Leong (Eds.), Mathematics instructional practices in Singapore secondary schools (pp. Cultivation of positive attitudes by experienced and competent mathematics teachers in Singapore secondary schools.
Engaging Learners, Empowering Teachers, Enabling Research, pp. (Proceedings of the 9th Asian Technology Conference in Mathematics: Technology in Mathematics. It also provides some research evidence to suggest that the use of LiveMath for exploring mathematics may enhance pupil learning. This paper looks at some examples of how educators can use LiveMath as an interactive tool for their pupils to explore algebra and calculus. Moreover the capability of LiveMath templates to be interactive even on Web pages opens up an exciting chapter in online mathematics learning. But with the advance of LiveMath (previously known as Theorist and MathView), an intriguing CAS that provides "a unique user interface that allows one to perform 'natural' algebraic maneuvers even more 'naturally' than one can achieve them on paper" (Kaput, 1992), there is now another way of using a CAS in the teaching and learning of mathematics, i.e., to explore algebraic and calculus concepts. However most educators do not see any purpose in their pupils learning a CAS to perform symbolic manipulations, such as factorisation, differentiation and integration, when formal assessments still require them to perform such skills by hand. Traditionally, most mathematicians, scientists and engineers have always used a CAS, such as Maple, to perform symbolic manipulations in order to solve algebraic and calculus problems. But most of them do not know of any computer algebra system (CAS) that can be used to explore algebra and calculus. Many mathematics educators in Singapore secondary schools are aware that The Geometer's Sketchpad, a dynamic geometry software, can be used to explore geometry. (Unpublished master’s thesis, National Institute of Education, Nanyang Technological University, Singapore DOI: 10.13140/RG.0881) This seemed to suggest that there was an inherent advantage of using IT to explore mathematical concepts. The pupils in the experimental class also showed a moderately positive affect towards the use of IT. The findings indicated a significant difference in pupils’ conceptual and procedural knowledge although there was no significant difference in their affect towards mathematics in general and towards the topic in particular. One class used an interactive computer algebra system called LiveMath, while the other did not have access to IT. In this study, both the experimental and control classes were taught using a guided discovery method to explore the characteristics of the exponential and logarithmic curves.
Many previous studies compared the effect of computer-assisted instruction with traditional teacher-directed teaching and any difference in performance might be due to a different pedagogical approach instead of the use of information technology (IT). The study investigated the effect of exploratory computer-based instruction on pupils’ conceptual and procedural knowledge of graphs, and the affective issues towards the use of computers in mathematics.
If the logarithm to the base b of x is equal to y, then b raised to the y power will give you the value x. The logarithm to the base b of the variable x is defined as the power to which you would raise b to get x. The most common base changes are from the natural log to base 10 log or vice versa. This can be proved from the definition and combination rules for logarithms. If the logarithm to the base a is known, then the logarithm to the base b can be obtained by the base change relationship: The general combination properties of logarithms are: HyperPhysics***** HyperMath***** Logarithms Logarithms may be manipulated with the combination rules. Although a logarithm may be defined with any base, the logs most often encountered are the logarithm to the base 10 which is called the common logarithmĪnd the logarithm to the base e which is called the natural logarithm.īase changes can be accomplished.