Engagement in Math: Three Places to Start

If a teacher sees students as disengaged and not liking math, what would be one good thing to watch, one good thing to read, one good thing to try?

Andrea Davis, later today in the comments:

Will you please give me the top three pieces of advice you have for the teachers of our youngest learners? We are K-6 and want to start now.

One, ask informal, relational questions (questioning, estimating, arguing, defining, etc.) as often as formal, operational questions (solving, calculating, simplifying).

Two, pose problems that have gaps in them — look up headless problems, tailless problems, and numberless problems, for three examples —Â and ask students to help you fill in those gaps. The most interesting problems are co-developed by teachers and students, not merely assigned in completed form by the teacher.

Three, before any explanation, create conditions that prepare students to learn from that explanation. These for example.

What are your suggestions for Andrea and Mark?

Play.

Let’s try to describe a big number using a small amount of syllables (Berry’s Paradox). For example, 777777 takes 20 syllables, but saying “777 times 1001” takes 15. For a number like “741” which is seven syllables, “Nine cubed plus twelve” is much better. More complicated expressions test our perception of order of operations. Have students come up with a scoring system to rank abbreviations.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

1. Bob Lochel

November 16, 2016 - 5:17 pm -

Before you provide vocabulary and definitions, provide experiences which invite students to describe ideas in their own words.

2. timteachesmath

November 16, 2016 - 5:45 pm -

Play.

Let’s try to describe a big number using a small amount of syllables (Berry’s Paradox). For example, 777777 takes 20 syllables, but saying “777 times 1001” takes 15. For a number like “741” which is seven syllables, “Nine cubed plus twelve” is much better. More complicated expressions test our perception of order of operations. Have students come up with a scoring system to rank abbreviations.

Bring up the game again anytime a new mathematical tool could help or students could incorporate a new tool into the game. “Let’s see how this new tool makes this expression less syllables.”

3. Andrea – 1) Count! Every.Single.Day. Not rote count; count collections, combine, regroup, estimate. Our youngest learners need to count. 2) Math Chats or Math Talk, or whatever you want to call them; but it’s not “free discovery” it’s skillfully guided discussions to let students build their own knowledge in a safe environment where it’s ok to conjecture. 3) Slow down. No matter what. Students need time to build number sense in PK-2, solid number sense, before they get to 3rd grade. The research is clear on this. We move students along with just surface knowledge. Don’t cave to pressure. It feels like you will fall behind, but that’s false. Moving ahead too quickly means they are always trying to catch up, fall for tricks, and never really understand. (Bonus: use manipulatives in every grade. Let kids use their fingers! No 5th grade student is going to use their fingers if they really don’t need to. If they are using them, they need that support; they aren’t being lazy!)

Mark – Wow. You know all the above responses. I’ve followed you. So my guess is this question isn’t something you are struggling with in terms of pedagogy. You’re a risk taker and will try new things; you listen to other’s ideas and test them out. I’m thinking you are dealing with something other than “teaching” math. So…ask. Ask what’s up. And listen. Really listen. Kids have so much bumping around in their heads and we can’t peek inside. Could be math. Could be this student is one of those who truly has a math learning disability. Most people don’t even know this is a very real neurological/biological/environmental disability. You know Daniel Ansari. He’s tops for the neuroscience part. The intervention part is a bit more tricky.

But…it could be outside stress; dynamics outside of your control, to an extent. What you can do is listen – hear. Then teach coping strategies using some age appropriate cognitive behavior techniques to combat negative self talk and cognitive distortions we create and play over and over in our heads. (If only I took my own advice!) You might not ever see the benefit of this; you might get push back. But I can guarantee, if you ask, and listen, no matter the response, this student will know that someone noticed and cared. And you will know you exhausted your toolkit. If help is needed that you can’t provide (for example if there is a learning disorder or personal stress), you have built the case it’s time to look for other reasons – like going to your general practitioner for a persistent health issue which finally requires seeing a specialist.

• Jennifer

November 22, 2016 - 2:26 pm -

This is my problem! I believe and preach all of these things, but I always feel the pressure to keep moving. At every level I have taught…K-8 and now college. There is only so much time in a year or a semester, especially when students are expected to perform well on that EOG or final exam. I struggle with this every day and often don’t feel like I have the right resources to be able to slow down to give mastery the time it needs to develop.

4. William CArey

November 18, 2016 - 2:21 am -

I’ve always had good success asking kids to move from the particular to the general, with feels a lot like play. For example, ask how many (distinct, proper; don’t necessarily use those words) fractions there are whose denominator Is less than five. Then six. Then nine. Then ten. That’s a task a class can work out successfully and easily. Then ask them for a rule that works for any number. Then ask them about patterns, any patterns. There are so many that even pretty disengaged kids start to see some.

5. Peter Gerdes

November 29, 2016 - 7:20 pm -

To answer this question I think you need to be clear about what kind of engagement you actually want.

For practical reasons (at least pre-computer) almost all pre-college mathematics (and much college math) focuses on techniques for solving certain kinds of problems. At least in my experience the more I grew interested in what I would call “real” math (i.e. proving/deriving results) the less interesting/engaging the game of trying to figure out a way of finding an elementary function representation of various integrals became. Indeed, my grades and classroom participation suffered substantially because my engagement focused on questions of why/how rather than what neat tricks helped solve a problem.

Now I don’t claim to be representative but I think this does reveal a general issue. Students aren’t dumb and if what your tests, homework or classroom exercises focus on is problem solving one can’t drive their engagement with discussion of why/how. My experience teaching and watching others teach inclines me to believe that if the performance you expect out of your students is problem solving (not clever reasoning/novel ideas) engagement comes out of making that problem solving into a fun game while attempting to explain too much about the why of the rules of that game just puts them to sleep and confuses them.

On the other hand if what you want is engagement with the ideas/concepts (i.e. real math) what you need to do is test/evaluate the students on clever arguments (be it proofs/derivations in a college class, novel ways of counting up winning hands in a HS probability class, or clever, non-rote, uses of property/set membership reasoning in a grade school class). However, I fear this later approach is impossible in a setting where there is an expectation that students leave the class knowing how to solve problems of a certain kind. (No, ‘fake’ creativity doesn’t count…even questions that require creative approaches the first time are rote solutions once the student becomes familiar with them).

6. Raymond Johnson

December 5, 2016 - 6:32 pm -

In reviewing recent research articles, I thought this one sounded rather relevant and timely:

Skilling, K., Bobis, J., Martin, A.J. et al. (2016). What secondary teachers think and do about student engagement in mathematics. Mathematics Education Research Journal, 28(4), 545-566. http://doi.org/10.1007/s13394-016-0179-x