**Q – Can you send me a list of language adjustments I need to make to communicate math more accurately to my students?**

A – Yes. ** Click on this link for a draft version of language and math. ** And please feel free to give me feedback through the website or through my email address: valerie_faulkner@ncsu.edu

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How do you break down the quadratic equation to your students? Would you mind posting a video showing how you break it into concepts and not procedures?

India – Thanks for this question! I need to work on this as I get this question often after people get excited about conceptual algebra. The key here is that students FIRST have a clear sense of what a linear equation is. If they do, many of the discussions regarding quadratic equations start to make more sense. Why do we have a different shape? (If kids don’t understand why a linear equation has the shape it has (a line) then how can you really have this next conversation?). Why is it possible to have 0, 1, or 2 points on the x axis? So, if you are teaching students who you presume understand linear algebra and you need to teach them quadratics, then start with re-teaching through dollar deals. It will go quickly. You can probably get through it in 2 or 3 days of lessons (for this group of students and for the purpose of re-teaching to lay groundwork for other discussions). then you have built a common language in the class that you can jump off of. So, if nothing else, I think you will be surprised if you just start there.

As for, a model for the quadratic, I am open to ideas. I started to play with a Gardening Story where you have a plot of land and need to consider the different possible lengths and widths for a given area. You would need to start with rectangular plots of land that are square rectangles and then build from there into other rectangles. Could that work? A problem here is that there is not negative area, of course. But I think that can be overcome with a discussion of all the possible mathematical solutions and then the solutions that fit the story. this is an important concept in general to discuss with students anyway. Let me know what you think.