An instrument for assessing primary students’ knowledge of information graphics in mathematics

Information graphics have become increasingly important in representing, organising and analysing information in a technological age. In classroom contexts, information graphics are typically associated with graphs, maps and number lines. However, all students need to become competent with the broad range of graphics that they will encounter in mathematical situations. This paper provides a rationale for creating a test to measure students’ knowledge of graphics. This instrument can be used in mass testing and individual (in-depth) situations. Our analysis of the utility of this instrument informs policy and practice. The results provide an appreciation of the relative difficulty of different information graphics; and provide the capacity to benchmark information about students’ knowledge of graphics. The implications for practice include the need to support the development of students’ knowledge of graphics, the existence of gender differences, the role of cross-curriculum applications in learning about graphics, and the need to explicate the links among graphics.

National numeracy tests : a graphic tells a thousand words

Mandatory numeracy tests have become commonplace in many countries, heralding a new era in school assessment. New forms of accountability and an increased emphasis on national and international standards (and benchmarks) have the potential to reshape mathematics curricula. It is noteworthy that the mathematics items used in these tests are rich in graphics. Many of the items, for example, require students to have an understanding of information graphics (e.g., maps, charts and graphs) in order to solve the tasks. This investigation classifies mathematics items in Australia’s inaugural national numeracy tests and considers the effect such standardised testing will have on practice. It is argued that the design of mathematics items are more likely to be a reliable indication of student performance if graphical, linguistic and contextual components are considered both in isolation and in integrated ways as essential elements of task design.

Chinese young children’s strategies on basic addition facts

Kindergartens in China offer structured full-day programs for children aged 3-6. Although formal schooling does not commence until age 7, the mathematics program in kindergartens is specifically focused on developing young children’s facility with simple addition and subtraction. This study explored young Chinese children’s strategies for solving basic addition facts as well as their intuitive understanding of addition via interview methods. Results indicate a strong impact that teacher-directed teaching methods have on young children’s cognitions in relation to addition.

Technological barriers to learning : designing hybrid pedagogy to minimise cognitive load and maximise understanding

Information and Communication Technologies (ICTs) provide great promise for the future of education. In the Asia-Pacific region, many nations have started working towards the comprehensive development of infrastructure to enable the development of strong networked educational systems. In Queensland there have been significant initiatives in the past decade to support the integration of technology in classrooms and to set the conditions for the enhancement of teaching and learning with technology. One of the great challenges is to develop our classrooms to make the most of these technologies for the benefit of student learning. Recent research and theory into cognitive load, suggests that complex information environments may well impose a barrier on student learning. Further, it suggests that teachers have the capacity to mitigate against cognitive load through the way they prepare and support students engaging with complex information environments. This chapter compares student learning at different levels of cognitive load to show that learning is enhanced when integrating pedagogies are employed to mitigate against high-load information environments. This suggests that a mature policy framework for ICTs in education needs to consider carefully the development of professional capacities to effectively design and integrate technologies for learning.

Taking a 'reality' check : expanding pre-service teachers' views on pedagogy and diversity

The outcomes of a two-pronged 'real-world' learning project, which aimed to expand the views of pre-service teachers about learning, pedagogy and diversity, will be discussed in this paper. Seventy-two fourth-year and 22 first-year students, enrolled in a Bachelor of Education degree in Queensland, Australia, were engaged in community sites outside of university lectures, and separate from their practicum. Using Butin's conceptual framework for service learning, we show evidence that this approach can enable pre-service teachers to see new realities about the dilemmas and ambiguities of performing as learners and as teachers. We contend that when such 'real-world' experiences have different foci at different times in their four-year degree, pre-service teachers have more opportunities to develop sophisticated understandings of pedagogy in diverse contexts for diverse learners.

Authentic and conventional assessment in Singapore schools : an empirical study of teacher assignments and student work

This is an empirical examination of the quality of teacher assignments and student work in Singapore schools. Using a theoretical framework based on principles of authentic assessment and intellectual quality, two sets of criteria and scoring rubrics were developed for the training of expert teachers to judge the quality of assignments and student work. Following rigorous training, the inter-rater reliability of expert teacher scoring was high. Samples of teacher assignments and student work were collected in English, social studies, mathematics, and science subject areas from a random stratified sample of 30 elementary schools and 29 high schools. For both grade levels, there were significant differences for the authentic intellectual quality of teachers’ assignments by subject area. Likewise, the differences of authentic intellectual quality for student work were significant and varied by subject area. Subject area effect was large. The correlations between the quality of teachers’ assignment tasks and student work were strong and significant at both grade levels. Where teachers set more intellectually demanding tasks, students were more likely to generate work or artefacts judged to be of higher quality. The findings suggest that teacher professional development in authentic intellectual assessment task design can contribute to the improvement of student learning and performance. It is argued that this will be a key requisite of educational systems like Singapore that are seeking to expand pedagogy and student outcomes beyond a focus on factual and rote knowledge.

Australia : The Challenges of Poverty, Pedagogy, and Pathways

A discussion of 2008/2009 developments in Australian educational policy, with specific reference to the adoption of US and UK trends in accountability, testing and school reform.

Does pedagogy still rule?

Theories on teaching and learning for adult learners are constantly being reviewed and discussed in the higher educational environment. Theories are not static and appear to be in a constant developmental process. This paper discusses three of these theories: pedagogy, andragogy and heutagogy. It is argued that although educators engage in many of the principles of either student-centered (andragogy) and self-determined (heutagogy) learning, it is not possible to fully implement either theory. The two main limitations are the requirements of both internal and external stakeholders, such as accrediting bodies and requirements to assess all student learning. A reversion to teacher-centered learning (pedagogy) ensues. In summary, we engage in many action-oriented learning activities but revert to teacher-centered approaches in terms of content and assessment.

Year 6 students' idiosyncratic notions of unitising, reunitising and regrouping decimal number places

Having flexible notions of the unit (e.g., 26 ones can be thought of as 2.6 tens, 1 ten 16 ones, 260 tenths, etc.) should be a major focus of elementary mathematics education. However, often these powerful notions are relegated to computations where the major emphasis is on "getting the right answer" thus procedural knowledge rather than conceptual knowledge becomes the primary focus. This paper reports on 22 high-performing students' reunitising processes ascertained from individual interviews on tasks requiring unitising, reunitising and regrouping; errors were categorised to depict particular thinking strategies. The results show that, even for high-performing students, regrouping is a cognitively complex task. This paper analyses this complexity and draws inferences for teaching.

Trouble and autoethnography in assessment genre : a case for postnational design in online internationalized pedagogy

This chapter is interested in the difference between local places with implicit codes and more global spaces with explicit directions, through the case study of the design and conduct of assessment in an online internationalized MBA unit. Online learning is understood to offer new ways of belonging in 'postnational' communities less reliant on locality for their frames of reference. This study reports and analyses firstly a series of troubles which erupted over the international students' desire for more explication of the desired genre for their assessment task. Then it analyses the different, 'autoethnographic' genre structure that emerged when students started to acknowledge the diverse backgrounds within the class.The chapter then offers practical considerations for the design of online internationalized programs.

University-industry partnership for pedagogy : some principles for practice

Industries demand a closer alignment of university learning curriculum to real work tasks to better meet the needs of organizations and learners. Both, industries and learners prefer the learning challenges to be based on the exigencies of work to precisely reflect real work circumstances that overtly add to business outcomes. However, such alignment is often complicated and challenging for academics and workplace managers alike. It demands partnerships between universities and industries, similar to arrangements forged for the vocational education and training sector. Such partnerships should allow active participation by learners, academics, workplaces and university administrators to move beyond a teaching orientation to a demonstrably effective learning arrangement through work integrated learning. This paper draws on a case study that negotiated a partnership between a non-government organization and an Australian university to design and facilitate a boutique curriculum that met the needs of learners and their workplace. Data were collected from interviews with participants, a focus group of the interviewees, and feedback from university staff involved in the course delivery. The paper presents a set of principles for universities and industries for partnership to enhance the alignment of academic curriculum to meet organizational and individual learning needs through work integrated learning.

Group metacognition during mathematical problem solving

Although various studies have shown that groups are more productive than individuals in complex mathematical problem solving, not all groups work together cooperatively. This review highlights that addressing organisational and cognitive factors to help scaffold group mathematical problem solving is necessary but not sufficient. Successful group problem solving also needs to incorporate metacognitive factors in order for groups to reflect on the organisational and cognitive factors influencing their group mathematical problem solving.

Implementation of an integrated, technology-based, discovery mode assessment item involving an incubation period to enhance learning outcomes for engineering maths students

In this paper we discuss our current efforts to develop and implement an exploratory, discovery mode assessment item into the total learning and assessment profile for a target group of about 100 second level engineering mathematics students. The assessment item under development is composed of 2 parts, namely, a set of "pre-lab" homework problems (which focus on relevant prior mathematical knowledge, concepts and skills), and complementary computing laboratory exercises which are undertaken within a fixed (1 hour) time frame. In particular, the computing exercises exploit the algebraic manipulation and visualisation capabilities of the symbolic algebra package MAPLE, with the aim of promoting understanding of certain mathematical concepts and skills via visual and intuitive reasoning, rather than a formal or rigorous approach. The assessment task we are developing is aimed at providing students with a significant learning experience, in addition to providing feedback on their individual knowledge and skills. To this end, a noteworthy feature of the scheme is that marks awarded for the laboratory work are primarily based on the extent to which reflective, critical thinking is demonstrated, rather than the amount of CBE-style tasks completed by the student within the allowed time. With regard to student learning outcomes, a novel and potentially critical feature of our scheme is that the assessment task is designed to be intimately linked to the overall course content, in that it aims to introduce important concepts and skills (via individual student exploration) which will be revisited somewhat later in the pedagogically more restrictive formal lecture component of the course (typically a large group plenary format). Furthermore, the time delay involved, or "incubation period", is also a deliberate design feature: it is intended to allow students the opportunity to undergo potentially important internal re-adjustments in their understanding, before being exposed to lectures on related course content which are invariably delivered in a more condensed, formal and mathematically rigorous manner. In our presentation, we will discuss in more detail our motivation and rationale for trailing such a scheme for the targeted student group. Some of the advantages and disadvantages of our approach (as we perceived them at the initial stages) will also be enumerated. In a companion paper, the theoretical framework for our approach will be more fully elaborated, and measures of student learning outcomes (as obtained from eg. student provided feedback) will be discussed.

Torres Strait Islander parents’ involvement in their children’s mathematics learning : a discussion paper

This paper is a beginning point for discussing what the literature states about parents’ involvement in their children’s mathematics education. Where possible it will focus on Torres Strait Islander Peoples. Little is known about how Torres Strait Islander parents approach their children’s learning of mathematics and how important early mathematics is to mothers. What is known is that is they are keen for their children to receive an education that provides them with opportunities for their present and future lives. However, gaining access to education is challenging given that the language of instruction in schools is written to English conventions, decontextualised and disconnected from the students’ culture, community and home language. This paper discusses some of the issues raised in the literature about what parents are confronted with when making decisions about their children’s education.

Getting skilled for education, training and employment : Indigenous Cultural Knowledges and mainstream knowledges of mathematics

This abstract is a preliminary discussion of the importance of blending of Indigenous cultural knowledges with mainstream knowledges of mathematics for supporting Indigenous young people. This import is emphasised in the documents Preparing the Ground for Partnership (Priest, 2005), The Indigenous Education Strategic Directions 2008–2011 (Department of Education, Training and the Arts, 2007) and the National Goals for Indigenous Education (Department of Education, Employment and Work Relations, 2008). These documents highlight the contextualising of literacy and numeracy to students’ community and culture (see Priest, 2005). Here, Community describes “a culture that is oriented primarily towards the needs of the group. Martin Nakata (2007) describes contextualising to culture as about that which already exists, that is, Torres Strait Islander community, cultural context and home languages (Nakata, 2007, p. 2). Continuing, Ezeife (2002) cites Hollins (1996) in stating that Indigenous people belong to “high-context culture groups” (p. 185). That is, “high-context cultures are characterized by a holistic (top-down) approach to information processing in which meaning is “extracted” from the environment and the situation. Low-context cultures use a linear, sequential building block (bottom-up) approach to information processing in which meaning is constructed” (p.185). In this regard, students who use holistic thought processing are more likely to be disadvantaged in mainstream mathematics classrooms. This is because Westernised mathematics is presented as broken into parts with limited connections made between concepts and with the students’ culture. It potentially conflicts with how they learn. If this is to change the curriculum needs to be made more culture-sensitive and community orientated so that students know and understand what they are learning and for what purposes.