Secondary Mathematics Research Articles

Secondary Mathematics Teachers’ Anticipations of Student Responses to Cognitively Demanding Tasks

ABSTRACT This study examines secondary mathematics teachers’ anticipations of student responses related to a series of cognitively demanding mathematics tasks from multiple mathematical domains presented in the context of voluntary and asynchronous online professional development modules. We analyze 283 anticipations made by 127 teachers to 17 mathematics tasks and present four distinct foci of teachers’ anticipations. Teachers participating in this study focused on actions students might take when engaging with the task — including the representations, strategies, and resources they might use — as well as aspects of students’ mathematical thinking, such as potential difficulties they might have, prior understandings they might use, and mathematical connections they might make. Teachers also attended to how students might react emotionally when presented with tasks and what actions they might take in advance or in response to their anticipations. We conclude with a discussion of ways our results can inform efforts to support improvements in mathematics teachers’ practice of anticipating.

AI활용교육에 대한 중등 수학교사의 인식 분석

Objectives The purpose of this study is to determine the level of awareness of secondary school mathematics teachers on the use of AI in mathematics education and the use of AI in various stages of lesson design. Methods A survey was conducted among 126 math teachers working in secondary schools. To analyze the survey results, the frequency, mean value, and standard deviation of each question were analyzed. In addition, in-dependent samples t-test and one-way analysis of variance were conducted to check the significance of differ-ences in respondents' characteristics as needed. Results The main findings of the study are as follows First, the results of the chi-square test were used to de-termine the statistical significance of whether the respondents had experience in teaching using A.I. Second, the chi-square test was used to determine whether the respondents had experience in teaching using A.I. The results showed that there were statistically significant differences in age and teaching experience, and the higher the age and teaching experience, the more teachers who had experience in teaching using A.I.. Third, the items that mathematics teachers expect more help from A.I. in lesson design are “diagnosing various learning problems by visualizing learner data (M=4.47),” “analyzing learning data such as learners' learning styles and learning patterns (M=4.4),” and “providing learning materials to overcome learning deficiencies (M=4.37)”. Fourth, when analyzing the perceptions of using AI in each stage of lesson design according to individual characteristics, the female mean (M=4.16) of ‘lesson design and development stage’ was higher than the male mean (M=3.88), and the difference was statistically significant. Conclusions Based on the results of the analysis, the following implications can be drawn for school math classes and lesson design activities. First, it is necessary to develop the professionalism of secondary math teachers so that math education using AI can be introduced and actively applied in the school field. Second, it is necessary to develop and disseminate teaching materials utilizing AI so that math education using AI can be activated. Third, research on AI-based math teaching and learning platforms is needed so that AI can be utilized in each stage of lesson design. Fourth, research and development of automatic grading systems utilizing AI technology should be conducted to support math education.

AN EXPLORATORY STUDY ON HOW MALE SECONDARY SCHOOL STUDENTS' ACADEMIC PERFORMANCE CONNECT TO THEIR MATHEMATICS ANXIETY

Given that it is a required subject in both elementary and postsecondary education, mathematics has been identified by some students as being challenging. Numerous studies have been conducted on various facets of mathematics. However, further research on the psychological characteristics of males in math classes in secondary schools in Delta State is needed, which is why this study was conducted. The study aimed to determine if test anxiety levels among male secondary school students and their academic performance in mathematics are related. Two research questions and two hypotheses were used in the study. The study's design was a correlation. The research population consisted of all 1650 senior secondary year two (SS2) math students in Delta State. A sample of 771 male students was selected using a multistage sampling process. The Mathematics Test Anxiety Questionnaire (MTAQ), which was validated by three experts, was the instrument used to collect data. The reliability coefficient, calculated using Cronbach's alpha, was 0.69. The students’ mathematics scores represent their academic performance. To analyze the data, Pearson product-moment correlation was employed. The study's findings demonstrated that test anxiety levels did not correlate academic performance of male students in secondary school mathematics. Furthermore, there was a sizable gap among male secondary students who had high and low anxiety in math.

Struggling as part of success: International Baccalaureate students’ productive struggle is strongly correlated to mathematical achievement

Productive struggle is an effective mathematics teaching practice that provides students opportunities to grapple with challenging mathematical concepts, connect prior knowledge, discover new ideas, and develop their critical thinking skills. Research has documented the benefits of secondary mathematics students engaging in productive struggle. Additional work is needed to detail how productive struggle relates to students’ mathematical achievement, specifically in the International Baccalaureate (IB) classroom. This study examined what correlation existed between 68 U.S. grade 11 and 12 IB mathematics students’ level of productive struggle exhibited during tasks of varying levels of cognitive demand and their mathematical achievement based on 10 IB established markschemes and a summative assessment. A strong, positive correlation was found between the level of productive struggle and mathematical achievement across all cognitive demand levels. These results support prior work emphasizing the importance of teachers making productive struggle a consistent, pervasive practice in their classrooms to foster student mathematical achievement and understanding.

How do pre-service teachers view Galois theory? A questionnaire study

Abstract algebra is an important part of mathematics teacher education as it provides the rigorous mathematical foundations for many mathematics topics covered in school classrooms. Throughout their academic career, many secondary mathematics teachers even enroll in more advanced algebra courses, which often culminate in Galois theory. However, very little is known about educational aspects of Galois theory and respective mathematics education research is scarce. We contribute to closing this gap by reporting on the results of an exploratory questionnaire study with a sample of n=39 pre-service mathematics teachers, inquiring about the raison d’être of incorporating Galois theory into teacher education: Is Galois theory viewed as useful for their later profession and which connections are drawn to the secondary mathematics classroom? On the one hand, the results of our study indicate that a vast majority of pre-service teachers do not perceive studying Galois theory as meaningful and struggle to exemplify connections between Galois theory and secondary school mathematics. On the other hand, a small share of the participants experienced Galois theory as an important part of mathematics that elegantly connects a variety of algebraic and geometric notions.

Comparing the teaching quality of alternatively certified teachers and traditionally certified teachers: findings from a large-scale study

The present study investigates whether alternatively and traditionally certified teachers differ in their teaching quality. We conducted doubly latent multilevel analysis using a large-scale dataset with student ratings on the quality of instruction provided by 1550 traditionally and 135 alternatively certified secondary school mathematics teachers in Germany. Findings show no evidence of differences in teaching quality between alternatively and traditionally certified teachers. Independent of the type of certification, novice teachers scored lower on classroom management than experienced teachers. Findings suggest that beginning teachers—whether alternatively or traditionally certified—need to be better prepared for classroom management before starting to teach.

Quantitative reasoning as a lens to examine changes in modelling competencies of secondary preservice teachers

AbstractThis study draws on quantitative reasoning research to explain how secondary mathematics preservice teachers’ (PSTs) modelling competencies changed as they participated in a teacher education programme that integrated modelling experience. Adopting a mixed methods approach, we documented 110 PSTs’ competencies in Vietnam using an adapted Modelling Competencies Questionnaire. The results show that PSTs improved their real-world-problem-statement, formulating-a-model, solving-mathematics, and interpreting-outcomes competencies. Showing their formulating-a-model and interpreting-outcomes competencies, PSTs enhanced their quantitative reasoning by properly interpreting the quantities and their relationships using different representations. In addition, the analysis showed a statistically significant correlation between PSTs’ modelling competencies and quantitative reasoning. Suggestions for programme design to enhance modelling competencies are included.

Good in theory, difficult in practice: An examination of secondary algebra teachers’ views about RtI

Research about response to intervention (RtI) programs has primarily focused on the elementary level, and there is a noticeable lack of research specific to secondary mathematics RtI programs. As such, the focus of this qualitative study was secondary algebra teachers’ perceptions and self-efficacy for the implementation of RtI. Research participants consisted of eight secondary algebra teachers that had implemented RtI programs and had at least five years of teaching experience. A semi-structured interview protocol was utilized to discuss the types of interventions they utilized, perceptions of the implementation, beliefs in their ability to effectively implement RtI, along with their view of the training they received. The researcher found student behavior, time, and training had negative impacts on teachers’ perceptions and self-efficacy towards implementing RtI programs. While participants in the study exhibited an understanding of the various tiers of intervention along with the processes involved in RtI, we conclude that there was an overall lack of preparation to work within an RtI system. The findings of this research study are of particular importance for school administrators and secondary mathematics teachers to better understand the latent barriers for successful RtI implementation. The findings of this study help these key individuals better understand the perceptions and barriers for implementing secondary mathematics RtI.

The Practice of Secondary Vocational Mathematics Teaching Reform in the Context of Vocational Education College Entrance Examination—Taking Nanning No. 1 Vocational and Technical School as an Example

The Practice of Secondary Vocational Mathematics Teaching Reform in the Context of Vocational Education College Entrance Examination—Taking Nanning No. 1 Vocational and Technical School as an Example

Changes in the Ghanaian schools’ mathematics curriculum – Exploring the need to raise awareness in the integration of the history of mathematical concepts as a pedagogical tool

There have been frequent changes to the Ghanaian mathematics curriculum content but with little or no regard for the pedagogical strategies to deliver the content. It was, therefore, important to explore teachers' awareness of integrating the history of mathematical concepts as a pedagogical strategy in teaching mathematics. The study employed the interpretive paradigm, using the qualitative inductive approach of an explorative case study with eight participating secondary school mathematics teachers. The interviews were conducted and transcribed for analysis using content analysis. The results indicated that while most teachers were enthusiastic about the use of the history of mathematical concepts as a strategy, they hardly employed it as a critical approach to teaching mathematics, and those who were aware of it merely used it as a form of introduction to their lessons. This limited the level of engagement of learners in the history of mathematical concepts in learning mathematics. Conclusions and recommendations were discussed.

The impact of graph theory and geometry based on some topics to develop critical thinking of secondary school mathematics’ students: A case of Mbulu district

The impact of graph theory and geometry based on some topics to develop critical thinking of secondary school mathematics’ students: A case of Mbulu district

Investigating the effect of instruction designed according to the ARCS model enriched with web 2.0 tools on students' mathematics achievement and motivation

This study aimed to investigate the effect of instruction designed according to the ARCS model enriched with Web 2.0 tools on the mathematics achievement and motivation of secondary school students and to examine student opinions regarding the applied instruction process. A mixed-methods approach was employed in the study since both quantitative and qualitative data were collected. To support quantitative data with qualitative data, a sequential explanatory design was chosen from mixed-methods designs. The research was conducted in the 2022–2023 academic year with the participation of 40 7th grade students enrolled in a public school in Niğde province. The research process was planned for 10 weeks, including a pretest administration in the first week, an eight-week intervention, and a posttest administration in the last week. In the experimental group, a mathematics instruction plan designed according to the ARCS model enriched with Web 2.0 tools was implemented, while in the control group, only the existing mathematics instruction plan was implemented. Quantitative data were collected using the ratio, proportion and percentage achievement tests and the mathematics motivation scale. Qualitative data were collected through focus group interviews with experimental group students. Data analysis was conducted, which included independent samples t-tests, paired samples t-tests, MANOVAs, and content analysis. The findings obtained from this study revealed that teaching with the ARCS model enriched with Web 2.0 tools had a positive effect on students' academic achievement. When the sub-dimensions of motivation were analyzed, no significant difference was found between the groups in the posttest motivation scores, but most of the participant students in the focus group interviews expressed positive opinions about the process and mentioned the effectiveness of the process. This study provides important information about the effectiveness of integrating Web 2.0 tools into the ARCS model in secondary school mathematics education in terms of the effectiveness of the teaching process and its contributions to students' achievement.

Enhancing user-centred educational design: Developing personas of mathematics school students

Persona development techniques are a well-established method to create relatable descriptions of representatives of target users of digital systems. In the field of education, research on learner characteristics has yielded comprehensive results that can help advance educational approaches. Nonetheless, these results often remain abstract and distant for researchers and practitioners. Personas offer a bridge to make this knowledge more accessible and to facilitate user-centred design processes. This study focuses on creating personas of mathematics school students to ease such accessibility. These personas are constructed based on an understanding of learners’ goals, needs, challenges and problems, joys, fears, feelings and emotions, and strategies. Data collection was conducted through a multifaceted approach, encompassing qualitative and quantitative data from web surveys, think-aloud protocols, and interviews. The target demographic comprised upper secondary school mathematics students in Austria. We found five distinct patterns of characteristics prevalent in this target group. The patterns of characteristics reflected by the personas complement the scientific body of knowledge obtained from traditional approaches investigating characteristics and needs of learners. In practical terms, these personas empower the development of user-centred digital systems, learning materials, and lessons, thus fostering an enriched educational experience for mathematics students.

Solving worded real-world problems using simultaneous equations by pre-service mathematics teachers in regional Australia: Performances and implications

<abstract> <p>Studies have shown that solving worded real-world problems is a difficult challenge for pre-service secondary mathematics teachers engaging study in most tertiary institutions. This case study reports the performances of three groups of regional pre-service mathematics teachers in their attempts to solve three different worded real-world problems through simultaneous equations in their formal assessments. These students were the first-year pre-service mathematics teachers enrolled in an undergraduate education program in a regional university in Australia. Their performances are compared by statistical analysis. The result of this study indicates that design of the word questions should consider challenging tasks appropriate for the students to achieve the pedagogical purpose in solving real-life problems that can best facilitate training the students towards becoming knowledgeable and motivated mathematics teachers for secondary schools, rather than ideologically making a levelling field with less challenging problems to achieve a high pass rate mandated by many institutions.</p> </abstract>

Analysis of secondary school mathematics textbooks in the context of digital competence

In today's world, where digitalization is inevitable and necessary, it is extremely important to raise individuals with digital competence. For this reason, it is of great importance that textbooks, which are important instruments of the education environment, are prepared in a way that contributes to digital competence skills. The aim of the study carried out in this context is to determine to what extent digital competence is included in secondary school mathematics textbooks. Document analysis, one of the qualitative research methods, was used in the study. The documents of the study consist of eight secondary school mathematics textbooks belonging to different publishers and being taught in public schools in the 2022-2023 academic year. The documents determined within the scope of the research were analyzed with the content analysis technique using a technology-supported qualitative data analysis software. The analysis of the data was based on the content, learning areas, and DigComp 2.2 framework that included digital competence. The results obtained from the study show that textbooks generally do not pay much attention to DigComp dimensions, more digital competence is included in the textbooks of MoNE Publications compared to the textbooks of other publishers, but in general, the concept of digital competence, which has an important place in the curriculum, is not sufficiently included in secondary school mathematics textbooks. In line with the results obtained from the study, suggestions were made to textbook authors and researchers.

Financial relationships and dependencies in Czech secondary school mathematics textbooks

This article analyses and compares four sets of Czech secondary school mathematics textbooks from the perspective of financial relationships and dependencies. We claim that understading of financial relationships and dependencies, such as inflation or relationship between potential return of an investment and its riskiness play an important role in financial literacy; this is why they are implicitly present in the Czech Financial Literacy Standard. The importance of the study lies in its focus on the connection between financial education and functional thinking, a link which has been missing in the literature we are familiar with. Functional thinking is an important prerequisite for understanding financial relationships and dependencies. On the other hand, financial topics may also be motivating and suitable contexts for developing functional thinking. Our comparative analyses indicates that Czech secondary mathematics textbooks do not provide teachers and pupils with opportunities to gain insights into the relationships and dependencies in financial education and that potential of the tasks with financial context for developing pupils’ functional thinking is not fully used in the analysed textbooks.

From Home to Classroom: Investigating Girls' Participation in Secondary Level Mathematics

This study explores the nuanced journey of girls' participation in secondary level mathematics, investigating the influences of early experiences at home and dynamics within the classroom. Focused on Grade IX students in Gurbhakot Municipality, Surkhet, the research adopts a quantitative approach through a survey design. Five secondary schools were selected using a convenience sampling method, aiming for diversity in community and geographical locations. Data collection involved Likert Scale points, encompassing 30 statements related to girls' participation in mathematics. The analysis revealed key insights, including positive attitudes towards academic engagement, varied opinions on gender perceptions, strong familial support, favorable learning environments at home, and diverse views on societal and parental influences. The study's significance lies in addressing a critical gap in literature by examining the transition from home to the classroom, offering valuable insights for educators and policymakers to enhance gender equity in mathematics education. The findings suggest areas for improvement, such as addressing gender perceptions, improving communication between parents and teachers, and enhancing the appeal of mathematics classes. Recognizing positive aspects, like strong family support and student interest, can contribute to fostering a more inclusive learning environment.

Reflections of COVID-19 on Teacher Education: A Metaphor Study for Distance Education

Due to the COVID-19 pandemic, distance education replaced face-to-face education in the 2019-2020 academic year in Turkey. This basic qualitative study was conducted to show the metaphorical perceptions of teacher candidates about synchronous distance university education. In this study, 178 teacher candidates, including 79 secondary mathematics, 49 science, and 50 elementary teacher candidates studying in a public university in the Central Anatolia Region in the 2019-2020 academic year, were selected with the convenience sampling method. The data were collected online due to the pandemic with an online form which includes the phrase “Distance university education is like… because…”. The teacher candidates provided 173 well-structured metaphors about distance education. The content analysis method was used for data analysis. The findings obtained in this study showed that comfort, YouTube, home, incomplete, comfort, holiday, and emptiness metaphors were particularly used. Metaphors used by teacher candidates were collected under 17 different categories as "hardware", "satisfaction", "interaction", "future", "need", "complex", "comfort", "obligation", "motivation", "spiritual", "virtual", "systemic", "responsibility", “accessibility”, “suitability”, “efficiency” and “time”. The content analysis results revealed thatmetaphors differed according to the needs and nature of the departments. It is recommended to create solutions specific to the departments and prefer distance education methods suitable for the lessons.

Mathematics teachers' perspectives on the use of math teaching materials

The aim of this study is to reveal the perspectives of secondary school mathematics teachers about the use of materials in mathematics teaching. For this purpose, the teachers' use of materials, the materials they have used, and their views on the role of using materials were analysed. In this context, the research was conducted with case study, one of the qualitative research designs. In accordance with the purpose of the research, easily accessible case sampling method was used to form the study group. The data of the study were collected from eight secondary school mathematics teachers working in different schools on a voluntary basis with a semi-structured interview form consisting of three open-ended questions about the use of materials in mathematics teaching. The interviews were audio recorded and the dialogues were transcribed. The data obtained were analysed by content analysis method. As a result of the study, it was determined that teachers' perspectives on the use of materials were built on four themes: the role of purpose of use, the role of effect on teaching, the role of effect on students and the materials used. Regarding the purpose of using the material, it was determined that most of the teachers emphasised the role of attracting attention to the lesson, the role of concretisation as the effect on teaching, and the role of facilitating understanding and remembering as the effect on students. Although the teachers stated that the use of materials had a positive effect, it was concluded that their use in the application dimension was at a low level. Another striking result of the study was that the concrete materials that some teachers stated that they used were actually course materials. When the focus was on what they used as materials, it was determined that all of the examples given were concrete materials actively used in the geometry learning domain. In addition, only one of the eight teachers participating in the study mentioned virtual learning objects (manipulatives) other than concrete materials as materials.

What Does Symmetry Look Like? A Qualitative Research Based on Mental Images

Symmetry, located within the field of transformation geometry, is a mathematical concept that plays an extremely important role as a problem-solving technique. Despite this, it seems that it is rarely used in solving mathematical problems in secondary school. This research was carried out to reveal the mental images of secondary school students regarding the concept of symmetry in the secondary school mathematics curriculum. In the study conducted based on a qualitative perspective, the metaphors developed by the students regarding the concept of symmetry and the visuals they drew were examined. The study was conducted in the spring semester of the 2022-2023 academic year with 223 students studying in the 5th, 6th and 7th grades at a public school in Ankara, selected according to the convenient sampling method. Content analysis was used to analyze and interpret the data obtained from the students. Looking at the results of the research; It turns out that secondary school students generally perceive the concept of symmetry as "having similar functionality", "visually overlapping" and "perfect and meeting in differences".