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.

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.

Keeping all students on the learning path

A powerful notion to guide thinking about whole-class mathematics teaching is Vygotsky’s zone of proximal development (ZPD). Our research with primary and secondary teachers over the last six years has identified roles of teachers in relation to the ZPD, and ways of overcoming some typical barriers to students’ movement through their zones. Methods have included focus groups of experts, video analysis of classroom interactions, classroom observation, and analysis of lesson plans and teachers’ reflections teaching processes their outcomes. The research has involved the gradual development, trailing, evaluation, and adjustment of a six-component model for planning and teaching mathematics. The focus of this paper is on the use of one of its components, “differentiated learning trajectories”.

Geocaching : a worldwide treasure hunt enhancing the mathematics classroom

Geocaching is a global treasure hunt that invites people of all ages to discover actively the beauty of their environment through the assistance of a Global Positioning Systems (GPS), mathematical know-how, and a bit of foraging. If you are seeking a new way to engage your students in a motivating and exciting real-life task, then geocaching might be the answer. The purpose of this article is to describe the experience of our shcool-based geocaching project undertaken with children in Prep (5-6) and the senior primary Grades (ages 10-12). We will share the potential for mathematical learning and engagement. It is argued that geocaching provides the opportunity for rich engagement with key mathematical concepts that goes beyond what can be acheived during a typical lesson.

Entry-level college mathematics success predictors : developmental performance, 'stopping-out' and demographics

Institutionally collected data identifying student demographics, course performance in both the precollege mathematics course and the college-level mathematics course, and 'stopping-out' time between the pre-college course and the college-level course were used to create a predictive model of academic success for 'high risk' college-level mathematics students. The two most significant factors were the pre-college mathematics course grade and the student's over-all college GPA.

First of all, I split the 24 : strategies for mental computation

In this article, the author sets out some goals and classroom activities for the teaching of mental computation. The author also discusses the importance of allowing children to help each other and explains that there is benefit in children listening to mathematical strategies given by other children.

Sex differences in achievement in year 12 mathematics and non-routine problem solving

In 1991 all Victorian year 12 students undertook the new Victorian Certificate of Education Mathematics Study designed by the Victorian Curriculum and Assessment Board. This paper presents the results of a study into sex difference in achievement in the new VCE Mathematics study in Victoria. An important goal of the study designers was to encourage more equal participation in senior secondary mathematics by females and males and to include assessment of mathematical skills previously not assessed in a year 12 course in Victoria. These new tasks could conceivably change the degree and direction of sex difference in achievement in senior secondary mathematics.

Understanding and developing structure - its importance for mathematics learning

This issue comes at a time when mathematics education research is becoming more intently focused on the development of "structure" as salient to generalised mathematics learning. Not surprisingly the attention on structure creates particular synergies with the increasingly rich field of research on algebraic thinking and arithmetic processes, particularly in the early years. In many ways, this special issue is concerned with describing the process of "structuring" that enables abstraction and generalisation. A recent MERJ special issue, Abstraction in Mathematics Education (Mitchelmore & White, 2007), illustrated theories of abstraction aligning these to notions of underlying structure. The importance of structure in the transition from school to university was also highlighted by Godfrey and Thomas (2008), and Novotna and Hoch (2008) in the previous special issue of MERJ (Thomas, 2008). In this special issue we present six papers that provide evidence of developing structure as critical for all learners of mathematics throughout schooling.

First of all I split the 24 : strategies for mental computation

Goals for mental computation are presented along with some ideas for teaching mental computation in the classroom. The understanding of number and the operations that come from developing mental computation strategies are useful for algebra and children should be encouraged to use more efficient and diverse mental strategies.

Teaching secondary school mathematics : research and practice for the 21st century

For the last decade or so, educational policy makers and researchers in many countries have been calling for significant changes to the way mathematics is taught in secondary schools. Australian mathematics curriculum documents now promote learning goals that go beyond mastery of a pre-determined body of knowledge and procedures - the traditional emphasis on facts, skills, formulae - to include mathematical reasoning and problem solving, communication, and real world applications. There is also pressure to move away from over-reliance on teacher-centred practices such as exposition and individual seatwork, towards activities that promote learners' involvement in constructing, applying, and evaluating mathematical ideas. Further impetus for reform comes from research recommending that if learners are to develop mathematically powerful forms of thinking and habits of mind, then classrooms should immerse them in the authentic practices of the discipline by supporting a culture of collaboration and sense-making. Teaching Secondary School Mathematics - incorporates recent developments in research and practice and applications to teaching mathematics in Australian secondary schools. Covering such areas as curriculum, pedagogy and assessment; teaching mathematical content; equity and diversity in the classroom; and professional and community engagement, it is an invaluable resource for all practising and pre-service mathematics teachers.

Mathematics: Launching Futures Proceedings of the 24th Biennial Conference of The Australian Association of Mathematics Teachers Inc.

‘Mathematics: Launching Futures’ was the theme for the 24th Biennial Conference of The Australian Association of Mathematics Teachers Inc.It was the first national conference on mathematics education since the introduction of the Australian Curriculum and so addresses the support educators will need to implement this curriculum. It also addressed concerns regarding  the low numbers of students studying higher level mathematics at school and university. A major aim of the conference was the sharing of knowledge to encourage  and support teachers at all
stages of their careers. This conference featured a joint day with the 36th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA), aiming to enhance collaboations between researchers and teachers.

A comparative study of content settings of mathematics curriculum standards from China, Australia, and Finland

The study investigated the mathematics curricula standards set by the governments in China, Australia(Victoria) and Finland in the aspects of the amount of content statements, the structure of content areas, level of details, level of requirement, the distribution of content, and the changes of content areas. The results show that China's mathematics standard has the biggest amount of and the most detailed content statements; that of Australia is in the second place; and Finnish standard has the least amount of content statements that are very general. The standards in all three countries emphasize numbers and operation and geometry.However,China's standards present a dynamic change, with different focus for different grades; Australian standards have similar proportion of each part of content for different grades and the amount of each part increases with grade; there is no fixed setting and proportion of content in Finnish standard, which is not confined by any mode.

Multi-dimensional assessment of student capabilities in mathematics and science

This study investigated relationships between students’ understanding, performance, and disposition in mathematics and science. The results indicated that assessments should be used to promote all aspects of student capability. Separate frameworks of student capability in mathematics and science need to be created to capture the individual nuances within each subject.