“Fill the gaps!” is the command of many well-intentioned educators. Math especially succumbs to this twisted pedagogy because math is more obviously hierarchical with lower building blocks being required to understand higher building blocks.

What is wrong with this “fill the gap” mentality?

First, it is wrong because it is joyless. Students need to spend more time on their strengths than their weaknesses because that’s where they derive the enjoyment of learning and the passion to persevere through their weaknesses. It is more exciting to do what you love!

Second, it is difficult for a teacher to micro-manage twenty students’ schedules so that each student is given the opportunity to “fill their gaps.”

Several years ago I was teaching a grade three class once every two weeks. I remember one girl–I’ll call her Heidi–who sat in the front row and was consistently slow to understand and poor in execution. I went through eight months of the school year with the impression that her math abilities were low.┬áIn retrospect, she was daydreamy. I also learned she was coming out of a violent home.

It all changed one day when I presented a tough puzzle. Many students thought they had solved it, but each time I showed them an inconsistency. Heidi then showed me a correct solution. She was the first. I told her that the two of us together were going to check other student solutions. I watched over her for the first several and she pinpointed the inconsistencies quickly and unerringly. I discretely withdrew leaving her in charge of assessing her classmates for five minutes. They lined up in front of her and she identified the errors in their solutions.

For the rest of the school year, she was the strongest student in the class. If we had focussed on Heidi’s gaps–there would have been no trouble finding them! That’s not what Heidi needed. She needed to find a strength and get inspired.

Heidi was a once-in-a-teaching-career student. She is definitely not typical. But, what was true for her is true for a majority of students with gaps. As the following video says… deal with the gaps, but don’t focus on them…