**By Jennifer Wilson, Posted June 8, 2015 – **

A few weeks ago, I overheard one student telling another, “Will you help me figure this out? Don’t just tell me how to do it.”

How many of the students in our care are thinking the same thing? How often do we tell them how to do mathematics? How often do we provide them with “Ask, Don’t Tell” opportunities to learn mathematics?

I used to tell my students how to determine whether a triangle is acute, right, or obtuse, given its three side lengths. Now I provide them an opportunity to determine the relationship between the squares of the side lengths so that they can generalize how to determine whether the triangle is acute, right, or obtuse.

For all the triangles, we used *a* ≤ *b*
≤ *c*, where *a*, *b*, and *c* are the three side lengths. Some
students wrote that a triangle is acute when *a*^{2} + *b*^{2}
> *c*^{2}; others wrote *c*^{2} < *a*^{2} + *b*^{2}.
Students already knew that a triangle is right when *a*^{2} + *b*^{2}
= *c*^{2} or *c*^{2} = *a*^{2} + *b*^{2}.
Students also determined that a triangle is obtuse when *a*^{2} + *b*^{2}
< *c*^{2} or *c*^{2} > *a*^{2} + *b*^{2}.
Students already knew that, for three lengths to form a
triangle, *a* + *b* > *c*, *a* + *c*
> *b*, and *b* + *c* > *a*.

I sent a Quick Poll to assess student understanding:

And I was surprised by the results. The
students had determined that for a triangle to be obtuse, *a*^{2} + *b*^{2}
< *c*^{2}. Why did one-third
of them miss the question? I had to think fast. I could have told them the
correct answer. And then I could have told them how to work the problem
correctly. Or I could have asked what misconception the students who marked
acute had. Would everyone have paid attention?

What I did instead was to show students the results without displaying the correct answer. I asked students to find another student in the room and construct a viable argument and critique the reasoning of others. I walked around and listened to their arguments. And I sent the poll again:

All students answered correctly; they had all learned from the mistake of those who had chosen acute (believing that 8 + 15 > 18 was enough ensure that the triangle was acute).

“Will you help me figure this out? Don’t just tell me how to do it.”

“Ask, Don’t Tell” learning opportunities allow the mathematics that we study to unfold through questions, conjectures, and exploration. “Ask, Don’t Tell” learning opportunities begin to activate students as owners of their learning.

What #AskDontTell opportunities do and can you provide?

**Resources for Pythagorean
Relationships:**

Pythagorean Relationships activity for TI-Nspire

Acute, Obtuse, Right Triangle Proof Geogebra applet

JENNIFER
WILSON, http://www.easingthehurrysyndrome.wordpress.com,
a National Board Certified Teacher, teaches and learns mathematics at Northwest
Rankin High School and is a curriculum specialist at the Rankin County School
District in Brandon, Mississippi. She is an instructor for TI’s Teachers
Teaching with Technology (T^{3}) program. She enjoys learning alongside
the Illustrative Mathematics community, and she is
a recipient of the Presidential Award for Excellence in Mathematics and Science
Teaching.

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majid saadat- 2/8/2018 5:12:31 PMverry good

طراحی سایت | طراحی وب سایت | طراحی سایت ارزان | طراحی سایت حرفه ای

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