Education Commons^™

Mathematical Connections Established In The Teaching Of Functions, Vesife Hatisaru

Research outputs 2022 to 2026

This study explores the types of mathematical connections established in the classroom in the teaching of functions. An extended model for mathematical connections (different representations (DR), procedural (PC), if-then (I-T), part-whole connections (PWC), feature/property (F/P), analogies, and instruction-oriented connections (IOC)) is used as the analytical framework. The context for the study is classroom observations of two secondary mathematics teachers teaching functions to Grade 9 students. The strength of teachers’ mathematical knowledge for teaching (MKT) the concept of function is different: one has stronger MKT, while the other has weaker MKT. A total of 485 connections are identified in a sample …

How Teachers Use Formative Assessment Strategies During Teaching: Evidence From The Classroom, Hem Chand Dayal

Australian Journal of Teacher Education

Using lesson observations, the study reported in this article explores how two practising secondary mathematics teachers implemented formative assessment actions in their classroom teaching. The study also investigated whether teachers’ beliefs about teaching and assessment could be mapped onto their classroom practices. In particular, while the two teachers were implementing student portfolio assessment in their own Year 9 mathematics lessons, the classroom observations focused on how they utilised formative assessment actions such as clarifying and sharing learning criteria intentions and criteria for success; activating students as instructional resources; and, providing feedback that moves learners forward. The findings suggest that one …

Does Mathematics Training Lead To Better Logical Thinking And Reasoning? A Cross-Sectional Assessment From Students To Professors, Clio Cresswell, Craig P. Speelman

Research outputs 2014 to 2021

© 2020 Cresswell, Speelman. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Mathematics is often promoted as endowing those who study it with transferable skills such as an ability to think logically and critically or to have improved investigative skills, resourcefulness and creativity in problem solving. However, there is scant evidence to back up such claims. This project tested participants with increasing levels of mathematics training on 11 well-studied rational and logical reasoning tasks …

Preservice Teachers As Document Detectives, Lorna Quinnell, Radha Iyer, Bronwyn Ewing

Australian Journal of Teacher Education

Literacy today relies on a readers’ ability to analyse text critically. This case study investigated preservice teachers’ critical analysis of media text containing visuals and representations. In particular, the analysis focused on mathematical factors that impact on readers’ interpretation of diverse visuals.

Data was gathered from the 23 preservice teachers, enrolled in the Graduate Diploma program at one Australian university. They participated in a series of mathematics learning sessions focused on the critical analysis of a selection of media items.

The paper argues that the ability to critically analyse graphs and visuals relies on mathematical knowledge and that the ability …

Primary School Teachers’ Experience Of Mathematics Education: A Phenomenological Study, Sarah Jane Tamburri

Theses: Doctorates and Masters

Researchers and policymakers agree that all children can learn mathematics, and research has shown that teaching practices have a significant impact on student learning and achievement. Therefore, it is important that teachers are supported in their development as professionals and mathematics educators. This research gives a voice to a small number of primary school mathematics teachers, providing insight into their experience of mathematics education, from their perspective. In-depth interviews form the basis of data collection and these have been analysed through a transcendental phenomenological approach. The insights gained into teachers’ experiences and perspectives provide a deeper understanding of their role …

Middle School Mathematics Pre-Service Teacher’S Responses To A Mathematics Content And Specific Mathematics Pedagogy Intervention, Stephen J. Norton

Australian Journal of Teacher Education

Prospective middle school pre-service teachers’ knowledge and affect in Australia has had little empirical research. In this study, 108 graduate entry pre-service teachers were surveyed for their knowledge of middle years’ mathematics, confidence, and self-efficacy at the commencement of a mathematics curriculum course. It was found that their memory of middle years’ mathematics was very poor and this was accompanied by low levels of confidence and self-efficacy. An intervention was undertaken to address these issues. The findings are discussed in the context of the “genericism” of pre-service teacher preparation. In particular, the findings call into question the justification for pre-service …

An Application Of The Solo Taxonomy To Classify Strategies Used By Pre-Service Teachers To Solve “One Question Problems”, Joanne C. Caniglia, Michelle Meadows

Australian Journal of Teacher Education

: The purpose of this article is to report on the strategies of secondary mathematics pre-service teachers (PSTs) as they solved conceptually rich problems. Using the Structure of Observed Learning Outcomes by Biggs and C (1982) (SOLO) Taxonomy, 15 PSTs’ solutions (in groups of 3 or 4) were analyzed by a panel of three mathematics educators. In addition, the authors studied questions posed by PSTs during their student teaching experiences through video analysis. Questions were then categorized using Crespo’s criteria of problem posing. Results showed a significant majority of the problems posed were procedural while PSTs own problem solutions showed …

Commercially Available Digital Game Technology In The Classroom: Improving Automaticity In Mental-Maths In Primary-Aged Students., John O'Rourke, Susan Main, Susan M. Hill

Australian Journal of Teacher Education

In this paper we report on a study of the implementation of handheld game consoles (HGCs) in 10 Year four/five classrooms to develop student automaticity of mathematical calculations. The automaticity of mathematical calculations was compared for those students using the HGC and those being taught using traditional teaching methods. Over a school term, students (n=236) who used the HGCs and Dr Kawashima’s Brain Training showed significant improvement in both the speed and accuracy of their mathematical calculations. Data collected in interviews during the intervention period from students, staff and parents were analysed to provide further information on the implementation and …

“I Learned Quite A Lot Of The Maths Stuff Now That I Think Of It”: Māori Medium Students Reflecting On Their Initial Teacher Education, Ngārewa Hāwera, Merilyn Taylor

Australian Journal of Teacher Education

Research involving preservice or initial teacher education (ITE) indicates that mathematics education is a vital component of study. Little is known however, of indigenous student views of their compulsory mathematics education courses for a teaching degree. This research contributes to that knowledge space as it explores Māori medium ITE students’ perceptions of mathematics education in Aotearoa New Zealand. A thematic and qualitative analysis of a focused group discussion provides insights into key factors that students reported as significant links between their university and practicum experiences (teaching practice in schools). Some suggestions for strengthening that programme were also expressed. Findings indicate …

Digital Story-Based Problem Solving Applications: Preservice Primary Teachers’ Experiences And Future Integration Plans, Çiğdem Kilic, Hatice Sancar-Tokmak

Australian Journal of Teacher Education

This case study investigates how preservice primary school teachers describe their experiences with digital story-based problem solving applications and their plans for the future integration of this technology into their teaching. Totally 113 preservice primary school teachers participated in the study. Data collection tools included a questionnaire with three open-ended questions and focus group interviews. The data were analyzed using content analysis by combining manifest and latent techniques. Most of the preservice primary teachers described positive experiences about digital story-based problem solving applications by emphasizing on that they contribute to both their own and their students’ learning, development, and attitudes. …

Developing Primary Pre-Service Teachers' Mathematical Content Knowledge During Practicum Teaching, Sharyn L. Livy, Colleen Vale, Sandra Herbert

Australian Journal of Teacher Education

While it is recognised that a teachers’ mathematical content knowledge (MCK) is crucial for teaching, less is known about when different categories of MCK develop during teacher education. This paper reports on two primary pre-service teachers, whose MCK was investigated during their practicum experiences in first, second and fourth years of a four-year Bachelor of Education program. The results identify when and under what conditions pre-service teachers’ developed different categories of their MCK during practicum. Factors that assisted pre-service teachers to develop their MCK included program structure providing breadth and depth of experiences; sustained engagement for learning MCK; and …

Exploring Links Between Pedagogical Knowledge Practices And Student Outcomes In Stem Education For Primary Schools, Peter Hudson, Lyn English, Les Dawes, Donna King, Steve Baker

Australian Journal of Teacher Education

Science, technology, engineering, and mathematics (STEM) education is an emerging initiative in Australia, particularly in primary schools. This qualitative research aimed to understand Year 4 students’ involvement in an integrated STEM education unit that focused on science concepts (e.g., states of matter, testing properties of materials) and mathematics concepts (e.g., 3D shapes and metric measurements) for designing, making and testing a strong and safe medical kit to insulate medicines (ice cubes) at desirable temperatures. Data collection tools included student work samples, photographs, written responses from students and the teacher, and researcher notes. In a post-hoc analysis, a pedagogical knowledge practice …

Valuing Assessment In Teacher Education - Multiple-Choice Competency Testing, Dona L. Martin, Diane Itter

Australian Journal of Teacher Education

When our focus is on assessment educators should work to value the nature of assessment. This paper presents a new approach to multiple-choice competency testing in mathematics education. The instrument discussed here reflects student competence, encourages self-regulatory learning behaviours and links content with current curriculum documents and with collaborative and cooperative learning episodes.

Mathematics, English And Gender Issues: Do Teachers Count?, Gilah C. Leder, Helen J. Forgasz, Glenda Jackson

Australian Journal of Teacher Education

Pedestrians were stopped in the street and asked about their views on the teaching and learning of mathematics and English for boys and girls. Many commented on the importance of teachers for both subject areas; some respondents self-identified as teachers. In this article we present findings on the gendering of mathematics and English and the impact that teachers can have on learning outcomes in these disciplines. The data reveal that mathematics is endorsed by many as a male domain and English as a female domain, and that teachers play an influential part in the learning outcomes – achievement, future participation, …

Teaching For Students' Confident Transition From Number To Algebra, Christina Lang Lee

Theses: Doctorates and Masters

The adoption by all states and territories of the national curriculum by 2013 saw students in schools across the country taught introductory algebraic concepts from Year Five. In the twenty first century the need to be algebraically competent has become a necessity much as computation was in the previous centuries.

The Researcher has found from experience that students who have struggled with number and number operations will then most probably make poor progress in their study of algebra. The transition from number to algebra requires a robust understanding of number and number operations

This study investigated the balance of instructional …

Second-Year Pre-Service Teachers’ Responses To Proportional Reasoning Test Items, Sharyn Livy, Sandra Herbert

Australian Journal of Teacher Education

A recent international study of pre-service teachers identified that proportional reasoning was problematic for pre-service teachers. Proportional reasoning is an important topic in the middle years of schooling and therefore it is critical that teachers understand this topic and can rely on their Mathematical Content Knowledge (MCK) when teaching. The focus of this paper is second-year Australian primary pre-service teachers’ MCK of real number items related to ratio, rate, proportion and proportional reasoning. This paper reports on strengths and weakness of pre-service teachers’ MCK when responding to test items; including a method suitable for analysing responses to five items and …

The Fitzroy Valley Numeracy Project: Assessment Of Early Changes In Teachers’ Self-Reported Pedagogic Content Knowledge And Classroom Practice, Lorraine Jacob, Andrew Mcconney

Australian Journal of Teacher Education

The Fitzroy Valley Numeracy Project (FVNP) was designed to improve numeracy outcomes for Indigenous students by developing a systematic, co-ordinated approach to teaching primary school mathematics. In this study, using early project data, we examine FVNP teachers’ self‑reported pedagogic content knowledge and classroom practice from initial and follow up questionnaires, as well as interviews from case study teachers. After the first FVNP year, teachers reported being better able to plan focused mathematics lessons and to monitor student learning. On the other hand, teachers also felt less able to make mathematics explicit to students and their confidence in providing engaging activities …

Numeracy Support For Year Two Students, Gillian Dawn Hurle

Theses: Doctorates and Masters

Research of teaching theories and intervention programs internationally and in Australia suggests that the implementation of numeracy support programs can improve student achievement levels (Fuchs, 2005; Ketterlin-Geller, Chard & Fien, 2008; Van Kraayenoord & Elkins, 2004). An intervention program was conducted for a small group of Year Two students with the aim of improving their numeracy skills over a 20 week period. Results of two mathematics assessments, together with information provided by teachers based on classroom observations and informal assessments were combined to select a group of twelve students who were considered to be at risk of developing mathematical difficulties. …

A Professional Experience Learning Community For Pre-Service Secondary Mathematics Teachers, Michael S. Cavanagh, Thomas Garvey

Australian Journal of Teacher Education

This paper reports the development and implementation of a collaborative professional experience learning community for a group of nine pre-service secondary mathematics teachers. The pre-service teachers and their methods lecturer made 12 school visits over one academic year to a local secondary school. The pre-service teachers observed and co-taught problem-solving lessons in two Year 8 classes. They discussed the lessons with the teacher and the university lecturer, and later posted reflective comments to an online forum. Data from questionnaires, interviews, and reflections indicate that participation in the learning community helped pre-service teachers make stronger links between theory and practice, learn …

Supporting Teachers’ Professional Learning At A Distance: A Model For Change In At-Risk Contexts, Elizabeth A. Warren, Janine Quine, Eva Devries

Australian Journal of Teacher Education

This paper examines the effectiveness of a professional learning model developed to support early years teachers in rural and remote communities in Queensland as they began to implement the Australian Curriculum in Mathematics. The data are drawn from 35 teachers at the initial stage of a large, four year longitudinal study RoleM (Representations, oral language and engagement in Mathematics). The particular aims of the longitudinal study are to (a) identify effective pedagogical practices that may assist young Indigenous Australian students to negotiate Western mathematical understanding, and (b) investigate professional learning models that best support teachers within this context. The data …

Enhancing The Teaching And Learning Of Computational Estimation In Year 6, Paula Mildenhall

Theses: Doctorates and Masters

There have been repeated calls for computational estimation to have a more prominent position in mathematics teaching and learning but there is still little evidence that quality time is being spent on this topic. Estimating numerical quantities is a useful skill for people to be able to use in their everyday lives in order to meet their personal needs. It is also accepted that number sense is an important component of mathematics learning (McIntosh, Reys, Reys, Bana, & Farrell, 1997; Paterson, 2004) and that computational estimation is an important part of number sense (Edwards, 1984; Markovits & Sowder, 1988; Schoen, …

Pemberton Hydroelectric Power Station: A Teacher Resource, Les Pereira, Phil Gregory, Helen Kuehs, Amanda Draper, Jenny Staker, Rosalie Tomlinson, Christa Pereira

Research outputs pre 2011

This publication provides a resource for teachers of students in years seven to ten. Teachers are able to address a range of outcomes pertinent to the Western Australian curriculum within the context of the Pemberton Hydroelectric Power Station. The resource contains plans for four units of work, one in each of the following Learning Areas: Science, Mathematics, English, and Society and Environment.

Computerized Adaptive Testing In Mathematics For Primary Schools In Thailand, Chaowprapha Chuesathuchon

Theses: Doctorates and Masters

A new system-wide educational change has been introduced in Thailand requiring, amongst other things, that technologies for education be utilized in all levels of education. This study focuses on Mathematics Computerized Adaptive Testing (CAT) designed to provide Thai primary school teachers with an innovative method of assessment, one of the effective tools of new technology to be used in Thai primary schools. This study aims to: (1) construct multiple-choice test items for a Mathematics course on the topic of Equations for Year 6 (Prathom Suksa 6) students in Thailand; (2) calibrate the test items using a Rasch Measurement Model, investigate …

An Exploratory Case Study Using An Expert Learning Process Designed To Promote Number Sense In A Year 6 Classroom, Paula Mildenhall

Theses: Doctorates and Masters

not available

Beyond Written Computation, Alistair Mcintosh, Len Sparrow

Research outputs pre 2011

This collection of papers based on research into aspects of number is a result of a writing conference held on Rottnest Island, near Perth, Western Australia. The concept of the conference emanated from Alistair Mcintosh and Len Sparrow and was based on two similar meetings organised by Cal Irons and Bob Reys.

All papers in this book were discussed at the Rottnest conference and subsequent changes were made by the authors based on comments and recommendations from the peer group who attended the conference.

The Effect Of Money As A Context On Students' Mental Computation Performance In Years 3, 5, 7 And 9, Anne Paterson

Theses: Doctorates and Masters

The purpose of this study was to research the effect of money as a context on school students’ mental computational performance and strategy choices across a range of ages. This study adds to existing research, which has compared students' mental computational methods with their written methods, by the provision of the single common context of money. The content topics of whole and other rational numbers (simple fractions, decimals, and some percentages) were covered. Forty-eight primary school students plus sixteen secondary school students were involved in this study, with equal numbers of both genders from the two primary schools and one …

Improving Aboriginal Numeracy: A Book For Education Systems, School Administrators, Teachers And Teacher Educators, Thelma Perso

Research outputs pre 2011

Aboriginal students have the right to access the same education that is available to non-Aboriginal children in Australian schools. At present, Aboriginal children have access to, the same curriculum that non-Aboriginal students have access to but it may not empower them. This might be for a variety of reasons: their different starting points, learning styles, underlying issues which are impediments to learning, and in particular, their previous experiences may not be understood by their classroom teachers.

The Relationship Between Estimation Skill And Computational Ability Of Students In Years 5, 7 And 9 For Whole And Rational Numbers, Phuntsho Dolma

Theses: Doctorates and Masters

This study explored the relationship between estimation skill and computational ability for whole and rational numbers. The methods carried out were both quantitative as well as qualitative and data were collected from three primary schools along with their associated high school in the Perth area. The year levels chosen were 5, 7 and 9. There were two classes from each chosen primary school representing Year 5 and Year 7 and three classes of Year 9 from the high school. The total number of students involved was 91, 77 and 73 from the three respective year levels. Instruments used for collecting …

The Computation Choices Made By Students In Years 5 To 7, Paul Swan

Theses: Doctorates and Masters

This study was designed to explore the computation choices made by 78 students in Years 5 to 7. The ability to choose and use a repertoire of computation methods is an important goal of mathematics education. While one might expect to find a great deal of research outlining the computation choices students make and why they make them, this was not the case; and as such it was decided to explore what computation choices students make and why they make them.

Phantom Classmates : A Case Study Of Talented Mathematics Students Learning Via Telematics, Leanne S. Clarke

Theses: Doctorates and Masters

The main advantages and disadvantages of the Telematics environment for talented mathematics students were investigated through a case study. The case study considered the interaction of, and opinions of 11 Year 9 students and the teacher/researcher. Participants were from nine schools in regional Western Australia, and were withdrawn from face-to-face classes to attend mathematics transmissions. Qualitative data were collected through student interviews, an anonymous questionnaire, tape recording of lessons, and teacher field notes. Students all agreed the main disadvantage occurred if timetabling for Telematics transmissions did not align with their local school class times for the same subject. The teacher …