I teach precalculus and calculus. This does not seem like a viable way to teach students in upper level courses. I do stress to my students, Don’t try to be like me and solve problems identically. Solve them in a correct manner (as long as it follows math rules). Students need to think logical and systematically, but giving them the answer will not be beneficial.

stevewyborney@gmail.comon September 6, 2015 at 3:20 pm

Hi, Bob. I have never taught precalculus or calculus so I can’t speak to specific examples in those levels. I have noticed, however, that this is most useful not when teaching new content, but when wanting students to delve deeper into foundational ideas that build toward the new content. Still not able to name specific examples, I wonder if there might be some foundational concepts that lead up to what you are teaching where it would be beneficial – from time to time – to provide students with the starting point and the ending point and ask for some possible connections between the two. Again, without specific examples, it’s difficult to detail this. In any case, thank you for making an excellent point and for reading and viewing the blog. It’s great to have a calculus teacher weighing in.

I don’t see why this couldn’t work from time to time as a class activity in calculus. The point is not to give them the solution but just the answer. Then discuss the many ways to get to the answer. A good one in calculus might be Q: Find the derivative of (x+1)(x-1)(x+2); A: 3x^2-4x-1. There are many ways to get there and talking about them will reinforce the validity of both expanding out and the product rule.

stevewyborney@gmail.comon January 31, 2016 at 8:09 pm

David, these are excellent points. Thanks for taking the time to read and to comment. I agree that this strategy could work very well at many different levels. I hope you try it in your calculus class.

I teach precalculus and calculus. This does not seem like a viable way to teach students in upper level courses. I do stress to my students, Don’t try to be like me and solve problems identically. Solve them in a correct manner (as long as it follows math rules). Students need to think logical and systematically, but giving them the answer will not be beneficial.

Hi, Bob. I have never taught precalculus or calculus so I can’t speak to specific examples in those levels. I have noticed, however, that this is most useful not when teaching new content, but when wanting students to delve deeper into foundational ideas that build toward the new content. Still not able to name specific examples, I wonder if there might be some foundational concepts that lead up to what you are teaching where it would be beneficial – from time to time – to provide students with the starting point and the ending point and ask for some possible connections between the two. Again, without specific examples, it’s difficult to detail this. In any case, thank you for making an excellent point and for reading and viewing the blog. It’s great to have a calculus teacher weighing in.

I don’t see why this couldn’t work from time to time as a class activity in calculus. The point is not to give them the solution but just the answer. Then discuss the many ways to get to the answer. A good one in calculus might be Q: Find the derivative of (x+1)(x-1)(x+2); A: 3x^2-4x-1. There are many ways to get there and talking about them will reinforce the validity of both expanding out and the product rule.

David, these are excellent points. Thanks for taking the time to read and to comment. I agree that this strategy could work very well at many different levels. I hope you try it in your calculus class.

Great blog! Looking forward to more posts!

Hi, Angie. After all this feedback I am excited to start setting up more tools!