Theses and Dissertations (Mathematics Education)
http://hdl.handle.net/10500/6440
2016-07-30T07:21:10ZLanguage practices of trilingual undergraduate students engaging with mathematics in Kenya
http://hdl.handle.net/10500/20134
Language practices of trilingual undergraduate students engaging with mathematics in Kenya
Njurai, Evelyn Wanjiru
This study explored language practices of trilingual undergraduate students of mathematics as they made sense of an algebraic task. Specifically, the study set out to explore whether, how and why trilingual undergraduate students used language(s) to make sense of mathematics. In this study a trilingual speaker is viewed as an individual proficient in three languages and whose proficiency in the languages is not necessarily equal. The speaker uses the three languages either separately or by switching between any two in ways that are determined by his/her communication needs.
Exploring language practices helped me to understand how students position themselves as they engage with a mathematics task using mathematical Discourses (capital D) in relation to their trilingual language facility. This facility involves the use of either the language of learning and teaching (LoLT) (English) or the switching between two or three of the languages they know. These languages were home languages, including Kiswahili of the students. In tertiary institutions, English is the LoLT while the home languages are neither taught nor used in the classroom.
The study used a qualitative inquiry process, specifically a case study approach. It was conducted at a public university in Kenya with a focus on first-year engineering students with mathematics in their programme. Data were collected using a students‟ questionnaire, and clinical and reflective interviews. A structured questionnaire was used to gather the baseline data, which was used for the selection of 15 interview participants. The clinical interviews provided information on language use as the students engaged with the task, explaining each step of the process, while the aim of the reflective interviews was to identify, ascertain and confirm various actions and different languages and language practices that were not apparent during the clinical interview. The interviews were transcribed and 11 paired transcripts were selected for analysis.
The data were analysed using the methods of Discourse analysis (Gee, 2005). This analysis explored how students used language in tandem with non-language “stuff” in a single language or when switching between any two languages and how and why each was used. The focus was on the activities and identities they enacted through their interpretation of the given task and in part of the solution process.
The findings revealed that when students engaged with mathematics, they drew on the LoLT only, or switched between the LoLT and their home languages or between the LoLT, home languages and Kiswahili. Those who switched did so when they were faced with interpretation challenges, when there was need to emphasise a point and due to habitual practices of switching. They commonly switched silently and communicated verbally in the LoLT. The purpose for code switching was to gain understanding of the task. On the other hand, a trilingual student is likely to remain in the LoLT because content has been taught and tasks presented in the LoLT.
The key contribution of this study is its focus on the trilingual language context of undergraduate students of mathematics, an area that has not been researched up to now. Furthermore, this study has added to scholarly work in this discipline by establishing that code switching is not the preserve of students who are learning the LoLT; rather, it is a reality for trilingual students who are competent in the LoLT when they engage with mathematics.
2015-01-01T00:00:00ZThe effect of using Lakatos' heuristic method to teach surface area of cone on students' learning : the case of secondary school mathematics students in Cyprus
http://hdl.handle.net/10500/20006
The effect of using Lakatos' heuristic method to teach surface area of cone on students' learning : the case of secondary school mathematics students in Cyprus
Dimitriou-Hadjichristou, Chrysoula
The purpose of this study was to examine the effect of using Lakatos’ heuristic
method to teach the surface area of the cone (SAC) on students’ learning. The Lakatos
(1976) heuristic framework and the Oh (2010) model of “the enhanced-conflict map”
were employed as framework for the study. The first research question examined the
impact of the Lakatosian heuristic method on students’ learning of the SAC, which
was addressed in three sub-questions: the impact of the method on the students’
achievement, the impact of the method on their conceptual learning and the impact of
the method on their higher order thinking skills. The second question examined
whether the heuristic method of teaching the SAC helped students to sustain their
learning better than the traditional method (Euclidean method). The third question
examined whether the heuristic method of teaching SAC could change students’
readiness level, according to Bloom’s taxonomy.
A pre-test and post-test quasi-experimental research design was used in the study that
involved a total of 198 Grade 11 students (98 in the experimental group and 100 in the
control group) from two schools in Cyprus.
The instruments used for data collection were cognitive tests, lesson observations
(video-recorded), interviews and questionnaire. Data was analysed using inferential
statistics and the Oh (2010) model of the enhanced conflict map. Student achievement
within time was the dependent variable and the method of training the independent
variable. Therefore, time was the “within” factor and each group was measured three
times (pre-test, post-test and delayed). The differences in students’ achievement
within each group over time were examined.
Results indicated that the average mean score achievement of the students in the
experimental group was double that of the students in the control group. The Jun-
Young Oh’s model of the enhanced conflict map showed that students in both groups
changed from alternative conceptions to scientific conceptions with the experimental
group showing greater improvement. It was also observed that from the post-test to
delayed test, the Lakatosian method of teaching the SAC has a significant positive
effect on students’ achievement at all levels of Bloom’s taxonomy, especially at the
higher order thinking (HOT) levels (application and analysis-synthesis levels) as compared to the Euclidean method of teaching. In addition, the Lakatosian method
helped the students to sustain their learning over time better than the Euclidean
method did and also helped them to change their readiness level, especially at the
HOT levels. The Lakatosian method helped students to foster skills that promote
active learning. Of great importance was the use of mathematical language, as well as,
the enhanced perception in the experimental group in comparison with the control
group, through the use of the Lakatosian method.
The results of this study are promising. It is recommended that pre-service teachers
should be trained on how to effectively implement the Lakatosian heuristic method in
their teaching.
2015-02-01T00:00:00ZAnxiety and lack of motivation as factors affecting success rates in bridging mathematics
http://hdl.handle.net/10500/19929
Anxiety and lack of motivation as factors affecting success rates in bridging mathematics
Sofowora, Samson Oluwaseun
The aversion to the study of mathematics and the resultant poor performance by students generally cannot be overemphasized and this still poses a great threat to the needed skills in the science, technology and commerce sector in South Africa. This study therefore tends to explore the importance of Mathematics to students and the economy globally by focusing on which contributive psychological factors are responsible for low performance in mathematics among Pre degree students as a case study.
In addition also, the teaching and learning strategies used in the classroom that will help curb mathematics anxiety among students will be looked into. Furthermore a test to ascertain if poor teaching methods or pedagogical content knowledge of mathematics’ teachers influence anxiety thereby leading to poor performance in mathematics will be carried out. By utilizing a mixed method approach, an integration of the qualitative and quantitative approaches, the study attempted to provide an insight into the poor performances in Mathematics by Pre-degree students in a Private Institution of higher learning by exploring the following affective domains: 1) Anxiety 2) Motivation (lack of either the Internal & External type) and also considering the teaching strategies adopted on the other hand.
The theoretical framework applied to this study was three fold in nature, namely, to investigate the nature of the relationship between mathematics anxiety and mathematics achievement on one side, secondly, to investigate the nature of the relationship between motivational orientation and mathematics achievement on the other side. Finally, it will investigate the relationship between teaching methods and mathematics achievement.
The major findings that emanated from this study were as follows: there is a strong impact of the affective factors (anxiety, beliefs, emotions and motivation) on mathematics learning and success rates among Pre-degree students in South Africa. This study shows the importance of affective factors (such as anxiety, negative attitude, lack of motivation) in determining the success and or failure of mathematics learning, with the intention of promoting and encouraging positive traits, attitudes and beliefs in the students.
The issue of teaching strategies was however not of a strong impact on success rates in bridging mathematics among the students as their lecturers were commended to be on top of their subject, but only that strategies to teaching mathematics must be dynamic, effective and varied as much as possible to meeting the students diverse learning styles .
2014-11-01T00:00:00ZThe impact of grade 10 learners' behaviour on their academic performance in mathematics
http://hdl.handle.net/10500/19833
The impact of grade 10 learners' behaviour on their academic performance in mathematics
Hagoramagara, Franco
The aim of this study was to identify types of behaviour manifested by learners during mathematics instruction, and the impact that this behaviour might have on the mathematics performance of learners. The study was conducted in Far East cluster of Johannesburg East District, in the province of Gauteng, South Africa. At the time of the study the Far East cluster of Johannesburg East District consisted of a population of seven public high schools, of which two schools were randomly sampled to participate in the study.
Participants consisted of (n=10) Grade 10 mathematics learners, 2 mathematics teachers and 2 heads of mathematics departments (HODs). Data from learners were collected using a set of their assessment scores accumulated over a period of six months, that is, from January 2014 to June 2014 (Section 1.3.3). Also, semi-structured interviews were carried out with learners to determine types of classroom behaviour they perceived to influence their mathematical performance. The aim of documenting learners‟ assessment scores (document analysis) was to determine their average performance in Grade 10 mathematics over a stipulated period. Teachers and HODs completed questionnaires to identify types of classroom behaviour that learners manifested during mathematics instruction.
The study followed a qualitative approach with phenomenology research design (Section 3.2). The study identified several types of classroom behaviour that characterized mathematics instruction in both schools, such as making noise and not doing classwork and homework activities. In addition, the study established that forms of behavioural patterns that are manifested by learners during a mathematics instruction influenced their performance in the subject. Huitt‟s (1997) model was used to conceptualize and interpret the results.
2015-10-01T00:00:00Z