The second of Howard Gardner’s eight forms of intelligence that combine in different ratios to define an individual, is that of mathematical and logical thinking. Logical mathematical intelligence may be formally defined as the capacity to reason, calculate, apply logic, think critically, and sometimes abstractly, all of which draw their basic principles from mathematics. Educational communities around the world recognize logical and mathematical reasoning to be essential parts not only of education, but of literacy itself. The American National Literacy Act of 1991 defines literacy as “an individual’s ability to read, write, and speak in English, and compute and solve problems at levels of proficiency necessary to function on the job and in society to achieve one’s goals, and develop one’s knowledge and potential”.
The role of technology in fostering mathematical and logical intelligence is obvious in that technology is built on the same mathematical principles and logic that drive life itself. The ancestors of modern digital gadgets – Pascal’s and Leibniz’s mechanical calculating machines, Napier’s logarithms, Babbage’s difference engine, Newman’s Colossus and Turing’s Bombe – have all been built on principles of logic and mathematics and in turn support mathematical developments. Jeanette Wing, in a seminal article, states that solving problems, designing systems, and understanding human behavior in real life can be closely related to the concepts fundamental to computer science and technology and coined the term “computational thinking ”, which must, in addition to reading, writing, and arithmetic, be added to every child’s education.
Technology can support mathematics education through dynamic software, anchored instruction, networked devices, participatory simulations, games, and construction kits. The challenge lies in developing technology that engages students with interesting and stimulating applications of mathematics that are relevant to the real world.
Concrete manipulatives – objects such as the Abacus, Cuisenaire Rods, Base 10 Blocks, and Fraction Circles – that have traditionally been used in teaching mathematics, can potentially be replaced by virtual manipulatives that are dynamic virtual representations of the concrete manipulatives, but with the added advantage that they can go beyond the capabilities of physical objects. The National Library of Virtual Manipulatives (NLVM) for example, offers interactive, web-based virtual manipulatives and concept tutorials for mathematics instruction. A comprehensive study by researchers at the Clayton State University on the use of concrete and virtual manipulatives in math education showed that while pre-service teachers found concrete manipulatives to be easier to use, students found both types of manipulatives useful to understand mathematical concepts. This is to be expected, as the teachers typically belong to the digital immigrant generation with a steep learning curve, while the students, in all likelihood, are digital natives, at home with technology. The study concluded that incorporating both types of manipulatives into the instruction of mathematics helps build better conceptual understanding and provides sound pedagogical strategies for use with future students.
Gaming offers a rich ground for mathematical and logical training. However, the use of games and simulations to teach and train in mathematics and logistics cannot follow the carrot-in-stick routine, such as the technique proposed by Michael Grove, the education secretary to the UK Government, where equations are solved “in order to get more ammo to shoot the aliens”. Mary Matthews of Blitz Games Studio, UK, aptly responds as “Using games for motivation is only one facet, [...] exploration, experimentation, team building, problem-solving and independent, personalised, differentiated experiences [will tap into] the full potential games can offer for learning”.
The NRICH Project, perhaps meets the goals of Matthews. It aims at enriching the mathematical experiences among learners and focuses on strategy games to develop essential problem-solving skills in a stimulating environment. NRICH’s strategy games are defined as being low-threshold, high-ceiling tasks where the child can easily access the game at its basic level and play ‘randomly’ while developing a winning strategy.
A simple search for online math tools produces hundreds of sites that offer various kinds of math training and education. Sites like A+ Click Math, Math Worksheets Lands, NumberBender , Get the Math and Math Worksheet Generator are some of many that offer supplementary practice problems in primary and secondary level mathematics. Math Pickle, featuring mathematics videos for students in kindergarten through twelfth grade, approaches mathematics from the standpoint of a problem solver instead of from the standpoint of a rules follower. These sites are but tip of the iceberg.
The current barriers to the use of technology in furthering mathematical and logical thinking include the general mindset that digital technologies are an add-on to learning mathematics and inadequate guidance on the use of technological tools in both statutory and non-statutory curriculum. According to a recent report by UK’s National Centre for Excellence in Teaching Mathematics, the main concerns among teachers of mathematics on the use of digital technologies are:
- lack of confidence with digital technologies;
- fears about resolving problems with technology;
- insecurity of knowing less than their learners who are digital natives;
- access to digital technologies;
- inappropriate training;
- lack of time for preparation;
- lack of awareness of how technology might support learning;
- not having technology use clearly embedded into schemes of work.
John Seely Brown, cofounder of the Institute for Research on Learning , and an expert in digital youth culture, digital media, and the application of technology to enable deep learning, states that the Web may be the first medium that honors the notion of multiple intelligences. Among the different types of intelligences classified by Gardner, Brown’s notion is best suited for mathematical and logical intelligence. But the sheer volume of “help” available online for mathematical and logical training could potentially render the effort futile. It is up to the instructor and user to use their judgement to choose tools that are relevant to their needs and development.
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