I live adjacent to the Northern California wine country, which makes wine tasting a fairly affordable and semi-regular kind of outing. (Pre-quar, of course.) But wine tasting makes me anxious and sweaty in ways that help me relate to students who hate math class.

- There’s a sharp division between who is considered an expert and a novice, and an obsession with status (there are four levels of sommelier!) that’s only exceeded by some religious orders.
- Experts seem to have very little interest in the intuitions and evolving understandings that novices bring to the tasting room. (What you’re supposed to be experiencing – the answer key – is written right there on the tasting menu!)
- The whole thing is arbitrary in ways that we’re all supposed to pretend we don’t notice. (In math: the order of operations, the names of concepts, the y-axis is vertical, etc. In wine: the relationship between price and appreciation.)

I basically only enjoy tasting with a friend of mine, Michael Kanbergs, who is the man at Mt. Tabor Fine Wines in Portland, OR, if you’re local. He has expert-level knowledge about wine and enthusiasm to match but is allergic to most ordering forces in the world, including the expert / novice distinction. So he wants to share with you his favorite wines but he’s hesitant to offer his own perception too early because that’d undermine his curiosity about how *you’re* perceiving the wine.

I’m grateful to Michael for modeling good teaching, and grateful to other wine experts for helping me empathize a little better with math students who might find me and my habits alienating in similar ways.

## 9 Comments

## Brandon Dorman

September 28, 2020 - 3:03 pm -Glad I’m not alone in the absurdity of wine knowledge levels

## john oberman

September 28, 2020 - 8:37 pm -Good Wine.I live around the corner of Mt.Tabor in the galilee.We also like their wines.

## Dick Fuller

September 29, 2020 - 6:09 am -Spot on, at least for an outsider looking in, and that is the way it usually feels. Seems to me there are two ways to look at education: (1) as a presentation of an official way to see the world, (2) as an environment where understanding can be discovered. For math the first is primarily academic; it prepares you for more of the same, and is essentially a dead end. It works for wine, presumably because there is wine at the end.

Students do have a mental life, They do recognize an animal they have never seen as as a “dog”. They were not taught, but they were around animals being dogs. Students do conceptual understanding, and at a fantastic rate. Since we don’t understand how they do it, we can’t test them. This doesn’t seem to bother us with the concept “dog”. Why not trust them to pick up math concepts that we could model.

“wine” is a percept we make from our taste perception. “Arithmetic” can be a concept we build by mental activity , conscious or not.

## Chester Draws

September 29, 2020 - 9:00 pm -Children in the wild do need to be taught that jackals, wolves, coyotes etc are not dogs. (Even in the modern world it is important that you teach your children that not all dogs are safe pets.) If people left this to experience rather a lot of children would be mauled — so we teach them *explicitly* what is a “dog” and what definitely is not.

Moreover, when my children got an animal wrong, I didn’t tell them what the animal really was and leave it at that. I explained what mistake they had made — goats have tails that go up, regardless of how sheep like they look, for example.

With animals and little kids it is often not much more relentless drill — lots of practice with very clear pictures.

We tend to romanticise “authentic” learning without examining that a whole pile of it is actually explicit instruction. Just not taught by teachers and not in a classroom. Hence the massive deficit that children that don’t get this teaching at home have compared to those that do — those left to their own devices simply do not learn anything like as much as those that are actively taught by their parents.

And I take exception that academic maths is a “dead end”. It is for most students only to the extent that they won’t take academic maths as such. But we teach it primarily so that they can use it in other subjects.

I like my architects to understand the way forces work, so that their buildings stay up. I like my pilots to understand wind sheer. I like my accountant to understand exponential growth. I personally needed quite a lot of calculus in my Chemistry degree (and those with weak Maths really stuggled).

## Dick Fuller

September 30, 2020 - 6:46 am -I just read the retweets. Any reaction to “I tweet therefore I am” or “I don’t tweet therefore I …?

## Dick Fuller

September 30, 2020 - 9:06 am -I just read the retweets. Any reaction to “I tweet therefore I am” or “I don’t tweet therefore I …?

## Dick Fuller

September 30, 2020 - 9:55 am -Think we are on the path to to the usual school math argument, no reason to believe we will settle an argument that’s been around forever.

I’ll stick to the importance of conceptual understanding to comprehending significant math.

Like your undergraduate experience in chemistry ,mine in freshman physics led me to asses the importance of the math carried from school. Why did so many students leave study in technical fields after their freshman year? None of them would have been admitted unless they had thrived in school math. What was missing?

The first and strongest hint came from the physics instructor before the third test: “I will not look at your calculation, show me you understand the problem.” He was credible, he did physics: understanding problems does not come from school mathematics. What did it overlook?

The long technical career that followed did not suggest another place to look for the answer.

Thanks for taking the time.

## Luciana Qu

November 1, 2020 - 5:37 pm -Hi Dan,

I really love this post. As a grad student currently pursuing secondary math certification, I’ve come to really realize and acknowledge the exclusive and almost elitist connotations in math proficiency. Many of us grew up in math classrooms where teachers assume prior knowledge and carry on lectures that provide students assessable, algorithm-based knowledge; however, we are starting to see that shift in math classrooms where this may soon be less the case.

Exploration and discussion-based strategies (like your friend Michael employs) helps mediate that divide between experts and novices because it provides the opportunity for students of all proficiencies to contribute to the discussion and feel valued. I think, in this sense, that math then becomes ever so slightly more approachable. For students and perhaps wine-tasters alike.

## Jake Lee

November 10, 2020 - 9:23 am -Hi Dan,

I enjoy this post a lot. The correlations you described about how wine tasting is and its connection to mathematics is totally relatable. I have had math teachers for sure that just expect students to know and do the mathematics without any questioning. There is a lack of exploration for students to engage in the material like the wine “experts” you discuss that do not want to help “novice” wine tasters learn. That feeling of anxiety that you talk about in wine tasting is what most students feel when they are learning about mathematics. They fear of being wrong or being questioned.

I actually really enjoyed your point on the arbitrariness there is in wine tasting as there are in mathematics. “Wine Experts” do not go into details as to why some things are the way they are, nor do they allow others to question why. I think in sense, we should allow math students to question the certain arbitrariness in mathematics which promotes better mathematical discussions. That seems to be what your good friend Michael sounds like he is doing when he talking about wine. That balance of talking to both experts and novices can really help see the value in wine tasting. Overall, I really did enjoy this metaphor and how it relates to why certain students do not enjoy mathematics.