It is often desirable to explain why standard methods work using pictures and blocks but these concrete materials should not be used as actual strategies for working through arithmetic problems – our ancestors moved beyond such primitive techniques centuries ago.
These convoluted strategies take up so much time that children are still working on basic arithmetic at the end of their primary school years when they should be moving on to more advanced topics such as fraction arithmetic and algebra, like their counterparts in high-performing jurisdictions like Singapore. Some Canadian children are left hopelessly confused by the multiple, convoluted strategies and do not master basic arithmetic at all.
This leaves them with shattered confidence and unprepared for learning further mathematics.
Further to this, inquiry-based or discovery-based learning has swept North American schools over the last several years. As if multiple strategies weren’t confusing enough, teachers are encouraged to use open-ended problems that have several possible solutions as a primary instructional tool for teaching novice learners. For example,
“The answer to my question is 62. What might my question be?” or
“Create a sentence that uses the numbers 22 and 73 and the words share and almost.”
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