# Tag Archives: parabola

Continuing our experiment to lead learning by following and responding to learner questions, Sam designed the following parabola investigation (ParabolaInvest.tns) for his learners. (Note: Sam teaches in a 1:1 MacBook program, so these files are designed to be viewed and investigated in computer view rather than handheld view.)

Here are the questions generated by Sam’s student-learners.

Wow! What an improvement in the number and the quality of questions.

The importance of collecting many questions is critical.  If we answer questions in the order they are asked, we might not get to the most interesting or most critical questions.

Sam reported that he is very pleased with the learners’ questions and their engagement with the mathematics.  He says he is encouraged to continue this method of teaching because of the change in participation and interest from his learners. It is fun to teach and  facilitate learning this way! He says:

Kids should interact with these graphs instead of memorizing facts.  I want to continue offering investigations where they control points and identify patterns. It’s a great way to learn!

He is busy working on an Ellipse Investigation, and he is already planning a Hyperbola Investigation too.

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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