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In this this article we discuss findings from an investigation of whether female student teachers would choose to study mathematics if it were optional for primary teacher education in Malawi. A mixed methods research methodology was used to collect data through survey and focus group discussions (FGDs). Five hundred and twenty three female students from 6 public teacher education colleges completed a questionnaire, and 160 of them participated in FGDs. A descriptive statistical analysis was conducted on the quantitative data while a thematic analysis was conducted on the qualitative data. The findings show that 68% of female students would choose to study mathematics while 32% would not. This correlated with the students' mathematics scores at the end of their secondary school national examination. Those students with high score passes opted for mathematics and those with low score passes did not, suggesting that performance at secondary school influenced their confidence in studying mathematics. Female student teachers' reasons for choosing or not choosing mathematics were it optional are classified into 5 categories: the perceived usefulness of mathematics, inner motivation to study mathematics, the nature of the college mathematics content, how mathematics courses are taught at colleges, and gender stereotype in mathematics lessons. We discuss these in relation to the Malawian government's agenda of increasing participation of females in mathematics, science, technology, and engineering.

In this paper we discuss findings of a study that investigated the resources and language that teachers in Malawi use to teach the concept of zero. In Malawi primary schools, textual resources available to teachers are mainly the curriculum materials in the form of syllabus, teacher guides and learner textbooks. The syllabus and teacher guides are in English while the learner textbooks are in Chichewa as teaching is in Chichewa or other local language in the first 4 years of primary school. We used the Mediating Primary Mathematics framework (Venkat and Askew in Educ Stud Math 97:71-92, 2018) and a qualitative case study of two teachers to explore the resources used, how the teachers interacted with the resources and how they moved between the two languages. Our findings include that the language and resources that the teachers used provided affordances as well as constraints for learning the concept of zero. We identified two types of challenges for the teachers; that of naming and that of representing the concept of zero. We discuss what the Malawi context illuminates about teaching zero in post-colonial multilingual settings.

This article discusses the findings of a case study that explored the use of explanatory talk in mathematics teacher education lessons on how to teach the concept of place value. The Mathematics Discourse in Instruction framework guided the study, in particular the element of naming in explanatory talk. Three teacher educators' lessons on the teaching of place value of whole numbers were observed and video recorded. Findings indicate that across all the lessons, 66% of the naming was mathematical and was seen to provide opportunities for student teachers to learn to use mathematical terms correctly, while 34% of the naming was non-mathematical and might have constrained student teachers' understanding of some concepts related to place value. Furthermore, two-thirds of the non-mathematical naming was use of ambiguous pronouns, which could have been avoided. The findings suggest that teacher educators need to pay more attention to correct mathematical naming of terms related to place value. How mathematical concepts are named in teacher education is important because correct naming is likely to help student teachers learn to regard mathematical talk as an important part of their work of teaching.

We re-examine a Malawian teacher's lessons which, using the framework of mathematic problem-solving developed by Polya, the typology of levels of task demand from Stein and colleagues and Malawi's description of learner-centred education (LCE), were described as teacher-centred and evaluated as 'not good'. We studied seven video-recorded circle geometry lessons taught by the teacher and analysed these first using an LCE framework and then the Mathematics Discourse in Instruction (MDI) framework, adapted to suit the analysis of geometry lessons. The LCE analysis revealed that while the lessons were undoubtedly teacher-centred, they were not at the extreme end of an LCE continuum. Analysis using an adapted MDI framework showed that the teacher's use of mediational means opened opportunities to learn mathematics. We argue that LCE frameworks are useful in mathematics education research as they do not dichotomise teaching practices, but they are insufficient. They can obscure opportunities made available to learn mathematics. Frameworks that illuminate such opportunities are needed to fully describe mathematics teaching practices. Furthermore, we identified links between the elements of LCE exhibited and the mathematical mediational means in use. These suggest that supporting teachers to strengthen their mathematical mediational means in use could enable movement towards more learner-centered teaching.

Purpose: The aim of the study is to better understand how lesson study (LS) contributes to challenging teachers' views of mathematics teaching and learning. Design/methodology/approach: This study is part of a wider ongoing project aiming at improving primary mathematics teaching in Malawi through professional development (PD) of teachers using a LS model. The units being analyzed are teachers' written reflections and lesson plans. The analytical approach is qualitative content analysis. Findings: Initially, the participating Malawian primary teachers report traditional views of mathematics teaching and learning. After having participated in a LS cycle, they reported on the need to work on how to involve and create space for learners' participation in mathematic lessons and highlight the importance for learners to discover mathematics on their own. Research limitations/implications: This is a small-scale study due to LS being quite new in the Malawian context and the need to test before possible upscaling. Practical implications The paper includes a description on how LS might contribute to challenging Malawian teachers' views of mathematics teaching and learning; this can be valuable information for others who are attempting to use LS in a similar context. Originality/value: This paper fulfills an identified need to learn more about how LS might contribute to challenging teachers' views of mathematics teaching and learning worldwide.

This paper reports on findings from a study that investigated reasons Malawian students have for preferring particular contexts in mathematics. The study explored students' preferences of contexts using a survey questionnaire that contained 27 contexts and asked students to indicate their level of interest for each context on a 4-point scale and to write down reasons for their most preferred contexts. There were 393 students of 14-20 years old. Findings include that most preferred contexts were of future career prospects, modern technology, health and community issues. Students' reasons for these preferences were in four categories of career prospects, curiosity, community well-being and personal well-being. Furthermore, future career prospects was the most common reason for the preferred contexts.

Understanding the proof problem is necessary in the development of geometric proof in schools. This paper discusses findings from a qualitative case study which explored the mathematical work done by teachers in helping students to understand geometric proof problems. Data were generated from two teachers through video-recorded observations of 30 lessons and tape-recorded post-lesson interviews. Both types of data were analysed using thematic analysis which involved coding of the data relating to the first stage of Polya's problem-solving framework. The findings suggest that supporting students to understand geometric proof problems involves several tasks, including defining key mathematical terms of the theorem, initiating activities for introducing the theorem and representing the theorem as a statement to be proved. Furthermore, conducting these aspects of mathematical work using empirical exploratory approaches offers students better opportunities to understand the proof problem.

We report on two case studies in which we investigated mathematics for teaching. We were interested in the mathematical knowledge teachers need to know, and know how to use, in order to teach mathematics well. The two case studies focused on the teaching of probability in Grade 8 and the teaching of functions in Grade 10. We discuss the mathematics for teaching probability and functions in terms of the mathematical 'problem solving' or 'mathematical work' demanded of the teachers as they taught the two topics. Among the findings are the interesting differences between the demands on the teaching of functions and the demands on the teaching of probability in these two cases. We argue that mathematics for teaching needs to be understood as shaped by the particular topic being taught, as well as by how teachers select to introduce and approach the ideas and concepts they are teaching. We conclude with a discussion of questions raised for mathematics teacher education, together with implications for practice.

In this paper, I discuss Universal Basic Education (UBE) in relation to the teaching and learning of mathematics in Southern Africa. I present the status of UBE for all countries in the region and then use 3 selected examples: Botswana, Malawi, and Zambia, to illustrate the provision of mathematics in the general framework of UBE in the countries. I draw from results of SACMEQ evaluations to compare the 3 countries' quality of primary education and also the mathematical achievement of learners. According to the evaluations, countries that have better age-appropriate enrolment and provide a better quality of primary education seem to have better mathematical achievement than countries that have less age-appropriate enrolment and less quality of primary education. While this might seem obvious, it is important to note because of the many challenges that some Southern African countries are facing in their efforts in providing quality mathematics education to all.

This paper looks at mathematics and its relevance in schools from the perspective of students' interests. It starts by discussing briefly the importance of paying attention to cultural and social relevance, and then it focuses on students' interests as one of the aspects of relevance. Findings are presented from a survey conducted in Malawi with 346 secondary school students. The study explored what students would find interesting to learn as contexts in school mathematics by indicating their preferences for some given contexts in form of a questionnaire, which was adapted from a very large cross country project (ROSME). Findings include that students are interested in mathematics for future careers and mathematics of modern technologies more than ethnomathematics and mathematics of agriculture, and there are no differences in preferences for contexts between female and male students. Most of the findings confirm findings from previous ROSME studies, particularly those situated in African countries, and therefore strengthen the arguments made earlier by these studies. This paper further argues that relevance for students includes their interests, and therefore should be considered as a factor in the development of curriculum materials and classroom activities.

The paper discusses findings of a study that investigated Malawian students' meanings for some probability vocabulary. The study explores the meanings that, prior to instruction, students assign to some words that are commonly used in teaching probability. The aim is to have some insight into the meanings that students bring to the classroom. The sample for the study consisted of 154 students in their first year of secondary school education and whose first language was Chichewa. The paper demonstrates that many of the students' preconceived meanings for probability vocabulary were distant from established conventional probability meanings. In addition, there was a wide range of meanings associated with each of the words. An attempt is made to analyse the students' meanings and to explain their possible sources, some of which are rooted in the students' first language. The paper highlights the importance of having an awareness of students' preconceived meanings, and also stresses the importance of language in learning probability.

This article discusses the findings of a case study that explored the use of explanatory talk in mathematics teacher education lessons on how to teach the concept of place value. The Mathematics Discourse in Instruction framework guided the study, in particular the element of naming in explanatory talk. Three teacher educators' lessons on the teaching of place value of whole numbers were observed and video recorded. Findings indicate that across all the lessons, 66% of the naming was mathematical and was seen to provide opportunities for student teachers to learn to use mathematical terms correctly, while 34% of the naming was non-mathematical and might have constrained student teachers' understanding of some concepts related to place value. Furthermore, two-thirds of the non-mathematical naming was use of ambiguous pronouns, which could have been avoided. The findings suggest that teacher educators need to pay more attention to correct mathematical naming of terms related to place value. How mathematical concepts are named in teacher education is important because correct naming is likely to help student teachers learn to regard mathematical talk as an important part of their work of teaching. [ABSTRACT FROM AUTHOR]

We re-examine a Malawian teacher's lessons which, using the framework of mathematic problem-solving developed by Polya, the typology of levels of task demand from Stein and colleagues and Malawi's description of learner-centred education (LCE), were described as teacher-centred and evaluated as 'not good'. We studied seven video-recorded circle geometry lessons taught by the teacher and analysed these first using an LCE framework and then the Mathematics Discourse in Instruction (MDI) framework, adapted to suit the analysis of geometry lessons. The LCE analysis revealed that while the lessons were undoubtedly teacher-centred, they were not at the extreme end of an LCE continuum. Analysis using an adapted MDI framework showed that the teacher's use of mediational means opened opportunities to learn mathematics. We argue that LCE frameworks are useful in mathematics education research as they do not dichotomise teaching practices, but they are insufficient. They can obscure opportunities made available to learn mathematics. Frameworks that illuminate such opportunities are needed to fully describe mathematics teaching practices. Furthermore, we identified links between the elements of LCE exhibited and the mathematical mediational means in use. These suggest that supporting teachers to strengthen their mathematical mediational means in use could enable movement towards more learner-centered teaching. [ABSTRACT FROM AUTHOR]

In this this article we discuss findings from an investigation of whether female student teachers would choose to study mathematics if it were optional for primary teacher education in Malawi. A mixed methods research methodology was used to collect data through survey and focus group discussions (FGDs). Five hundred and twenty three female students from 6 public teacher education colleges completed a questionnaire, and 160 of them participated in FGDs. A descriptive statistical analysis was conducted on the quantitative data while a thematic analysis was conducted on the qualitative data. The findings show that 68% of female students would choose to study mathematics while 32% would not. This correlated with the students' mathematics scores at the end of their secondary school national examination. Those students with high score passes opted for mathematics and those with low score passes did not, suggesting that performance at secondary school influenced their confidence in studying mathematics. Female student teachers' reasons for choosing or not choosing mathematics were it optional are classified into 5 categories: the perceived usefulness of mathematics, inner motivation to study mathematics, the nature of the college mathematics content, how mathematics courses are taught at colleges, and gender stereotype in mathematics lessons. We discuss these in relation to the Malawian government's agenda of increasing participation of females in mathematics, science, technology, and engineering. [ABSTRACT FROM AUTHOR]

Understanding the proof problem is necessary in the development of geometric proof in schools. This paper discusses findings from a qualitative case study which explored the mathematical work done by teachers in helping students to understand geometric proof problems. Data were generated from two teachers through video-recorded observations of 30 lessons and tape-recorded post-lesson interviews. Both types of data were analysed using thematic analysis which involved coding of the data relating to the first stage of Polya's problem-solving framework. The findings suggest that supporting students to understand geometric proof problems involves several tasks, including defining key mathematical terms of the theorem, initiating activities for introducing the theorem and representing the theorem as a statement to be proved. Furthermore, conducting these aspects of mathematical work using empirical exploratory approaches offers students better opportunities to understand the proof problem. [ABSTRACT FROM AUTHOR]

We report on two case studies in which we investigated mathematics for teaching. We were interested in the mathematical knowledge teachers need to know, and know how to use, in order to teach mathematics well. The two case studies focused on the teaching of probability in Grade 8 and the teaching of functions in Grade 10. We discuss the mathematics for teaching probability and functions in terms of the mathematical 'problem solving' or 'mathematical work' demanded of the teachers as they taught the two topics. Among the findings are the interesting differences between the demands on the teaching of functions and the demands on the teaching of probability in these two cases. We argue that mathematics for teaching needs to be understood as shaped by the particular topic being taught, as well as by how teachers select to introduce and approach the ideas and concepts they are teaching. We conclude with a discussion of questions raised for mathematics teacher education, together with implications for practice. [ABSTRACT FROM AUTHOR]