Tag Archives: conics

Ellipse Investigation – #AskDon’tTell

One more learning investigation from our experiment – see Circle Investigation – #AskDon’tTell and Parabola Investigation – #AskDon’t Tell.

Sam designed the following ellipse investigation (EllipseInvest.tns).


Look at the continued improvement in the learners’ questions:

Ellipse_Investigation_Q1 Ellipse_Investigation_Q2.jpg

Sam notes that his learners are beginning to ask more mathematically relevant questions. Isn’t this exciting? Can you imagine learning math this way?

I’m pretty sure there is a hyperbola lesson coming soon.

Parabola Investigation – #AskDon’tTell

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.

Circle Investigation – #AskDon’tTell

What if we facilitate learning episodes by following the learners questions? How might we set up opportunities for learners to explore and think PRIOR to a show-and-tell scaffolded lecture?

What if we gave learners the a TI-Nspire document and asked them to explore it for a few minutes? What if we asked them to jot down observations, patterns, and questions  that come to them as they play with the document?

So, here’s the hypothesis:  We can teach just as much (or more) by responding to the learners’ questions.  What if we tried an experiment with a one page Nspire document and a protocol for question generation?

Sam Gough, Algebra II teacher at The Westminster Schools, was brave enough to try this experiment with his learners.  Here’s the original plan:

Using the TI-Nspire document CircleInvest.tns, facilitate a 3-12-3 protocol to generate student questions.

  • 3 minutes: Independent investigation of the CircleInvest.TNS file.
  • 12 minutes: Work with a partner to share questions, convert closed questions to open questions, and generate additional questions. Partners should identify their top 2-3 questions.
  • 3 minutes: Use the TI-Nspire Navigator to collect each student’s top question.

Using the TI-Nspire Navigator for Networked Computers, he sent his learners the circle investigation shown below and challenged them to interact with the document and record questions.


Using the 3-12-3 protocol combined with the ideas in Dan Rothstein’s Make Just One Change: Teach Students to Ask Their Own Questionshe coached his learners to investigate the TI-Nspire document and generate open-ended rather than closed questions. Below are the questions generated and submitted by his learners.


Pretty interesting, huh? Not bad for a first try.  Sam reported that he did teach what was in his original lesson. He was intrigued by the pattern question asked by his learners.  He said that he is concerned that when the lesson is more challenging than investigating a circle, he may not get the results he wants.  He also mentioned that the times might need to be 3-9-3 instead of 3-12-3.  I wondered if they might need more time as they improved as investigators and questioners.

Acknowledging that one trial does not make an experiment, we are going to try again tomorrow with a Parabola Investigation.