Middle School Mathematics Research Articles

Middle School Mathematics Teachers' Views on The Concept of Mathematical Game

In this study, the views of middle school mathematics teachers on the concept of mathematical games were investigated. The participants of the study consisted of 13 middle school mathematics teachers. Phenomenology, one of the qualitative research methods, was used in the study. Interviews were used for the collection of data. The data were analyzed through content analysis. As a result of the research, the teachers mostly used the expressions instructive and fun in their definitions of mathematical games. It was found that the participants explained the relationship between mathematics and games with the presence of mathematics in games and mathematics making sense of games. It was observed that teachers used mathematical games for cognitive/academic and affective purposes. In terms of the benefits of mathematical games, the focus was on the benefits for the subject, the student and the teacher. Similarly, it was emphasized that mathematical games have various effects on students' learning, attitudes toward the lesson, personal development and social development. However, it was determined that teachers experienced various difficulties during the game design/planning and teaching process.

The Process of Teaching and Learning from the Views of Prospective Mathematics Teachers: The Case of Algebraic Inequalities

This study explores the views of prospective mathematics teachers on the process of teaching and learning about algebraic inequalities. Phenomenology, one of the qualitative research methods, was used in the study. The participants of the study consisted of 6 prospective middle school mathematics teachers studying in the last year of the Elementary Mathematics Teacher Education Program of a university in the Central Anatolia Region of Türkiye in the spring semester of the 2021-2022 academic year. Data were collected through semi-structured interviews. The obtained data were analyzed using content analysis, one of the qualitative analysis methods. As a result of the analysis of the interviews with the prospective middle school mathematics teachers, three main themes were obtained. Teaching inequalities, the difficulties that students may experience in inequalities, and the methods that can be used to overcome difficulties were the main categories that emerged. Direct quotations from the prospective teachers’ views were also included in the presentation of the findings. As a result of the study, it is recommended that more practice should be included in teacher education programs to improve prospective mathematics teachers' knowledge and experience of meaningful learning and overcoming difficulties.

A comparison of functions in Finnish, Singaporean, and Taiwanese middle-school mathematics textbooks

A comparison of functions in Finnish, Singaporean, and Taiwanese middle-school mathematics textbooks

Investigation on the Present Situation of Mathematics Large Unit Teaching in Middle Schools in Anyang and Its Improvement Countermeasures

Under the background of educational reform, large-unit teaching strategy is of great significance to improve the quality of middle school mathematics teaching and promote students' deep learning. Based on the integration of pedagogy theory and practice, this paper deeply analyzes the challenges and opportunities faced by middle school mathematics teachers in Anyang when implementing large-unit teaching strategies, and puts forward targeted professional development strategies for teachers at different stages, such as rookie, backbone and senior. At the same time, this paper also discusses how to combine teachers' internal motivation and external support to build an effective strategy system. These research results not only provide concrete guidance for middle school mathematics teachers to implement large-unit teaching strategies, but also provide in-depth insights and references for educators to promote the sustainable development and innovation of middle school mathematics education.

The Effectiveness of Feedback Provided by Middle School Mathematics Teachers and Preservice teachers on Student Solutions: An Evaluative Study

The aim of this study is to reveal the suggestions of middle school mathematics teachers and preservice mathematics teachers that can both correct errors in students’ incorrect solutions and contribute to the advancement of students who have provided correct solutions. The study is based on the case study method. Initially, six problems related to proportional reasoning were posed to middle school students in a public school, and the solutions obtained from the students were classified according to their proportional reasoning strategies. These solutions were then examined by the students' mathematics teachers and by preservice mathematics teachers. Two questions were asked to mathematics teachers and preservice mathematics teachers during these examinations. After the examination, interviews were conducted to discuss the suggestions made to (1) correct the errors in incorrect solutions and (2) advance the proportional reasoning skills of students who obtained correct solutions. The findings indicate that both mathematics teachers and preservice mathematics teachers were adequate in providing suggestions to correct errors in students’ incorrect solutions. However, it was also found that both groups had difficulties in making suggestions to further the advancement of students who provided correct solutions.

Evaluation of Questions in Middle School Mathematics Textbooks in Terms of Problem Solving Strategies

Purpose: This study aims to analyze solved problems in mathematics textbooks, focusing on both general and specific problem-solving strategies. By conducting a detailed analysis of each general strategy, the study seeks to provide a comprehensive evaluation of the problem-solving approaches presented in the textbooks. Design/Methodology/Approach: The document analysis method was utilized in this study. Solved problems from the mathematics textbooks published by the Ministry of National Education (MoNE) for 5th, 6th, 7th, and 8th grades during the 2023-2024 academic year were examined. Data were collected using the “Solved Problems Checklist” and “Problem-Solving Strategies Determination Form” developed by Hatay (2020). A qualitative descriptive analysis method was employed to analyze the data, with percentage and frequency values calculated to present the findings. Findings: The analysis revealed that the stages of planning and implementing a solution plan were prominently featured in the middle school mathematics textbooks. Specifically, the initial stage of understanding the problem often included visual aids such as figures, diagrams, tables, and pictures. In the planning phase, the predominant solutions involved discussions of mathematical operations. Highlights: The study’s findings indicate that while problem-solving strategies are generally emphasized in mathematics education, certain steps, such as solution evaluation, are given greater focus. Additionally, the research highlights a significant gap in the inclusion of the problem-posing stage, the final step of general problem-solving strategies, in the analyzed mathematics textbooks.

Exploring Sources of Bias to Improve the Universal Design of Mathematical Problem-Solving Tests

ABSTRACT Advancement of testing of mathematical problem-solving skills calls for open-ended, realistic tasks particularly susceptible to bias, compromising the score validity and fairness of tests. Informed by universal design principles, this study framed 360 prototype items developed for the Problem-solving Measures Grades 6–8 Computer Adaptive Tests as a bounded case to illuminate sources of bias in middle-school mathematics assessment. Experts’ shared understandings of potential sources of bias were collected using an iterative Delphi technique. Four themes in sources emerged from a thematic analysis of 201 sources of bias identified: assumed lived experiences, language use, item presentation, and stereotypes. These sources potentially placed subgroups of students from certain sociocultural backgrounds (e.g. culture, gender, race/ethnicity, socioeconomic status) at a disadvantage by challenging them in ways unrelated to mathematical problem solving. Recommendations for minimizing potential sources of bias in test development to achieve equitable K-12 mathematics problem-solving tests are discussed.

Evaluating large language models in analysing classroom dialogue

This study explores the use of Large Language Models (LLMs), specifically GPT-4, in analysing classroom dialogue—a key task for teaching diagnosis and quality improvement. Traditional qualitative methods are both knowledge- and labour-intensive. This research investigates the potential of LLMs to streamline and enhance this process. Using datasets from middle school mathematics and Chinese classes, classroom dialogues were manually coded by experts and then analysed with a customised GPT-4 model. The study compares manual annotations with GPT-4 outputs to evaluate efficacy. Metrics include time efficiency, inter-coder agreement, and reliability between human coders and GPT-4. Results show significant time savings and high coding consistency between the model and human coders, with minor discrepancies. These findings highlight the strong potential of LLMs in teaching evaluation and facilitation.

Understanding Barriers to STEM: Teachers' Insights on African American Underrepresentation

This study focuses on the development of a measurement instrument to identify Middle and High School mathematics and science teachers’ beliefs about the main factors of underrepresentation of African American students in STEM (Science, Technology, Engineering, and Mathematics) fields. The research method using the stages of instrument development were (1) test design which involved construction of initial item pool by conducting extensive review of literature and coding of participating teachers personal statements (2) determination of validity which involved expert review process to confirm construct and face validity of items, (3) pilot testing which involved collecting data from a second set of participants, (4) determination of reliability which involves conducting a reliability analysis based on data collected from pilot testing and (5) determination of factorial structure which involved Exploratory Factor Analysis (EFA) to identify underlying factors in participating teachers’ belief structures. First, to obtain trustworthy information, voluntary middle and high school mathematics and science teachers were asked to write personal statements where they explain their main reasons for choosing teaching as a career. Secondly, qualitative data obtained from participating teachers’ personal statements were coded. Coding was applied to identify and to group the phrases or sentences that convey the same or similar reasons. Then results from an extensive literature review on this topic were blended in teachers’ common expressions which were determined because of coding procedure. Then 8 content experts assessed content validity and face validity. Finally, the survey was piloted to African American middle and high school mathematics and science teachers. Fifty-three (53) surveys were completed and received back from teachers. Then, exploratory factor analysis was conducted to identify any underlying factors in the scale. Reliability analyses were also conducted for both the entire survey and for each of the factors. Results of the study suggested four underlying components: (1) Access and Resources, (2) Role Models and Representation, (3) Bias and Discrimination, (4) Curriculum and Pedagogy.

Research on the Problems and Improvement of Junior Middle School Mathematics Examination Review Teaching under the Background of “Double New”

With the deepening and reform of our education enterprise, the traditional teaching way can hardly satisfy the new demand for students’ development. Therefore, educators must actively renew the educational concept, optimize the teaching strategy, push the students to the deeper study. In view of this, this article briefly summarizes the significance of the total review of junior middle school mathematics, analyzes the difficulties faced in teaching and discusses the teaching strategies such as clear teaching objectives, consolidating the foundation of students and adopting diversified teaching methods, so as to hope that these strategies can provide useful reference for educators.

An examination of the cognitive demand levels posed by problems in the middle grades mathematics textbooks

This research investigated the cognitive demand levels of mathematics tasks within the middle school mathematics textbooks endorsed by the Ministry of National Education for the academic year of the 2023-2024. To achieve this, a qualitative research method was utilized, and document analysis was performed. In this direction, the textbooks were analyzed using descriptive analysis. The tasks within the textbooks were examined through the lens of Smith and Stein’s (1998) theoretical framework. The findings indicate that the majority of mathematics tasks in middle school mathematics textbooks exhibit a low level of cognitive demand. It was found that over 80% of the tasks fell into the categories of memorization and procedures without connections levels. It has been revealed that tasks at the levels of procedures with connections and doing mathematics, which are high cognitive demand levels, are uncommon. This shows that textbooks do not sufficiently support the potential of students to develop mathematical thinking and problem-solving skills. Based on these results, various suggestions have been made for textbooks. The most important of these suggestions include ensuring that students are cognitively exposed to higher level tasks and increasing the number of tasks that will improve their mathematical thinking skills. Thus, it will be possible for students to have a more effective learning process by deepening their mathematical understanding.

Developing an assessment instrument for strengthening the Pancasila student profile in web-based middle school mathematics teaching

This study aims to develop an assessment instrument for strengthening students' Pancasila profile in middle school mathematics teaching, which teachers can use. This research follows a development process using the Plomp model, consisting of three phases. The respondents involved in this study were six experts in mathematics education and information technology, 23 middle school mathematics teachers, and 1,297 students. The research results show that Aiken's V value is 0.89, which exceeds the v-table of 0.630, indicating good validity. The Cronbach Alpha reliability analysis results indicate a strong outcome, with a value of 0.751. Confirmatory factor analysis using the R program showed significant factor loadings with a p-value < 0.05. Apart from that, the achievement percentage for all dimensions is in the good category, with an average achievement of 87.06%. These results prove that the assessment instrument developed is suitable for teachers to measure the strengthening of Pancasila student profiles in mathematics teaching at school. The developed instrument can be used as an effective evaluation tool in mathematics teaching to strengthen the Pancasila Learner Profile and help identify areas that require improvement in teaching to achieve a more balanced profile across all dimensions.

Perceptions versus performance: Assessing teacher learning in asynchronous online professional development

AbstractTeacher learning in asynchronous online professional development (PD) is often measured by self-reported instruments, despite uncertainties regarding teachers’ accuracy in their self-assessment of learning. This study explored whether teachers’ self-reported gains in content knowledge for teaching aligned with those measured by direct assessments. Through quantitative analyses of data collected from 57 middle school mathematics teachers who participated in a fully asynchronous online PD program, we found no significant correlation between teachers’ self-reported knowledge gains and those measured by direct assessments. Additionally, we examined the role of teachers’ use of self-regulated learning (SRL) strategies, namely organization, elaboration, and monitoring, in their learning from the PD program by conducting linear regression analyses. Our results indicated that teachers who frequently monitored their understanding of the PD content demonstrated greater gains in their content knowledge as measured by direct assessments. However, none of the SRL strategies predicted the accuracy of teachers’ self-assessments of knowledge gains from the asynchronous online PD program. These findings raise concerns about relying solely on self-reported instruments to capture teachers’ learning in asynchronous online PD programs, and they emphasize the need for more robust and accurate outcome measures in the asynchronous online learning context.

Predicting Marginalized Students’ Mathematics Achievement in High School

ABSTRACT The current study is a conceptual replication of the influence of an advanced educational opportunity and several student propensities to learn on a college-readiness assessment for mathematics (ACT scores) among an important and under-studied group of students. We focused on a sample of predominantly Black students from economically-disadvantaged homes in the U.S. (n = 329; 80% Black, 59% female, 66% whose parents had a high-school diploma or less). Accelerated course placement (high-school math course in 8th grade) was a unique predictor of math ACT scores above and beyond prior math achievement and other variables (B = 1.5). In line with a fade-out model, executive function skill in 6th grade was not a unique predictor with other predictors in the model. In line with emerging findings with marginalized students, mathematics self-concept in 6th grade was also not a unique predictor. Finally, students’ mathematics achievement at age 4 predicted their math ACT scores in 12th grade (B = .69), as did their middle-school mathematics achievement in number, algebra, and geometry (B = .43–.67), which mediated the relation between mathematics achievement at age 4 and math ACT scores. Findings highlight the importance of advanced academic opportunities, which national data indicates marginalized students are less likely to receive, the diminishing role of individual differences in executive function skill as children develop domain knowledge, the diminished role of math self-concept for predicting achievement among marginalized students, and the strong stability in math achievement.

Quadrilaterals hierarchical classification and properties of the diagonals: A study with pre-service mathematics teachers

The aim of this research is to investigate the main characteristics of the processes of constructing a hierarchical classification of quadrilaterals and identifying properties of their diagonals by pre-service middle and secondary school mathematics teachers (PMTs), when involved in whole-class discussions with the teacher educators, after having solved tasks focused on those topics. Data collection comprised video recordings of the sessions and PMTs’ written work, analyzed qualitatively. Findings indicate that constructing the hierarchical classification of quadrilaterals involved the PMTs in prototypical judgments, and dichotomous comparisons. In comparison the identification of the diagonals’ properties was influenced more by definitions and logical relationships, reflected in judgments and comparisons. It was concluded that participation in these processes, with whole-class discussions and development of schemes to illustrate inclusion relationships, may assist PMTs with prototypical phenomenon and dichotomous comparisons, benefiting their future teaching practice.

Research on the BOPPPS Teaching Mode of Number and Algebra in Junior Middle School Mathematics

BOPPPS teaching mode is a goal-oriented and student-centered teaching mode. It emphasizes students' participatory learning and attaches great importance to classroom interaction and inquiry. In order to change the disadvantages of traditional teaching, this paper discusses the perfect fit between this model and the "number and algebra" classroom in junior high school mathematics. On this basis, a series of teaching strategies are provided for reference. The teaching process of "number and algebra" under the BOPPPS teaching mode is constructed. This provides experience for junior high school mathematics teaching.

Teacher and Student Opinions on Teaching Four Operations with Integer Numbers in 7th Grade with Counting Stamps

The study examines the views of middle school mathematics teachers and 7th-grade students on using counting stamps to teach four operations with integers. The study was conducted with ten mathematics teachers with different professional seniority and ten 7th-grade students studying in these schools. The teachers were asked six open-ended opinion form questions, and the students were simultaneously asked five open-ended opinion form questions. In this qualitative study, the interview technique was used to analyze the views of teachers and students. A structured interview form was preferred as a data collection tool. A qualitative research method was adopted in collecting, analyzing, and interpreting the data of this study. Content analysis was used to analyze and interpret the data. According to the study results, it was determined that teachers and students did not find counting stamps functional and that they needed to be more adequate in operations with integers. Therefore, there is a need for new models that can replace counting stamps.

Unleashing the potential: spatializing middle school mathematics for enhanced learning

Unleashing the potential: spatializing middle school mathematics for enhanced learning

Learning together: A mixed methods analysis of team-based learning in mathematics

To provide meaningful, high-quality learning experiences for students with diverse academic backgrounds, a critical consideration for mathematics educators is student engagement. The approach of team-based learning has allowed for an increase in student-centered class time and demonstrated positive results in tertiary education across multiple disciplines. However, this approach has been primarily used at the tertiary level and has not yet been empirically examined in middle school mathematics. Our mixed methods study of team-based learning in an eighth-grade mathematics class examined the influence of students’ team type (i.e., mixed sex, same-sex) and perceptions of team members’ contributions on students’ engagement in their mathematics class. Results of the study provide evidence for the positive effect of team-based learning on engagement as well as support for the critical role of peer interactions. Our findings provide implications for implementing team-based learning in secondary mathematics education for educators and researchers.

An engineering design-based mathematics activity example based on STEM approach in middle school: Cold storage design

Engineering design practices in STEM education focus on reflecting the discipline-specific work of engineers in a manner that is suitable for the student level and course learning objectives. Using an engineering design context also facilitates student identification of global problems and feasible solutions to address such problems. In this article, within the framework of STEM approach, an engineering design activity that can be applied in middle school mathematics course is presented. Additionally, examples of students’ experiences of the engineering design-based mathematics activity are given. The "Cold Storage Design Activity" was executed in a classroom setting, and the implementation process underwent examination and evaluation. 12 eighth-grade students from a middle school in Turkey took part in the implementation. The middle school were able to successfully perform an engineering design process and effectively overcome challenges through teamwork. The results of the activity show that middle school students are excited and eager to participate in a design activity.