Ordinary Level Mathematics Research Articles

Challenges and Effects of Dialogue and Argumentation in Teaching Ordinary Level Mathematics in Zimbabwe

The purpose of the study was to examine the effect of challenges that affect the teaching of ordinary level mathematics using dialogue and argumentation approach in the mathematics classrooms in Zimbabwe. A descriptive survey was the method employed for the research. The subjects of this study consisted of approximately 100 Ordinary level Mathematics teachers and ten Mathematics Head of Departments selected from 72 public high schools in Gutu district of Masvingo province in Zimbabwe. Purposive sampling was used for selecting ten participating Mathematics Head of Departments for qualitative data. Random sampling was used for selecting samples of teachers for quantitative research. Quantitative data analysis was done using two statistical metrics namely the mean and the standard deviation while qualitative data was analysed by thematic analysis. The empirical findings of the study indicated that challenges such as class size, planning, attitudes, heterogeneity, lack of confidence, and lack of proficiency among challenges that have a significant but negative influence on the application of dialogue and argumentation in the teaching of Ordinary level mathematics. The main study limitation was that the results may not be transferable nationally since the study was limited to schools in the Gutu district of Masvingo province in Zimbabwe. These results have implications on the need for mathematics teachers to receive training on how to plan and implement the dialogue and argumentation teaching approach in the mathematics classrooms.

Effect of the Dialogue and Argumentation Strategy on the Academic Achievement of Ordinary Level Students in Zimbabwe

The purpose of the study was to examine the effect of the dialogue and argumentation strategy on the academic achievement of mathematics students studying the subject at ordinary level. The research strategy used was a descriptive survey. A quantitative approach that used a structured questionnaire for data collection from a sample of 100 O’ level Mathematics teachers was used. Data validation was done using Confirmatory Factor Analysis (CFA). The Structural Equation Modelling (SEM) was used for data analysis. The empirical findings of the study indicated that all the factors of dialogue and argumentation strategy namely: collective teaching, purposeful teaching, supportive teaching, reciprocal teaching, cumulative teaching and pedagogical repertoires have a significant and positive influence on the teaching of ordinary level mathematics. These results demonstrate that the dialogue and argumentation strategy has a significant effect on the academic achievement of ordinary level mathematics students. The main study limitation was that the findings of this study might not be transferable nationally since the study was delimitated to only schools in Gutu district of Masvingo province in Zimbabwe. These results have implications on the effective teaching of ordinary mathematics in secondary schools in Zimbabwe.

Secondary School Students’ Mathematics Anxiety: A Zimbabwean Perspective

This study employed a mixed-methods technique to examine the spectrum of mathematics anxiety levels felt and expressed by Zimbabwean students studying Ordinary level mathematics. Ninety-one pupils from forms 3 and 4 (N = 91) made up the convenient sample; of them, 41 were male and 50 were female. The instrument used was the Hopko-adapted amalgamated mathematics anxiety scale (aMAS) (2003). While focus group conversations were audio recorded and transcribed to explore in-depth, social settings and learning environments that cause anxiety, the quantitative data was analysed using SPSS, version 23.0. The key categories were then thematically classified and analysed with quantitative information. To test a hypothesis based on the data, an independent samples t-test was run to see whether males and females’ anxiety levels differed by mean. The results showed that the participants experienced significant mathematics anxiety, and many situations—including parental and social pressure, instructional methods, and learning environments—reinforce math fear. Findings also show that, society exerts significant pressure on learners due to high expectations of success in mathematics. Additionally, some teachers were viewed as fuelling the anxiety through their repertoire and that classroom environments may unintentionally cause discomfort to mathematically challenge peers. Interesting suggestions were made by respondents regarding how to help people with math anxiety. The study offers a compelling case for its relevance to teacher education, research, and instructional practice. The study also recommends conducting comparative studies as one method of comprehending the issue. Keywords: Cognitive achievement, Mathematics-anxiety, Teaching-learning, Gender issues, Social phenomena.

Secondary mathematics teachers’ use of learners’ responses to foster justification skills

This study aimed to understand how secondary mathematics teachers engage with learners during the teaching and learning process. A sample of six participants was purposively selected from a population of ordinary level mathematics teachers in one urban setting in Zimbabwe. Field notes from lesson observations and audio-taped teachers’ narrations from interviews constituted data for the study to which thematic analysis technique was then applied to determine levels of mathematical intimacy and integrity displayed by the teachers as they interacted with the students. The study revealed some inadequacies in the manner in which the teachers handled students’ responses as they strive to promote justification skills during problem solving, in particular teachers did not ask students to explain wrong answers. The teachers indicated that they did not have sufficient time to engage learners in authentic problem-solving activities since they would be rushing to complete syllabus for examination purposes. On the basis of these findings, we suggest teachers to appreciate the need to pay special attention to the kinds of responses given by learners during problem-solving in order to promote justification skills among learners.

COVID-19 AS AN AGENT OF CHANGE IN TEACHING AND LEARNING STEM SUBJECTS

The closing of schools due to Covid-19 has brought a dimension of uncertainty into STEM education. Despite the closing of schools due to the need to observe physical distancing, some schools have found ways to continue teaching and learning on virtual platforms enabled by increasingly pervasive fourth industrial revolution environments. In this study, the teaching of Ordinary level mathematics and science in pursuit of STEM education goals as enabled by the Internet of Things (IoT) in online classrooms was therefore, explored. Using an interpretive case study, relevant data were collected from two mathematics and three science teachers during semi-structured interviews. These participants communicated their experiences in transitioning from face-to-face to online classrooms as they worked to promote STEM education during the Covid-19 pandemic. The findings reveal teachers’ experiences of this transition and their selection of particular Web 2.0 tools to establish online classrooms. Notably, mobile instant messaging tools proved to be a popular option for being cheap, user-friendly, temporal, and multimodal. The findings also revealed that teachers struggled to adapt the hands-on activities to suit online teaching resulting in the use of teacher-centred approaches. Keywords: Covid-19, mathematics and science, online learning, STEM education, virtual platforms

Rurality and Exclusion in Ordinary Level Mathematics in Zimbabwe: A Document Analysis

This conceptual paper fuses literature review and document analysis in examining the nexus between rurality and social exclusion in Ordinary level mathematics education in Zimbabwe. The paper utilizes Bourdieu’s cultural capital theory to examine the content and context of mathematics problems in textbooks and examinations focusing on language and cultural experiences. Globally, rural education has been neglected and Zimbabwe is no exception. I argue that the role of nonmaterial deterrents like lack of cultural and language capital in achievement in mathematics education has not been accorded due attention. I conclude that the context of mathematics problems in textbooks and examinations is alien to rural learners. The readability of textbooks is also beyond the reach of many rural learners. I recommend that the mathematics curriculum should be inclusive of the diverse cultural experiences of learners and the language used should be intelligible to all. The mathematics educators and related stakeholders should know that every child is capable of doing mathematics hence all forms of social closure should be eradicated. https://doi.org/10.26803/ijlter.19.6.22

Exploring the Conceptual Understanding of the Quadratic Function Concept in Teachers’ Colleges in Zimbabwe

This paper reports on an exploration of preservice teachers’ understanding of the quadratic function concept in Zimbabwe. These concepts were taught to preservice teachers studying for a diploma in Education wishing to specialize in the teaching of Ordinary level mathematics. Concerns about high Mathematics failure rate in Zimbabwean Secondary Schools have prompted this investigation into finding out if teachers’ understanding of quadratic function concept could be the cause. The study adopted the APOS (action-process-object-schema) to investigate their conceptual understanding of the concepts. Data were generated from students’ responses to a written task and follow up interviews were used to solicit information from the preservice teachers. A designed genetic decomposition for quadratic concepts was used as an analysis tool. The findings of the study also revealed majority of the pre-service teachers seemed to be operating at the action level of understanding, with very few teachers who have reached the object level. It was noted that the preliminary genetic decomposition failed to accommodate all students’ responses which lead to the development of a modified genetic decomposition.

The Effects of Using Assessment Rubrics on the Assessment and Grading of Pupils Conceptual Understanding of Algebra

In an effort to improve performance in mathematics, this quasi-experimental non-equivalent control group pre-test post-test study was designed to establish the effects of using assessment rubrics on the assessment and grading of pupil’s conceptual understanding of algebra. This was done using Algebra Achievement Test (α=0.9) and Attitude Questionnaire Math (α=0.832) as data collection instruments. In the study, two groups of pupils (control, n=30 and experimental, n=34) doing 10th grade ordinary level mathematics were randomly selected at Muyombe Boarding Secondary School. Both groups received Problem Based classroom instructions on the topic. Then the experimental group was assessed using assessment rubrics. Data collected were analyzed using statistical tests through SPSS version 16. The independent t-test results showed that the experimental group exhibited a statistical significance with higher Mean Achievement Score (μ =62.76 SD=21.844) than the control group (μ =49.72 SD=14.027), t (62, 0.05) =3.590, p<0.05). The Manny Whitney U test also showed that the experimental group (μ=92.92, SD=3.11) had a statistical significance with a higher positive attitude toward mathematics than the control group (μ=84.35, SD=8.59), p<0.001. The results of the study showed that assessment rubrics could serve as a powerful tool for assessment and grading of pupils’ work that led to improved performance in mathematics. The study recommended that teacher educators should consider including assessment rubrics in their respective methodologies and assessment courses for pre-service teachers, and suggestions were provided for further research studies.

Secondary School Mathematics Teachers’ Use of Students’ Learning Styles When Teaching Functions: A Case of Zimbabwean Schools

This paper reports on a research that was done to explore how ordinary level mathematics teachers used their knowledge of their students’ learning styles when teaching functions. The study was carried out at eight secondary schools in the Makoni District of Manicaland Province in Zimbabwe. The schools were selected using stratified random sampling. Twenty-five mathematics teachers at the selected schools participated in the research. Data were obtained through face to face interviews and document analysis. The findings revealed that the mathematics teachers’ teaching and assessment strategies were not based on their knowledge of their students’ learning styles. Information and communication technology (ICT) and audio teaching aids were not used by most of the teachers. The researchers recommended that the mathematics teachers be in-serviced on the implications of students’ learning styles for mathematics teaching. The teachers also needed some in-service training on how to use different forms of ICT in mathematics teaching.

Post-primary students’ images of mathematics: findings from a survey of Irish ordinary level mathematics students

ABSTRACTA questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination – the final examination for students in second-level or post-primary education. At the time this study was conducted, ordinary level mathematics students constituted approximately 72% of Leaving Certificate students. Students were aged between 15 and 18 years. A definition for ‘image of mathematics’ was adapted from Lim and Wilson, with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. A questionnaire was composed incorporating 84 fixed-response items chosen from eight pre-established scales by Aiken, Fennema and Sherman, Gourgey and Schoenfeld. This paper focuses on the findings from the questionnaire survey. Students’ images of mathematics are compared with regard to gender, type of post-primary school attended and prior mathematical achievement.

Trend in the G.C.E. Ordinary Level mathematics performance of students in the North West region of Cameroon.

This work seeks to portray the trend (pattern) in the General Certificate of Education (GCE), Ordinary Level mathematics performance of secondary school students of the North West Region of Cameroon, across the years 2007-2013. To achieve this, an expost facto research design was used. Furthermore, the population of the study was all the 171,187 Form Five secondary school students of the North West Region of Cameroon that sat for this examination across the years 2007-2013. No sampling was used since the results of all the students in the population were considered in the study. The instrument for data collection was the “ North West Region Students’ GCE O’Level Mathematics Results ” Data CD which was officially collected from the headquarters of the Cameroon GCE Board, Buea. Moreover, students’ mean mathematics performance for the various years was used to describe the trend in the students’ performance. Though the results did not show any systematic pattern, it was noticed that 2009 showed the best mathematics performance, with performance dropping steadily across the years 2011-2013. Keywords: mathematics achievement, performance trend, secondary education, GCE Ordinary Level

The image of mathematics held by Irish post-primary students

The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for ‘image of mathematics’ was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research focused on students studying ordinary level mathematics for the Irish Leaving Certificate examination – the final examination for students in second-level or post-primary education. Students were aged between 15 and 18 years. A questionnaire was constructed with both quantitative and qualitative aspects. The questionnaire survey was completed by 356 post-primary students. Responses were analysed quantitatively using Statistical Package for the Social Sciences (SPSS) and qualitatively using the constant comparative method of analysis and by reviewing individual responses. Findings provide an insight into Irish post-primary students’ images of mathematics and offer a means for constructing a theoretical model of image of mathematics which could be beneficial for future research.

The Teaching of Geometric (Isometric) Transformations at Secondary School Level: What Approach to Use and Why?

The topic of Geometric transformation is topic number 10 out of 11 topics on the national ordinary level mathematics syllabus. It involves both analytic and algebraic geometry. Analytic because it can be approached using the graphical perceptive, and algebraic because matrix theory can be applied. It requires learners to have a good grasp of a number of skills, the so called assumed knowledge. Thus Teachers of mathematics before designing, selecting and implementing a lesson, ought to understand the knowledge that their students already have (or do not have). This is because one mathematical topic depends on another, early strengths support later progress while earlier weaknesses compound into greater debility. Such information is extremely useful for planning instruction. Assumed knowledge base covers topics such as vectors, construction of shapes, symmetry, properties of shapes, Cartesian equations and graphs, similarity and congruency, etc. Because of such demands learners are found wanting especially where it involves deciding the type of transformation. It is thus the thrust of this paper to approach transformations first by using graphs. Such an approach may cause understanding and enjoyment amongst teachers and learners in the topic. This approach aims at exposing the student to real practical experiences with transformations. Brief synopses on issues of the subject content are provided.

Classification and comparison of mathematics examinations—methods based on Bloom's taxonomy

This paper describes an exploratory investigation of the use of an adaptation of Bloom's taxonomy to classify and compare mathematics questions and papers on the basis of the questions alone. It starts with some background comments on the secondary level public examination system in England and Wales. A critical review of classification schemes for mathematics questions, including a detailed discussion of Bloom's taxonomy, is then given, and this is followed by examples of how a suggested version of Bloom's taxonomy might be used in analysing General Certificate of Education Ordinary level Mathematics papers. Some recommendations for further research are contained in the conclusions section.

Mastery of simple probability ideas among G.C.E. ordinary level mathematics candidates

The apparent difficulty of the probability items on mathematics examination papers taken by bright 15‐16‐year‐olds is reported, together with the fact that these items discriminated to a surprising extent between boys and girls taught together in mixed schools. In an attempt to explain this the processes involved in the questions are analysed and tentatively related to the stages of cognitive development one might have expected such pupils to have attained.

Short notices - Exercises on modern accounts. Books 1 and 2, by N. McCrone and others. Pp 125, 154. £1·95 each. 1974. SBN 0 245 52216 6/52218 2 (Harrap) - The geometry of environment, by Lionel March and Philip Steadman. Pp 360. £2·90. Reprinted 1974. SBN 416 82707 0 (Methuen) - Geometry and trigonometry for calculus, by Peter H. Selby.

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Hints for Ordinary Level Mathematics. By L. H. Clarke. (Decimal Currency Edition.) Pp. 58. 1969. (Heinemann.)

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Ordinary Level Mathematics, with answers. Decimal Currency Edition. By L.H. Clarke. Pp. xiv. 474. 90p. 1969. (Heinemann Educational Books Ltd.) - Mathematics Two, Three and Four. Decimal Currency Edition. By L.H. Clarke. Two Pp. xii, 324. 65p. Three pp. xv, 350. 75p. Four pp. xii, 317. 80p. 1969. (Heinemann Educational Books Ltd.) - Decimals through Experience. By M. Holt. Pp.

Ordinary Level Mathematics, with answers. Decimal Currency Edition. By L.H. Clarke. Pp. xiv. 474. 90p. 1969. (Heinemann Educational Books Ltd.) - Mathematics Two, Three and Four. Decimal Currency Edition. By L.H. Clarke. Two Pp. xii, 324. 65p. Three pp. xv, 350. 75p. Four pp. xii, 317. 80p. 1969. (Heinemann Educational Books Ltd.) - Decimals through Experience. By M. Holt. Pp. 22. 20p. 1969. (Blond Educational Ltd.) - Decimal Currency and You. By L.H. Clarke. Pp. 13. 7½p. 1969. (Heinemann Educational Books Ltd.) - Volume 55 Issue 391

The Future of Applied Mathematics

I want to start by explaining some of the terms I shall use in this lecture. First, there is pure mathematics. Anyone who has done Ordinary Level Mathematics has some idea of what pure mathematics is about. Degree, or postgraduate pure mathematics for that matter, is—to quote A. N. Whitehead—“the science concerned with the logical deduction of consequences from general premisses”. The humbler algebra and geometry of school mathematics is concerned with exactly this, or should be. And in both cases, it is all done, at least in principle, for the fun of the thing with no application to the real world in mind.