To my last post, “No more broccoli ice cream” David Griswold challenged me with a very serious and thoughtful reply.

The phrase, “No more broccoli ice cream” came from this meme that I saved. I collect these memes, just because the provide interesting fodder for conversations about math in class.

So who is Denise Gaskins? She is a home school parent who specializes in K-6 math (I am inferring this from her website and the books / content she talks about. I could be wrong about the grade levels.) She tweets and has a FaceBook page under the name “Lets Play Math.” It is clear she has a focus on making math fun, interesting, and engaging. At that age, my experience is that learners are very much into mathematics. I saw this bulletin board in a hallway last year.

If you zoom in, you will see that almost every single one of those 4th graders said their favorite subject was math, or they enjoyed math, or they were good at math. 2 out of the 15 had no positive mention of math. A bulletin board next door to it had a similar proportion. When I saw this board, I wrote a post called “Where does the joy go?” This issue is one that I have been struggling with for a while. Why are young children excited about math, but junior or high school learners typically are not?

I believe it is because at some point, I and my fellow teachers stop thinking about math as joyful, and start thinking about it as “serious work.” We can’t have fun solving these equations, this is “serious business.” But that is true of all subjects in high school. It isn’t just math teachers, but English teachers, history teachers, and other teachers. We turn our subjects into these “serious business” topics that must be “mastered” and “assessed.” If you don’t pass the classes, then you can’t graduate, you can’t be successful in life without knowing “algebra.”

[yes, I used a lot of scare quotes in that paragraph because I do not want anyone to infer that there is an agreed upon meaning of those terms.]

Here is what David said in his questioning of my post:

I’m not sure I completely agree with this, or Lockhart for that matter. There are a lot of people who find joy and beauty in the curriculum, and there are lots of ways to encourage and celebrate that joyousness without throwing too much out. Will some people hate it? Sure. I didn’t like AP US History very much, though I liked my teacher. But I had friends who thrived there. And I’m okay with that.

Personally, I don’t think the ice cream metaphor is realistic. Math isn’t ice cream. Nothing is ice cream. No field or subject is as universally loved and delicious as ice cream, certainly nothing with any practical application. Math isn’t ice cream, it’s vegetables! So maybe “textbook math” is steamed broccoli and it’s up to us to add peas and roasted cauliflower and sweet potatoes (maybe even with some marshmallows on top) and even pickles, but the fact is some people don’t like ANY vegetables and some people like simple steamed broccoli the best and some people like ALL vegetables and, importantly, all of them are part of a well balanced diet. So our job is to be a math nutritionist.

The first paragraph I will not reply to, because it is his personal feelings and I don’t think there is anything there to discuss. It is real.

The second paragraph is the challenge. “No field or subject is as universally loved and delicious as ice cream.” But … I don’t like ice cream. I eat it maybe one time every four or five months, because my wife wants to share something.

And, guess what? Yes, math is as loved as ice cream at the lower grades. I have observed 4th and 5th grade classrooms where the learners are excited, joyful, and enthusiastic about math. The bulletin board above is anecdotal evidence.

I think we need to stop saying it is the subject that is like vegetables, and accept the fact that it is the way we teach the subject that turns it into vegetables.

Watch this video (it is 5 minutes) of these middle school learners struggle and succeed in math.

There is honest to goodness joy there.

They ate some yummy ice cream in that lesson. Why can’t we do that every day?

To answer David. Is math like vegetables? I think it can be. Is math like ice cream? I think it can be. The choice is mine.

If I get to choose whether math is more like vegetables or like ice cream in my classroom, I will choose ice cream (even though I don’t like ice cream).

I choose this not for myself, but for my learners. And David is right. Not everyone will love every subject. I am okay with that. But if I choose to present math like brussel sprouts instead of chocolate fudge peanut butter ripple, then I have denied some learners even the ability to choose whether or not they enjoy math.

And then, how do I make my pre-service teachers understand that it is a choice they can make too? [Wow, that is a whole different can of worms.]

So, is math like ice cream? For my classroom, for my pre-service teachers, the answer must be Yes.

David responded on Twitter with these series of tweets. I think they add a great deal to the conversation.

@gwaddellnvhs @letsplaymath My only problem with this response (which is lovely) is that my point is vegetables are BETTER than ice cream.

— David Griswold (@DavidGriswoldHH) September 9, 2016

@gwaddellnvhs they are more varied, more sustainable, and more nutritious. With variability comes dislike but also love.

— David Griswold (@DavidGriswoldHH) September 9, 2016

@gwaddellnvhs I don’t want to avoid all math that some or even many dislike. I make it clear why I like it and why it is good for them.

— David Griswold (@DavidGriswoldHH) September 9, 2016

Thank you David for making me think.

I am a pre-service teacher studying mathematics and education. I am a new follower of your blog because I think that you have posted some interesting things, so I am excited to start following you!

I would like to address a statement you made above. You said that “we need to stop saying it is the subject that is like vegetables, and accept the fact that it is the way we teach the subject that turns it into vegetables.”

1. I feel like David’s argument was really just pointing out some of the flaws in the analogy, something that all analogies will have. I think that your analogy works, and I have to agree with what you say about evaluating how we are teaching math and if that is producing people who are genuinely interested in math.

2. I think that I have found your statement to be rather true, and to summarize what I am understanding about what you say is that as we progress through math education we have the ‘ice cream’ turned into a vegetable because of the way it is taught, and then later on I would be willing to say that in college we see this vegetable turn into a very bland vegetable that is poorly seasoned.

I say this because a trend I have noticed in my abstract group and ring theory course along with other math courses I have taken is that there are moments that math is glorious and delicious, but also that those moments are few. I have noticed that math in college is often taught through regurgitating the textbook in real-time on the blackboard. That is literally the most bland vegetable that has ever touched my mouth.

3. So this leads to two questions I have for you about some things I have been thinking about lately. To what extent do you think our high school math education is influenced by our experiences in collegiate level math? Do you think that we should also be looking towards and pushing for reform in collegiate level math education?

Mathew, Those are big chunks of questions, and I end up addressing them often in my courses I teach. My response would be yes, to both. I think that the college experience in mathematics definitely influences how mathematics is taught in the high school. We take a group of people who love mathematics enough to sit through the lectures, learn from the lectures, and build knowledge from the lectures, and then turn them loose in high schools. Then we are surprised when these same people lecture in high school?

There are reforms underway. You can learn about some of them here: http://www.ams.org/programs/edu-support/Innovations-College-Level I know of others, but they are in my office. I will come back to this I think.

Thank you Mathew, and I hope your teaching is awesome!

Thank you for responding, I think it is cool to see what types of reforms universities are making in that fashion, and I would imagine that if we can make these types of innovations for engineering and science majors, that it would only be a matter of time for innovations to also impact mathematics majors in more abstract proof based courses.