In my cognitive
science group this spring, we read Daniel Willingham’s Why Don’t Students Like School?. One of the sections suggests that there’s a compelling question in
every lesson:
“There is a conflict in almost any lesson plan, if you look for it. This is another way of saying that the material we want students to know if the answer to a question—and the question is the conflict.”
Building off of
this idea, one of the ideas that our facilitators/coaches had us focus on was
how were we motivating the content in our class.
Lesson
A compelling
__________________ drives the content.

Questions:

Making a Lesson More Compelling:
With this in mind, I spent much of the spring thinking about what makes a question/problem compelling. Here’s one example of two different
lessons which share the same goal of introducing the idea of standard form linear
equations with solutions as different possible combinations. I did the first attempt with only one of my sections and then the next day revised to the second attempt with all of my sections.
Attempt #1 (Less Compelling)
This lesson certainly revolved around a
problem, but kids (and to be honest, I) didn’t find it particularly compelling.
Attempt #2 (More Compelling)
After talking with one of the coaches in my cognitive science group, I came up with the problem above. When I launched the problem, the kids got this
task card and I held an actual box with the candies in it. After some work time (which
involved a class discussion about 10 minutes in with one possible solution to
make sure everyone understood the problem), each table wrote down the total
number of solutions they had found on a notecard (to keep them honest). Tables
raised their hands (and kept them up) for 2 solutions, 3 solutions, 4
solutions, more. I then told them the total number of packs of candy in the box
and gave them a couple minutes to write their final answer on the notecard.
Last step, open the box and group members with the correct final answer get a
starburst. I think this was more compelling to my students for a bunch of
reasons—fewer words, the mystery, the possibility of finding all the
options, verifying a guess, and last but not least candy.
A Framework:
I have been guilty of a lot of lessons
like the first one, which are based on the expectation that students come to
school and do “their job” of engaging in whatever I put in front of them. But I
think that students deserve better. Students deserve to have something
that is compelling in every class. I am not sure that every class can have a
compelling conflict. But I think that different
categories of lessons—concept introduction, practice, and transfer (and I
think that transfer problems often introduce new topics)—lend themselves to
different avenues for being compelling.
Compelling Question Options
Useful for concept introduction/transfer lessons and
practice lessons
 Gamification:
 “Can you find all of the possible options?
 “How few moves can you do this in?”
 Understanding:
 Why isn’t [common misconception]? Why would someone think [common misconception]?
 Why would someone [(new) math tool]?
 When would you use [(new) math tool]?
 Comparison:
 What’s the difference/the same between?
 Debatable: (thanks Chris Luzniak)
 What is the best/worst, weirdest/coolest, most efficient (method, solution, first/next step…)?
 What should they do first/next/now…?
 What is the biggest/smallest/most ___ solution?
Compelling Problem Options
Useful for concept introduction/transfer lessons
Problem Genre

Examples

Relevant Routines

Looking at/watching this makes me
wonder…

 3Acts

 3Acts
 Math Forum’s Notice
& Wonder
 Brian Bushart’s Numberless
Word Problems




Making a prediction and then determine
if you are right/who is closest

 Dan Meyer’s
Pool Table 3Act
 Chistopher Danielson’s Put
the Point on the Line Desmos Activity


Problems that create a need for a math
tool in order to introduce it

 Dan
Meyer’s aspirin and headache series


Problems that initially seem really long
and annoying, but have cool shortcut(s)

 Evaluate:
81 – 72 + 63 – 54 – 45 + 36 + 27 – 18 + 9
 Inspired by CME “Maintain your
Skills” Section (this would fall under the practice category):
a) 7 x 102
b) 8 x 102
c) 15 x 102
d) 80 x 102
e) 35 x 102

 Grace
Kelemanik and Amy Lucenta’s Contemplate
then Calculate

Real life connections that are actually
interesting


Compelling Practice Options
Useful for practice lessons
See my blog post here
for the practice structures I have tried.
So that’s what I’ve got so far. What
needs to be added or changed in this framework?
Hola! I think this is a really great framework. I've also been thinking about compelling questions that are a bit more abstract (and perhaps are meant for older students then?).
ReplyDeleteFor instance, when I've taught Electricity and Magnetism at the undergrad level, a "type" of compelling question that I've found myself revisiting over and over again is "Why do we care? Why would someone want to define what this is in the first place?"
As an example (from Newtonian Mechanics), we define this quantity called MOMENTUM, and it's given by the mass times the velocity of an object. When I first thought of how to teach this, I asked myself "Why do we even care about momentum? SOMEONE defined this value, and it continually shows up in the curriculum, so it must be important to SOMEONE. But why?"
This helped me to think about all the things that can be achieved with momentum. In particular, knowing the momentum of a system allows us to predict the subsequent motion of objects in the system (under certain conditions).
SO, the reason we care at all, then, is because momentum gives us predictive power. If it were some other quantity (for example, the mass squared times the velocity) that were conserved, then we would have named THAT instead and be learning about it instead of momentum.
All this is to say, maybe this can help us as educators think of compelling questionsif we ourselves sit and think about WHY this is important. Who uses this and for what? Why did someone find that they needed this concept in the first place? What does this concept allow us to do vs. other concepts that we already know or are in place?
~Amanda
Thanks for the thoughts Amanda! I think you're exactly right that it's not going to be compelling for students if we as teachers haven't thought through why what we are teaching is important or useful (beyond they need it to be successful in next year's math class/on this particular test). I think turning this need into a question for students could fall under Dan's aspirin/headache idea or the question stems of why do we/when do we.
DeleteHi Nicole,
ReplyDeleteSomething I might add to the problem types is "puzzle" (though maybe that is too broad). I'm thinking about, for example, the seniors in AMDM in the SPRING who got pretty into graph theory  I think largely because it was such a puzzle! That doesn't seem to fall into your categories.
A next question I have is ...
 Is it better to think about what is most compelling to students OR is it better to match the question/problem type to the content?
Seems like you're really set up to use the Amanda tracker, and as I think we talked about, get students involved in assessing their own motivation.
Hi Sarah! I agree that the puzzle category can be really engaging for students. I think it's related to the gamification questions, but I would probably put puzzle under compelling problems (not questions). Do you have ideas for what the characteristics of a puzzle problem might be?
DeleteI think that both what is most compelling to students and what is the best fit for content are important to think aboutand they are probably related. I think there needs to be a good fit with content for kids to find it compelling and actually learn what I hope they will learn.