Zambian University Student Teachers’ Conceptions of Algebraic Proofs

This paper reports on a case study that aimed to evaluate the perceptions of 73 student teachers at Mukuba University on the nature and purpose of mathematical proof. They were presented with a mathematical reasoning and proof arguments assessment tool followed by a 10-member focus group interview. Algebraic tasks presented to them involved (i) proof construction on simple number and set theory, (ii) assessment of given mathematical statements and arguments to validate them, and (iii) validating formally structured inductive proofs. More than 75% of the student teachers had limited understanding of the nature and purpose of mathematical proofs and they believed that proof construction and validation entailed inspection of a few examples and the testing of single extreme cases. Concrete examples of empirical forms of mathematical arguments which student teachers perceived as valid were found but these demonstrated limited forms of mathematical reasoning and comprehension. It is proposed that paying attention to analytical and deductive mathematical arguments in school based assessment will alleviate mathematical learning problems and improve the quality of mathematics education. Keywords: student teachers, algebraic proof, conceptions of proof, mathematical reasoning, school based assessment.

Fostering students’ mathematical reasoning through a cooperative learning model

This study sought to ascertain whether the student teams-achievement division (STAD) model of cooperative learning is effective in fostering students’ mathematical reasoning. Using the cluster random sampling technique, 301 eleventh-grade students between the ages of 14 and 20 were chosen from six public secondary schools within one district in Zambia. Students were given tasks on quadratic equations and functions both before and after the intervention. A robust analysis of the covariance test revealed that students’ mathematical reasoning abilities were significantly higher for the group that received instruction using the STAD approach than for the group that was taught using conventional methods of instruction at each of the five design points where regression slopes were comparable. A Chi-square test of independence further revealed that the STAD learning approach was associated with a greater proportion of students who demonstrated an appropriate degree of mathematical reasoning ability for each of the three indicators (conjecturing, justifying, and mathematizing). These results demonstrate that enhancing students’ mathematical reasoning abilities through the integration of classroom activities that engage students intellectually, physically, and socially is beneficial

Learning Time of Day and Students’ Academic Achievement at School Certificate Level: A Case Study of Chibote Girls’ Secondary School.

A case study presented here is an investigation into whether time of day for instruction has an effect on students’ academic achievement in Mathematics, Science, Biology and English at school certificate level by focusing on the grades candidates obtained after sitting for national examinations. The focus is primarily on 33 randomly selected morning and afternoon pupils at Chibote Girls Secondary School. We hypothesized that morning pupils perform better than afternoon pupils owing to the fact that pupils who learn in the morning have a higher retention rate as compared to those who learn in the afternoon when the temperature is quite high. This hypothesis was tested using a non-parametric Mann-Whitney U test which showed that there was no statistically significant difference across the categories of the two learning modes in Mathematics, Science and English. Furthermore, the same results were analysed through a component plot in rotated space (factor analysis) which showed a significant difference in students’ performance between Mathematics and English for both learning modes. Descriptive statistics were computed and the general picture was that pupils performed poorly in all the four subjects with mathematics placed at the tail and English in the lead. Keywords: Learning time, Academic achievement, Core subjects

An Investigation into Challenges Faced by Secondary School Teachers and Pupils in Algebraic Linear Equations: A Case of Mufulira District, Zambia

This paper investigates the challenges faced by secondary school teachers and pupils in the teaching and learning of algebraic linear equations. The study involved 80 grade 11 pupils and 15 teachers of mathematics, drawn from 4 selected secondary schools in Mufulira district, Zambia in Central Africa. A descriptive survey method was employed to obtain in-depth and richer information about the central issues under study. To address the three research questions, an assessment test for the pupils was administered followed by separate interviews for teachers and pupils respectively. Some identified challenges include: (i) lack of pre-requisite knowledge by pupils, (ii) lack of conceptual, procedural and strategic knowledge and skills required for solving linear equations and (iii) inappropriate approaches and methods used in the teaching of algebraic linear equations. The study also compared responses on items from teachers’ and pupil’s interviews and found out that there was a strong relationship between teachers’ and pupils’ opinions on the challenges that pupils face in solving algebraic linear equations and what needs to be done to improve the situation. It is therefore, proposed that the teaching and learning of secondary school mathematics need to focus on transforming the quality land scape that has been identified especially the transition from arithmetic to algebra. Pupils need to be exposed to formulating equations from situations with which they are familiar and that teachers get regular refresher courses to keep them up-dated with new developments in the teaching and learning of mathematics. Keywords: Challenges, Algebra, Linear equations, Secondary school teachers and pupils

MEDIATING EFFECT OF SELF-EFFICACY ON THE RELATIONSHIP BETWEEN INSTRUCTION AND STUDENTS’ MATHEMATICAL REASONING

Literature is well-stocked with studies confirming that an instructional approach, self-efficacy, and mathematical reasoning skills are critical for enhancing students’ conceptual understanding and achievement in mathematics. However, there has been little emphasis on establishing whether being able to reason mathematically depends only on the instructional approach or students’ self-efficacy beliefs about mathematics also play a hidden role. A quasi-experimental study involving 301 grade 11 students from six public secondary schools in one district was carried out to investigate the mediating effect of self-efficacy on the relationship between instruction and students’ mathematical reasoning. Participants of the study were selected using the cluster random sampling method. Data were collected before and after the intervention via a mathematical reasoning test and a mathematics self-efficacy beliefs questionnaire. A Parallel Multiple Mediator Model in SPSS using the PROCESS custom dialogue version 3.4 was employed for data analysis. Findings suggest that mathematics self-efficacy and task-specific self-efficacy beliefs collectively and significantly mediate the effect of the instructional approach on students’ mathematical reasoning. The Student Teams-Achievement Division (STAD) was found to be an effective approach for enhancing students’ mathematical reasoning alongside self-efficacy beliefs. These findings provide evidence on the need to select an instructional approach that does not only focus on developing students’ cognitive abilities such as mathematical reasoning but also fosters students’ affective attributes such as maths self-efficacy beliefs

From what makes students dislike mathematics towards its effective teaching practices

This paper presents the findings of a descriptive survey research that investigated what makes students dislike mathematics and seeks potentially effective mathematics teaching practices, to boost their interest. The study involved 94 participants, including 60 lower-level secondary school students and 34 mathematics teachers from 5 schools in Karongi District, Western Province, Rwanda. Both students’ and teachers’ questionnaire responses were analyzed using descriptive statistics. We found that what makes students dislike mathematics is related to how mathematics is taught. Low scores in tests or exams, teachers’ harshness, and carelessness were reported among the factors demotivating students to like mathematics. Being able to show the relevance of Mathematics in an everyday situation, teaching students to remember mathematical facts, and showing them lots of worked examples were mentioned by most of the teachers as indicators of effective mathematics teaching practices. Together with these indicators, preparing the lesson before teaching, providing exercises and homework to students, and making research to update teachers’ teaching skills have been drawn and recommended for teachers as potentially effective teaching practices

An Analysis of Prospective Teachers’ Mathematical Reasoning on Number Concepts

This paper presents and discusses the results of a case study that was carried out to understand the mathematical reasoning of 73 second-year student teachers at a university in Zambia.  The paper also demonstrates why it is important to develop the reasoning abilities of mathematics student teachers during their initial training programs. The questionnaire items presented to student teachers required them to justify the validity of selected algebraic statements and arguments on odd and even numbers. Factors that influenced participants’ modes of argumentation were also identified, clearly highlighting their implications for mathematics teacher education. Findings of the study revealed that 70% of the participants gave explanations that were aligned to an empirical or inductive mode of argumentation while 7% used the analytical or deductive argumentation mode. The rest of the participants gave explanations that did not reflect valid mathematical justification of the given algebraic statements and arguments. These results clearly indicate that only the minority of participants exhibited an adequate understanding of representing odd and even numbers in general form. Analysing and developing prospective teachers’ mathematical reasoning abilities are necessary to anticipate how they would practice when they are professionally qualified

Insights of teachers and students on mathematics teaching and learning in selected Rwandan secondary schools

Effective teaching and learning of mathematics are vital not only for examination or assessment purposes but also for empowering learners to live in a modern age of science, mathematics, and engineering and enable them to role-play to the social and economic development of the developing countries and the whole world as well. This study reveals insights of teachers and students regarding mathematics teaching and learning in Rwanda. The study was a survey designed involving 217 ordinary level secondary school students and 25 secondary school teachers who teach Mathematics, from 5 schools in Karongi District, Western Province, in Rwanda. The results analysis was confined to three components namely; preferred mathematics teaching methods, motivation to teach and learn mathematics, and the usability of mathematics in daily life. Descriptive statistics and all the statistical tables/graphs were generated using SPSS and MS Excel. As results, peer learning and group work and expository were found to be the most applied teaching methods in the selected schools. This study has underlined that not only parents but also siblings have an impact on their young brothers/sisters’ education. In terms of its utilitarian value, respondents revealed that mathematics increases critical thinking, problem-solving skills, and creativity of students. Teachers need to be more knowledgeable in the subject matter, through lesson preparations and linking mathematical concepts to real-world experiences

Teacher efforts towards the development of students’ mathematical reasoning skills

Research shows that improved mathematical reasoning results in improved conceptual understanding and the application of mathematical knowledge to a variety of real-world contexts. The assessment of teacher efforts to help students develop their mathematical reasoning, however, and the identification of classroom practices that encourage this growth have received less attention in previous studies. A descriptive survey was conducted with 62 mathematics teachers from six randomly chosen public secondary schools in one district. Lesson observations were carried out in six randomly selected grade 11 classrooms from all participating schools to supplement teachers' questionnaire replies. Results show that more than 53% of the teachers believed that they had been making enormous efforts towards the development of students' mathematical reasoning skills. Nonetheless, some teachers were not found to be as supportive of students' mathematical reasoning as they believed they were. Additionally, the teachers did not leverage all of the opportunities that arose during instruction to support students’ mathematical reasoning. These results show the need for greater professional development opportunities geared towards orienting both in-service and prospective teachers on useful teaching strategies for fostering students' mathematical reasoning