What questions could we ask to help our learners investigate and “discover the rules” for the number of roots or zeros of a quadratic function?

Should we start by questioning their understanding vocabulary?  Can we questions our learners to connect roots, x-intercepts, and zeros?  Can we listen to the learners’ questions to take their path instead of our carefully scaffolded plan?

What questions should be asked to lead our learners to move them identifying no real roots,  1 real root, and 2 real roots graphically to identifying the number of roots using the equation and the discriminant?

Remember, we ask questions; we do not tell rules or definitions.  The art of questioning must be practiced and honed.

Want to explore the investigation? Here’s how:

• Clicking on the screenshot should enable you to download the TI-Nspire document and open it if you have the TI-Nspire software on your computer.
• Clicking on the Launch Player button should open a player file where you can interact with the document without having TI-Nspire software. (Be patient; it is a little slow to launch.)

I would love to hear your thoughts and feedback.  Also, what questions would you ask, and what questions do you hope your learners ask?

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1. Cool! You got the document player to work on a blog! Instead of just laying out the discriminant rules, you could use this document to let students discover the secrets of the discriminant.

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2. Right! The key is in the art of questioning, listening, and observing. Do you have a set of questions in mind just in case your learners need a little coaching? I want to post my set of questions, but I am waiting to hear from others.

Thanks for letting me know that the player is working for you. Steve has helped me work on this. It is the second post with a player file.

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3. […] writing LEARNing: Linear Functions Investigation – #AskDon’tTell and LEARNing: Quadratic Functions Investigation Zeros and Roots – #AskDon’tTell, I’ve been trying to work out an idea for prompting student investigation and questioning […]

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