Hops, steps and jumps : mathematical progress in the early years

While curriculum frameworks ale major influences on learning, teachers know that children progress at different rates. Sometimes this is evident within a particular topic. and at other times more obvious across different topics. In this paper. we present the hops, steps, and jumps of numeracy learning of some 3000 Australian children. All were assessed using I Can Do Maths, and their achievements mapped to provide a detailed picture of how children hop, step and jump on their numeracy journey. This mapping provides teachers with infonnation about key hurdles to numeracy learning for Australian children.

Time to make a difference: using action research to foster student engagement

This paper reports on a project, funded by the Victorian Department of Education and Training (Australia), undertaken to explore the capacity for teachers to develop innovative teaching and learning strategies aimed at improving the educational experiences of students in the middle years. Central to this charter was the need for local schools to form Clusters, share ideas and develop strategies designed to improve student engagement and connection. In forming the Buxton (pseudonym) Cluster, four schools came together to declare their shared interest in improving student connection through the teaching and learning of mathematics. The 22 teachers involved in the project shared a broad concern that the traditional pedagogies built up around the maths discipline were contributing to the wider level of student disconnection observed in the middle years. In thinking about change, the group were attracted to constructivist approaches to pedagogy in which learning opportunities and tasks are varied sufficiently to appeal to the various learning styles and aptitudes of learners. Favouring an action research framework teachers involved in the project embarked on the implementation of pedagogic reforms aimed at improving levels of student engagement.

How to review a mathematics textbook

This article provides guidelines for maths primary teachers on how to review a mathematics textbook or curriculum system.

Opening up open-ended mathematics tasks

This discussion has evolved from ideas in Peter Sullivan and Pat Lilburn's Open-Ended Maths Activities; Using 'Good' Questions to Enhance Learning (1997). This is a compilation of open-ended questions, and methods for generating open-ended questions, along with a brief rationale for using such questions. This classroom-oriented teaching resource developed from earlier research and teaching development work by Peter Sullivan and David Clarke, and others. Two methods are offered for constructing a 'good question'.

How big is a billion?

The counting techniques used in the subject of mathematics is discussed in this article. The various numeration methods are also explained which can be used so that the children can easily understand maths.

Effect of social background on the development of probabilistic concepts

This research explores how the social backgrounds of a group of students contributed to their intuitive knowledge in probabilistic reasoning, and influenced their processing of the associated mathematics. A group of Year 11 students who came from families for whom the phenomenon of track gambling formed an important part of their cultural background was identified. Another group consisting of students in the same mathematics course (Year 11 Maths in Society) but from families for whom the phenomenon of gambling in any form was totally absent from their social backgrounds was identified. Twenty students were selected from each group. The research employed a qualitative methodology in which a phenomenographic approach was used to investigate the qualitatively different ways in which individuals within the two groups thought about concepts involving probabilistic reasoning, and processed the related mathematical skills and concepts. The cognitive processes involved in the applications of probabilistic and related mathematical concepts in a variety of both gambling and non-gambling situations were studied in order to determine whether this culturally based knowledge could be viewed as a type of ‘ethnomathematics.’ Data were obtained through individual structured interviews which enabled patterns of reasoning to be compared and contrasted. Analyses of these data enabled intuitive mathematical understandings possessed by the gamblers not only to be identified, but also to be linked with their social backgrounds. Also differences between how individuals in the two groups processed probabilistic and associated mathematical knowledge were determined. This research complements and extends existing knowledge and theories related to culturally-based mathematical knowledge. Implications for further research, for classroom teaching, and for curriculum development in the study of probability in senior secondary mathematics classes are discussed.

Towards an integration of theories of achievement motivation

This thesis investigated children's school achievement in terms of an integration of three theories of achievement motivation. The three theoretical outlooks were expectancy-value theory (EVT), implicit theories of intelligence (ITI), and flow theory (FT). The first of two studies was an exploratory investigation of the effectiveness of each theory independently and combined to predict children's achievement in four school subjects. The subject areas were maths, reading, instrumental music and sport. Participants were 84 children (40 females and 44 males) aged 9 to 10 years, one of each child's parents, and school teachers of each child in the four subject areas. All data were collected through questionnaires based on the three models. The results indicated that EVT and FT but not ITI accounted for a significant amount of the variance in children's achievement, including effects for subject area and gender. A second confirmatory study tested EVT, FT and an integrated model for the prediction of achievement in maths, reading and instrumental music. The participants were a further 141 children (74 females and 67 males) aged 10 to 11 years, and a parent and teachers of each child. Data collection using questionnaires occurred early in the school year (Timel) and approximately five months later (Time2). For EVT, children and parents’ competence beliefs were significant predictors of children's achievement in each subject area. Females tended to believe themselves more competent at reading and instrumental music and also valued these subjects more highly than boys. Modeling results for flow theory indicated that children's emotional responses to classes (happiness and confusion) were significant predictors of achievement, the type of emotion varying between subject areas and time periods. Females generally had a more positive emotional reaction to reading and instrumental music classes than males did. The integrated model results indicated significant relationships between EVT and flow theories for each subject area, with EVT explaining most achievement variance in the integrated model. Children's and parents’ competence beliefs were the main predictors of achievement at Timel and 2, Subject area and gender differences were found which provide direction for future research. Anecdotal reports of parents and teachers often attest to individual differences in children's involvement in various school domains. Even among children of apparently similar intelligence, it is not uncommon to find one who likes nothing better than to work on a mathematics problem while another much prefers to read a novel or play a musical instrument Some children appear to achieve good results for most of the activities in which they are engaged while others achieve in a less consistent manner, sometimes particularly excelling in one activity. Some children respond to failure experiences with a determination to improve their performance in the future while others react with resignation and acceptance of their low ability. Some children appear to become totally absorbed in the activity of playing sport while others cannot wait for the game to end. The primary research objective guiding the current thesis is how children's thoughts and feelings about school subjects differ and are related to their school achievement. A perusal of the achievement motivation literature indicates several possible models and concepts that can be applied to explain individual differences in children's school achievement. Concepts such as academic self-concept, multiple intelligences, intrinsic and extrinsic motivation, self-beliefs, competence beliefs, subjective task values, mastery and performance goals, ‘Flow’ experiences and social motivation are just some of the constructs used to explain children's achievement motivation, both within and between various activity domains. These constructs are proposed by researchers from different theoretical perspectives to achievement motivation. Although there is much literature relevant to each perspective, there is little research indicating how the various perspectives may relate to each other. The current thesis will begin by reviewing three currently popular theoretical orientations cited in achievement motivation research: subjective beliefs and values; implicit theories of intelligence, and flow experience and family complexity. Following this review, a framework will be proposed for testing the determinants of children's school achievement, both within each of the three theoretical perspectives and also in combination.

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”.

Make a DIY mathematics trail.

A mathematics trail is an excellent activity. A mathematics trail might be something that students make themselves, possibly for other students to use, or for a Family Maths occasion, or for a community event. Presenting the making of a mathematics trail as an opportunity for inquiry-based learning (which is probably similar to, but not the same as passing the buck) could save the teacher a lot of time in preparing the trail. Pedagogically, it shifts some of the where-is-the-mathematics-in-this? type of thinking to the students - activating the maths curse and stimulating their own creativity! (Catchy expressions such as "ownership", "constructivism" and "student-centred" also spring to mind).

Examining the aesthetic dimensions of teaching : relationships between teacher knowledge, identity and passion

Having an appreciation for the subject, their students and what the subject can offer their students has both cognitive and emotional dimensions for teachers. This paper uses empirical data to explore the efficacy of a Deweyan inspired framework called “Aesthetic Understanding” to scrutinise relationships between teacher knowledge, identity and passion. The paper uses case study data of three teachers of maths and/or science generated from a video study to illustrate the relationships between the three elements of Aesthetic Understanding. The need to value the aesthetic dimensions of teaching when examining the subject-specific nature of secondary teaching is discussed.

The joy of teaching

Why do people become teachers? Some of the reasons for entering science and mathematics teaching include: wanting to make a difference, good job conditions, liking young people, loving science and maths, being good at teaching, having had a good maths/science teacher, a shortage of teachers, and a love of learning.

We need good teachers, and especially teachers with good science and chemistry backgrounds. It is also true of all school levels, including primary. Job satisfaction and the joy of teaching are not enough. Everyone needs encouragement, acknowledgement and respect. Everyone needs to know that they and their work are valued. Teachers need these too. It is a good investment in the nation’s future.

Finding a common story : synthesising findings from two research programs

In this research the authors tackled the issue of synthesising the findings of two independent research programs with common themes into a coherent analysis of teaching and learning across disciplines and school sectors. Through an ongoing dialogue and iterative exploration of emerging themes a synthesis generated new understandings of the use of narrative pedagogies in maths, science and technology, and the aesthetic nature of such learning experiences. This process demonstrates how a comparative lens enables a higher level of analysis of both research programs and generates broader narratives that can be applied to contexts beyond the original research foci.

Once upon a time: children's literature and mathematics

What was your favourite book as a child? Remember the joy of reading it over and over again until the pages were worn and the corners curled. Have you thought about introducing your favourite book into a mathematics classroom? Utilising books in mathematics can engage and benefit every child in your class. Building on children’s wonder of literature can enhance their experience in mathematics. Building on children’s wonder of mathematics can enhance their experience of literature. In this paper we present the joy and value of employing children’s literature in the middle to upper primary mathematics classroom supported with engaging tasks that will have your students noticing maths in every story they read.

Engineering fundamentals in a new undergraduate curriculum

CONTEXTIn recent years there has been a push in Engineering education to change the basic model fromstudents learning discrete subjects, followed by design projects in third and fourth year, to learningand practicing the design process from the first year. At the same time, there has also been a pushtowards “active learning” (Prince, 2004) as opposed to the more traditional lecture/tutorial/practicalapproach. This year, Deakin University has launched a new design-centred curriculum inundergraduate engineering. Named “Project-Oriented Design-Based Learning” (PODBL), the newcourse structure is running in first and second years. In semester one of first year in the new course,students enrol in one double-unit of design, one unit of maths, and one unit of fundamental science.PURPOSEThis work seeks to determine whether a new fundamental-science unit called “EngineeringFundamentals” fulfils the educational needs of first-year students in the PODBL curriculum. It alsoseeks to determine student perceptions of the new unit.APPROACHThe unit was first offered in semester-one, 2016 to two separate on-campus cohorts and an offcampuscohort. Innovations in this unit include using the CADET model for teaching combinedpractical-tutorial seminars, a shift in lectures from delivering conceptual content to teaching problemsolving and applications (flipping the classroom), and extensive use of online videos and study guidesfor delivering primary content (Cloud Learning). Student learning was assessed by means of problembasedonline quizzes, practical reports, and a final exam. Student perceptions were queried by astandard unit-evaluation system and by a more focussed set of surveys given to students in threeseparate cohorts.RESULTSThe academic results in this unit were compared with those in the previous unit. No substantialdifferences were observed in the marks of this unit in 2016 compared with the 2015 marks of thecorresponding previous physics unit. On-campus students showed more general satisfaction with theunit than did off-campus students. However, not all on-campus students were happy with the flippedclassroommodel.CONCLUSIONSAs the course changes from a traditional approach to a design and project-based approach, it is best ifall units in the course adapt in some way to the new teaching style. Not all units need be completelyproject or design based. In the case of “Engineering Fundamentals,” we believe that due to the widevariety of topics covered, making the entire unit design-based is inappropriate. However, some designand project components can be built into the unit via the practicals. Semester one 2016 was asuccessful first offering of the unit. We recommend that in future years a design/project component beconsidered for the unit’s practicals.