The graphic calculator as a thinking tool: perspectives from the classroom

For over a decade the graphic calculator has been promoted not only as a computational tool but also as a thinking tool — for example, as an aid to enhance conceptual understanding, as a problem-solving tool and as a means of enabling students to engage in meaningful investigations. However, research studies focusing on these aspects have shown mixed results and have mostly focused on graphs and functions. This paper reports on one aspect of a case study in a year 10 mathematics classroom — the role of the graphic calculator as a thinking tool. Data from observations of nine statistics lessons and interviews with the teacher and five students are analysed from three perspectives: the teacher’s intentions with respect to the use of the graphic calculator as a tool to promote conceptual understanding as opposed to procedural competence; the opportunities afforded during the lessons for student investigation; and students’ views of how the graphic calculator enhanced conceptual understanding. The results provide insights into ways in which students perceive the graphic calculator as promoting conceptual understanding, as well as some of the difficulties encountered in practice in a classroom.

The graphic calculator as a thinking tool : perspectives from the classroom

For over a decade, the graphic calculator has been promoted not only as a computational tool, but also as a thinking tool - for example, as an aid to enhance conceptual understanding, as a problem-solving tool and as a means of enabling students to engage in meaningful investigations. However, research studies focusing on these aspects have shown mixed results and have mostly focused on graphs and functions.

This paper reports on one aspect of a case study in a year 10 mathematics classroom - the role of the graphic calculator as a thinking tool. Data from observations of nine statistics lessons and interviews with the teacher and five students, are analysed from three perspective's: the teacher's intentions with respect to the use of the graphic calculator as a tool to promote conceptual understanding as opposed to procedural competence; the opportunities afforded during the lessons for student investigation; and students' views of how the graphic calculator enhanced conceptual understanding.

The results provide insights into ways in which students perceive the graphic calculator as promoting conceptual understanding, as well as some of the difficulties encountered in practice in a classroom where the teacher clearly intends to use the graphic calculator as a thinking tool.

A simple-to-use calculator for determining the total solar heat gain of a glazing system

Architects and designers could readily use a quick and easy tool to determine the solar heat gains of their selected glazing systems for particular orientations, tilts and climate data. Speedy results under variable solar angles and degree of irradiance would be welcomed by most. Furthermore, a newly proposed program should utilise the outputs of existing glazing tools and their standard information, such as the use of U-values and Solar Heat Gain Coefficients (SHGC’s) as generated for numerous glazing configurations by the well-known program WINDOW 6.0 (LBNL, 2001). The results of this tool provide interior glass surface temperature and transmitted solar radiation which link into comfort analysis inputs required by the ASHRAE Thermal Comfort Tool –V2 (ASHRAE, 2011). This tool is a simple-to-use calculator providing the total solar heat gain of a glazing system exposed to various angles of solar incidence. Given basic climate (solar) data, as well as the orientation of the glazing under consideration the solar heat gain can be calculated. The calculation incorporates the Solar Heat Gain Coefficient function produced for the glazing system under various angles of solar incidence WINDOW 6.0 (LBNL, 2001). The significance of this work rests in providing an orientation-based heat transfer calculator through an easy-to-use tool (using Microsoft EXCEL) for user inputs of climate and Solar Heat Gain Coefficient (WINDOW-6) data. We address the factors to be considered such as solar position and the incident angles to the horizontal and the window surface, and the fact that the solar heat gain coefficient is a function of the angle of incidence. We also discuss the effect of the diffuse components of radiation from the sky and those from ground surface reflection, which require refinement of the calculation methods. The calculator is implemented in an Excel workbook allowing the user to input a dataset and immediately produce the resulting solar gain. We compare this calculated total solar heat gain with measurements from a test facility described elsewhere in this conference (Luther et.al., 2012).

The next step in energy rating: the international ETTV method vs. BCA Section-J glazing calculator

The most important prevention in minimizing energy transfer in commercial buildings is the treatment of glazing in the building facade. In a commercial building, while the impacts of roof, walls and floors on the overall heating and cooling loads of the building have low effects, glazing is likely to be the most important factor. This paper investigates the BCA Section-J glazing calculator and the ETTV (Envelope Thermal Transfer Value) methods and tries to look for differences as well as similarities in calculation of building envelopes energy performance. For this investigation, a hypothetical high-rise commercial building in Melbourne, Australia is considered when evaluating the energy performance of the envelope through these two methods. Both methods consider the U-Value of glass and wall materials as well as Solar Heat Gain Coefficient (SHGC) and Shading Coefficient (SC) of the glass. Findings in this research project indicate differences and significant discrepancies between the BCA Section-J and ETTV methods in evaluating the energy performance of commercial building façades. Issues of calculation weaknesses are identified with the lack of air leakage and infiltration of a particular façade design or window to wall ratio (WWR). Suggestions have been made where improvement to the overall energy calculation through facades of a commercial building is needed.

"Hey, I'm learning this"

The article offers a look at the benefits, as well as the negative impact, of using games in mathematics education. The views of teachers on the benefits of using games in teaching mathematics are explored. Information on the guestimate calculator game is provided. Details of a study on the use of guestimate game on Year 5 and 6 students is presented.

Students` impressions of the value of games for the learning of mathematics

The use of mathematical games in primary classrooms is commonplace in Australia. This paper reports on key findings from a larger investigation exploring the impact of games on mathematical learning, student attitudes, and behaviours. 222 Grade 5 and 6 children were taught multiplication and division of decimal numbers using calculator games. This paper raises questions about the students’ attitudes towards games as a vehicle for learning mathematics. One aspect reported in this paper is an apparent difference between students’ attitudes to games usage when data were
collected quantitatively compared with qualitatively.

Students' conflicting attitudes towards games as a vehicle for learning mathematics : a methodological dilemma

Mathematics games are widely employed in school classrooms for such reasons as a reward for early finishers or to enhance students' attitude towards mathematics. During a four week period, a total of 222 Grade 5 and 6 (9 to 12 years old) children from Melbourne, Australia, were taught multiplication and division of decimal numbers using calculator games or rich mathematical activities. Likert scale surveys of the children's attitudes towards games as a vehicle for learning mathematics revealed unexpectedly high proportions of negative attitudes at the conclusion of the research. In contrast, student interview data revealed positive associations between games and mathematical learning. This article reports on the methodological dilemma of resultant conflicting attitudinal data related to game- playing. Concerns arising from the divergence in the results are raised in this article. Implications based on the experience of this study may inform educational researchers about future methodological choices involving attitudinal research.

Estimating the increasing cost of commercial buildings in Australia due to greenhouse emissions trading

The ratification of the Kyoto Protocol by most industrial nations will result in an international greenhouse emissions trading market by or before 2008. Calculating the quantity of embodied energy in commercial buildings has therefore taken on added significance because it is in the creation of energy that most greenhouse gas that causes global warming is released. For energy efficient commercial buildings in Australia, the embodied energy can typically represent between 10 and 20 years of operational energy. When greenhouse emissions trading is introduced in Australia the cost of energy will rise significantly, particularly electricity which relies primarily on burning fossil fuels for generation. This will affect not only the operating energy costs of buildings (light, power & heating/cooling) but also the cost of building materials and construction. Early estimates of the potential cost of future greenhouse emission permits in Australia vary between $IO/tonne to $180Itonne. This cost would be imposed primarily on the producers of energy and passed on by them to consumers via higher energy costs. For a typical commercial building this could lead to an increase in the total procurement cost of buildings of up to 20% due to the energy embodied during the construction or refurbishment of the building. To assist in evaluating these potential cost increases McKean & Park, Sinclair Knight Merz and Deakin University have developed a web-based Carbon Cost Calculator for commercial buildings.

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.

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.

In the office SFX

In the Office SFX is a sound effect of a busy office.

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.

Consumer response to unit pricing for mobile telephony

This project is a co-operative study between ACCAN and Deakin University. It focuses on Unit Pricing, the practice of displaying the price of goods or services based on a standard quantity, to allow a direct comparison between competitive offers. This study aimed at gauging whether the new unit pricing information for mobile phone contracts assists consumers in assessing and comparing the value provided across alternative contracts within and between suppliers. Some 24 in-depth interviews were conducted with consumers who had recently bought or renewed a mobile phone contract.
The research showed that most consumers could use unit pricing information and some found it useful. Where consumers’ plans had unlimited or infinite capacity, unit pricing information was not relevant. Many consumers preferred voice allowances to be expressed in minutes, rather than in dollar allowances. Data was the most problematic category, as consumers typically had only limited understanding of the amount of data that various applications used. Most did have a broad understanding of what total capacity in data they would need, typically expressed in gigabytes.
Consumers commonly sought simplicity in deciding on which plan they would purchase or renew. A key issue for consumers was not “going over”, that is not exceeding their call, text or data allowances. For that reason, they were prepared to choose a plan that commonly resulted in them not using their full allowances each month. Some consumers used Apps on their smartphones to monitor their usage. Not all consumers had experienced advisory messages about nearing the limits of their plan’s allowances.
The Report recommended that:

R1. Unit pricing should be maintained
R2. Where unit pricing is provided for call costs, these should be expressed in terms of a one-minute call.
R3 Unit pricing for data should be expressed in terms of gigabytes or part thereof.
R4 In advertising mobile phone plans and at point of sales, customers should be provided with three levels of information – 1) overall plan features, 2) unit pricing information and 3) a data calculator.
R5 Level 2 and 3 information should be provided in a standard format across the industry, enabling consumers to make ready comparisons between plans and between competitive offers from different providers.
R6. Continuing public education is needed.
R7. Warnings about going over should always include the date when the allowance period ends and tell consumers what the rate will be if they “go over” based on the Level 2 information.
R8. The Consumer Protection Code should be reviewed in the light of these findings and recommendations.

Out of touch

In June 2016, an Australian on minimum wage earned $656.90 per week. That is $34,159 a year, before tax. According to the Australian Tax Office’s ‘simple tax calculator’, the tax owed would be $3030, leaving a take-home salary of $31,128. Let’s call it $600 a week.It’s fair to say that many of us would struggle to make ends meet on that income – $600 a week does not go very far in modern Australia.