Development of fourth-grade students’ understanding of experimental and theoretical probability

Students explored variation and expectation in a probability activity at the end of the first year of a 3-year longitudinal study across grades 4-6. The activity involved experiments in tossing coins both manually and with simulation using the graphing software, TinkerPlots. Initial responses indicated that the students were aware of uncertainty, although an understanding of chance concepts appeared limited. Predicting outcomes of 10 tosses reflected an intuitive notion of equiprobability, with little awareness of variation. Understanding the relationship between experimental and theoretical probability did not emerge until multiple outcomes and representations were generated with the software.

Engaging students (and their teachers) in STEM through robotics

Robotics@QUT is a university outreach program aimed at building pre- and in-service teacher capacity to encourage interest in Science, Technology, Engineering and Mathematics (STEM) subjects with school children from low socio-economic status areas. Currently over 35 schools are involved in the outreach program. Professional Development workshops are provided to teachers to build their knowledge in implementing robotics-based STEM activities in their classrooms, robotics loan kits are provided, and pre-service teacher visits arranged to provide the teachers with on-going support. The program also provides opportunities for school students to engage in robotics-based on-campus activities and competitions and is seen as a way to build aspirations for university. This paper presents an interim evaluation that examines the value of the Robotics@QUT program for the teachers, pre-service teachers and school students participating in the program. Surveys were administered to determine the participants’ perceived benefits of being involved and their perceptions of the program. The data gathered from the teachers showed that they had gained knowledge and confidence and felt that the Robotics@QUT program had assisted them to deliver engaging robotics-based STEM activities in their classrooms. The pre-service teachers’ responses focused on benefits for themselves, for their future teaching careers and for the school students involved. The school students’ responses focused on their increased knowledge and confidence to pursue future STEM studies and careers.

Problem solving in a 21st century mathematics curriculum

Research on problem solving in the mathematics curriculum has spanned many decades, yielding pendulum-like swings in recommendations on various issues. Ongoing debates concern the effectiveness of teaching general strategies and heuristics, the role of mathematical content (as the means versus the learning goal of problem solving), the role of context, and the proper emphasis on the social and affective dimensions of problem solving (e.g., Lesh & Zawojewski, 2007; Lester, 2013; Lester & Kehle, 2003; Schoenfeld, 1985, 2008; Silver, 1985). Various scholarly perspectives—including cognitive and behavioral science, neuroscience, the discipline of mathematics, educational philosophy, and sociocultural stances—have informed these debates, often generating divergent resolutions. Perhaps due to this uncertainty, educators’ efforts over the years to improve students’ mathematical problem-solving skills have had disappointing results. Qualitative and quantitative studies consistently reveal mathematics students’ struggles to solve problems more significant than routine exercises (OECD, 2014; Boaler, 2009)...

Challenges in embedding numeracy throughout the curriculum in three Queensland secondary schools

The Australian Curriculum identified seven General Capabilities, including numeracy, to be embedded in all learning areas. However, it has been left to individual schools to manage this. Whilst there is a growing body of literature about pedagogies that embed numeracy in various learning areas, there are few studies from the management perspective. A social constructivist perspective and a multiple case study approach were used to explore the actions of school managers and mathematics teachers in three Queensland secondary schools, in order to investigate how they meet the Australian Curriculum requirement to embed numeracy throughout the curriculum. The study found a lack of coordinated cross-curricular approaches to numeracy in any of the schools studied. It illustrates the difficulties that arise when teachers do not share the Australian Curriculum cross-curricular vision of numeracy. Schools and curriculum authorities have not acknowledged the challenges for teachers in implementing cross-curricular numeracy, which include: limited understanding of numeracy; a lack of commitment; and inadequate skills. Successful embedding of numeracy in all learning areas requires: the commitment and support of school leaders, a review of school curriculum documents and pedagogical practices, professional development of teachers, and adequate funding to support these activities.

Expectation and variation with a virtual die

By the time students reach the middle years they have experienced many chance activities based on dice. Common among these are rolling one die to explore the relationship of frequency and theoretical probability, and rolling two dice and summing the outcomes to consider their probabilities. Although dice may be considered overused by some, the advantage they offer is a familiar context within which to explore much more complex concepts. If the basic chance mechanism of the device is understood, it is possible to enter quickly into an arena of more complex concepts. This is what happened with a two hour activity engaged in by four classes of Grade 6 students in the same school. The activity targeted the concepts of variation and expectation. The teachers held extended discussions with their classes on variation and expectation at the beginning of the activity, with students contributing examples of the two concepts from their own experience. These notions are quite sophisticated for Grade 6, but the underlying concepts describe phenomena that students encounter every day. For example, time varies continuously; sporting results vary from game to game; the maximum temperature varies from day to day. However, there is an expectation about tomorrow’s maximum temperature based on the expert advice from the weather bureau. There may also be an expectation about a sporting result based on the participants’ previous results. It is this juxtaposition that makes life interesting. Variation hence describes the differences we see in phenomena around us. In a scenario displaying variation, expectation describes the effort to characterise or summarise the variation and perhaps make a prediction about the message arising from the scenario. The explicit purpose of the activity described here was to use the familiar scenario of rolling a die to expose these two concepts. Because the students had previously experienced rolling physical dice they knew instinctively about the variation that occurs across many rolls and about the theoretical expectation that each side should “come up” one-sixth of the time. They had observed the instances of the concepts in action, but had not consolidated the underlying terminology to describe it. As the two concepts are so fundamental to understanding statistics, we felt it would be useful to begin building in the familiar environment of rolling a die. Because hand-held dice limit the explorations students can undertake, the classes used the soft-ware TinkerPlots (Konold & Miller, 2011) to simulate rolling a die multiple times.

The potential benefits of divergent thinking and metacognitive skills in STEAM learning: A discussion paper

In the wake of an almost decade long economic downturn and increasing competition from developing economies, a new agenda in the Australian Government for science, technology, engineering, and mathematics (STEM) education and research has emerged as a national priority. However, to art and design educators, the pervasiveness and apparent exclusivity of STEM can be viewed as another instance of art and design education being relegated to the margins of curriculum (Greene, 1995). In the spirit of interdisciplinarity, there have been some recent calls to expand STEM education to include the arts and design, transforming STEM into STEAM in education (Maeda, 2013). As with STEM, STEAM education emphasises the connections between previously disparate disciplines, meaning that education has been conceptualised in different ways, such as focusing on the creative design thinking process that is fundamental to engineering and art (Bequette & Bequette, 2012). In this article, we discuss divergent creative design thinking process and metacognitive skills, how, and why they may enhance learning in STEM and STEAM.

Investigating feelings towards mathematics among Chinese kindergarten children

Prior to entering schooling settings, many children exhibit intuitive knowledge of mathematics and many have mastered basic addition combinations. However, often as a result of formal instruction, some children begin to dislike or fear mathematics. In this study, children at a kindergarten in China took a smiley-face survey to determine how their feelings and beliefs about mathematics were affected throughout their kindergarten years.Results suggest that even children in this study have a better number sense and mathematics achievement, they appear to develop mathematics anxiety in Chinese cultural context.

Assessment in tertiary mathematics

There is a growing consensus among many educators that the goals of teaching and learning mathematics are to help students solve real-life problems, participate intelligently in daily affairs, and prepare them for jobs (Gardiner, 1994; Roeber, 1995). These goals suggest that the role of routine procedural skills should be diminished while more emphasis ought to be placed on learners gaining conceptual insights and analytical skills that appear essential in real-life mathematical problem solving (Schoenfeld, 1993; Stenmark, 1989).

Report on Innovation Working Group : The Mathematics Education into the 21st Century Project. Dresden, Saxony

This document reports on the Innovations Working Group that met at the 10th International Conference “Models in Developing Mathematics Education” from the 11-17th September 2009 in Dresden, Saxony. It briefly describes the over arching and consistent themes that emerged from the numerous papers presented. The authors and titles of each of the papers presented will be listed in Table 2.

Torres Strait Island 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.