*The human mind is essentially one, but the directions it may take are many, and it is easy to see that people in general divide into those with a bent toward numbers and science and those who take naturally to literature, history, and the arts.*

-Jacques Barzun, Begin Here

[dropcap]I[/dropcap] suppose if I must choose, I will say that I am a literature, history, and arts person — that I am *not* a numbers person. I disliked math until about age ten, when it started to make sense to me. After that, I rather enjoyed it. But I always needed a good teacher or tutor, being disinclined to figure it out for myself. I was not a natural “numbers person.”

It’s easy for those of us who are not numbers people to get a little nervous about teaching math in our homeschools. Math was *hard*, we might say, and so who are we to think we could teach it?

While it’s true that we need to *know and understand* math in order to teach it, it is *not* true, it turns out, that only numbers people can teach math. In fact, Jacques Barzun rather questions the idea:

[T]he mind that feels at home with math is likely to lack the qualities that make a good teacher.

The way he explains it makes loads of sense. To numbers people, certain things are obvious which are emphatically Not Obvious to the rest of us. Numbers people often make great leaps when they try to instruct others {because, to them, the leaps are obvious}, and these leaps leave gaps in understanding for the average not-a-numbers person.

[O]mitting assumptions in teaching will produce in the student mind a gap in understanding that may last for years.

My guess is that a numbers person teaching a not-a-numbers person is much worse than a numbers person teaching another numbers person. The latter just might make giant leaps together and enjoy it immensely.

The problem Barzun is addressing lies in the fact that math teachers have to talk aloud — they have to explain what they are doing in words a student can understand. And since they are not *words* people, this tends to get them into trouble, especially when we’re talking about the rare situation of an extreme numbers person trying to teach something like elementary arithmetic.

But the point of this post is not to debate whether or not a numbers person could successfully teach math to a not-a-numbers student. Rather, it’s to encourage those of you who are discouraged by the fact that you are not a numbers person.

**What do you need to have in order to be a good teacher?** Barzun says that first, you have to have enough smarts to be baffled by Eduspeak. *You know*. That secret language they use at Teachers College? That’s what he’s talking about — that made-up language spoken only by experts.

Next, you need to have “a strong interest in some branch of learning.” Even better, a lot of branches. That’s his third criteria: interests *beyond* a particular specialty. Learn stuff, says Barzun:

In bearing, in manner of thinking and talking, a teacher should quite naturally appear to be

a person with a mental life, a person who reads books…

Imagine that. He’s prescribing scholé, or Mother Culture.

So. You’re not a numbers person? It’s okay. Barzun says you can teach math anyhow. In fact, it might be to your advantage because

teaching is par excellence the adaptation of one particular mind to another

and who can understand the child struggling with math better than one who struggled with the same thing, once upon a time? You have the compassion necessary to reach out to the child and help him along. Couple that with a decent curriculum, and you’re good to go.

## 23 Comments

EXACTLY,

You have the compassion necessary to reach out to the child and help him along. Couple that with a decent curriculum, and you’re good to go.

What a truth.

I’m proof of redeeming math teaching/learning with my non math daughters. We are both submitting to math, and going through it together, with a bit more vision from me -not much, I’m relearning, but not longer scared at what’s coming and I don’t know, because I know I can learn it, and she may even help-, (I can look at the upcoming lessons), happily, my girls are arriving at good math on their own, the good program does not allow me to pass on my pitiful notions and bad habits and wrong scripts. And a good program starts taking away your anxiety and showing you lovely things math shows and does!

Speaking of the beauty of math, have you ladies read Lockhart’s A Mathematician’s Lament? While I didn’t agree with all of it, it really made me think and changed my view of math.

Ooh! No! It’s going on my list. 🙂

Actually, you can read it for free online. 🙂 https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

Ooh, Nelleke! I could hug you.

Well, except for the thousands of miles between us. 😉

That actually makes sense. Yes, the author talked about how Israel was infected by “fuzzy math” even after it was passé in California because teachers were in US universities. He lead a campaign for Israel to adopt Singapore math instead of the latest innovation in constructivist math from education departments. It may end up being an update on the state of Israeli math education. I did end up switching to Singapore math for my daughter and she is doing much better. But, I suspect most of the difference from other things that we tried is that I am doing a better job of teaching all of the layers of understanding more than the particular curriculum.

I am a math person, at least through the lower math levels. I am also a pretty good word person, but I do struggle to explain math. Honestly I think it comes from being an extreme intuative. I just see certain patterns and I can’t explain how I got from A to D. I just…saw. So, my extreme un-intuative daughter was struggling with tens and subtraction (like 4-2) and ABAB patterns and we were really struggling. Then I found a book called Arithemtic for Parents by Ron Ahroni. The author was a math professor turned elementary math teacher who really worked at his craft. He opened my eyes to all of the ways in which I was making leaps that my daughter couldn’t jump. My goodness was that book helpful to a math person working with a less math person. Honestly, I am grateful to be homeschooling my daughter because it would have been hard for a classroom NOT to lose her. Between distractions and her poor visualizations, she would have struggled without extremely good teachers. I may not be extremely good, but at least I can stay put on a topic with no pressure to move ahead until we chip away at progress. Even if she never gets as far, I think she has a much better shot at a respectable foundation (and not saying obnoxious things in the progress.) I admit one of my pet peeves is people who scoff at math like anyone who is good at it has some magic power that they applied effortlessly. I think that math is on the whole, work, even for people who “see” it well.

So this book — Arithmetic for Parents — do you recommend it? I really don’t have many books on math, so I’m intrigued!

And I LOVE all your thoughts here, Lena! 🙂

Yes. It is one of those unknown gems. He does an amazing job of showing a lot of the nuance of arithmetic. It would probably be great for anyone who isn’t enthused about arithmetic as a liberal art to get more excited. And he does a great job of laying out processes and why they work like they do. He wrote the book for parents so they would be better at helping with math homework, so it really is meant to coach you as a parent to help with math. The author was a professor of math in Israel that went to teach arithmetic at a kibbutz and so he is clearly a super mathmetician who was charmed again by arithmetic when he went back.

I am totally buying this. It sounds so great! 🙂

Oh my goodness, Lena! Did you see there is a new edition coming out next month. I don’t normally spend that much on paperbacks, but I couldn’t resist…my birthday is in May, so I pre-ordered myself a gift, I guess. 🙂

So, I pulled the book out again last night after I wrote this. I forgot that he begins the book with a meditation on the beauty of math! My favorite homeschool book in general is the liberal arts by Jain and Clark. But arithmetic for parents helped me see more depth in arithmetic as a liberal art AND it helped me solve my daughters problems with interpreting even the simplest word problems wrong. Double benefit. I wonder what was changed for the revision?

It said something about covering current politics regarding math. Does your book have a chapter on that? Something about the way it was worded made me think that was the part that was either added or revised.

ps. I noticed that about the beauty of math and that is really what pushed me over the edge in buying it. 🙂

Yes! I now know that happened for a reason – as do all things 😉

Hi Brandy, I apologise for the long comment, but this post has really got me thinking, so I have a LOT to say …

I would say there are wordy number people and non wordy number people.

I am definitely a numbers person…..but I’m also a words person..…I also consider myself an arts person. I took maths, English and art for my A’levels (my focus subjects before university). I chose to continue with maths because, while I could develop my skills in art and english by myself, maths would come to a standstill. But you see I could’ve gone any way.

I think the key to teaching is valuing a need to understand and giving meaning to the subject. Learning is enhanced when things become meaningful . It is a struggle when the student feels like they’re in the dark. So I think in order to *be* a good teacher you have to be wordy – but that doesn’t necessarily mean that numbers people are not words people, which it seems (from your post) is what Barzun was implying; and you also have to see the obstacles.

My mind gets into a fog many times, (being an introvert I have lots happening in my head and its hard to organise). With new concepts, even mathematical ones, it may seem like I dont get maths. But it takes time for me to grasp ANY kind of idea fully. Anyway, I was blessed with many excellent maths teachers all the way up to college (high school) who were prepared to explain until I got it…..and when I got it, I got it. I also had a couple of books that my brother had at home, which explained maths and physics in really fun, interesting and living ways…In a way that made us realise that maths and physics were happening around us.

I reached university……and now I was taught by university professors, you know the ones that make GREAT leaps. I could no longer see connections…and now I began to feel like I was in the dark…that awful feeling that tells you you don’t like this subject or that you’re no good. Suffice to say, I didn’t do as well as I had done, pre-uni. But! I still loved maths, and I knew it was more to do with the teaching than myself. I went through school bored with the monotony of geography, history and biology, and feeling like I just didn’t get them…while now I’m simply amazed at what I discover in these subjects. While I was younger, I always thought I didn’t like these subjects, now I realise it, was more to do with how the teachers didn’t use their words meaningfully enough, and so topics seemed so abstract.

After uni I ended up as a maths teacher (and an arts teacher) (and I couldn’t help giving the children read alouds) (and I wanted to link every subject to every subject, because connections were important, if you wanted to make sense of things). I valued that need to understand, having experienced being a numbers person in the dark in MATHS CLASSES!!! and also having had good teachers who persevered. So in ageement with points the other commenters made, I will keep on explaining and reexplaining any concept to a student, approaching from different angles until he/she gets it. Because I don’t believe these concepts are beyond anyone (“barring specific learning disabilities”), but I accept that they may presently be in a little fog.

You make a lot of sense, HC! 🙂 And also: I do think that Barzun, at least in that particular essay, fails to point to an ideal of being a crossover. While we all have natural strengths and weakness, I really do think that being BOTH is ideal!

And another thought…while I’m comfortable as an adult with classifying myself as a “word” person rather than a “math” person, I’m really cautious about classifying my children too soon. I don’t want them ever to think “math is just not my thing” and use it as an excuse. Math is hard, but I’m confident that anyone (barring specific learning disabilities) can learn it. Some might have to learn it slower than others, and some might need to approach it in a more creative way.

This is good for me to know as a teacher, too…even though I am not a math person and don’t know enough math right now, I can still learn whatever I need to know in order to guide my children.

Amen amen, Nelleke! I completely agree with not classifying our children young, unless perhaps it is so obvious it can’t be avoided. Even then, I try to resist labeling my children, even if it’s true!

This post immediately brought The Spark, by Kristine Barnett, to mind. I remember being struck by a portion of the book (why, oh why, didn’t I write it down?) where she talks about how her son (a mathematical genius) is very good at explaining math to people who don’t understand it. She said it was because he understands that there are many ways to approach math. Where most teachers only have a few ways to approach any given problem, he has many more and just keeps trying different ones until a person “gets it.” So a patient math person may be a good teacher.

(This was a very interesting book, by the way. Have you read it? I couldn’t put it down, quite literally…which may or may not be a good thing when a person has multiple children under six. lol.)

That is super interesting! And no, I haven’t read the book, but I think I need to, from the sound of it. 🙂

I remember one time reading about a sort of “bell curve” of genius. So on one side, you have those who can teach it, but have a hard time understanding. In the middle, you have those who understand really, really well, but can’t really explain it to others. On the far right, you have those who fully understand AND understand well enough to explain to others. Sounds like her son is on that side of the curve! I believe Einstein was like that — totally a genius, but able to explain to the common man. That is truly a gift! ♥

Love this! I am not a numbers person (though I got As in math). I am a letters person. For my first three years of teaching, I taught middle school English and history. I didn’t understand why some kids didn’t “get” it. Then, my administration told me they were switching me to math and science. I cried. But then I loved teaching middle school math! When it didn’t make sense, I understood why it might not make sense. I was able to teach concepts the numbers-brain way as well as the letters-brain way.

I love this, Mariel! I also love how God directing our lives often makes it better than we think it is going to be. 🙂