An evaluation of personal greenhouse gas calculators

Personal greenhouse gas calculators (PGGC) are important tools to raise awareness of the impact of personal behaviour on carbon dioxide emissions. Per capita, Australians are the highest emitters of greenhouse gases in the world and the task for them to reduce emissions to sustainable levels will be particularly challenging. This paper reviews six PGGC promoted in Australia and evaluates them for their consistency. The emissions for an individual currently practicing a modest green lifestyle are calculated and compared. Emission calculations were found to differ by an order of magnitude in some cases. It was also found that users of PGGC are not adequately informed about the limitations of the calculators. The adoption of modest and radical green lifestyles reduced greenhouse gas emissions to 83% and 53% of the average Australian, indicating that behavioural changes by consumers alone will be insufficient to reduce emissions to sustainable levels.

Using activity theory in researching young children's use of calculators

Constructivist and socio-cultural perspectives in mathematics education highlight the crucial role that activity plays in mathematical development and learning. Activity theory provides a socio-cultural lens to help analyse human behaviour, including that which occurs in classrooms. It provides a framework for co-ordinating constructivist and socio-cultural perspectives in mathematics learning. In this paper, we adopt Cole and Engeström's (1991) model of activity theory to examine the mediation offered by the calculator as a tool for creating and supporting learning processes of young children in the social environment of their classroom. By adopting this framework, data on young children's learning outcomes in number, when given free access to calculators, can be examined not only in terms of the mediating role of the calculator, but also within the broader context of the classroom community, the teachers' beliefs and intentions, and the classroom norms and the division of labour. Use of this model in a post hoc situation suggests that activity theory can play a significant role in the planning of future classroom research.

Using graphics calculators and spreadsheets in chemistry : solving equilibrium problems

Discusses tabular and graphical approaches to equilibrium calculations.

Calculators, mathematics and young children : a study of six children using calculators as part of the mathematics curriculum during their first two years of school

The thesis investigates the role a calculator can play in the developing number knowledge of three girls and three boys as part of their mathematics program, during their first two years at primary school. Random sampling was used initially to select six girls and six boys from the twenty-four children entering a 1993 prep class. These twelve children were interviewed on entrance to school and based on the performance of the twelve children on the initial interview, a girl and a boy were chosen from the higher, middle and lower achievers to take part in the full study. The class teachers involved were previously participants in the ‘Calculators in Primary Mathematics’ research program and were committed to the use of calculators in their mathematics program. A case study approach using qualitative methods within the activity theory framework is used to collect relevant data and information, an analysis of five interviews with each child and observations of the children in forty-one classroom lessons provides comprehensive data on the children's developing number knowledge during the two years. The analysis questionnaires establishes each teacher's perceptions of the children's number learning at the beginning and end of each year, compares teacher expectations with children's actual performance for the year and compares curriculum expectations with children's actual performance. A teacher interview established reasons for changes in teaching style; teacher expectations; children's number learning; and was used to confirm my research findings. An activity theory framework provides an appropriate means of co-coordinating perspectives within this research to enable a description of the child's number learning within a social environment. This framework allows for highlighting the mediation offered by the calculator supporting the children's number learning in the classroom. Levels of children's developing number knowledge reached when working with a calculator and as a result of calculator use are mapped against the levels recommended in ‘Mathematics in the National Curriculum’ (National Curriculum Council, December 1988), and the Curriculum and Standards Framework: Mathematics (Board of Studies 2000). Findings from this comparison illustrate that the six children's performance in number was enhanced when using a calculator and indicate that on-going development and understanding of number concepts occurred at levels of performance at least two years in advance of curriculum recommendations for the first two years of school.

Algebra skills and traps and diagnostic teaching for the future

Explores on some research about teaching and learning algebra and related classroom issues. Diagnostic instruments that may be used by senior secondary teachers in teaching algebra to senior classes; Strategies for remediating algebraic difficulties and misconceptions; Impact of technology on the algebra curriculum; Usefulness of copying algebraic expressions while using Computer Algebra Systems or mathematics processing software in a calculus class.

A problem-based learning project supported by the internet

This case study looks at how bank sites with interactive calculators can be used to enhance directed investigations of students in a Mathematics Studies course. In the course of these investigations, students access simulated contexts which enabled them to have a feel of how they would spend money in the real world. This case study reveals the confidence of students in carrying out searches and transferring data, learning about bank calculators and their role in real life, how hidden costs are incorporated into loans and being able to validate what is presented in these calculators with their own calculations. This case study also highlights the perceptions of the teacher regarding this strategy in teaching this topic and the areas that need improvement. This paper analyses what has happened in the teaching and learning process and endeavours to shed some light into how the Internet can be used to promote a quality mathematics education.

The mechanics of computation and human thought

Thousands of students are preparing for chemistry examinations in June. An unresolved debate is whether they should be permitted to use graphics and programmable calculators in those examinations. Some educators have not only advocated the use of graphics calculators, but have also pointed to the Danish system in which students are permitted to use computers in senior school examinations.

In some Australian jurisdictions, graphics calculators are permitted in year 12 mathematics examinations, but not in chemistry examinations. The reasoning is that information or methods of solving numerical chemical problems can be stored in the memory of graphics calculators, giving some students an unfair advantage. This means that chemistry students either have to learn how to use (and buy!) two types of calculators or, if they only have one calculator, are disadvantaged in using non-programmable calculators in mathematics examinations.

The use of technology (or its lack thereof) can limit how and what students learn. “The mechanics of computation and human thought” is an allusion to Asimov’s short story, “A Feeling of Power” in which, overuse of technology has caused people to forget how to do simple arithmetic. In our current assessment system, the insistence that students must be able to do simple chemical calculations has lead to underuse of available technology. The misperception is that the ability to do calculations is linked to understanding of concepts.

Graphics calculators, programmable calculators and computers are tools. Instead of banning or limiting technology, we should take the opportunity to rethink what is being assessed and how it is assessed. It is the proper use of technology, by combining the mechanics of computation and human thought to deepen understanding and to ask probing questions that truly leads to a feeling of power.

The effect of mathematical games on on-task behaviours in the primary classroom

A challenge for primary classroom teachers is to maintain students’ engagement with learning tasks while catering for their diverse needs, capabilities and interests. Multiple pedagogical approaches are employed to promote on-task behaviours in the mathematics classroom. There is a general assumption by educators that games ignite children’s on-task behaviours, but there is little systemically researched empirical data to support this claim. This paper compares students’ on-task behaviours during non-digital game-playing lessons compared with non-game-playing lessons. Six randomly selected grade 5 and 6 students (9–12 year olds) were observed during ten mathematics lessons. A total of 2,100 observations were recorded via an observational schedule and analysed by comparing the percentage of exhibited behaviours. The study found the children spent 93 % of the class-time exhibiting on-task engagement during the game-playing lessons compared with 72 % during the non-game-playing lessons. The game-playing lessons also promoted greater incidents of student talk related to the mathematical task (34 %) compared with the non-game playing lessons (11 %). These results support the argument that games serve to increase students’ time-on-task in mathematics lessons. Therefore, it is contended that use of games explicitly addressing the mathematical content being taught in a classroom is one way to increase engagement and, in turn, potential for learning.

Introducing linear functions: an alternative statistical approach

The introduction of linear functions is the turning point where many students decide if mathematics is useful or not. This means the role of parameters and variables in linear functions could be considered to be ‘threshold concepts’. There is recognition that linear functions can be taught in context through the exploration of linear modelling examples, but this has its limitations. Currently, statistical data is easily attainable, and graphics or computer algebra system (CAS) calculators are common in many classrooms. The use of this technology provides ease of access to different representations of linear functions as well as the ability to fit a least-squares line for real-life data. This means these calculators could support a possible alternative approach to the introduction of linear functions. This study compares the results of an end-oftopic test for two classes of Australian middle secondary students at a regional school to determine if such an alternative approach is feasible. In this study, test questions were grouped by concept and subjected to concept by concept analysis of the means of test results of the two classes. This analysis revealed that the students following the alternative approach demonstrated greater competence with non-standard questions.