Investigation into the skill levels achieved by mathematics students in the V.C.E. and the H.S.C. mathematics courses

This study examines whether recent changes to the mathematics courses offered in the final year of secondary school (Year 12) in the state of Victoria, Australia have affected the learning outcomes of students in terms of then: skill levels in algebra, calculus and problem solving; and in terms of their preparation for a tertiary mathematics unit. The impact of these changes on the transition from secondary to tertiary mathematics is also considered. A comparison is made between students who attempted a first year mathematics unit at the University of Melbourne (U. of M.) having completed the new V.C.E. (Victorian Certificate of Education) mathematics courses and mathematics courses from the previous H.S.C. (Higher School Certificate) system. The comparison involves the use of tests administered upon entrance to a tertiary mathematics unit at the U. of M., and questionnaires. In 1991, V.C.E, students and H.S.C. students attempted the same mathematics test at the U. of M. and their results were compared. In 1992, the tests were attempted by V.C.E. students only. To compare new V.C.E. students and H.S.C. students, questions on the 1991 test were matched with similar questions on the 1992 tests and a panel of experts determined what the H.S.C. students who attempted the 1991 test would have been expected to average on these matched questions on the 1992 tests had they attempted them. These expected average scores were then compared with the actual scores of the new V.C.E. students. The scores of the groups were scaled when necessary. Questionnaires were administered to 1991 U. of M, mathematics students who were part of the V.C.E. pilot group in 1990, secondary mathematics educators, tertiary mathematics educators, and 1991 V.C.E. (1992 U. of M.) students. The mathematical misconceptions exhibited by new V.C.E. students are discussed and their frequencies stated. The research indicates that the new V.C.E. mathematics courses have provided the V.C.E. mathematics students in this study with significantly lower skill levels and a significantly poorer preparation for a tertiary mathematics unit than those which were previously provided by the H.S.C. mathematics courses.

Teacher professional growth : a study of primary teachers involved in mathematics professional development

The overall purpose of this study was to examine whether professional development programs can act as appropriate vehicles for the professional growth of teachers of primary mathematics. A longitudinal study was conducted of primary teachers involved in a Victorian mathematics professional development program — Exploring Mathematics In Classrooms (EMIC). The professional growth of six teacher participants in one EMIC course was examined over a period of 18 months. The teachers selected were from four different schools located in the southern metropolitan region of Melbourne. The central interest of this study was in teacher professional growth and accordingly the perspective sought was predominantly that of the teacher. A case study research approach was adopted and data were gathered through observations, interviews, questionnaire, and the collection of teacher work documents. A theoretical model of teacher professional growth was used to represent the teachers' growth. The study generated data on the nature of teacher professional growth and the features of professional development programs likely to influence teacher professional growth. All of the teachers reported and demonstrated growth with respect to their mathematics teaching, in areas associated with their: Classroom Practice, Knowledge and Beliefs, and Professional Attributes. The teachers' growth was highly individualistic, with no two teachers demonstrating exactly the same professional growth outcomes, or the same growth processes. The data provided evidence to confirm that teacher growth is a complex and gradual learning process. For each of the teachers several different routes to change and growth were evident, drawing attention to the non-linear nature of growth. The teachers' responses to the professional development program were influenced by various contextual and personal factors. The data provided evidence of a strong link between the content and outcomes of professional development programs — the outcomes reported and demonstrated by the teachers reflected the content of the EMIC program. Key factors associated with mathematics professional development programs perceived as influencing growth were: program content; program structure; and program presentation. A significant finding was the strong influence on teacher growth of the presenters of professional development programs—some data suggested that the 'quality' of the program presenter is fundamental to the success of any professional development program. The study provided insight into the processes involved in teacher professional growth and factors associated with the way in which professional development programs influence growth. The theoretical model of teacher professional growth used in this study has been elaborated and recommendations which might inform the design and implementation of future professional development programs have been made.

Implementation of student active learning in primary mathematics in Indonesia

Twenty years after the first pilot projects began to develop Student Active Learning (SAL) in Indonesia, and four years since it was adopted for use in the last provinces, this research investigates the implementation of Student Active Learning in Indonesian primary mathematics classrooms. A study of the relevant literature indicates that teaching based on constructivist principles is unlikely to be implemented well in mathematics classrooms unless there are high quality teachers, readily available manipulative materials, and a supportive learning environment. As Indonesian schools often lack one or more of these aspects, it seemed likely that Student Active Learning principles might not be ‘fully’ implemented in Indonesian primary mathematics classrooms. Thus a smaller scale, parallel study was carried out in Australian schools where there is no policy of Student Active Learning, but where its underlying principles are compatible with the stated views about learning and teaching mathematics. The study employed a qualitative interpretive methodology. Sixteen primary teachers from four urban and four rural Indonesian schools and four teachers from two Victorian schools were observed for four mathematics lessons each. The twenty teachers, as well as fourteen Indonesian headteachers and other education professionals, were interviewed in order to establish links between the background and beliefs of participants, and their implementation of Student Active Learning. Information on perceived constraints on the implementation of SAL was also sought. The results of this study suggest that Student Active learning has been implemented at four levels in Indonesian primary mathematics classrooms, ranging from essentially no implementation to a relatively high level of implementation, with an even higher level of implementation in three of the four Australian classrooms observed. Indonesian teachers, headteachers and supervisors hold a range of views of SAL and also of mathematics learning and teaching. These views largely depended on their in-service training in SAL and, more particularly, on their participation in the PEQIP project Typically, participants’ expressed views of SAL were at the same or higher level as their views of mathematics learning and teaching, with a similar pattern being observed in the relationship between these latter views and their implementation of SAL principles. Three factors were identified as influencing teacher change in terms of implementation of SAL: policy, curricular and organisational, and attitudes. Recommendations arising from this study include the adoption of reflection as an underlying principle in the theory of SAL, the continuation and extension of PEQIP type projects, changes in government policy on curriculum coverage and pre-service teacher training, and more support for teachers at the school and local authority levels.

Using everyday experiences in teaching secondary mathematics in Malawi : possibilities and constraints for change

Proponents of socially and culturally oriented mathematics education have argued that teaching approaches which value and connect with the learner's prior knowledge and everyday experience are more likely to promote active, meaningful, relevant and liberatory learning than approaches which rely on transmission and abstract presentation of mathematical content. In Malawi, proposals to reform the outdated secondary mathematics curriculum have been made with the aim of aligning mathematics instruction with the social and political changes in the current Malawian society. Using a case study approach, this study investigated the extent to which everyday experiences could be used as a vehicle for changing the learning and teaching of secondary mathematics in Malawi. The study was collaborative, taking place over a period of five months in severely overcrowded and poorly resourced classes in two schools. It involved three mathematics teachers in a cycle of planning and teaching mathematics lessons based on the use of everyday experiences, and observation of and reflection on these lessons, in order to document the effects of using everyday experiences on student learning and teachers' teaching practices. The data was collected through student questionnaires; classroom observations and fieldnotes; interviews and reflective meetings with teachers; and informal meetings with key education officials in Malawi. Mathematics examination results from students involved in this study and a corresponding group from the previous year were collected. A reflective and critical approach was adopted in the interpretation and discussion of the data. Teachers' participation in this study resulted in heightened awareness of their teaching roles and the value of linking school mathematics with everyday experience. The study also shows that students found mathematics interesting and important to learn despite their lack of success in it. In addition, the study documented a number of constraints to change in mathematics instruction such as teachers' focus on mathematics content and examination requirements, and students' resistance to inquiry learning. It also recorded possibilities and barriers to collaboration both between teachers and researchers, and teachers themselves. The findings of this study are timely since they could serve to inform the reform of the Malawian secondary mathematics curriculum currently being undertaken, which began without a critical examination of the classroom conditions necessary to accommodate a socio-politically relevant mathematics education.

Mathematics as a second language : looking for a bridge between mathematical language and the language of thought

Our thoughts are in one language, and mathematical results are expressed in a language foreign to the way we think. Mathematics is a unique foreign language with all the components of a language; it has its own grammar, vocabulary, conventions, synonyms, sentence structure, and paragraph structure. Students need to learn these components to partake in a thorough discussion of how to read, write, speak and think mathematics. Beginning with the students natural language and expanding that language to include symbolism and logic is the key. Providing lessons in concrete, pictorial, written and verbal terms allows the instructor to create a translation bridge between the grammar of the mother language and the grammar of mathematics. This papers presents methods to create the translation bridge for students so that they become articulate members of the mathematics community. The students "mother" language, expanded to include the symbols of mathematics and logic, is the the key to both the learning of mathematics and its effective application to problem situations. The use of appropriate language is the key to making mathematics understandable.

Teaching mathematics using the internet

This paper examines teachers' use of the Internet in the teaching and learning of Mathematics. The study draws upon data collected via an online survey and interviews with six teachers. It reports on their beliefs, strategies for use and their perceptions on how it impacts on students and their learning of mathematics. Some comparisons are made between the ways teachers used the Internet.

Web mathematics anyone?

The World Wide Web has had an impact on many areas of teaching and learning. Mathematics teaching however has only recently begun to utilise and develop this educational resource. This paper outlines a research program, which aims to uncover the extent the Internet, in particular the World Wide Web, is being used for High School mathematics education. The program includes searching out discernible Web-based teaching strategies and examining their impact on mathematics teaching and learning attitudes and achievements. Of particular interest is the extent to which deployment of the Web in mathematics teaching might increase student interest in mathematics. The first step in this
process is to develop a preliminary typology of mathematical elements on the Web. The nature of these elements, their categorisation and their possible roles in the teaching and learning of mathematics are discussed.

Implementing cooperative learning in grade four mathematics classes in Thailand

This study showed that successful implementation of cooperative learning in Thai primary mathematics classrooms requires three components: preparation of teachers, preparation of instructional materials and the preparation of pupils. In addition, cooperative learning was found to have a positive effect on pupils' mathematics achievement and their attitude towards mathematics.

Fostering meaningful learning by using word problems in post-secondary mathematics

This research is a case study of action research investigating the effects of using word problems with Chinese Malaysian post-secondary students studying mathematics as an enabling science. A variety of word problems, a discussion method, reflective and peer learning, specific values in mathematics, and relevant socio-cultural and language issues were explored.