Ask, Don’t Tell (Part 2): Pythagorean Relationships
By Jennifer Wilson, Posted June 8, 2015 –
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
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 a2 + b2
> c2; others wrote c2 < a2 + b2.
Students already knew that a triangle is right when a2 + b2
= c2 or c2 = a2 + b2.
Students also determined that a triangle is obtuse when a2 + b2
< c2 or c2 > a2 + b2.
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
And I was surprised by the results. The
students had determined that for a triangle to be obtuse, a2 + b2
< c2. 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
Pythagorean Relationships activity for
Obtuse, Right Triangle Proof Geogebra applet
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 (T3) program. She enjoys learning alongside
the Illustrative Mathematics community, and she is
a recipient of the Presidential Award for Excellence in Mathematics and Science