Senior Secondary Mathematics Research Articles

Effect of 7Es Instructional Cycle on Senior Secondary Mathematics Students Learning Outcomes in Gusau, Zamfara State, Nigeria

The study investigated the effects of 7Es instructional cycle on senior secondary mathematics school students learning outcomes in Gusau, Zamfara State, Nigeria. A pre-test post-test quasi experimental research design was adopted where two research questions and two null research hypotheses guided the study. The target population was 6,466 (3,154 male and female 3,312). The sample consists of 216 (103 male and 113 female) senior secondary school two mathematics students using an intact class. A total of 40 multiple choice objective questions were used for data collection at pre-intervention test and post-intervention test. Geometry Achievement Test (GAT) was instrument developed for the study. The instrument was validated by experts and pilot tested. A reliability coefficient of 0.75 was obtained for Geometry Achievement test using Pearson Product Moment Correlation (PPMC) and the instruments were reliable for the study. Mean and Standard Deviations was used to answer the research questions and Analysis of Variance (ANOVA) was used for testing the hypotheses at 0.05 level of significance. Findings revealed that there was significant difference in the mean achievement scores of senior secondary school male and female students taught mathematics using 7Es instructional cycle strategies and those taught with lecture method. that there was significant difference in the mean retention scores of senior secondary school male and female students taught mathematics using 7Ess instructional cycle strategies and those taught with lecture method. It was recommended among others that Geometry teacher’s awareness of 7Es instructional cycle of teaching should be created through workshops, seminars and conferences on teaching strategies.

Challenges Faced by Students in the Application of CBE in Senior Secondary Mathematics Education in Sri Lanka

Challenges Faced by Students in the Application of CBE in Senior Secondary Mathematics Education in Sri Lanka

Novel Feature-Based Difficulty Prediction Method for Mathematics Items Using XGBoost-Based SHAP Model

The level of difficulty of mathematical test items is a critical aspect for evaluating test quality and educational outcomes. Accurately predicting item difficulty during test creation is thus significantly important for producing effective test papers. This study used more than ten years of content and score data from China’s Henan Provincial College Entrance Examination in Mathematics as an evaluation criterion for test difficulty, and all data were obtained from the Henan Provincial Department of Education. Based on the framework established by the National Center for Education Statistics (NCES) for test item assessment methodology, this paper proposes a new framework containing eight features considering the uniqueness of mathematics. Next, this paper proposes an XGBoost-based SHAP model for analyzing the difficulty of mathematics tests. By coupling the XGBoost method with the SHAP method, the model not only evaluates the difficulty of mathematics tests but also analyzes the contribution of specific features to item difficulty, thereby increasing transparency and mitigating the “black box” nature of machine learning models. The model has a high prediction accuracy of 0.99 for the training set and 0.806 for the test set. With the model, we found that parameter-level features and reasoning-level features are significant factors influencing the difficulty of subjective items in the exam. In addition, we divided senior secondary mathematics knowledge into nine units based on Chinese curriculum standards and found significant differences in the distribution of the eight features across these different knowledge units, which can help teachers place different emphasis on different units during the teaching process. In summary, our proposed approach significantly improves the accuracy of item difficulty prediction, which is crucial for intelligent educational applications such as knowledge tracking, automatic test item generation, and intelligent paper generation. These results provide tools that are better aligned with and responsive to students’ learning needs, thus effectively informing educational practice.

The Van Hiele Model’s Effects on Student Attitudes and Achievement in Geometry Content of Senior Secondary Mathematics

The Van Hiele Model’s Effects on Student Attitudes and Achievement in Geometry Content of Senior Secondary Mathematics

Espial of Concept Difficulties in the New Africans’ Secondary School Mathematics Curriculum: CTCA Recommended

The value of teaching-learning the subject mathematics has been one of the foremost challenges and concerns of educators. This study employed a mixed method design aimed at investigating difficult concepts in the new senior secondary mathematics curriculum as perceived by students in Ghana and Nigeria. Guided by two research questions and the sample was 1,252 SS 1-3 students from 34 public and 66 private senior secondary (SS). The students are from both urban (62.9%) and rural (35.1%). The mean age of the students was 15 years, the class streams are science, commercial, and arts classes. The instruments were validated and the reliability was established using Cronbach’s Alpha method, and a reliability index of 0.78 using the test-retest method. The data obtained were analyzed using mean ranking in the IBM-SPSS 23 and Ms. Excel for qualitative analysis into themes and graphical representations. From the data gathered, we found 39 topics that students perceived to be difficult in the new mathematics curriculum. It was recommended amongst others that the CTCA should be used for the teaching-learning of mathematics in African schools based on its effectiveness in STEM related subjects in African and beyond.

MATHEMATICS FOR SUSTAINABLE DEVELOPMENT: IMPROVING STUDENTS’ LEARNING THROUGH RICH MATHEMATICAL TASKS STRATEGY

Mathematics is needed to achieve sustainable development goal 4, which targets inclusive, equitable education cum lifelong learning. Nonetheless, the students’ achievement in senior secondary mathematics is below average. Thus, this study examined the effects of the Rich Task strategy and numerical ability on senior secondary mathematics achievement. The sample comprised 203 pupils from two public senior secondary schools in Ijebu-Ode Local Government Area, Ogun State, selected on purpose. Three data collection instruments are the Mathematics Achievement Test (r = 0.84), the Numerical Ability Test (r = 0.79), and the Treatment Instructional Package. The data collected were analysed with descriptive and inferential statistics at 0.05 significance. The study discovered that the treatment significantly influenced students’ academic achievement, with the Rich Task instructional strategy found to be more effective than the conventional method. The findings also showed that numerical ability significantly impacted academic achievement, with high-ability students outperforming low and medium-ability students. However, there was no significant interaction effect between instructional strategies and numerical ability on students’ academic achievement. The study recommended that teachers employ Rich Task Strategy to meet their students’ different learning requirements and skills, and the implications for achieving sustainable development Goal 4 were identified.

Influences on student decisions to enrol in higher-level mathematics courses

Addressing the participation rates in senior secondary mathematics courses in Australian schools remains a critically important issue. In this paper, the authors report on quantitative findings from a study in which all year 11 and year 12 (aged 17–18 years) Australian Tertiary Admissions Ranking (ATAR) students in Western Australia were invited to participate. The aim was to explore the perceptions of these students regarding their enrolment in higher-level mathematics courses. Data from 1633 students were collected using a survey instrument comprised of 12, 5-point, Likert-scale items. Data were analysed by applying two statistical procedures: calculating frequencies of the 12 items in the scale and examining associations with demographic characteristics and individual items through generalised linear modelling. Analyses indicated most students agreed that other courses of study were more attractive, with almost half indicating that they did not like mathematics. In addition, approximately half of the students said that they did not need to enrol in any mathematics course for ATAR or for university entrance. Significant findings were also identified for gender, school type, and school gender. The knowledge gained from this research is valuable in understanding students’ reasons for choosing not to enrol in higher-level mathematics courses when they have the option to do so and, more broadly, to address persistently low or declining participation rates in these areas of study.

Concept Maps as a Resource to Enhance Teaching and Learning of Mathematics at Senior Secondary Level

Research has identified conceptual understanding as central to students’ mathematics comprehension. However, limited research is available to help teachers link mathematics concepts from junior to senior subjects during teaching and learning in Queensland. This mixed methods study is underpinned by constructivism. It explores teachers’ perceptions on how visual representations such as concept maps that link junior concepts (years 7 to 10) to senior concepts (year 11 and 12) can enhance the teaching and learning of conceptual knowledge at senior secondary mathematics. Surveys that include Likert scale items and open-ended questions were conducted with sixteen senior secondary mathematics teachers. To gain deeper understanding, eight semi-structured interviews were also conducted. Results show teachers hold the perception that when concept maps are used to link junior (years 7 to 10) to secondary concepts (year 11 and 12) they can be a resource that enhances conceptual knowledge, consolidation, and assessment of students’ mathematical knowledge. The role of visual representations in mathematics teaching and learning that is enhanced by concept maps is an area that needs more attention to help improve students’ participation and achievement.

Espial of Concept Difficulties in the New Africans’ Secondary School Mathematics Curriculum: CTCA Recommended

The value of teaching-learning the subject mathematics has been one of the foremost challenges and concerns of educators. This study employed a mixed method design aimed at investigating difficult concepts in the new senior secondary mathematics curriculum as perceived by students in Ghana and Nigeria. Guided by two research questions and the sample was 1,252 SS 1-3 students from 34 public and 66 private senior secondary (SS). The students are from both urban (62.9%) and rural (35.1%). The mean age of the students was 15 years, the class streams are science, commercial, and arts classes. The instruments were validated and the reliability was established using Cronbach’s Alpha method, and a reliability index of 0.78 using the test-retest method. The data obtained were analyzed using mean ranking in the IBM-SPSS 23 and Ms. Excel for qualitative analysis into themes and graphical representations. From the data gathered, we found 39 topics that students perceived to be difficult in the new mathematics curriculum. It was recommended amongst others that the CTCA should be used for the teaching-learning of mathematics in African schools based on its effectiveness in STEM related subjects in African and beyond

The stability of mathematics students’ beliefs about working with CAS

In Victoria, Australia, senior secondary mathematics students are expected to use technology and thus need to make decisions about using pen-and-paper (P&P) or technology when solving mathematics problems. The predominant technology is a Computer Algebra System (CAS). This study investigated the beliefs about CAS held by twelve Year 11 students as they learnt to use CAS and whether these beliefs were stable over time. These students held a range of beliefs related to the usefulness of CAS, speed of CAS compared to P&P, whether CAS is proper mathematics, choice of CAS or P&P, ease of use, the correctness of answers and solving problems in Mathematical Methods (i.e. the mathematics subject studied). Beliefs are often described as being stable (e.g. McLeod, 1992), but some researchers stress stability needs to be determined empirically rather than being seen as a characteristic of beliefs (e.g. Liljedahl et al., 2012). For this sample of students, stability (rather than instability) is a feature of students’ beliefs about CAS.

A Comparative Study of Chinese and Australian Senior Secondary Mathematics Teaching Materials—Exponential, Logarithmic Functions as an Example

A Comparative Study of Chinese and Australian Senior Secondary Mathematics Teaching Materials—Exponential, Logarithmic Functions as an Example

Pattern and Dynamics of Teacher Emotions during Teaching: A Case Study of a Senior Secondary Mathematics Teacher

Understanding the emotional dimension of classroom practices benefits sustainable education. However, the dynamic nature of teacher emotions during teaching remains understudied. To acquire an “in-depth” description of the emotional phenomena during teaching, a case study was adopted to examine the pattern and dynamics of a senior secondary mathematics teacher’s teaching-related emotions. Seven new mathematics lessons were observed and videotaped, and three video-stimulated, post-lesson teacher interviews were conducted. Based on appraisal theories of emotions, thematic analysis and content analysis were mainly used to analyse the data. The study revealed that the teacher most frequently experienced happiness/satisfaction as positive emotions and confusion/surprise as negative emotions. The emotions followed a three-stage process: perceptions, multilevel appraisals, and responses. The teacher most often perceived her students’ cognitive accuracy and adopted goal/need conduciveness/attainment, the discrepancy from expectations, and causal attribution as core appraisal dimensions. Teacher emotions in classrooms were also often hierarchical and cumulative, shifting from more negative at the beginning of a new semester to more positive at the middle of the semester. This study shed light on the dynamic development of teacher emotions, extending the theories and process models of emotions from the psychological field to educational research and facilitating teachers’ sustainable professional development.

Evolution over Two Decades of CAS-Active Senior Secondary Mathematics Curriculum and Assessment

The Victorian Curriculum and Assessment Authority (VCAA) introduced the use of Computer Algebra System (CAS) technology (calculator and software) into the senior secondary mathematics curriculum and examination assessment in three phases, starting with a research-based pilot from 2000, followed by parallel implementation of CAS and non-CAS subjects from 2006 and culminating in transition to CAS-assumed subjects in 2010. This paper reports reflections on these developments over two decades from the perspectives of a researcher and the state mathematics manager (the authors) in consultation with four implementing teachers (the consultants). The authors critically examined the strategic design decisions that were made for the initiative over time. Then, with contributions from the four consultants, technical design issues relating to assessment and to teaching and the changes over a decade were investigated. A range of modifications have been made over the two decades, driven by changes in device capability and progressively increasing teaching expertise. The place of CAS in senior mathematics is now widely accepted, partly because an examination component not allowing any technology has been implemented. Examination questions have become more general, which may have added difficulty, but more questions involve setting up a real situation mathematically.

Analysing senior secondary mathematics teaching using the Knowledge Quartet

Analysing senior secondary mathematics teaching using the Knowledge Quartet

Effect of Constructivist Instructional Strategy on Students Achievement in Secondary School Mathematics Curriculum in Rivers State, Nigeria

The study examined effect of constructivist strategy on students Achievement in Senior Secondary Mathematics in Rivers State. The research was guided by three research questions and corresponding hypotheses. The population is all the thirty four thousand, one hundred and sixty eight (34,168) of all Senior secondary II (SS11) students in Rivers State during the 2018/2019 Academic year. A sample size of 280 students in four intact classes were selected through purposive sampling technique. Two of each of the classes were used as experimental and control groups. Non randomized pre-test, post test control group design was used for the study. Instrument used for the study was Mathematics Achievement Test (MAT) made up of 25 items drawn from simple statistics and Lesson Packages. The instrument was validated by experts and reliability coefficient of the instrument was obtained through test-retest method. The scores obtained were subjected to Pearson product moment correlation coefficient analysis and the result yielded 0.82. Analysis of Covariance (ANCOVA), Mean and Multiple Classification Analysis (MCA) were used in analyzing the data. Findings reveals that constructivist strategy was more effective in facilitating students achievement in Mathematics than expository method. The result did not show a significant difference in students’ achievement in Mathematics in terms of gender and school type. The study therefore recommended among others the use of constructivist strategy in the teaching and learning of Mathematics in schools.

Effect of Problem-Based Learning Approach on Students’ Academic Performance in Senior Secondary Mathematics

Conventional teaching method alone cannot enhance the mathematical creativity and thinking skills needed in the 21st Century. Therefore, modern teaching methods are needed to facilitate students’ problem-solving skills. This study examined the effect of the problem-based learning (PBL) approach on students’ academic performance in senior secondary Mathematics. The pretest-posttest control, quasi-experimental design, was adopted in the study. An intact class of Senior Secondary School (II) Mathematics students (108) from two randomly Selected Senior Secondary schools in Akinyele Local Government Area, Oyo State, Nigeria, were used selected. Four null hypotheses were formulated and tested using Analysis of Covariance at the alpha level of 0.05. Results revealed that problem-based learning approach enhanced students’ academic performance in Mathematics (F1, 108= 7.130; p = (.009) < .05). It also revealed that gender has no main effect on the academic performance of students (F1, 108= .051; p = (.821) > .05). In addition, there was no significant interaction effect of PBL and gender on students’ academic performance in Mathematics (F1, 108= .000; p = (.985) > .05), and; there is a significant main effect of PBL on the quantitative ability of students (F1, 108= 6.756; p = (.010) < .05). It was recommended that stakeholders in education and the government need to train and retrain teachers on adopting the PBL approach in Mathematics classrooms to enhance students’ academic performance.

The relationships between teacher emotions and classroom instruction: Evidence from senior secondary mathematics teachers in China

This study conducted a questionnaire survey with a sample of 221 senior secondary mathematics teachers, to examine the relationships between teacher emotions and classroom instruction in the context of China. Confirmatory factor analysis and structural equation modelling were used to analyse the data. The results showed that the mathematics teachers experienced enjoyment and satisfaction more frequently than anger and anxiety, with these emotions varying with age, grade, teaching experience, and professional title. Inquiry-based instruction positively predicted enjoyment and satisfaction and negatively anger and anxiety, while direct instruction positively predicted anger and anxiety. Teachers’ satisfaction can also be a positive predictor of inquiry-based instruction. This study enriches research on teaching–emotion relationships, extending them to the context of Chinese mathematics education.

When girls do masculinity like boys do: establishing gender heteroglossia in school mathematics participation

While mathematics education research has become increasingly concerned with issues of equity, including girls’ participation in the subject, the field remains troubled with conceptualising and operationalising gender. To date, few studies of gender and school mathematics participation have moved beyond conflating gender with sex or categorising masculinities and femininities through the body. This failure to engage with gender conceptualisation has persisted despite the apparent intractability of girls’ underrepresentation in senior secondary mathematics in many contexts, including Australia. In this article, I provide fresh insights into girls’ mathematics participation by employing a conceptualisation of gender as heteroglossic to explore the post-compulsory mathematics participation choices of two school students, one girl and one boy. Using these theoretical tools to decentre the students’ bodies, I demonstrate that the reasons why these students chose to participate in Mathematics Advanced do not distinguish them by their sex/gender, as would be expected in the monoglossic gender system. While femininity was performed, both students’ subject choices were primarily characterised as masculine performances, including establishing themselves as having mathematics brains and seeking to use their mathematics participation to attain prestige. I argue that recognising and normalising girls’ masculinity and boys' femininity, rather than simply categorising gender differences, will be essential to increasing girls’ belonging and participation in mathematics. This will require greater attention to the differences within, and similarities between, the categories of boy and girl.

Girls are still being ‘counted out’: teacher expectations of high-level mathematics students

Girls’ underrepresentation in high-level post-compulsory mathematics is a longstanding issue of concern in many Western nations, with innumerable efforts to increase their participation producing little impact. In this paper, we shed new light on girls’ underrepresentation through a post-structural feminist investigation of mathematics teachers’ discursive constructions of high-level senior secondary mathematics students. Our analysis of semi-structured interviews with 22 Australian mathematics teachers revealed gendered views that serve to exclude many students from the high-level mathematics student category. Most concerning was their recurring naturalised construction of successful high-level mathematics students as endowed with the right, invariably male, brain. In so doing, teachers repeatedly closed off the possibility of success to those lacking such a ‘mathematics gift’, effectively ‘counting girls out’. We argue that increasing girls’ participation in mathematics requires moving beyond current efforts to raise female interest and confidence to, more profoundly, disrupt enduring discourses of male superiority in mathematics.

Melody of Functions and Graphs: Improving Senior Secondary Mathematics Students’ Understanding of the Function Concept by Active Integration of Mathematics and Music

Melody of Functions and Graphs: Improving Senior Secondary Mathematics Students’ Understanding of the Function Concept by Active Integration of Mathematics and Music