCs (e.g., DEs) and TECs (e.g., signal processing (SP)). Background: Textbooks stand as one of the main resources for teaching and learning mathematics. Previous research has highlighted differences in how mathematical concepts are discussed in ISCs and TECs. These disparities might hinder students' opportunities to learn mathematics and identify the importance of mathematics in engineering. Intended Outcomes: The findings have the potential to increase awareness of mathematics and engineering instructors regarding the teaching and learning of the LT in ISCs and TECs. Additionally, it could result in the identification of several suggestions for textbook authors of DEs and SP, ultimately contributing to the improvement of engineering education for (electrical) engineering students. Application Design: This study uses the praxeological analysis rooted in the Anthropological Theory of the Didactic to analyze two textbooks. One is tailored for teaching and learning DEs, while the other addresses teaching and learning SP, a mandatory course for electrical engineering students in many countries. Findings: The findings indicate that there are several differences between the two textbooks, including differences in the purpose/motivation of presenting this topic and the definitions provided for the LT.

Contribution: Visual maps that illustrate how mathematics, physics, and electrical engineering classes are connected to each other during the first two years of the electrical engineering curriculum were developed. Key terminology and differences in presentation between fields are discussed. Background: Experience has shown that engineering students struggle when they need to use an approach from their mathematics or physics courses in their first- or second-year engineering courses. In particular, students have difficulty making connections between what they learned in mathematics and physics and how it applies to engineering problems. Improving students' ability to identify the connections between fields could increase student resilience in their engineering coursework. Research Questions: 1) Can visual representations of topic connections between fields across the entry-level engineering curriculum increase student's motivation for learning topics in physics and mathematics and improve their problem solving ability? 2) Are there language barriers or other differences between fields that hinder student learning? Methodology: A multidisciplinary team of faculty members from mathematics, physics, and electrical engineering developed visual representations of the links between the core electrical engineering, physics, and mathematics concepts required to solve problems that students will see in their early electrical engineering coursework. Inconsistencies in terminology or notation were explored and documented. Findings: The developed visual aids, coined systematic approach to problem solving (SAPS) maps, describe a mechanism for linking concepts and skills across the technical courses in the first two years of the electrical engineering curriculum.

Formal teacher leader programs that develop, position, and reward teachers to work with peers to improve instruction are a growing reform effort in the United States, yet there are few published studies of their efficacy. In this paper, we examine the impacts of one district's teacher leadership program on students' annual state test performance. The program placed full-time instructional coaches and partly released English language arts (ELA) and mathematics content specialists in each of 11 district schools. To assess the program's impact, we examined five years of student-level state test data; two years before the adoption of the intervention and three years afterwards. Using an interrupted time series design, we examined trends in performance before and after the adoption of the intervention. Overall, there were no significant effects in ELA, and a small negative effect in mathematics. By contrast, in the stable sub-sample of students who were in the district for the five years examined in the study, there was a large significant positive effect in mathematics and large but non-significant positive effect in ELA. We conclude with a discussion the implications of these findings for research and policy.

The study involved 2,575 students selected through a combination of probability and non-probability sampling procedures. Explanatory sequential mixed methods design was used. Participants completed the FennemaSherman Mathematics Attitude Scales (FSMAS) to provide the quantitative data for the research. The qualitative data were gathered through interviews. The arithmetic mean from the survey data for each of the students was used to shortlist 140 students for focus group interviews. The findings revealed that some of the impetuses that drive the respondents' positive attitudes towards mathematics were mathematics as a compulsory subject, good teaching strategies by teachers, the utility of mathematics, career aspirations, and encouragement from parents, guardian or peers. The study recommended that stakeholders should encourage, enhance and promote these factors. Teachers, educators, and researchers are encouraged to dig deeper to unearth more of such factors.

Implementing an equity agenda in the classroom is both necessary and challenging for classes containing pre-service teachers. For this intervention, we chose to begin our History of Mathematics course for preservice middle school teachers with a cultural simulation training exercise: Bafa Bafa. After participating in the exercise, pre-service teachers were asked to write a reflection paper and were later interviewed about their experiences in the course. Although participants found Bafa Bafa an uncomfortable experience, it was not an unsafe one, and the preservice teachers agreed that this exercise helped them better understand, articulate, and notice experiences with microaggressions.

To optimize teacher support, administrators need subject-specific knowledge, skills, and beliefs to lead, not just manage, instructional change. Professional development (PD) is needed with the many roles administrators are already called to fill. In this study, 38 elementary administrators participated in PD in mathematics instructional leadership. Findings from the Administrator Self-Efficacy Survey for Mathematics, derived from the Principal Self-Efficacy Survey (Smith & Guarino, 2005), show that subject-specific, district-led PD designed around sources of self-efficacy (Bandura, 1977, 1982, 1986) had a significant impact on increasing administrators' mathematics instructional leadership self-efficacy. Specifically, administrators increased their beliefs to influence effective mathematics practice, apply district PD to instructional leadership practices, and justify change during reform. These results show promise for future mathematics-specific instructional leadership development. Results from this study can inform PD design for districts and leaders aiming to promote and support school administrators as instructional leaders and advocates for evidence-based practice.

Mathematics is a challenging subject for most students in technical and vocational institutions. The institutions apply great effort towards developing mathematics knowledge and skills, mainly by influencing students' motivations. This study tries: (1) to present evidence for the validity of an instrument for measuring students' motivational beliefs as their beliefs, self-efficacy, and intrinsic-extrinsic goal orientations regarding mathematics; (2) to explore the relationship between institutional context and the instrument's scores as students' motivational beliefs. The data collected from 1,239 students from two different Chilean institutions were analyzed. The psychometric analysis provided evidence of the reliability and validity of the instrument. The instrument suggests differences in the level of motivational beliefs associated with students' age and the type of institutions. The instrument allows educators to study the relationships between motivational beliefs and the institutional context of technical and vocational schools. It can also be used for the prediction of student success in their mathematics course by the understanding of their motivational beliefs towards mathematics.

Critical thinking ability is a very important basic ability in learning mathematics. In the era of technological advances and digitalization, a comprehensive learning approach is needed that accommodates critical thinking skills. The controversial problem-based multimodal approach with ethnomathematics is seen as being able to improve this ability. This can be seen from the characteristics of the learning model with the Ethnomathematically Controversial Problem-Based Multimodal approach that accommodates visual, auditory, and kinesthetic learning styles. However, there is no empirical evidence that the combination of that approach and ethnomathematics (Balinese culture) in digital learning can improve students' critical thinking skills. This study aims to comprehend the impact of digital learning with a controversial problem-based multimodal approach, incorporating Meru and Jejaitan Bali ethnomathematics on students' critical thinking skills. Quasi-experimental research uses a Randomized Complete Block Design (RCBD) applied to measure students' initial abilities, namely students with low, medium, and high initial abilities. The instrument used in this research is a test of critical thinking skills which contains controversial issues with ethnomathematical nuances in the cases of the sacred building of Meru. The population consists of 202 grade IX students, with 48 in the experimental group and 52 in the control group. The ANOVA test results demonstrated that using this approach was effective in improving students' critical thinking skills. (This can be seen from the value of sig. 0.00 < =0.05 which means that there is a difference in students' critical thinking skills between the experimental class and the control class). According to the t-test results, students in the experimental group had significantly higher critical thinking skills than students in the control group. Tukey's test shows that critical thinking ability varies depending on the student's beginning ability. In conclusion, this combination is effective in improving students' critical thinking skills, especially on the topic of geometry.

The purpose of this study was to investigate the influence of cognitive training (CT) using mobile applications on attentional control and impulsivity among pre-service teachers. Pre-service teachers were divided into two groups: experimental (n=25) and control (n=14) groups, they were selected from a large sample (n=718). Over 28 sessions, the training group engaged in CT tasks (the tower of Hanoi [TOH] and simple reaction time [SRT]), whereas the control group did not participate in training sessions or understand the main goal of the study. In the criterion tasks (matching familiar figures and numerical Stroop), all participants were pre- and post-tested. CT using mobile applications helps us see how the trained group's attentional control and impulsivity had influenced. we also observed the progress of trained group as measured by number of moves or time for TOH, and reaction time (RT) for SRT. Other effects were observed in comparison to a control group that underwent no training. There were changes in impulsivity in post-test in favor of training group according to number of moves, and time component of matching familiar figures test. Corresponding to attentional control, the finding indicated that there were changes in (number and size) RT component in post-test in favor of training group.

Research in mentoring has shown that students may at times be more willing and able to absorb information that is delivered to them by their near-peers, rather than by traditional figures of authority, like teachers and professors. In this study, underrepresented minority high school students participated in an informal learning experience that was led by college students who were "near-peers" to the high schoolers. Students were engaged by participating in interactive MathShows, following a Math Social Media Campaign, and attending a summer Math Internship. Participants in the quantitative component of the study included N = 559 U.S. high schoolers who were from predominantly (>99%) Hispanic ethnic backgrounds. The qualitative component of the study involved another 19 students from the same school. The mixed methods study addresses associations between high schoolers' attitudes toward mathematics and their identity alignment, as well as classes of reasons that students gave for their identity alignment. Interactions with the college near-peers that occurred during the experiential learning intervention are also discussed. Results of this study address the goal of broadening participation of underrepresented student groups in STEM careers.

This is a comprehensive study aiming to examine pre-service primary school teachers' (PPST) mathematical disposition levels in terms of various variables, and to explain the results thoroughly. It employed the explanatory sequential design among the mixed method research designs. The data were collected through Mathematics Dispositional Functions Inventory (MDFI) and semi-structured interviews. The participants consisted of 361 PPSTs in the quantitative phase, and six PPSTs in the qualitative phase. Quantitative data were analyzed with descriptive and inferential statistics, while qualitative data were analyzed with descriptive analysis. The PPSTs' mathematical disposition levels did not differ significantly in terms of grade level, high school type, area of education at high school and ability area variables; however, their scores in the attitude toward mathematics lesson factor of MDFI differed significantly in terms of area of education at high school and ability area variables. There were significant, positive, and low-level relationships between PPSTs' mathematical disposition levels and their levels of mathematics learning experience in primary, middle and high schools, and their perception level of mathematics teaching efficacy. The PPSTs' scores in attitude toward mathematics lesson factor related to ability area were consistent with their statements in the interviews. The quantitative analysis results regarding mathematics learning experience levels and mathematics teaching efficacy perception levels, defined as continuous variables, overlapped with the qualitative analysis results.

The purpose of this study was to examine the mathematical creativity of gifted and non-gifted students through the indicators of creativity (fluency, flexibility, and originality). The study involved 12 secondary school students (six gifted and six non-gifted) from different cities in the Black Sea Region of Türkiye. The data were collected through clinical interviews regarding the solutions developed by the students for a problem-posing activity developed by Balka (1974). Each student was interviewed twice over a two-week period. Prior to the interviews, the students were asked to pose as many different and varied problems as possible. In the clinical interviews, the students' solutions were discussed deeply without evaluating their correctness. Using the theoretical framework developed by Taskin (2016), data were analyzed using fluency, flexibility, and originality indicators of creativity. The results revealed no clear difference between gifted and non-gifted students in terms of fluency indicators, but gifted students generally pose problems more creatively and flexibly than their non-gifted peers. It has been suggested that problem-posing activities be used to compare the creativity of gifted and non-gifted students. The indicators of originality and flexibility can also be weighted differently for calculating students' final scores of mathematical creativity because they are more effective at distinguishing gifted from non-gifted students.

This study aimed to examine whether a computational thinking (CT) intervention related to (a) number knowledge and arithmetic (b) algebra, and (c) geometry impacts students' learning performance in primary schools. To this end, a quasi-experimental, nonequivalent group design was employed, with 61 students assigned to the experimental group and 47 students to the control group (n = 108). The experimental group comprised students in primary school who were to be followed across the second and third grades. The experimental group underwent work with digital CT activities, while the control group did not receive such interventions. A one-way analysis of variance (ANOVA) was performed on the data gathered to assess the ability differences between students from the experimental and control groups. The pre-and post-test results revealed that the experimental group's performance was significantly better than the control group's performance for the content areas involving CT activities.

Problem-solving and enquiry-based learning are integral in the Mathematics and Science curriculum in South Africa through online-based assessment. Online assessment has rapidly gained recognition because of technology. In this paper, the authors explored the views of online baseline assessment among Senior Phase First-year Mathematics Student Teachers. The researchers adopted a qualitative research method. Data was collected from the participants using an online Google form developed into a questionnaire. The participants in this study were first-year students enrolled for the Bachelor of Education in Mathematics at a university in a rural province of South Africa. The first-year student teachers were exposed to the senior phase baseline assessments through the licensed online Computer Aided Mathematics Instruction (CAMI) tool. One hundred and sixteen (116) senior-phase student teachers completed the online questionnaire. This study used convenience sampling since it was the most appropriate method to conveniently invite the participant. The findings revealed that first-year student teachers were enthusiastic and motivated to write the baseline assessment on computers for the first time. The result also showed that several first-year student teachers experienced difficulties solving mathematics problems using computers. This study recommends more intensive research on student teachers' views on online assessment regarding gender and time.

The outbreak of COVID-19 and the consequent lockdown took the world by surprise, forcing the trimming of the school curriculum and institutions of higher learning to urgently adopt online platforms to continue teaching and learning. This article is a case study that explores the use of a social media platform, WhatsApp, to improve peer learning and peer support in a South African context. The study sought to explore the nature of peer-to-peer learning that took place, and how peer support contributed positively to a student's conceptual understanding of the mathematics concepts. It involved a cohort of 180 entry-level students of an undergraduate engineering mathematics course. Guided by social constructivism, we analysed the data qualitatively using grounded theory. The results suggest that WhatsApp served as a viable platform for communication and peer-to-peer learning of engineering mathematics concepts. The study also found that the WhatsApp postings peer support alleviated the negative effects of remote learning. Some implications of the study as well as recommendations are suggested.

Ticks and crosses (TCs) are a common aspect of teachers' classroom practice in relation to assessment in many learning areas including mathematics. Putting TCs in learners' written work is a strategy of feedback. Even though these TCs are frequently used in different types of mathematics assessments, there is limited research in relation to what they actually stand for and what functions they are designed for and especially what purpose they eventually serve in practice. This article emerged from a broader study that aimed at exploring classroom formative assessment practices of Grades 4-6 mathematics teachers, a learning goals and documentary analysis. Since this study was qualitative in nature, we used qualitative, non-probability sampling to recruit respondents according to pre-selected criteria relevant to our research questions. The study participants were 43 qualified and experienced Intermediate Phase mathematics teachers and 95 Grades 4-6 learners from the Tshwane South district, where a phenomenon of low achievement was of great concern. We engaged in document analysis of all the 95 learners' mathematics workbooks. Questionnaires were administered to the 43 teachers. We report on an analysis of teachers' assessment practices of Grades 4-6 learners' mathematics work. We narrate the extent of the use of TCs among teachers from selected schools in Tshwane South district in Gauteng, South Africa. Our analysis shows that while there is prevalent use of TCs among teachers, there are critical gaps in relation to knowledge of TCs in assessing mathematics. We present a qualitative and quantitative data analysis to illustrate how these were used in connection with assessment of learners' mathematics work linked to the concepts of numerical, geometric, and graphical relationships. We use our analysis of the vignettes to explore and argue that teachers use TCs without adequate understanding of what these actually mean in relation to assessment broadly and assessment intended at collecting and clarifying goals for mathematical learning specifically. Despite teachers having mathematical qualifications and a repertoire of experience for teaching, the majority of teachers grappled with understanding mathematical concepts as evidence in how they marked learners' mathematics work. The study also found that teachers' understandings of assessment of mathematics were diverse and largely inconsistent with the formal definitions of mathematics.

The goal of this research was to provide a general assessment framework of students' statistical reasoning in medicine, then build three scales to assess students' statistical reasoning ability in solving practical medical problems, including Description, Interpretation and Prediction. On that basis, the study designed a set of tools to assess students' statistical reasoning ability in solving practical medical problems. Through the analysis of the students' performance, assessments of the students' statistical reasoning in medicine were done. These research results were suitable for student assessment in medical statistics courses, useful for faculty and students in teaching and learning medical statistics.

Optimization is a vital mathematical concept widely applied in various engineering fields. However, teaching this subject to engineering students often involves abstract materials, making it challenging for them to grasp. To address this issue, a group of five mathematics lecturers collaborated on designing a practical lesson on optimization for first-year engineering students. The aim was to present the concept through a real-world problem, making it more accessible and applicable. The lesson focused on the design of water channels used for transferring water from sources to farms, showcasing how engineers can create optimal water channels with different geometrical cross-sections for agricultural purposes. This approach allowed students to see the direct application of mathematics in the real-world. The lesson was conducted as a three-hour workshop and attended by 38 volunteer first-year engineering students at a Malaysian university. Data were collected through observations and interviews and analyzed using the thematic analysis method. Feedback from both the lecturers and the participating students indicated that this teaching method significantly enhanced their conceptual understanding of mathematical optimization. Moreover, it fostered the development of problem-solving skills in real-world scenarios, bridging the gap between engineering and mathematics.

Studying students' performance in learning differentiability is essential since it requires them to perform proceptual thinking. This case study research investigates students' proceptual thinking outcomes in learning the differentiability concept using Desmos Classroom Activities (DCA) based on the Three Worlds of Mathematics (TWM) framework. In this study, DCA facilitates students' learning of differentiability with a sensible approach and exposes them to the graphical exploration of non-differentiable functions. Students succeeded in concluding that continuity does not imply differentiability. With its graphical, computational, and symbol manipulation capabilities, DCA has facilitated students to perform proceptual thinking in learning differentiability through a richer learning experience. Many students (76%) could perform at the procept level when solving the differentiability problem. Also, twenty-two students (about 88%) had no limitations in the graphical representation. The result of this study confirms that DCA based on the TWM as a generic organizer can contribute to students' proceptual thinking outcomes in learning differentiability.

This research aimed to reveal the effectiveness of using a Problem-Based Learning (PBL) physics pocketbook integrating augmented reality (AR) with the local wisdom of catapults in improving the mathematical and graphical representation abilities of high school students. This study is a quasi-experiment with a pretest-posttest control group design. The data collection was carried out in two stages, namely empirical testing and effectiveness testing stages. The empirical test was conducted on 276 grade XII students, while the effectiveness test was conducted on three science classes of grade XI students of State Senior High School (SMAN) 10 Yogyakarta. The three classes consisted of 36 students in the experimental class, 36 students in the Contrast Class 1, and 36 students in the Contrast 2 Class. The mathematical and graphical representation abilities were measured through a test instrument that passes the analysis of the empirical test using the QUEST program. General Linear Model (GLM) was utilized to analyze the effectiveness test, which was supported by the SPSS software. The result of the General Linear Model (GLM) analysis in the experimental class showed a significant value of 0.000 on the mathematical and graphical representation ability variables. The findings of this study indicate that the use of the developed Problem-Based Learning physics pocketbook integrating augmented reality with local wisdom is effective in increasing the mathematical and graphical representation abilities of grade XI students, with an effective contribution of 82.6% and 84.4% each.

This study aims to develop a scale to identify the factors influencing mathematics teachers' grading practices regarding students' in-class performance. The study was carried out with 180 secondary and 140 high school mathematics teachers from the southwestern region of Türkiye. The scale's construct validity was determined using item analysis, exploratory factor analysis (EFA), and confirmatory factor analysis (CFA). The EFA results showed that the scale consisted of a 5-point Likert-type scale with 36 items under eight factors (mathematical knowledge and skills, social behaviors, affective skills, effort, homework performance, follow-up test results, academic exam results, and external benchmarks). The scale explained 70.02% of the total variance, with factor loadings ranging from 0.50 to 0.92. The item-total correlations ranged from 0.36 to 0.64, and t-test results for the item discrimination index were significant. The Cronbach's alpha coefficient for the overall scale was calculated to be 0.92. The CFA results indicated that the scale model had a good fit (Chi-square/df = 1.39; RMSEA = 0.051; IFI = 0.98; NNFI = 0.97; CFI= 0.98; and SRMR = 0.062). Based on the findings, the scale is a valid and reliable instrument that may be used in determining the factors influencing mathematics teachers' grading practices.

This project focused on how two technology coaches, a K-12 Technology Coach and a Science Technology Engineering Mathematics (STEM) Coach collaborated with their coach colleagues and tech-industry partners to offer teachers resources and embedded professional learning (PL). As part of a multiple-case study of coaching models of PL, over the course of two academic years, the researchers gathered observational data during classroom coaching sessions, small group professional learning sessions, and professional development workshops hosted by a tech-industry partner. Additionally, the coaches and a subset of middle school teachers participated in one-on-one interviews and the coaches had discussions in a focus group. Data analyses distilled two main themes: (1) coaches appeal to and collaborate with tech-industry partners; and (2) coaches solicit support and collaborate with school district administrators. Conclusions suggest that technology and STEM coaches serve an integral role in the implementation of technology across the district when collaborating with tech-industry partners. Recommendations include the need for technology coaches to be resourceful and initiate and foster tech-industry partnerships as well as dedicate time to collaborate with other coaches to enhance their own professional knowledge and skills.

Computational Thinking (CT) has emerged in recent years as a thematic trend in education in many countries and several initiatives have been developed for its inclusion in school curricula. There are many pedagogical strategies to promote the development of elementary school students' CT skills and knowledge. Unplugged learning tasks, block-based programming projects, and educational robotics are 3 of the most used strategies. This paper aimed to analyze the effect of Scratch-based activities, developed during one scholar year, on the computational thinking skills developed and concepts achieved by 4th-grade students. The study involved 189 students from two school clusters organized into an experimental group and a control group. To assess students' computational knowledge, the Beginners Computational Thinking Test developed by Several Zapata-Cáceres "et al." (2020) was used. The results indicate statistically significant differences between the groups, in which students in the experimental group (who performed activities with scratch) scored higher on the test than students in the control group (who did not use Scratch).

This research evaluated the influence of technology-based teaching models on the development of critical thinking abilities in elementary school mathematics teacher candidates, as measured using Facione's (1990) criteria. The research was conducted with fourth-grade students studying in the Faculty of Education, Elementary Mathematics Education at a state university in the Marmara Region of Türkiye during the 2019-2020 Fall Semester. A case study research design was used to obtain a qualitative understanding of the participants' experiences. Two pre-service teachers were video-recorded throughout the research implementation process (5 weeks in total, from the 3rd week when the teaching model practices started to the 7th week when it ended). The dialogues in the video recording were analyzed using the descriptive analysis technique. Keywords and sentences describing the critical thinking sub-skills identified by Facione (1990) were observed to be included in the student dialogues, especially in the implementations of the designed teaching model that required the use of GeoGebra. These dialogues concluded that the proposed instructional model programs are consistent with the critical thinking competencies, include activities to use critical thinking skills, and can provide opportunities for developing critical thinking skills.

This article is an excerpt from a master's thesis developed in Brazil, in which we approach recurrent and linear sequences, given some intriguing particularities in their definitions and the scarcity of discussion of this topic in the literature of the History of Mathematics, especially with regard to its geometric representation. Thus, we aim to present the identities of Fibonacci, Lucas, Jacobsthal and Padovan in a three-dimensional visualization with the contribution of GeoGebra software. The research methodology chosen was bibliographical, exploratory in nature, where we have theoretical support in works such as Oliveira and Alves (2019), Silva (2017), Souza and Alves (2018), Vieira and Alves (2020). This research brings as results a set of geometric constructions of the identities of the proposed sequences, in three-dimensional perspective, being a support for future works developed around this theme. GeoGebra was essential in the process of constructing and visualizing the sequences, as it provided strategies for understanding the recurrence relations and the properties of the Fibonacci, Lucas, Jacobsthal and Padovan sequences, through the behavior of the visual representations of these identities.

This research aimed to investigate the relationship between mathematical epistemological beliefs and the mathematics motivation of high school students. The survey model was employed in the research. Four hundred twenty-four high school students constitute the study group from public high school. Data were collected through the "Mathematics-Oriented Epistemological Belief Scale" and the "Mathematics Motivation Scale." The Mann-Whitney U and Kruskal-Wallis H tests were used to analyze the data. The findings showed a significant positive relationship at a moderate level between the belief that learning depends on effort with motivation, a weak and negative significant relationship between the belief that learning depends on ability with motivation and a negative and insignificant relationship between the belief that there is only one truth with motivation. The mathematical epistemological beliefs and mathematical motivations of high school students differ statistically in terms of gender, mother's education level, and daily studying time. However, they do not differ statistically regarding out-of-school support, technology, internet use, class level, father's education level, or perceived income level.

Education for Sustainable Development (ESD) is an initiative of the United Nations' Sustainable Development Goals (SDGs). ESD contributes to a sustainable community by teaching students about their personal impact on their community to help them make resourceful decisions. The researchers are interested in principals' role when implementing ESD within their schools. This was a qualitative study, which included six school principal interviews. The findings included the following themes: math and reading were a priority, social and emotional needs were prioritized, ESD was seen as extracurricular, and current events and students' interests influence learning content and activities.

Studies show that indigenous languages have exhibited enormous impact on the evolution and didactics of counting and place value. However, Ghana systems have different perspectives and pose varied successes on the didactics of counting and place value. In this study, we explored a mixed methods design to examine the mismatch between Ghanaian and Hindu-Arabic systems. With a sample of 178 participants, we further examined not only student-teachers' knowledge and transitioning but also their skills and conceptualisation in didactising nine Ghanaian languages with respective to the Hindu-Arabic system. Both quantitative and qualitative data were collected through test and interview instruments. They were analysed by utilising T-test, ANOVA and verbal narratives which complemented and corroborated each other. The one-sample t-test result indicates that there was no impact of Ghanaian languages on counting and place value systems. However, the ANOVA test result infers that there is an impact of indigenous Ghanaian language on counting and place value systems. The qualitative results confirmed that the student-teachers had average skills in didactising counting and place value systems in the Ghanaian indigenous languages. It was therefore recommended, among other things that, measures should be taken not only to synchronise the Ghanaian languages but also to finetune the languages in tandem with the Hindu.

Early mathematicians viewed mathematics as a beautiful and ethereal art form. However, the pupils in school appear to have no idea of this beauty. Misconceptions about mathematics among students, parents, and instructors are thought to be one of the root causes of the problem. Mathematical misconceptions and myths among instructors, parents, and students were examined in this study. These findings were obtained using a descriptive qualitative method of investigation. Research participants included elementary school pupils and their parents from East Java, Indonesia as well as 10 instructors, 10 students, and 10 parents. Random selection was used to pick the respondents. The results of this study showed that teachers, parents, and students have a wide range of misconceptions about mathematics. Among the misconceptions that occur among students, teachers and parents are: i) The conception of mathematics; ii) The aim of learning mathematics is only to train students to count and memorize formulas; iii) Mathematical ability is a genetic talent and only people who have talent will be proficient in mathematics; and iv) Mathematics is a non-applicable. The consequences of widespread misconceptions about mathematics among teachers, parents, and students are detrimental to the learning process and hinder the development of strong mathematical skills.

This research is an ethnomathematical research that aims to explore the mathematical abilities of the Bugis people in weaving the "lipa' sabbe." This study applies a qualitative method with an ethnographic approach. The data were collected through observation, interviews, and documentation. Based on the results, it can be explained that in the process of weaving silk, the craftsmen combine the techniques of counting, designing, placing, and measuring as mathematical activity to produce various motifs. The weaver's ability to count and design motifs produces geometric planes that are transformed through a combination of reflection, translation, and dilatation. In making visualized motifs resembling curved planes such as the "lagosi" motif, the "phinisi" or the "batumesang" motif, they are approximated by using a collection of rectangular pixels from the arrangement of warp, weft and other motif yarns such as gold or viscose. The redesign of the silk motif uses the the number patterns identified on the arrangement of the yarns. In algebra, the "lipa' sabbe" motif can be represented by a set of constant functions, parallel linear functions, or degree-n polynomial. The results of this study indicate that the mathematical concepts in "lipa' sabbe" motifs are not only in the form of geometric concepts, but also include the concepts of number pattern, and algebra. Based on the manufacturing process and the resulting motifs indicate that the craftsmen have unique mathematical abilities.

To assess the integration of information and communication technologies (ICTs) in teaching and learning, a new construct for ICT competence was developed by the Programme for International Student Assessment (PISA) in 2022. The framework for ICT assessment involves four major dimensions; access to ICT, use of ICT, students' ICT competencies, and subject-related ICT use. In this paper, we analysed this ICT assessment in terms of validity construction of test scores with data from PISA 2018 and investigated ICT competence in relation to the variables of mathematics, science, and reading literacy. The analyses were based on public data from PISA 2018 for Turkey (N = 6890). After removal of univariate and multivariate outliers from the Turkish sample, factor analysis, correlation analysis, and structural equation modelling were performed on 5438 data items. In the study, we confirmed the four-dimensional structure of ICT competence for the Turkish sample. In this study, the construct validity of the PISA 2018 application ICT test was verified using the Turkish sample. The ESCS variable was included as a control variable in the analyses due to its significant impact on the relevant variables. The analysis showed that the mathematical literacy scores of the PISA 2018 Turkish students were positively low affected by the availability of ICT, negatively low affected by the entertainment of ICT, and positively low affected by the interest and perceived competence in ICT, use of ICT for educational purposes at school and outside school, and the use of ICT related to the subject. Considering the ICT variables that affected the PISA 2018 students' science literacy scores; the entertainment of ICT and the interest and perceived competence in ICT significantly low affected the students' use of ICT on the subject. On the other hand, the availability of ICT negative significantly low affect their science literacy scores. While the entertainment of ICT negatively low affected the science literacy scores, interest and perceived competence in ICT and use of ICT for educational purposes at school and outside school positively low affected the students' use of ICT on the subject. Finally, when we look at the ICT variables that low affected the students' reading literacy scores; and use of ICT for educational purposes at school and outside school and the interest and perceived competence in ICT significantly positive low affected the use of ICT on the subject. On the other hand, the availability of ICT negative significantly low affect reading literacy scores. While the entertainment of ICT negatively low affected reading literacy scores; interest and perceived competence in ICT positively low affected the use of ICT on the subject.

Students are encouraged to develop a set of scientific skills and disciplinary practices common across the STEM disciplines. These skills (scientific inquiry, quantitative skills, laboratory and computational skills, communication skills, teamwork/interpersonal skills, interdisciplinary competency) are highlighted as important in discipline-based guiding documents -- biology (Vision and Change in Undergraduate Biology Education: A Call to Action), chemistry (American Chemical Society Guidelines and Evaluation Procedures for Bachelor's Degree Programs), and mathematics (A Common Vision for Undergraduate Mathematical Sciences Programs in 2025) -- for undergraduate teaching of biology, chemistry, and mathematics, and for the professional success of STEM college graduates. To promote interdisciplinary teaching and learning of STEM, we present a comprehensive comparison of the different disciplines' competency statements for undergraduate education. This organization and comparison of commonalities in scientific skills and disciplinary practices can be used by faculty and departments to come together to break down traditional silos, help their students more easily apply learning from one STEM discipline to another, and to create institutional change.

In this article, we discuss Micro Assignment Guided Inquiry and Collaboration (MAGIC), an active learning method that draws on the merits of inquiry-based learning in STEM courses. We describe the use of Micro Assignments (MAs) consisting of a series of short, instructive guiding questions that scaffold the course material. Students work through these questions and present solutions to the class. The instructor facilitates learning as well as collaboration among the students during face-to-face interactions, providing the Guided Inquiry and Collaboration (GIC). We present a qualitative discussion about this active learning approach that achieves some of the documented benefits, such as deep student engagement with the material and familiarity with communicating arguments. This method also helps students develop the skills they need as they move from lower- to upper-level courses, such as collaborating, active reading, and breaking down involved assignments and problems into manageable steps. Through GIC and use of the MAs, the instructor guides students to become more abstract thinkers who desire evidence, evaluate arguments, and no longer follow step-by-step formulas but rather produce logical thought processes.

This study explores calculus students' opportunities to learn the concepts of integral by examining one mathematician's videotaped lessons and the textbook. Results show that both lessons and the textbook introduce important cognitive resources briefly and focus on other units of knowledge. Implications to these results are also discussed.