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Published on May 27, 2014;
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Mathematics
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Education
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Published on May 27, 2014 by Mario Pineda, Ph.D.
at http://drpineda.ca/math-education-in-the-21st-century.html

The universe is inherently mathematical and the purpose of mathematics is ultimately to be a tool helping us gaining understanding and insight into the nature of our world, or in Dan Meyer's words *Math makes sense of the world. Math is the vocabulary for your own intuition.*. Despite this, mathematics is often perceived by students as being disconnected from the real world and without having a real world application. One reason for this attitude may stem from the way mathematics has been taught in schools, with a focus on staged problems and rote memorization with little emphasis on understanding and solving open ended problem. For mathematics to be useful it needs to be presented and experienced in the context of real world scenarios. Over the last few years Alberta Education has taken upon itself to revise the mathematics curriculum in Alberta by integrating current research, developments and trends in mathematics learning and teaching and bringing the curriculum into the 21st century. While the idea that the world is inherently mathematical does not necessarily by itself make mathematics more authentic or accessible to students. For example, while the physicist Max Tegmark provides a compelling argument that the universe is entirely mathematical, and as much as I appreciate his short educational video clip and his somewhat longer book on the subject, his rational is probably not going to make students be in awe of the role of mathematics in cosmology. The same argument is made, however, in a video clip produced by Alberta Education but with the key difference that it is pitched to students and educators.

One way of making mathematics more authentic for students is by presenting students with real world open ended problems. For example, in Dan Meyer's TED talk "Math class needs a makeover" he uses an example from a standard mathematics text book where students are asked to calculate how long it will take for a hexagonal container to be filled with water. In the text book formulation of the problem the students is given a clip art-looking figure with the dimensions of the container and is given precisely the information required (nothing more or less) in order to solve the problem using a formula sheet. The question is also subdivided into several sub-questions that incrementally guide the student towards the final solution by asking for various intermediate results. This is an example of a staged problem where the mathematics is dumbed down requiring a minimum of understanding and where the student, rather than engaging in constructive problem solving, tries to identify a formula into which to plug in the given information. In his TED talk Dan Meyer advocates a more open needed approach, with minimal amount of information at the outset and with no real right answer at the end. The basic tenet of this approach is that rather than having students mindlessly extracting the required information from the question (which only contains the required information) just to plug it into a provided formula, students need to engage the higher-levels of Blooms taxonomy and create their own solutions, including developing their own formulas. This approach is not only a more authentic approach as to how problems are solved in the real world but it also provides the necessary components for students to actually understand how to develop and apply their mathematical skills.

Lynn McGarvey makes a similar point in her CBC interview (starts at 26 minutes) where she discusses the recent movement among some parents in Alberta towards a "back to the basics" approach for teaching mathematics. While the "back to the basics" proponents argue that rote memorization is an important teaching strategy required in order for children to learn mathematical concepts, McGarvey makes the deft argument that it provides no deeper understanding of mathematical patterns and connections. For example, McGarvey asks, why is it that 6x4 = 3x8. Learning multiplication tables by rote memorization, something that the "back to the basics proponents" forced the current education minister to reintroduce, will teach children that 6x4=24 and 3x8=24, but provides them with no insight as to why this is the case and, more importantly, how this could be generalized and used in solving more complex mathematical problems.

Traditionally the emphasis in mathematics education has been focused on the view that success in mathematics meant being able to compute accurately and quickly (Kirkpatrick et al. 1999). In today's world, however, as Conrad Wolfram argues in his TED talk "Teaching kids real math with computers", we are saturated by information and we all carry around "computers" in our pockets that can do calculations vastly faster and more accurate that any human being (perhaps with the exception of the TED talk featuring the mathemagician Arthur Benjamin) we are in the unique and quite wonderful position of being able to shift the focus of our mathematics education from drills, rote memorization, mindless and endless calculation to a focus on having our students spend much more effort on learning on how to conceptualize problems and apply their knowledge in mathematics to solve real world authentic problems (Steen, 1999).

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