Kids haven’t changed, but…

This is a response to this opinion from @RobynUrback.

@RobynUrback, I agree with your assertion that our kids deserve better when it comes to their education in mathematics; however, you have misdiagnosed the problem.

You are right to say that kids haven’t changed, but you have not addressed the fact that the world for which we are preparing them has changed (and will continue to change), nor have you addressed the fact that what we know about how students learn has also changed.

You point to the change in the math curriculum as the problem that needs to be fixed, but you have not addressed the problems in its implementation. The math curriculum has changed, but teacher preparation has not. The math curriculum has changed but the metrics that we use to monitor student progress has not.

Kids haven’t changed; but the world for which we are preparing them has.

Computation that used to take a great deal of time can now be done almost instantaneously with tools that are cheap and ubiquitous. In a few minutes, students can analyze data on their home computers with a degree of sophistication that used to require small teams of undergraduate research assistants. Complex algebraic equations can be solved instantly and for free. In fact, some sites will even show you step-by-step solutions so that you can make your teacher think that you did it by hand. The stuff of a traditional mathematics curriculum, like being able to do a multi-digit division problem or factor a quadratic equation quickly and accurately is not an asset when a smartphone will always be faster and more consistently accurate. What is an asset in such a context is the ability to identify problems, select appropriate tools to solve them, and reflect on the validity and accuracy of the solution(s). Unfortunately, traditional math curricula tend to do this work for students, robbing them of opportunity to learn how to do it themselves. Dan Meyer has described this well here.

Kids haven’t changed; but what we know about how they learn has changed.

Traditional mathematics curricula are predicated on the idea that students are empty vessels who need to be filled with knowledge about numbers. We know now that this is not true. From infancy, children build their understanding of the world through observation and experience. This includes concepts of quantity, shape and chance. Skilled teachers facilitate this process by identifying misconceptions and then creating experiences that help students revise and extend their understanding. This is discovery. The danger of treating students like empty vessels is that the misconceptions that students bring to the material are ignored and sometimes they are accidentally reinforced. There is also the risk that students will come to see mathematics as something that is foreign and disconnected from their lives when, in fact, it is deeply rooted in their intuition and daily experience.

Returning to a traditional curriculum will not fix the problem, but I can think of a few things that might.

Equip teachers to implement the new curriculum effectively.

Asking teachers to teach mathematics in a way that is profoundly different from the way they learned it is unfair. Most of today’s teachers will have learned math as a series of separate skills rather than a set of interrelated concepts. Their education did not prepare them for the future in which we now find ourselves. Most of the instructional resources they have to work with prioritize computation for its own sake, rather than as a step in the larger process of problem-solving. It would be irresponsible to put a taxi driver in the cockpit of an airplane and say, “this is the way of the future, figure it out!”, but that is essentially what we have done with teachers. They need time, resources and support to implement a current curriculum effectively.

Measure what matters, not what is easy.

The impact of a traditional mathematics curriculum is easy to measure in large-scale, standardized assessments. Computational skills can easily be assessed with multiple-choice and fill-in-the-blank tests that can been marked by machines. It is much more difficult (and expensive) to assess conceptual understanding and problem-solving skills. Many of the standardized tests that are used to monitor the success of the curriculum favour computational skills which means that they are not fully aligned with the goals of a modern approach to teaching and learning. To claim that the curriculum is failing without considering the validity of assessment used to measure its success is to oversimplify the issue.

Canada’s children deserve an education that will equip them to succeed in a rapidly changing world. This cannot be achieved by reverting to the techniques of the past. Our children deserve an education that is evidence-based, thoughtfully implemented and properly resourced.



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