Prompt: What would you do differently?

I’m not sure – do I teach with formulas, or not?

1. millikinjax

I totally feel your pain right now. I feel a strong desire to show students WHERE the formulas come from and I love how the area formulas all eloquently related back to the familiar rectangle. However, after the “discovery” of the formula, students quickly forget how we derived it and what the meanings were for the different aspects of the formula. They are taking a quiz tomorrow so I will have a better idea of what I need to do differently next year. I think models will help

• Wendy Menard

Thanks for reading. We could have derived the formula; it worked when we did the area of triangles and Law of Sines. There’s always next year…

2. Pat Ciula

Apparently everything that is confusing (like base and height) to 7th graders is still confusing in 11th grade.
I wonder if working with formulas (derived by others) should be postponed as long as possible. If students are given opportunities to make sense of measurements and relationships between shapes and develop their own formulas that work (and most likely look similar to “official” formulas), why not let them continue to use them? I wonder if jumping too quickly to formulas sends the wrong message about the value of their work, which may be why they abandon them and their meaning.
One idea that popped into my head was to use nets more intentionally. Kids love cutting them out and taping them into 3-D shapes; its “fun” and almost magical. But I have found it difficult to get learning from it. What if students examine a variety of nets– ask them to locate the base, the perimeter of it, it’s base and height, the height of the solid, maybe using colored pencils to trace and mark measurements. I think it would stretch their brains to “see” these measurements on a net and may help them make sense of the confusing vocabulary. There could be a lot of noticing and wondering going on, which is way better than cutting and taping.

• Wendy Menard

I totally agree about formulas, but when my students seek additional support online, that’s the first thing they find.

We started with nets of rectangular prisms, where it’s not so easy to determine which face is the base. They translate base to mean ‘bottom’ (not unreasonably) so when they encounter a triangular prism lying on its side, they have a hard time seeing that the triangles are the bases. I like idea of using nets throughout to help with that confusion. Thanks!