University of Macau / Faculty of Education

University of Macau / Faculty of Education

published_or_final_version / abstract / toc / Education / Master / Master of Education

In 2004, the Transition Mathematics Project (TMP), funded by the state of Washington and The Bill and Melinda Gates Foundation, was established to create projects to help high school students gain the necessary skills to become college and work-ready. Aligned to TMP's College Readiness Mathematics Standards, a fourth-year capstone mathematics course was developed and implemented, titled Applications in Mathematical Reasoning (AMR), a rigorous course option for students to take during their senior year of high school. The purpose of this study was to explore any relationship between taking the AMR course and preparation for college level mathematics. Using causal-comparative study design and matching participants in the sample, variables were examined based on the number of precollege courses taken; college level math course completed and grade earned; and placement test results for students who took the AMR course compared to those students who took no mathematics during their high school senior year. Though findings for precollege and college level course-taking were inconclusive, mathematics placement test scores were found to be significantly higher for those students who completed the AMR course. The placement test findings supported other research that links rigorous mathematics courses taken in high school with improved college placement and persistence. Based on the research examined and the study findings, there was support to consider the following: (a) creating alternate but rigorous math course offerings for the high school senior year; (b) striving toward a four-years of mathematics graduation requirement for all high schools; (c) enacting mandatory placement at the community college for students placing into precollege courses; and (d) reducing barriers to successful transition between high schools and post secondary institutions by fostering K-16 communication, aligning standards, and improving course alignment. / Graduation date: 2012

The main purpose of this study was to assess the relationship between students' achievement in mathematics and teachers' background, professional development and teaching practices. A self report instrument - Mathematics Teaching Opinionate Scale (MaTOS) was used to collect data from Form C (Grade 10) mathematics teachers in the Maseru District in Lesotho, Southern Africa. Stratified random sampling technique was adopted for the study in the selection of participants screened on the basis of type of ownership of schools. The simple random format was subsequently utilized to pick 40 teachers on the basis of school population. Out of the total participants of 40 teachers, 18 (45.0%) were males while 22(55.0%) were female. Simple correlation and regression statistics at the 0.01 and 0.05 significance levels were utilized for data analysis. Findings indicated a significant positive relationship between students' academic achievement in mathematics and teachers' background (i.e. teachers' qualifications, subject majors and years of experience especially from six years of teaching) with r = 0.552, P < 0.01. Furthermore, regression analysis showed that teachers' qualifications (&#946; = 0.77, P < 0.05), subject majors (&#946; = 0.35, P < 0.05) and experience (&#946; = 0.16, P < 0.05) were predictors of students' achievement in mathematics [F(3,39) = 4.321; P < 0.05)]. The findings therefore suggest that if all mathematics teachers have a degree, are specialized in mathematics or mathematics education and have more than five years teaching experience the students' achievement in mathematics would likely improve. / MATH, SCIENCE and TECH EDU / MSC (MATHS,SCIENCE OR T/EDU)

It is widely recognized that educational research and theory should be motivated by the desire to continually improve the practice of teaching. However, bridging the divide between theoretical research outcomes and the practical constraints of classroom-based teaching has proved somewhat challenging. The involvement of teachers as the 'bridge-builders' between theory and practice could provide an effective mechanism for achieving this integration. The purpose of this study is thus to investigate whether the involvement of teachers in developing and implementing a theory-based teaching module would improve teaching practice in the classroom. A teaching module was collaboratively developed by a group of teachers for Grade 9 linear functions using: the principles of mathematical proficiency postulated by Kilpatrick, Swafford and Findell, (2001); the teaching phases formulated by van Hiele (1986); and the cognitive classification of classroom activities developed by Stein and Smith (1998). This module was then taught to six Grade 9 classes by four teachers in one school in the Eastern Cape, South Africa over a period of 5 weeks. The effectiveness of the module, and its application in the classroom, was assessed in terms of: (i) the extent to which theory could be used to inform the design and development of teaching materials; (ii) the efficacy of this teaching material in promoting teaching for mathematical proficiency; and (iii) the effects of extraneous influences on the usefulness of the module in teaching for mathematical proficiency. While the theoretical framework provided a sound basis for developing the teaching module, it was found that collaboratively transforming this theory into a teaching module for practical use in the classroom is certainly possible, but it requires considerable time and effort that practising teachers do not have. Developing the depth of understanding required for mathematical proficiency also takes time - a commodity often in short supply as teachers grapple with the demands of the curriculum. Teaching for mathematical proficiency is a layered process. It starts with thinking about an idea (like a graph) that is developed out of a related concept that then has a set of characteristic algorithms and actions which are learnt and performed in sequence. Building understanding in this way ends with a student being able to visualize and conceive the graph as a structure that can be described as if it were an object (encapsulating all the previous concepts belonging to similar graphs in one idea). This development of understanding is important for mathematical proficiency but is not necessarily easy. When teaching with the module, it was necessary to create an extra opportunity for students to use procedural knowledge and repetition in order to provide enough examples to help them see the link: between linear number patterns and linear graphs. Extraneous influences on teaching for mathematical proficiency were grouped into two categories - endogenous and exogenous influences. Endogenous influences were teacher related and included the attitudes, decisions and disposition of the teacher. Exogenous influences were more contextual (and in effect out of the control of the teacher) and included teaching time available, curriculum, external assessments etc. Both of these influences were seen to affect teaching for mathematical proficiency, either promoting or inhibiting it. This research affirmed the central role that teachers play in teaching for mathematical proficiency. It is considered critical that research actively involve teachers in the evolution of mathematical theory. The development of an enabling environment (including institutional support, time, capacity, resources, skills and tools) for teachers will further enhance their capacity to teach for mathematical proficiency.

Cell phones have become a ubiquitous part of daily life for both teachers and learners alike. The educational potential afforded by cell phones is diverse. The challenge for teachers is to capitalise on this ubiquity and make use of cell phones for educational purposes. This study investigates how cell phones can be used in the teaching of Mathematics using VITALmaths video clips. Five VITALmaths video clips were uploaded onto cell phones which were used in the classroom to explore the Theorem of Pythagoras in a visually appealing way that supported a conceptual understanding of the basis of the theorem. The study was conducted in two high schools in Grahamstown, South Africa. It involved two teachers from each school and a total number of 47 Grade 10 Mathematics students. The participating teachers were chosen from a group of Mathematics teachers taking part in the Mathematics Teacher Enrichment Programme (MTEP) of the FirstRand Foundation Mathematics Education Chair hosted by Rhodes University. This study is framed as a case study and is grounded within the interpretive paradigm. The study captures teachers’ and learners’ experiences in using cell phones as instructional aids within the pedagogical context of the classroom. This research suggests that cell phones can be a useful resource to support teaching and learning in the classroom, particularly in under-resourced schools. The use of VITALmaths video clips as mathematical content, and cell phones as a vehicle of delivery, enhanced active participation and concentration, sped up lessons, encouraged collaboration as well as interaction and hands-on exploration, and promoted both student autonomy as well as teacher enrichment.

Mathematics has become increasingly important, as it is a pre-requisite for careers like architecture, science, engineering and medicine. Therefore it becomes imperative for the learners to understand and love it. In other words a sound foundation of mathematical skills and knowledge in the early stages is required. Often we hear learners asking questions like "when and where are we going to use these symbols x and y in our lives? " These questions might indicate that learners cannot link mathematics with daily life occurrences or even their own background experiences. This study is an exploration through hands-on activities of mathematical concepts embedded in beadwork artifacts. Learners' background experiences on bead work artifacts are acknowledged and explored for mathematical understanding. It is a case study, consisting of 44 learners in Grade 9 in two schools in Grahamstown. An interpretive approach is used. In order for the learners to be able to explore beadwork artifacts, they visited the Albany Museum (AM) and Msithandane Women's Project (MWP) in the community. Learners gathered information from these two sources. Beadwork artifacts in this study were used as a mediation and integration tool between culture and mathematics. Beadwork artifacts are found in the learners' cultures serving different purposes. In this study the focus was on Xhosa bead work artifacts. The hands-on activities posed challenges to learners because of their different background experiences. Some were able to draw designs but were unable to thread what they designed, whereas others were able to thread beads but were unable to draw designs. In this study learners had to use both completed bead work artifacts and drawn up designs for the investigation of mathematical concepts. Learners were able to identify symmetries in dress and in South African flag designs. Number patterns discovered were linked to their prior number pattern knowledge. The economic value of beadwork artifacts linked mathematics to the economics learning area. This study ties up with the new curriculum (C2005) and RNCS, which advocate the inclusion and integration of learning areas. In this instance, art and culture were used in mathematical activities. The study also encouraged the inclusion of participants' cultural background as a starting point for motivating them towards utilizing mathematical resources existing in their real life situations. The purpose was to make them aware that mathematics is found everywhere around us.

The disparate numbers of boys and girls who elect to continue with mathemalics and/or physical science in the higher slandards of the school system has recently attracted much research atlention and the complexity of the interrelaledness of causal factors has become obvious. The broad aim of the study was to investigale the significant drop-out rate of girls at the end of the junior secondary phase of education (approximate age of fourteen lo fifteen). This was to be carried out for mathematics and physical science and undertaken using a cross-sectional and a longitudinal study. The cross-sectional study entailed administering mathematics and physical science attitude questionnaires to 3531 standard six, seven and eight pupils from 4 co-educational, 2 allgirls' and 2 all-boys' schools, from middle and upper socioeconomic communities with similar language and cultural backgrounds . The longitudinal study involved pupils from two coeducational schools and one all-girls' school. It was a progressively-focused study starting with questionnaires administered to 358 standard six girls and boys, narrowing down to questionnaires and interviews used with 50 girls and 28 boys in standard seven and finally to interviews with 10 girls from standard eight. The parents of these ten girls were interviewed at the end of the study. The attilude questionnaires yielded strong sex differences which favoured the boys in both subjects for all the attitudes measured and also pointed to a progressive deterioralion of altitudes over the three-standard span. They also established significant differences in attitudes which favoured the pupils from Single-sex schools. It was further concluded that the girls were more strongly guided by their attitudes when making their subject-choice decisions. In the longitudinal study, reasons were suggested for pupils either taking or dropping mathematics and physical science. The introduction of algebra in the first year of high school presented a problem to pupils. In physical science, electricity was singled out as giving the subject a male bias. Socialization influences in the home were the main issue dealt with from the parent interviews . Sex-roles and stereotypes were dealt with in depth. Recommendations were made involving classroom strategies, curriculum possibilities, school policies and further research

The study examined the use of multiple representations such as the real world, written symbols, spoken symbols, diagrams and manipulatives by learners to promote the learning of percentages and fractions through social interaction. This investigation was carried out through a teaching and learning programme which was developed and implemented by me, the researcher. The effect of the implemented programme was the main focus of the research. The qualitative study was oriented in the interpretive paradigm – a paradigm that seeks to understand the meaning attached to human actions. Twenty learners participated in the implementation of the programme and 9 learners were selected for focus group interviews. The purpose of the interviews was to explore learners' understanding and feelings about the use of multiple representations in the learning of percentages and fractions through social interactions. The other tools employed in this study were pre-and-post diagnostic tests, observations, learners' work and a journal. The pre-test was used to determine learners' prior knowledge for the program design and implementation, while the post-test and learners' work were used to analyze the effect of the programme. Observations were used to investigate how multiple representations promoted or did not promote the learning of percentages and fractions. The teacher's journal was to record and reflect on any relevant information gathered on each lesson observed. The data shows that the effective use of multiple representations helped learners learn the concept of percentages and fractions better. Learners were able to look at representations in useful ways; multiple representations made some aspects of the concept clear; and multiple representations enabled learners to correct errors. Through the interaction between the teacher and learners, the following was found: all the learners changed words to change focus; learners made links between multiple representations; the learners deepened their concepts of percentages and fractions; learners could convert between fractions using multiple representations; learners could work out percentages of a quantity; and learners could express one quantity as a percentage of another. Furthermore, through the interaction between learners and learners all learners could identify more equivalent fractions of an initial fraction which was given to them; and they could increase and decrease a quantity by a given percentage. On the basis of this research, it can be concluded that the programme promoted the learning of percentages and fractions through three effective methodologies. The first methodology consisted of the effective use of multiple representations; the second methodology concerned the interaction between the teacher and learner during the learning process and the last methodology related to the interaction between the learners - interactions that were not strongly mediated by the teacher. I would recommend that teachers use these three effective approaches when teaching percentages and fractions to promote the learning of the concepts.