Visual Models vs Algorithms

There has been a substantial increase in the use of visual models in my class compared to last year. As a beginner teacher with no experience, I taught like how I was taught. This year however, I understand how important conceptual knowledge can be, and what a better way than to visualize it. It's the reason why some of the weaker classes can keep up. Visual models are good for everyone. Just because a student is in the algorithmic stage (as in, they can solve a problem algorithmically), doesn't mean that they have the conceptual knowledge.

I have been wondering lately though, when should I take students off of visual models and move them onto the division w/ fraction algorithm? Some higher level students are annoyed with drawing models, but I want them to understand that this is a tool they have in their disposal at any point in time, not something that's disposable just because there is a faster way.

We have been doing a lot of division with fractions lately, and we've gone as far as division with fractions with uncommon denominators. And I must say, it did occur to me that the model for division with fractions is a piece of extra work when the algorithm is so easy to follow.

VS.

 

The downside to the algorithm is that it literally conveys no conceptual knowledge at all. I want to make sure students have a solid foundation of what division is before moving onto the next topics (long division/GCF/LCM). In the long run, I'd rather be safe than sorry. I think when students have shown that they can compute or solve word problems fluently with the visual model, then I can teach the algorithm and we can move on.