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Mathematics education is looking for innovative methods to foster problem-solving skills in students. This research develops a problem-solving assessment using GeoGebra Classroom, a versatile interactive mathematics software, to revolutionize mathematics formative assessment and improve students' problem-solving skills. This study adopted the analysis, design, development, implementation, and evaluation (ADDIE) instructional design model stages. The design stage created a comprehensive assessment blueprint, incorporating GeoGebra Classroom functions to create interactive problem-solving tasks. Data analysis used both quantitative and qualitative approaches. Qualitative data consisted of feedback and suggestions from assessment experts, mathematicians, and GeoGebra specialists. Meanwhile, quantitative data included expert scores and cognitive tests that measured students' problem-solving abilities. A cognitive post-test was conducted to measure the progress of students' understanding while using the assessment product. The results of the content validity analysis, assessed using Aiken's V, ranged from 0.85 to 0.92, indicating a high level of validity for the problem-solving skills assessment in terms of content and construction. Some revisions were made to the design of the developed media to make it more interactive for students. These findings suggest that we can further use problem-solving questions integrated with GeoGebra Classroom to uncover the problem-solving skills of junior high school students.

The fear of failure stops students from thinking logically and processing information in mathematics. Creating an appropriate classroom climate based on every student's ability is crucial to overcoming the prejudices associated with mathematics. In this regard, this study aims to create the best classroom climate approach that will increase interest in mathematics and ensure academic success. For this purpose, mathematicians' views on the classroom climate approach and how they create them were discussed by using qualitative techniques. It was considered that teachers participating in this research are working in 9th grade in state high schools affiliated with the Turkish Republic of North Cyprus Ministry of Education, accepting students through examination. The researchers collected teacher views through a semistructured interview form and analyzed them using context analysis. The findings showed that teachers were in a hurry to teach and generally paid attention to creating a comfortable classroom climate in which students could express their thoughts and opinions. This situation also revealed a lack of adequate classroom climate approach skills among teachers. Therefore, the classroom climate approaches discussed in this study are expected to make a significant contribution to this field by offering solutions to teachers in creating a supportive classroom climate.

Purpose: The language load within mathematics test items can lead to inaccuracy in assessing "Orang Asli" pupils' mathematical ability due to their struggle in comprehending the academic language. This study aims to determine the validity of using test accommodations in the form of oral academic language and oral native language when administering mathematics computation and word problem test items among the "Orang Asli" pupils. Methodology: By employing a quantitative approach, this study utilised random equivalent group design to examine the validity of using oral test accommodations among 334 Grade Four "Orang Asli" pupils. Three testlets were constructed and used in this study: written test in the academic language (WAL), oral test in the academic language (OAL), and oral test in the native language (ONL). The three testlets comprised Paper 1 and Paper 2, each consisting of 20 mathematics computation and 20-word problem test items, respectively. One-way ANOVA was used to analyse and examine if there were differences in the mathematics performance between the three groups of tests administered to the "Orang Asli" pupils. Findings: The results indicated that the test scores of the pupils on the oral tests were higher compared to the written test administered to the pupils for both mathematics computation and word problem items. For computation items, the pupils performed better in the OAL testlet, followed by the ONL testlet. On the other hand, the pupils obtained the highest test scores in the ONL testlet compared to the OAL testlet for word problem items. Furthermore, the results illustrate that there is a difference in the mathematics performance of the "Orang Asli" pupils between the oral tests in both languages and written tests in the academic language. Significant: This study clearly shows that language plays a prominent role in affecting the "Orang Asli" pupils' mathematics performance. By utilising the oral test as a promising test accommodation, this measure could help address the language barrier faced by the "Orang Asli" pupils in mathematics testing.

The aim of this study is to develop a theoretically sound, valid, and reliable scale to examine seventh and eighth grade students' attitudes towards so-called skill-based mathematics questions (SBMQ). The sample of the study was 820 seventh and eighth grade students at three different middle schools in Etimesgut District of Ankara Province. A draft item pool was crafted after a detailed literature review and the scale was finalized for the implementation after receiving expert opinions. This version of scale was administered shortly before the national examination which included skill-based questions in the 2022-2023 academic year. Exploratory and confirmatory factor analysis methods were used to examine the construct validity of the scale. The analysis resulted in 16 items in three factors (affective, cognitive, and motivational) which explained 46% of the total variance. Cronbach's alpha and composite reliability scores were above 0.70 for each factor and whole scale. The results indicated that the Attitudes Towards SBMQ Scale developed for seventh and eighth grade students is valid and reliable.

The study reported on here was conducted to explore four Grade 7 mathematics teachers' understanding of the relationship between the objectives indicated in the CAPS for teaching different topics/concepts and instructional time stipulated for doing so. Seven lessons were studied in 4 primary schools in the Vhembe district of the Limpopo province, South Africa. A constructivist philosophical approach was used. The data collection methods included interviews and classroom observations. The main finding indicates teachers' understanding of instructional time as either a regulatory or a teaching tool. The ability to translate instructional time into social time depends on the level of teachers' curriculum literacy. Consideration of how CAPS objectives could be fulfilled based on the topic/concept to be taught and the stipulated instructional time, influenced the learners' conceptual understanding, procedural fluency, and competency in mathematics. The conclusion underscores the importance of instructional time as both an essential authoritative regulatory tool and signal of a pedagogic device and communication required to advance the instructional objectives.

The COVID-19 pandemic compelled higher education institutions to adopt an alternative approach to learning. For mathematics education, supporting students through blended learning has become increasingly important as it will ensure students' learning is sustained in such a situation. This practical change has illuminated how cloud technology can be employed in mathematics education to improve the instruction process. Using a cloud classroom blended learning-instructional framework for integrating educational cloud tools into mathematics teaching, this study analysed students' metacognitive ability in mathematical problem-solving. A pre-experimental research using a one group pre-test-post-test design was conducted. The sample comprised sixty undergraduate mathematics students enrolled on a Numerical Analysis course. Sample selection was carried out using a simple random sampling technique. Data were analysed using a descriptive analysis, parametric tests, and n-gain. The results revealed that, firstly, the majority of students (90%) achieved a post-test score of metacognitive ability in mathematical problem-solving -- this exceeded the 60% threshold. Secondly, students' post-test score of metacognitive ability in mathematical problem-solving (mean score of 82.14, S.D. = 8.29) increased significantly compared to the pre-test score (mean score of 73.54, S.D. = 8.38). Further, the effect size was large. Thirdly, there was an enhancement of metacognitive ability in the mathematical problem-solving of students with a mean n-gain of 0.34, which is in the moderate category. Thus, cloud classroom blended learning significantly improved metacognitive ability in mathematical problem-solving among undergraduate students. Educators can apply the results to assess mathematics learning in order to improve the quality of metacognitive ability in mathematical problem-solving.

The first step to access information; it is possible to perceive it by hearing, seeing and touching. It is necessary to make sense of this gained knowledge. Therefore, having some basic skills forms the basis of all disciplines. The purpose of this research is to determine skills through activities prepared with an interdisciplinary approach. The research was designed as a case study. Purposeful sampling method was used to determine the study group of the research; the study was conducted with third grade primary school teaching students as the study group. As data collection tools in the study; skill target list, in-class skill observation form, semi-structured interview form and student products were used. At the end of the research, the students' skills were determined and in terms of science skills; it was revealed that life skills and innovative thinking skills were sufficient, but scientific process skills were not sufficient. In terms of language skills, reading and writing skills were found to be at an intermediate level. However, speaking skills, which are self-expression skills, were found to be at a low level. In terms of mathematical skills, it was observed that their problem solving skills were high, but their level of using basic mathematical skills was low. Technology skills; it has been found that it is sufficient in terms of algorithm creation, but not in the context of science acquisition. In addition, it has been observed that the activities prepared through the task-oriented teaching method make the lesson interesting and are effective in revealing creativity.

Background: The Mental Starters Assessment Project (MSAP) seeks to address poor performance in Grade 3 mathematics. The programme focusses on eliminating inefficient counting methods and promoting strategic mathematical skills, including numerical sense, mental calculation and rapid recall skills. Additionally, MSAP supports teachers' professional growth by providing them with a toolkit of effective calculation strategies to bridge the performance gap and enhance mathematical education. Aim: This paper explores the insight gained from reflections of final year Bachelor of Foundation Phase (FP) initial teacher educators (ITE) students in South Africa. Setting: Grade 3 classrooms. Methods: The ITE students were given training and materials to implement the MSAP, and this occurred over a 4-week teaching practicum, after which they completed a reflective task on the implementation. A total of 20 students were selected from a cohort of 138 based on their academic performance. Results: The analysis of the reflections showed that ITE students benefitted from reflecting on their practice and highlighted important elements of their professional learning. The reflections raised issues related to challenges in their pedagogical content knowledge (PCK) as well as their confidence and competence to teach mathematics and manage the classroom context. Conclusion: With a multi-dimensional model of reflection, ITE students can achieve a deeper understanding of mathematics teaching and learning when building learners' mental strategies, fostering professional growth and elevating the overall quality of mathematics education. Contribution: Overall, the findings provide insight into the benefits of reflective practices for ITE students' professional development and the improvement of mathematics education.

Developmental mathematics courses play a critical role in ensuring that students have the foundational mathematical skills necessary to succeed in higher educational mathematics coursework. With the introduction of the corequisite format in recent educational reforms, there has been a growing trend towards transferring developmental mathematics courses to computerized adaptive learning platforms such as computer aided instruction (CAI) and mastery-based learning for developmental math content. While this trend has led to increased accessibility and flexibility for students, it has also raised concerns about the effectiveness in supporting students' acquisition of essential mathematical knowledge, particularly for the students categorized as needing developmental mathematics. In this article, the authors advocate for the use of computerized platforms alongside alternative teaching methods rather than as a substitute for in-person instruction and interaction.

Mathematics is a collection of cognitive products that have unique characteristics from other scientific disciplines. As cognitive products, mathematics, and thought processes are two things that cannot be separated. Although in the literature there have been many approaches proposed to support the analysis of students' thinking processes, not many have used Harel's theory of thinking to reveal the characteristics of students' mathematical thinking. Therefore, this research aims to describe the thinking process of class IX students in solving algebra problems based on Harel's thinking characteristics. To achieve this goal, qualitative research was conducted with a case study design. The questions on the topic of algebra were adapted and developed from questions from the National Examination (UN) and the International Program for Student Assessment (PISA). Next, a test was given to 30 class IX students followed by interviews. The results of the data analysis concluded that in general students still use non-referential symbolic thinking and only a few have algebraic invariance thinking or proportional and deductive thinking. This shows that there are still many students who have difficulty understanding algebra. In increasingly complex problems, students' thinking processes become less flexible, and concepts are understood separately (procedural).

Detailed mathematical reasoning abilities can help students to understand higher mathematical abilities, including proving, problem-solving, and critical thinking. However, based on surveys and research, students' mathematical reasoning abilities are low and require significant attention. Therefore, this study aims to gain a detailed picture of the mathematical reasoning abilities of students who got the social cognitive learning (SCL) model and students who got the problem-based learning (PBL) model by considering the students' mathematical self-efficacy (MSE). The study used a quasi-experimental Nonequivalent post-test-only group design with 70 students from class 11 SMA in one school in Bandung. The data collection used a Mathematical Reasoning Ability test and a mathematical Self-efficacy Questionnaire to classify MSE levels as low, moderate, or high. The data were analyzed using two-way ANOVA and a 3x2 factorial design. According to the study results, students taught using the SCL model had better mathematical reasoning abilities than those taught using the PBL model. Moreover, students with high MSE levels exceed low MSE levels in math abilities. The SCL model enhances students' mathematical reasoning abilities and expands the range of social cognitive theory's applicability of mathematics.

This paper argues that engaging students in informal statistical reasoning from early school years is essential for the development of statistical understanding. We investigated if and how children aged six-seven years old identified variation in a table of data and made predictions through the design of a teaching experiment. The classroom teaching experiment was comprised of four 45 minutes lessons addressing the understanding and interpretation of data sets. In order to describe students' informal predictive reasoning, we used the framework of "data lenses". More specifically, we analyzed the different types of answers the students produced as they engaged in predictive reasoning during an interview given before and after the teaching experiment. The participation of students in (classroom) and out-of-school (family) communities of practice was also taken into consideration. Our results demonstrate that the students benefited from their learning experience and developed data understanding.

In contemporary society, students' analytical thinking and reasoning skills are crucial for their future development. The fourth grade (ages 9-10) is a critical stage for cultivating higher-level cognitive skills in students. Mathematics plays a significant role during this period, serving as a fundamental tool for fostering students' analytical thinking and reasoning abilities. Collaborative inquiry-based learning is considered beneficial for enhancing students' analytical thinking and reasoning skills. Therefore, this study aims to design a collaborative inquiry-based instructional model based on the characteristics of mathematics textbooks. The study extensively analyzes primary school mathematics textbooks published by Beijing Normal University and integrates the essential elements of collaborative inquiry-based learning to devise an instructional model tailored to the characteristics of mathematics textbooks. The model comprises six parts: Contextual Introduction (Question 1), Collaborative Inquiry (Question 2), Communication and Sharing (First round), Collaborative Inquiry (Question 3), Communication and Sharing (Second round), Review and Conclusion. The model is designed to assist students in acquiring knowledge through collaborative inquiry, stimulate their curiosity through contextualized learning, improve their analytical thinking and reasoning skills through collaborative inquiry, foster cognitive development through effective communication and sharing, and ultimately solidify acquired knowledge through reflection and conclusion. Theoretically, the analysis suggests that this model may positively impact students' analytical thinking and reasoning abilities, providing a valuable reference for practical teaching.

This paper presents a replication study investigating the effectiveness of a strategy to assist students with learning difficulties in adding fractions. Drawing on the research conducted by Grünke et al. (2023), this single-case analysis extends the application of the "Look, Ask, Pick" (LAP) mnemonic technique initially introduced by Test and Ellis (2005) to struggling sixth-grade students. Employing a multiple-baseline design, we implemented the LAP strategy with four participants in a time lagged fashion. Significant improvements were observed in their fraction performance, demonstrating the intervention's potential to enhance understanding and proficiency. The students highly appreciated the strategy, deeming it of great importance. In conclusion, we address the limitations of our study, propose directions for future research, and delve into the implications for teachers. This research contributes to the understanding of fraction interventions and offers valuable insights into facilitating the mathematical progress of students facing challenges.

In this paper, we propose novel transdisciplinary STEAM practices to enable students and teachers to model architecture using technology. Architectural modelling can foster students' mathematical knowledge and computational thinking while connecting them to other disciplines such as culture and history. Our study focuses on enabling architectural, cultural, and historical diversity in educational practices. Moreover, the study tries to foster participants' modelling skills and innovative technology use as augmented reality and 3D printing. Thus, this paper will describe three case studies from Austria, Libya, and Indonesia and how these STEAM practices were used in different ways to allow participants to express their diversities through modelling diverse architectural constructions cross-culturally. We followed a qualitative data analysis approach for the participants' interviews, questionnaires and artefacts including architectural modelling, disciplines connections and lesson plans. The data analysis resulted in emerging themes emphasizing STEAM practices' possibilities to connect architecture to culture and history and highlighting the participants' cultural diversities in each of the three case studies.

Developing algebraic thinking is a key factor in learning mathematics. Despite its importance, many students still struggle with algebraic concepts. This research investigates students' achievements in algebraic thinking using Demetriou's test across 7th (approximately 12-13 years old), 8th (approximately 13-14 years old), and 9th (approximately 14-15 years old) grades. The study analyzes performance in different levels of algebraic tasks (i.e., [1] extrapolation of relationships, [2] coordinating simple structures, [3] operating with undefined symbolic structures, and [4] coordination with undefined structures), revealing a significant developmental leap in algebraic abilities during the 9th grade. While no statistically significant differences were found in the first level, 9th grade students demonstrated superior performance in levels 2, 3, and 4, suggesting cognitive readiness for abstract algebraic concepts around the age of 14. The research unveils a disjointed development in algebraic abilities, indicating a progression from basic arithmetic operations to proportional reasoning before the full integration of algebraic thinking. Notably, tasks involving variables in the third level pose persistent challenges for students. The findings contribute to understanding the optimal age for introducing algebraic concepts and underscore the importance of considering cognitive development in mathematics education. The study proposes implications for educators, such as emphasizing proportional reasoning in earlier grades and employing differentiated instruction based on individual students' abilities.

This study aims to map the landscape of the importance of previous research on computational thinking (CT) in mathematics learning over the last decade. This research is a literature review research, there are 113 publications collected from the Scopus database which are then analyzed using the bibliometric analysis method assisted by the Vosviewer application. The data taken from the Scopus database was refined so that it became 113 publications. The results of the study show that publications are spread across various continents, including America, Asia, Africa, and Europe. The United States and the United Kingdom are the most influential countries and have high cooperation with other countries in this field. The main conclusion from this study is that computational thinking has an important role in learning mathematics and STEM. The integration of computational thinking in the mathematics curriculum can improve students' understanding of mathematics and help them face the challenges of the digital age. In addition, the development of effective training methods for mathematics teachers as well as the assessment of good computational thinking learning tools and platforms can help improve the effectiveness of computational thinking teaching in mathematics contexts. These innovations will help better understand how computational thinking can be effectively integrated in mathematics learning and prepare students for a future filled with digital technologies.

In learning mathematics in the 21st century and after the COVID-19 pandemic, a multimodal role in the process of drawing conclusions involving mathematical symbols or signs is very much needed. This process is called multimodal semiotic reasoning. This research aims to study the literature on multimodal semiotic reasoning research articles. Until April 2023, there were 32 articles on the keyword multimodal semiotic reasoning with the subject of mathematics in the Scopus, Science Direct, and ERIC databases. Furthermore, it is identified based on a) suitability of criteria; b) the similarity of the articles in the three databases. Finally obtained 24 articles that meet the requirements for further research. A literature review on multimodal semiotic reasoning is explored based on a) kinds of mathematical reasoning involving symbols and signs using multimodal, b) multimodal used in research, c) the most researched mathematical concepts and the mathematization process that occurs, d) the role of multimodal semiotic reasoning in mathematics education. The results showed that a) the most dominant type of mathematical reasoning involving objects, symbols, and signs using multimodal was Algorithmic Reasoning (AR), b) the most multimodal source was verbal answers, c) the concept of geometry through a process of vertical-horizontal mathematization was the most researched, and 4) the biggest role of multimodal semiotic reasoning for the benefit of knowledge of mathematics education. In conclusion, multimodal semiotic reasoning has had a major impact on mathematics education and research on this multimodal semiotic reasoning will continue to thrive in the future. [Note: The publication year (2023) shown in the citation on the PDF is incorrect. The correct publication year is 2024.]

In today's world, it is important for individuals to have critical thinking and mathematical thinking skills, which are high-level thinking skills. In advanced education systems, it is among the important priorities that students not only learn knowledge but also acquire high-level thinking skills. This study aims to examine the relationship between mathematical and critical thinking skills and academic achievements of secondary school students. In the study, relational screening model, one of the quantitative research models, was used. The research was carried out in a province located in the southern region of Turkey in the 2022-2023 academic year with students studying in secondary school (n=346) who were determined by maximum variation method selected from the types of purposeful sampling. Mathematical thinking scale and critical thinking scale was used as a data collection tool. In the process of analyzing the data, one-way analysis of variance and regression analysis techniques were used. According to the research findings, it was observed that there was a relationship between the critical thinking and mathematical thinking skills of the students, both the critical and mathematical thinking skills of the students did not differ significantly according to gender, and the mathematical thinking skills differed significantly according to the grade level. In addition, it was concluded that both mathematical and critical thinking skills of the students increased according to their grade levels. In addition, students' critical skills and academic achievement together explained 25.0% of the total variance of mathematical thinking skills. In other words, as students' critical thinking skills and academic achievement increase, their mathematical thinking skills also increase.

Considering the negative situations faced by the migrating societies, it is known that the language and culture factors exert a stronger influence on the mathematics course than the other undesirable conditions. From this perspective, it is known that the mathematical performance of individuals is likely to increase by placing the concept of number sense in the center. Therefore, the present study aimed to examine the number sense skills of Syrian immigrant students with reference to gender and duration of stay as an immigrant as well as to determine their conceptual awareness of number sense-related components. The descriptive correlational design was used in this study in which 152 immigrant students participated. Web-based two-tiertest was used in the data collection process, and descriptive statistical values and t-test for independent samples in the analysis of the data. As a result, it was found that male students compared to female students, as well as those who had been immigrants in Turkey for a long time compared to those for a shortertime showed higher number sense performances,though most of the students were at a low number sense level. In addition, the differences appeared significantly in relation to the variables of gender and duration of stay as an immigrant. A surprising result is that most students preferred number sense-based solutions as the basis for their answers. It can thus be concluded that the number sense performances of Syrian immigrant students are lower than expected and that future studies are needed not only to focus on teachers but also on teaching methods and materials in order to take immigrant problems under control and to come up with solutions with a view to overcome such challenges.

This manuscript reports the results of an investigation of the simultaneous prompting procedure to teach a five-step algorithm for solving three addition basic facts. Four preschool students receiving Tier 1 services in their school's multi-tier system of supports (MTSS) framework participated. A multiple probe across participants single case design was employed, and a visual analysis of the data indicate a functional relationship between the independent and dependent variable. Three of the participants achieved the mastery criterion and maintained the targeted learning outcome for 2-6 weeks. These participants applied the five-step algorithm to three sets of novel addition facts and acquired incidental information consisting of mathematics terminology. The fourth participant voluntarily discontinued her involvement in the study but, prior to her withdrawal, her data were similar to that of the other three participants. Social validity data from the participants' teachers confirmed their satisfaction with the study's procedures and participants' learning outcomes. The results extend those from related research and validate simultaneous prompting's effectiveness in teaching mathematics to students receiving Tier 1 and Tier 3 services in an MTSS framework. Topics for future research are discussed, and include investigating the effectiveness of simultaneous prompting to teach mathematics across students receiving services through all MTSS tiers.

Society is in an incessant process of reflection, but the educational system is not following the same path, creating an urgent need for a quality educational renovation in which new methodologies, approaches and educational resources are developed based on creation, collaboration and learning by doing. In this sense, the integrated education of science, technology, engineering, art, and mathematics (STEAM) is postulated as an educational approach through which to transform the teaching-learning processes into processes that contribute to the development of critical, creative, and scientific thinking. Proof of this is the continuous increase in publications in this line of research. This article presents a systematic review with a total of 19 studies published in high-impact journals with the aim of making a critical reflection and evaluating the real scope of incorporating STEAM projects in education to improve the students' mathematical skills. In particular, five areas of interest have been evaluated: active learning in the teaching of STEAM subjects, the development of technological resources, the design and implementation of educational proposals, the evaluation of STEAM education and teacher training in STEAM education. Considering the results, we emphasize the need to continue working on the theoretical foundation and educational practice of this approach to allow teachers to implement it effectively.

Critical thinking is a key transversal competency of the 21st century, but some students have difficulty, especially during the transition to online learning due to the COVID-19 pandemic. This study aims to identify epistemological obstacles in critical thinking related to proof, generalization, alternative answers, and problem-solving. This online learning involved 30 prospective mathematics teachers through video conferences. An exploratory case study was conducted on 9 mathematics teacher candidates with the highest exam scores. Data were collected from the results of 4 mathematical critical thinking questions. The data were analyzed and described based on a predetermined framework. The results show various epistemological obstacles in critical thinking, namely difficulty in proving the relationship between two concepts, generalizing the relationship, finding multiple alternative solutions, and solving problems. The epistemological obstacles found can be the focus of lecturers in creating more structured online learning. Online learning needs to be well-planned in terms of the use of learning resources, learning media, and integration with technology. Learning should pay more attention to understanding the relationship between concepts, the flexibility of concepts and procedures, as well as the habit of drawing in geometry learning.

In recent years, science, technology, engineering and mathematics (STEM) approaches in education have received growing attention in the political arena and in educational research and practice. A concern consistently raised in the research literature regarding interdisciplinary STEM education is that the role played by mathematics is understated such that it may be overshadowed by the other disciplines. This study contributes to the discussion by presenting a review of 4,812 studies, of which 37 with descriptions of STEM activities were selected, analysed and synthesised to identify the various roles played by mathematics in these STEM activities. This process produced an analytical framework that captures the various roles mathematics can play, which can be categorised into two major categories: mathematics as the specific aim of the activity or mathematics utilised as a tool. Two cases selected from the review are presented in this study to demonstrate how the framework can be employed in analysing STEM activities. Furthermore, we propose using the framework when developing STEM activities as a tool to ensure explicit awareness of the various roles mathematics can play.

A cohort of pre-service mathematics students was exposed to a teaching strategy based on retrieval practice and test-potentiated learning. The aim of the study was to determine how high and low prior topic knowledge study participants compare in terms of their procedural fluency and conceptual understanding after exposure to the teaching strategy. A pre-test and post-test repeated measures design was employed in the study to compare within groups. A revised taxonomy table based on Bloom's taxonomy was utilised to categorise test items. Findings indicate significant differences between pre-test and post-test scores within groups. Results from the independent samples t-test show a significant difference between the two groups. Outcomes confirm that the benefits of retrieval practice are greatest for unfamiliar content. Findings indicate that for low prior topic knowledge students, procedural fluency is enhanced and retained more than conceptual understanding whereas for the high prior topic knowledge students it was the reverse. The strategy was not as effective for improving conceptual understanding.

The ability to relate mathematics teaching to real life is the common goal of many countries' mathematics curriculum National Society for Experiential Education's (NSEE) [2011] "Eight Principles of Good Practice for All Experiential Learning Activities." (intention, originality, planning, clarity, monitoring and evaluation, reflection, evaluation, and acknowledgement) recommend that students' experiences and the meaning and learning they derive from those experiences should be consolidated. Students' ability to develop mathematical skills is directly linked to their ability to relate, which includes skills such as "problem solving, reasoning, communication." Bringing real-world contexts to mathematics lessons can affect students' attitudes towards mathematics and also support their mathematical association skills. In this context, it is important to analyze how the activities in the textbooks, which are the first resources in the classroom, are prepared and to what extent they connect the student with real life. In this regard, the focus is on the activities in the primary school mathematics textbook. In this study, the relationship of the activities in the Greek Primary School 3rd-grade textbook with real life was analyzed based on Gainsburg's (2008) classification. The document analysis method was used in the study, which was conducted on the basis of qualitative research. The data source of the research is the Greek Primary School 3rd grade mathematics textbook. The data obtained was analyzed using the descriptive analysis method. As a result of analyzing a total of 147 activities, it was determined that the activities were collected in the type of classical word problems and partially included activity types associated with real life.

There is a dearth of empirical data to support the positive effects of problem solving (PS) combined with digital technology in the classroom, despite claims that these activities improve students' algebraic thinking abilities. Therefore, the purpose of this study was to evaluate how the teaching method known as Polya's problem solving with digital bar model (PSDMB) affected the seventh graders' ability to think algebraically. Ralston's framework, which covers Generalised Arithmetic, Function, and Modelling within the topic of Linear Equation, served as the foundation for the evaluation of algebraic thinking abilities. A quasi-experimental pre-test and post-test control group design was employed. A total of 90 seventh graders, aged twelve- to thirteen-year-olds, from a secondary school in Tambunan, Sabah, Malaysia, made up the sample. Three teaching groups were formed out of these randomly chosen students: PSDMB (n = 30), Bar Model (MB) (n = 30), and Conventional Problem Solving (CPS) (n = 30). Both the pre- and post-algebraic thinking tests were taken by students. The post-test results were analysed using MANCOVA with the students' pre-test results acting as covariates. The results indicated that students in the PSDMB group performed notably better in Generalised Arithmetic, Function, and Modelling than those in the MB group, who, in turn, outperformed those in the CPS group. These results imply that incorporating digital bar model into problem-based learning is a successful strategy for improving seventh graders' algebraic thinking abilities.

Algebraic thinking is the ability to generalize about numbers and calculations, find concepts from patterns and functions and form ideas using symbols. It is important to know the student's algebraic thinking process, by knowing the student's thinking process one can find out the location of student difficulties and the causes of these difficulties. This study aims to analyze students' algebraic thinking processes in constructing new knowledge of high-ability students based on the Cognitive System of Marzano's Taxonomy. The subjects in this study were twenty one mathematics teacher candidates who took linear programming courses. The algebraic thought process of prospective instructors in solving linear equation problems is described using a qualitative descriptive technique in this study. The data collection technique starts with giving algebraic thinking questions and interviews/observations. Data reduction, data display, and deriving conclusions are the data analysis techniques employed. The results of the research show that algebraic thinking processes with types "Generasional Representasi Sequential Concrete" students are able to extract conclusions and organize better. Algebraic thought processes with types "Generational Representation of Concrete Random" students are able to build models and form generalizations but their representation is not good enough that they cannot be communicated properly.

Poor numeracy skills among remedial pupils remained a critical issue for Malaysia to achieve educational goals. This systematic literature review identified research trends and evidence-based practices on teaching aids to enhance remedial mathematics instruction. The review followed PRISMA model through four phases, searching WoS and Scopus databases to analyze 29 studies from 2014 to 2023 that met the inclusion criteria. The predominant focus was on Indonesia, Taiwan, Malaysia and the United States. Mainly quantitative and qualitative research designs were utilized. Findings revealed diverse teaching aids were proposed, including digital technologies such as systems, smartphone apps, games, multimedia, augmented reality, virtual reality, as well as manipulatives, number lines and instructional modules. Both digital and handson manipulative teaching aids have been applied in remedial mathematics interventions with promising results. Key findings indicate the effectiveness of teaching aids depends on alignment with pupils' individual needs and suitable pedagogical approaches based on local context. Implications emerge for developing new teaching aids and teacher training tailored to local remedial mathematics learners. Rigorous research is needed, particularly in the Malaysian context, to evaluate the usability of teaching aids over time. Investing in specialized teaching aids and aligned instruction will help provide quality remedial mathematics education. This review highlights promising teaching aids and gaps to build essential numeracy skills among remedial pupils in Malaysia for equitable math outcomes.

Many educators and professional organizations recommend Quantitative Reasoning as the best entrylevel postsecondary mathematics course for non-STEM majors. However, novice and veteran instructors who have no prior experience in teaching a QR course often express their ignorance of the content to choose for this course, the instruction to offer students, and the assessments to measure student learning. We conducted a case study to investigate the initial implementation of an entry-level university quantitative reasoning course during fall semester, 2018. The participants were the course instructor and students. We examined the instructor's motives and actions and the students' responses to the course. The instructor had no prior experience teaching a QR course but did have 15 years of experience teaching student-centered mathematics. Data included course artifacts, class observations, an instructor interview, and students' written reflections. Because this was a new course--and to adapt to student needs--the instructor employed his instructional autonomy and remained flexible in designing and enacting the course content, instruction, and assessment. His instructional decision making and flexible approach helped the instructor tailor the learning activities and teaching practices to the needs and interests of the students. The students generally appreciated and benefited from this approach, enjoyed the course, and provided positive remarks about the instructors' practices.

Mathematics is one of the essential subjects for students because it focuses more on the ability to remember, memorize, and interpret. In addition, gamification in mathematics is excellent since it promotes critical and creative problem-solving and enhances children's metacognitive abilities. This experimental study investigates the impact of digital gamification and metacognitive skills on the mathematical problem-solving capabilities of primary school students. This type of research is quasi-experimental with a pretest-posttest control group design. The number of samples used was 108 students consisting of 55 students in the experimental class and 53 in the control class. The research data was collected with the MAI (Metacognitive Awareness Inventory) instrument for metacognitive skills and problem-solving tests. The data analysis technique used is Two Way Anova. This study yielded several findings. Among them, there are significant differences in students' solving abilities based on the application of gamification in learning. Second, there is a significant difference in students' problem-solving abilities based on metacognitive skills. In addition, there is an interaction between digital gamification and metacognitive skills on students' mathematical problem-solving abilities.

This research centers on implementing Quantitative Reasoning (QR) within a differential equations course at an urban public community college. As a participant in the Numeracy Infusion for College Educators (NICE) faculty development program, I sought to integrate QR skills into my curriculum. Students in the course were introduced to QR goals using real-world data sets, particularly those related to population growth, which aim to enhance their understanding, sharpen their problem-solving abilities, and cultivate a positive perspective on the real-world relevance of mathematics. Preliminary findings indicate varied levels of QR skill development among students. These results underscore the potential benefits of infusing QR into mathematics courses and provide insights for educators looking to adopt similar strategies in their teaching.

This study aimed to describe students' semantic representation obstacles in solving geometric problems. There are three types of obstacles, that are ontogeny, epistemology, and didactics obstacles. This study was carried out on three subjects with different obstacles and focused on math semantic representations in solving geometry problems. The research subjects were 65 students, consisting of 20 male students and 45 female students. Subjects with different obstacles are called subject ontogeny (SO), subject epistemology (SE), and subject didactic (SD). The purpose of the subject is to receive descriptions of the three types of obstacles. The instrument used in this research was a geometry problem-solving test which was validated by two expert validators. The instrument test on problem-solving questions was about Euclidean geometry course material. The representations that surface for SO Subjects navigating ontogenic obstacles include verbal, symbolic, and visual representations. In the identification stage, the SO showed symbolic and verbal representation. In the verification stage, the SO showed symbolic and verbal representations. Meanwhile, SE dealt with an epistemological obstacle consisting of all types of symbolic and verbal representations in all stages. The last SD subject dealing with didactic obstacles showed only a visual representation.

This research aims to enhance mathematical proficiency and stimulate creative thinking among 10th-grade students through the implementation of the 5E Inquiry-Based Learning approach with Supplementary Media. The study explores the effectiveness of this pedagogical approach in transforming the learning experience and outcomes in mathematics education. The study focused on comparing students' performance before and after the intervention, as well as investigating their creative thinking abilities in terms of flexibility, originality, fluency, and elaboration. The participants consisted of 10th-grade students from a large-sized school in the northeastern region of Thailand, specifically one classroom comprising 40 students. The tools include Lesson plans, Mathematics Proficiency test and Creative thinking skills test. The results revealed a significant improvement in mathematical proficiency following the implementation of the 5E Inquiry-Based Learning Approach with supplementary media, with a notable increase of 37.25%. Prior to the intervention, students scored an average of 4.64 out of 20, which increased to 12.08 out of 20 post-intervention. Furthermore, the investigation into creative thinking skills indicated that students exhibited a proficient level overall, with an average score of 22.60 out of a maximum of 32 points. The analysis of specific dimensions of creative thinking revealed average scores of 5.60 for Originality, 5.78 for Fluency, 5.63 for Flexibility, and 5.60 for Elaboration.

The incorporation of Computer Science teaching in educational systems has increased in recent years. Given international interest, Chile has promoted projects to promote the development of students' digital skills. Focusing on this new educational context, this research reports the results regarding the identification of computational concepts and practices that can be articulated with the contents and skills of the curriculum. of Chilean mathematics. for first grade of primary school based on the use of the Bee-Bot robot. For this, the study followed a qualitative approach, developing a case study of the Chilean study program with the content analysis technique and using, as analysis categories, computational concepts and practices from the field of educational computing. In total, 30 learning objectives of the study program were analyzed. The results indicate that, although there is little articulation between computational concepts and first grade content proposed in the curriculum, there is greater articulation between computational practices and mathematical skills suggested in the Chilean curriculum. It is concluded that Computational Thinking can be developed from the earliest school levels using the Bee-Bot robot (or similar), and this is demonstrated by the structure of the Chilean primary mathematics curricular program.

Mathematical literacy stands as a critical skill imperative for navigating the complexities of the 21st century. Enhancing students' mathematical literacy necessitates comprehensive engagement across the educational landscape. This aligns with the "Guru Penggerak" (GP) initiative, established by the government to serve as educational leaders, propelling the entire educational system forward. Nonetheless, the current GP program needs more specific provisions addressing mathematical literacy, and the existing learning environments for mathematical literacy remain constrained. Consequently, there is a pressing need to develop a dedicated mathematical literacy learning environment within the GP framework. This study endeavors to create a mathematically literate learning environment that is both valid and practical, potentially impacting the GP program significantly. Employing a design research approach, the study progresses through three key stages: preliminary, prototyping, and assessment. Seven teachers participated as subjects, using data collection methodologies including walkthroughs, observations, questionnaires, and interviews, which were analyzed descriptively. Findings indicate the development of a model for a mathematical literacy learning environment termed D-C-C with the LEPscO framework, which is deemed valid due to its alignment with the PISA framework, Indonesian educational curriculum, and unambiguous language. Moreover, the model proves practical for implementation within the GP program, exhibiting potential effects such as enhanced teacher satisfaction, learning, organizational support, and utilization of new knowledge, alongside improved student outcomes reflecting heightened mathematical literacy proficiency. This research contributes to educational discourse by introducing the LEPscO Framework, encompassing a Digital-Class-Community learning environment, structured learning processes encompassing training, classroom implementation, knowledge sharing, and community development, and targeted learning outcomes focusing on teachers' comprehension and reinforcement of mathematical literacy in education.

Abstraction is essential to learning mathematics because the mathematical concepts obtained through abstraction will be more meaningful than directly receiving these concepts. This study aims to describe the pre-service teachers' abstraction in constructing relationships among quadrilaterals. This research method was explorative qualitative research with a purposive sampling technique. The subject of this research was a pre-service mathematics teacher who had taken a geometry course. The data analysis techniques used in this study were data condensation, data display, drawing and verifying conclusions. The research results showed that the participant used epistemic actions in an abstraction, such as recognising each quadrilateral type, building-with their properties, constructing relationships among them, and consolidating the abstract results made. Thus, the abstraction in constructing relationships among quadrilaterals can be observed from the epistemic actions: recognising, building-with, constructing, and consolidation, known as RBC+C.

Growth mindset has received more focus in schools in the past fifteen years as a possible way to improve various educational outcomes. There are important possible benefits if students believe in the malleability of intelligence and the potential to improve in ability and various human qualities. Students with growth mindsets set self-improvement as achievement goals, use all of their resources, seek feedback, attribute failure to something that is under their control, and work harder when faced with setbacks. For mathematics, these beliefs and outcomes of a growth mindset are especially important as students may view mathematics as too difficult and a barrier or detterent to a possible career. The notion that only some students can do well in mathematics is important to counter. The purpose of this article to review the research on growth mindset in high school mathematics education since 2007. Directions for future research are discussed including the importance of teachers in growth mindset interventions and students developing growth mindsets through having successful mathematics learning experiences.

The capacity to generate prediction is indispensable in daily existence, particularly amidst the swift transformations that are occurring on a global scale. Therefore, this study aimed to analyze the levels of prediction ability among mathematics students when presented with data in graphs. A qualitative approach was adopted, involving 37 mathematics students, using taskbased tests and interviews as data collection techniques. The results showed that the ability of most students to make a prediction based on the COVID-19 graph was at a multi-structural level of 35.14%. This level was characterized by students making predictions based on the trends of the pandemic graph patterns, but they tended to overlook the overall patterns. The prediction generated at the unistrutural, multistructural, relational, and extended abstract levels was considered reasonable because of the graph or data provided. These findings indicated the existence of predictive reasoning conducted by students in making predictions of problems related to the COVID-19 graph. The insights gained into the prediction ability prompted teachers to enhance graphic literacy instruction, to equip students with the skills needed to thrive in the 21st century.

This study aimed to examine the effect of using the flipped classroom model on students' proportional reasoning. In this context, the study focused on students' achievement and solution strategies for proportional reasoning problems. The participants of the study were 56 seventh-grade students, who were determined by convenience sampling method. In line with the purpose of the research, the concept of proportion was taught to the experimental group using the flipped classroom model and to the control group through teaching in accordance with the mathematics curriculum. The data of the study were collected through the Proportional Reasoning Test. The results of the study showed that the flipped classroom model was more effective in terms of mathematics achievement than the teaching method in line with the curriculum. In addition, the experimental group students used more correct solution strategies and fewer incorrect solution strategies than the control group students while solving the problems.

This article aims to identify the mutual relationship between the awareness of the importance of mathematical competencies for the acquisition of work-related skills and the perceived importance of the latter for performance in future work and successful participation in the labor market. How these issues relate to math anxiety is also explored. The above is examined on a sample of university students in the selected education institution (HEI) N =297 in the Czech Republic in 2022. Subsequently, a series of semi-structured interviews were conducted with the students in 2023. It was found that by improving work-related skills for a future career, math anxiety increases. A crucial finding is up to 47 % of the perceived importance of competencies for future job performance can be explained by understanding the importance of mathematics for their acquisition. The findings of this study have the potential to contribute to the improvement of mathematics education and the development of a more skilled and capable workforce, which can ultimately lead to greater economic growth and social progress. In addition, this article contains practical recommendations on how to use these findings in the practice of mathematics education not only in the selected higher education institution.

Students have different study habits from one another and from location to location. It is a crucial component of education since students' study practices have a big effect on their achievement in academics. Parents, educators, administrators, and members of the public are increasingly concerned about the poor level of mathematical comprehension in our country. Researchers and educators have worked very hard to determine the causes of the low performance in the subject. Despite all of these initiatives, the issues persist. Students' study habits are a powerful indicator of both their academic performance in mathematics and the quality of their education. It is unrealistic to expect students to acquire all there is to know about a subject from their teachers in the classroom; students' study habits are a combination of what they learn in and outside of the classroom. Sorenson (1991) listed several beneficial study habits, one of which is that the main goal of study should be understanding. One must focus on this for an extended period of time rather than rushing through. Effective study techniques, according to Crow & Crow (1992), include setting up a specific workspace, creating a timetable, and taking concise, well-organized notes.

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.

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.

The research aimed to achieve the following objectives: 1)Assess the effectiveness of cooperative learning management utilizing the STAD technique and KWDL technique among PrathomSuksa 6 students in solving decimal problems, with a target of achieving a 75/75 criterion, 2) Enhance the problem-solving abilities of grade 6 students in mathematics by implementing cooperative learning management using the combined STAD technique and KWDL technique, compared to a 75 percent criterion, 3) Improve the learning achievement in mathematics of grade 6 students in solving decimal problems through cooperative learning management, employing the STAD technique and KWDL technique, in line with a 75 percent criterion. The research was conducted with a selected group of 33 students from Prathomsuksa 6/1, first semester, academic year 2022, at Ban Chiang Yuen School. The research tools employed were: 1) a cooperative learning plan incorporating the STAD and KWDL techniques, 2) a mathematics problem-solving ability test, and 3) a mathematics learning achievement test. Data analysis involved the use of percentage, mean, standard deviation, and efficiency (E1/E2). The findings of the study indicated the following: Cooperative learning management using the STAD technique and KWDL technique exhibited an efficiency of 76.14/75.45, satisfying the 75/75 criterion. The average mathematics score post-intervention was 75.76 percent, surpassing the 75 percent criterion. Mathematics learning achievement, as measured by the average score post-intervention, reached 75.45 percent, fulfilling the 75 percent criterion.

In the 21st century, the demand for proficiency in mathematics has escalated, as it underpins critical thinking, problem-solving, and innovation in various fields. Recognizing the significance of mathematics education, after-school programs have emerged as potent supplementary platforms to enhance students' mathematical skills and achievement. This study aimed to determine the impact of the after-school program on fostering mathematics in the 21st century. The study was conducted at Chaparral Middle School of Alamogordo Public Schools District in New Mexico, USA to middle school students enrolled for the school year 2023-2024. The research method is experimental. The after-school program students were exposed to the mathematics resources in the 21st century such as Khan Academy, ALEKS, Peer-Assisted Learning Strategies, Illustrative Math, and the like. Evidence-based resources were used to foster students' mathematics achievement. A standardized test that measures mathematics achievement was the main instrument used in the study. The mean, standard deviation, and t-test were used to analyze the data collected. The analysis with a t-value of 7.889 and probability value of 0.000 revealed that students exposed to the after-school program performed significantly in terms of mathematics achievement. Researchers recommend that teachers may use the after-school program to foster mathematics achievement. Teachers might also incorporate activities into their Mathematics teaching that demand students to engage resource materials to foster students' mathematics potential in the 21st century.