Mathematical Content Research Articles

Level of Students' Mathematical Literacy Based on Cognitive Conceptual Tempo (Reflective-Impulsive)

This research aims to describe students' mathematical literacy abilities based on their cognitive conceptual tempo. The research method used in this study is a qualitative descriptive approach. The research was conducted at SMKN 1 Ngasem in class XI-2 Design, Modeling, and Building Information. Data collection techniques in this research involved the use of tests and interviews. The tests were divided into two parts: the Matching Familiar Figures Test (MFFT) to gather data on students' cognitive styles (conceptual tempo) and a mathematical literacy test to assess the level of mathematical literacy abilities of the students. The results of this research indicate that reflective subjects were able to achieve a mathematical literacy level of 3 for S1 and level 4 for S2. Reflective students fall within the medium scale. Meanwhile, impulsive subjects achieved mathematical literacy indicators at level 1 and level 4 for S3, and level 1, level 3, and level 4 for S4. Impulsive students also fall within the medium scale. Furthermore, future researchers can explore more extensive mathematical literacy content and contexts.

Analysis of Mathematics Content Knowledge of Mathematics Teachers Based on Bloom's Taxonomy Revision

This study aims to assess mathematics teachers' understanding of Mathematics Content Knowledge based on the Revised Bloom Taxonomy. The method used is quantitative descriptive research with a survey approach. The respondents of this study were mathematics teachers who taught at SMP/MTs in Losari District, Brebes Regency. Data was collected using non-test instruments in the form of questionnaires and question tests. Data analysis involves presenting data, testing differences, and concluding. The results showed that teachers' understanding of Mathematics Content Knowledge in teaching and mastery of the material was categorized as strong. Based on Bloom's revised taxonomy, teachers have good mastery, especially in knowledge dimensions such as factual, conceptual, procedural, and metacognitive knowledge, which are categorized as high. There was no significant difference in the average Mathematics Content Knowledge score of teachers, either with a working period of less than 10 years, 10-15 years, or more than 15 years.

Ethnomathematics in Intermediate Phase: Reflections on the Morabaraba Game as Indigenous Mathematical knowledge

Mathematics education remains a worrisome issue in the South African education system. This dilemma presents itself in the underperformance of learners in Intermediate Phase mathematics. In an effort to address this challenge and develop alternative approaches to the teaching of mathematics, a university-based project was initiated. As part of the project, this article reflects on the experiences of five project members who observed the implementation of Morabaraba, which is an Indigenous game, rich in mathematical relevance. This qualitative case study explored how mathematics teachers implemented the Morabaraba game to teach Intermediate Phase mathematics content. The method used to capture the data entailed reflections of the team that were derived from the observation of mathematics lessons in the Intermediate Phase. From these observations the researchers found that teachers invented their own rules when integrating mathematical concepts; they reinvented the game to cater for the complexity of mathematical content and experienced challenges in the playing of the game. We conclude that the Morabaraba game can be implemented, with practical adjustments, to comply with the objectives of the mathematics concept. The recommendation is that ethnomathematical games be employed as a teaching strategy as they are found to encourage active learning. Future research endeavours include exploring how ethnomathematical games can be sustained for future use.

Game-Based Learning Model with Baamboozle Media Based on Artificial Intelligence Increases Student Engagement and Learning Outcomes

The rise of students who have low learning outcomes and student engagement. Low mathematics learning outcomes are caused by models or learning media that are unsuitable for use in learning. This research aims to test the effectiveness of using the Game-Based Learning learning model with the assistance of Baamboozle media on Student Engagement and student learning outcomes. The research method used in this research is a quasi-experiment with a one-group pre-test and post-test design. The total sample for this research was 27 third-grade elementary school students. Data collection methods in this research are observation, questionnaires, and tests. The instrument used to collect data is test questions. Data analysis techniques use inferential statistics. The research results, namely the post-test results, show that all students completed the KKM. The t-test results showed differences in the pre-test and post-test after using the Game-Based Learning learning model with Baamboozle media. The results of questionnaires and teacher observations show that Student Engagement has increased. It was concluded that the Game-Based Learning learning model using Baamboozle media effectively improved learning outcomes and Student Engagement in mathematics content.

A literature review: Mathematics vocabulary intervention for students with mathematics difficulty

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

Flipped Classroom Approach and Acquisition of Problem Solving Skills in Mathematics in Secondary Schools in Turkana County

In a flipped classroom, learners study structured mathematics content prior to the lesson via watching relevant videos outside the lesson. This study initiated the use of flipped classroom approach in mathematics classrooms in order to strengthen learners’ problem- solving skills and impact performance. Reviewed literature shows a positive correlation between using flipped classroom approach and problem solving. The study design is quasi-experimental. One group of participants was instructed via flipped classroom approach and the other conventional methods. A comparison of problem-solving ability between the groups was made. The form two students and their mathematics teachers were the target population. Data was collected by means of an achievement test and means calculated per group. The inferential statistic, t-test was used to determine if the difference in means between the experimental and control group in the achievement test was significant. The study found that where flipped classroom approach is used, learners performed better in mathematics problem-solving than their counterparts instructed via conventional methods.

What Mathematics Teachers’ Perceptions of The Integration of Educational Drama in Mathematics Instruction: A Mixed-Methods Study

This research aimed to explore mathematics teachers' perspectives on the integration of educational drama in mathematics instruction, specifically focusing on mathematical knowledge, classroom discourse and affective aspects. Using a mixed-methods approach and a sequential explanatory design, the study first employed a quantitative phase, applying a scale to gauge teachers’ views on incorporating educational drama into mathematics instruction. The questionnaire covered three key dimensions: the advancement of mathematical knowledge, facilitation of classroom discourse, and emotional elements. The framework was developed based on established theoretical models. Following this, interview protocols were designed, based on the quantitative outcomes, to explore the insights provided in greater depth. The results indicated a predominantly positive reception among mathematics educators for the use of drama in mathematics education, with consistent agreement observed across all aspects of the scale. The mean scores for the development of mathematical knowledge, classroom dialogue and emotional dimensions were notably high, reflecting substantial alignment among the participants. Qualitative analysis of the teacher interviews highlighted the beneficial aspects of employing drama in mathematics education. The teachers noted the role of drama in reinforcing concepts, enhancing specific mathematical skills and positively affecting student engagement. However, concerns were raised regarding the potential for students' focus to be diverted from core mathematical content. In terms of classroom discourse and emotional development, drama was acknowledged for its role in fostering interactive exchanges, refining students’ speaking abilities, and nurturing self-confidence and motivation. Nonetheless, there were caveats concerning the suitability of drama for all student cohorts, pointing to the need for tailored approaches.

Discussion on the Skillful Use of Mind Maps in High School Mathematics Teaching

With the continuous development of China’s education, the social requirements for high school teaching are constantly improving. The teaching of high school mathematics is a key point in the high school curriculum, but also a major difficulty. Due to the strong logic and abstraction of the content of high school mathematics, some students find it very difficult to learn. In order to solve this problem, high school mathematics teachers can make use of mind maps to teach, so that students can exercise their thinking ability, and realize the improvement of comprehensive ability in mathematics. This paper analyzes the shortcomings of high school mathematics classrooms under the background of new curriculum reform and discusses the significance and methods of applying mind maps in high school mathematics classrooms, so as to put forward reasonable suggestions for realizing the efficient teaching of high school mathematics.

Mathematics self-concept and response pattern in higher education examinations: differences between genders

The study examined how mathematics self-concept, mathematics anxiety and endorsement of mathematics gender stereotypes may impact female students’ response pattern in multiple-choice examinations in courses with mathematical content. Questionnaires measuring these three variables were completed by 435 undergraduates (327 enrolled in a non-mathematical course and 108 in a course with mathematical content). Achievement was measured via multiple-choice examinations, thus allowing us to analyse students’ response patterns (i.e. not only their mark but also the number of hits, errors and unanswered questions). In females, a poorer mathematics self-concept and higher levels of mathematics anxiety (compared with male classmates) did not impact negatively on their final mark in the course with mathematical content. However, the response pattern in this course differed according to gender and mathematics self-concept: a poorer mathematics self-concept was associated with a higher number of unanswered questions in women and a tendency toward a greater number of errors in men. This suggests that a poorer mathematics self-concept leads women to be more cautious during multiple-choice examinations so as to minimise mistakes, whereas in males it tends to be associated with a risk-taking response strategy. These results raise further concerns about the use of multiple-choice examinations, particularly for assessing mathematical knowledge in students with low mathematics self-concept.

Student visual attention during group instruction phases in collaborative geometry problem solving

AbstractTeacher gestures support mathematics learning and promote student collaboration. Aligned with speech, gestures can help students to notice the important visual information of geometry tasks. However, students’ visual attention to the teacher’s gestural cues during collaborative problem solving remains a largely unexplored field in mathematics education research. This mixed-method case study investigated relations between students’ visual attention, teacher gestures, and students’ collaborative problem-solving process on a geometry task. The data were collected with video cameras and mobile gaze trackers on four students simultaneously in two Finnish 9th-grade mathematics lessons with the same teacher. The findings show that the students attended to their own papers most of the time during the teacher's gestures, but differences in student attention between the gesture types emerged. The qualitative analysis showed that the teacher’s tracing, pointing, and representational gestures helped in directing student attention to targets relevant to the situational learning process. We conclude that teacher gestures can both convey mathematical contents and direct student attention, which intermediates mathematical thinking in problem solving.

The Relation Between Soft Skills and Arithmetic Performance

Arithmetic achievement holds particular significance in contemporary times; however, students continue to encounter difficulties in this domain. Researchers and organizations are actively seeking factors that can support students in navigating mathematical content. To address this gap, we propose an examination of the role played by six soft skills (adaptability, curiosity, initiative, leadership, perseverance, and social awareness), alongside self-regulated learning strategies, academic motivation, achievement emotions, and fluid reasoning abilities, in students’ performance on standardized arithmetic tasks. Data were gathered from 551 Italian students aged 11–18 through classroom-based paper-and-pencil tasks and questionnaires. Path analysis results reveal that only fluid reasoning abilities, academic motivation, and negative achievement emotions significantly correlate with arithmetic performance. Soft skills demonstrate an indirect relationship with arithmetic performance, mediated by negative achievement emotions and academic motivation (while not mediated by positive achievement emotions and self-regulated learning strategies). These findings underscore the increasingly recognized significance of soft skills and expand their relevance to arithmetic achievement, potentially suggesting novel psychoeducational interventions to bolster students’ performance in this realm.

Introducing the role of being an advocate in mathematics teacher education

AbstractMathematics teacher education is often described in terms of the mathematical content and pedagogy that teachers need. However, recent calls for equity in mathematics education demand a broadening of this view. In this article, we articulate a theoretical description of what the role of being an advocate in language-diverse classrooms could involve and some of the practical challenges that mathematics teacher educators may have when introducing it, using empirical examples from our teacher education courses for teachers of Grades 1–7 in Norway. In the theoretical description of the role of being an advocate into mathematics teacher education, we distinguish between in-class advocacy and advocacy beyond the classroom and what these different kinds of advocacy might entail in language-diverse classrooms. The practical issues that we identified in raising different aspects of the role indicate the need for further research into how to raise preservice teachers’ awareness about the role of being an advocate, in and outside of the classroom, in different cultural settings and how this knowledge could be used in teacher education to challenge preservice teachers’ language ideologies and raise non-trivial issues.

Mathematical Content Knowledge and Problem-Solving Skills of Preservice Teachers in the Era of Distance Learning

Mathematical Content Knowledge and Problem-Solving Skills of Preservice Teachers in the Era of Distance Learning

The effectiveness of using educational robots in enhancing engineering mathematics skills among students in basic school

Educational robots foster engaging, democratic, and collaborative learning environments, enhancing students' mathematical and engineering abilities by enabling them to interact, solve problems, assimilate information, and communicate effectively within the classroom. This study aims to examine the impact of educational robots on the development of engineering mathematics skills. The study uses a quantitative approach with a quasi-experimental design for a single pre- and post-test group. The sample consisted of 40 fifth grade students who initially studied geometry using traditional methods, followed by studying the same content using the educational robot. The study found that robot-based education significantly improved engineering mathematics skills. It was concluded that using educational robotics as a tool for teaching mathematics improved computational thinking, engineering mathematics, motivation, creativity, cooperation, and teamwork. It is possible to argue that the study's results corroborate relevant research showing how educational robots raise students' academic performance and improve their critical thinking. These results lend credence to the idea that educational robots improve learning beyond traditional approaches by actively involving students, giving subjects greater concreteness, and capturing their interest and attention. The study recommends the creation of new mathematical activities using educational robots across various mathematical contents and educational stages, further enhancing engineering mathematics among students.

Application of Model Concept Teaching Practice in Middle Schools in Lhasa: Taking the Fibonacci Series as an Example

The concept of a mathematical model is the main expression of the core quality of mathematics in junior middle school, which runs through all the contents of mathematics teaching in middle school. In the “2022 Compulsory Education Curriculum Standards,” mathematics teaching requires an overall grasp of mathematical ideas. Teachers should pay attention to the model concept of the ideological method of explanation and application in the teaching process, which can improve the teaching ability of teachers and is more conducive to students’ development. The new curriculum reform further improves students’ application awareness in the cultivation of core competencies.

MATH ANXIETY

Mathematics anxiety has been the subject of growing academic interest, as it can significantly impact academic performance and individuals’ relationship with mathematical content throughout their lives. This narrative review aims to understand the conceptual evolution, causes and possible interventions associated with mathematics anxiety. Using a bibliographic methodology, articles, books and reports published in renowned academic databases were analyzed. As the main theoretical framework, the cognitive-behavioral perspective was adopted, which understands mathematical anxiety as a result of interactions between cognitive, behavioral and environmental processes. The results point to a multifaceted understanding of the phenomenon, highlighting not only individual factors, such as self-efficacy and past experiences, but also external factors, such as teaching methods and teachers’ attitudes. Interventions aimed at reducing mathematics anxiety have focused on both pedagogical strategies and psychotherapeutic approaches, demonstrating the need for an interdisciplinary approach to tackle the problem. This work contributes to the literature by consolidating dispersed knowledge and indicating future paths for educational research and practice.

When algebra makes you smile: Playful engagement with early algebraic practices

BackgroundThe typical competitive and results-driven approach to school mathematics has traditionally been conceived as devoid of play, joy, and positive affect. AimsIn this paper we address the following questions: What markers of positive affect are observed while students are doing early algebra? Specifically, how are students’ markers of joy related to early algebraic practices? What are the characteristics of playful stances to learning early algebra that are observed when children express positive epistemic affect? SampleWe analyze three cases in which elementary school students engaged in tasks from an early algebra classroom teaching experiment. MethodsDrawing from two theoretical frameworks, epistemic affect and early algebra, we conducted microgenetic analyses of lesson transcripts to identify markers of joy and early algebraic practices. We conducted frequency analyses to determine their co-occurrence. ResultsOur results indicate that children expressed joy while engaging in early algebraic practices, evidence of positive epistemic affect. We describe the aspects of each of the cases we present in terms of prior literature on playful stances to learning to further bolster our claims about the relationship between joy and engagement with the early algebraic practices. ConclusionsWe conclude that mathematical learning environments should include open opportunities for students to engage with mathematical content, with multiple entry points and ways to respond. We also conclude that early algebraic practices provide opportunities for playfully engagement and positive epistemic affect.

TPACK competence of mathematics education students in designing constructivist learning

The problem and the aim of the study. This study examines mathematics education students' TPACK (Technological Pedagogical Content Knowledge) and constructivist learning skills. The major issue is mathematical education students' ability to integrate technology, pedagogical expertise, and mathematical content knowledge in a constructivist learning setting. The study topics include how well students employ constructivist ideas in learning design, how technology supports mathematics learning, and what variables impact their TPACK abilities. By studying it more, this research may help enhance the mathematics education curriculum and teacher training to meet 21st-century education needs. Research methods. Qualitative case study research is used in this work. 23 students of the mathematics education program at Universitas Negeri Surabaya were selected. After observing students in constructivist mathematics learning design activities, in-depth interviews were conducted to understand better their views on TPACK and the constructivist approach, and their learning plans were analyzed. Students' TPACK abilities in constructivist learning will be assessed using thematic and triangulated data analysis. The research findings may help explain the problems and opportunities of constructing a mathematics education curriculum, particularly when merging TPACK and constructivist techniques. Results. The average TPACK competency of math education students is 78.4%, according to studies. According to the TPACK component analysis, students scored 85.2% on the Technology Knowledge Test (TK), 79.6% on the Pedagogical Knowledge Test (PK), and 75.8% on the Content Knowledge Test (CK). However, CK component proficiency varied, suggesting mathematical content knowledge should be improved. In-depth interviews showed that students with formal educational technology training or courses had higher TPACK ratings (M = 82.1%) than those without (M = 76.3%). These data show that formal education and training improve TPACK abilities. To optimize the constructivist method, the CK component must be improved. This research shows that technology integration and mathematics subject mastery are crucial to constructivist learning curricula and training programs for mathematics education students. Conclusion. The constructivist learning TPACK skills of mathematics education students are examined in this study. Students demonstrated technology integration, instructional competency, and mathematical topic knowledge with an average TPACK score of 78.4%. According to TPACK component analysis, pupils have good technical skills (TK) but varied mathematics topic knowledge. TPACK scores are higher for technology education students, demonstrating the role of formal learning in competency. These findings show that CK needs to include constructivism better. In conclusion, comprehensive training and mathematical content additions can improve students' TPACK skills, enabling constructivist technology usage. These insights may assist in improving mathematics curriculum and training.

The expertise of novices: A framework for prospective teacher’s noticing of children’s mathematical thinking

The purpose of this study was to articulate nuances within the process of learning to notice and to provide a framework for characterizing the capabilities of noticing in prospective mathematics teachers. We collected and analyzed data on teacher noticing based on classroom videos from prospective teachers in a mathematics content course. We analyzed data in accordance with existing research-based frameworks on noticing and in consideration with literature on expertise. We provide the Framework for the Expertise of Noticing, which describes noticing expertise along five dimensions: Evidence-based Noticing; Concrete vs. Abstract Characteristics in Noticing; Individual vs. Pattern Focus in Noticing; Task vs. Contextualized Perspective in Noticing; and Cognitive vs. Metacognitive Characteristics in Noticing. The framework is a tool for mathematics education researchers and teacher educators who study and support the development of noticing in prospective teachers.

The Effect of Training Program Based on Instructional Practices According to the (NCTM) Standards on Improving the Pedagogical Knowledge among Mathematics Teachers in Jordan

The current study aims at revealing the effect of a training program based on teaching practices according to NCTM standards in improving the pedagogical knowledge of mathematics teachers. The study followed the semi- experimental method. To achieve the aims of the research, a training program that is based on the standards of NCTM was designed. The program consists of eight packages which are (Establish mathematics goals to focus learning, implement tasks that promote reasoning and problem solving, Use and connect mathematical representations, facilitate meaningful mathematical discourse, pose purposeful questions, build procedural FLuency from conceptual understanding, support productive struggle in learning mathematics, Elicit and use evidence of student thinking). After confirming the validity of the tool, a sample of (20) male and female teachers from Deir Ala Directorate of Education in the academic year 2020-2021.To reveal the effectiveness of the program, a test in pedagogical knowledge was prepared. The test consists of six respects which are identification of mathematics content, the pedagogical knowledge of the mathematical content and knowing students' thinking. The test validity and reliability were checked. The results of the study showed that there were statistically significant differences between measuring averages in the post application of the test. These results were pro- sample in all dimensions and in the total degree. Depending on these results, the study asserted the necessity for the training department in the Jordanian Ministry of Education to benefit from the suggested and used program in the study to focus more on the teaching practices.