Why Is Reading Math Different from Reading Text?

[jack476]

Normally I have very good reading comprehension, but when I try to read mathematical statements I'm finding that even though I know what they mean it feels like they don't register fully.

When you read math, do you read it to yourself translated into plain English? Or is there another way I'm supposed to think about it?

 

[jim hardy]

I have to reproduce with pencil and paper every math step that an author takes.
Else it's "in one ear and out the other" , nothing sticks in between.

It takes some rigor to train the mind to associate the right "feelings" with words.Here's what Einstein said on the subject:

Here's a longer extract from Einstein's answer:

"(A) The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be "voluntarily" reproduced and combined. There is, of course, a certain connection between those elements and relevant logical concepts. It is also clear that the desire to arrive finally at logically connected concepts is the emotional basis of this rather vague play with the above-mentioned elements. But taken from a psychological viewpoint, this combinatory play seems to be the essential feature in productive thought--before there is any connection with logical construction in words or other kinds of signs which can be communicated to others.

(B) The above-mentioned elements are, in my case, of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will.

(C) According to what has been said, the play with the mentioned elements is aimed to be analogous to certain logical connections one is searching for.

(D) Visual and motor. In a stage when words intervene at all, they are, in my case, purely auditive, but they interfere only in a secondary stage, as already mentioned.

(E) It seems to me that what you call full consciousness is a limit case which can never be fully accomplished. This seems to me connected with the fact called the narrowness of consciousness (Enge des Bewusstseins)"

From "A Mathematician's Mind, Testimonial for An Essay on the Psychology of Invention in the Mathematical Field by Jacques S. Hadamard, Princeton University Press, 1945." in Ideas and Opinions.

I suppose there are people who think in equations. I envy them.

 

[symbolipoint]

Normally I have very good reading comprehension, but when I try to read mathematical statements I'm finding that even though I know what they mean it feels like they don't register fully.

When you read math, do you read it to yourself translated into plain English? Or is there another way I'm supposed to think about it?

Not sure what you mean. Do you refer to the discussion passages or to symbolism? Learning to read the symbolism is a lengthy process and requires dedicated practice and exercise and study. A person will soon enough learn to read some of the symbolism very quickly. SOME of this relies on the ability to see patterns, when they occur.

 

[symbolipoint]

Normally I have very good reading comprehension, but when I try to read mathematical statements I'm finding that even though I know what they mean it feels like they don't register fully.

When you read math, do you read it to yourself translated into plain English? Or is there another way I'm supposed to think about it?

One more comment:
I myself rarely, maybe never, translate any algebraic or arithmetic expression or statement into English from the symbolism. I READ what I see, in symbols!

 

[NascentOxygen]

When you read math, do you read it to yourself translated into plain English?

I read maths aloud (in my mind) as precisely worded perfect English grammar, and I encourage my students to work towards this as their goal. It has served me well through both under- and post-graduate Maths studies.

 

[jim hardy]

I read maths aloud (in my mind) as precisely worded perfect English grammar, and I encourage my studients to work towards this as their goal. It has served me well through both under- and post-graduate Maths studies.

Now there's exemplary rigor. Bravo, Sir.

 

[symbolipoint]

Now there's exemplary rigor. Bravo, Sir.

I read maths aloud (in my mind) as precisely worded perfect English grammar, and I encourage my students to work towards this as their goal. It has served me well through both under- and post-graduate Maths studies.

Given enough study, one can read the symbolic expressions or statements without translation. This becomes visual.

 

[sonofagun]

Normally I have very good reading comprehension, but when I try to read mathematical statements I'm finding that even though I know what they mean it feels like they don't register fully.

When you read math, do you read it to yourself translated into plain English? Or is there another way I'm supposed to think about it?

New topics always involve new notation/symbols, or a rehashing of familiar notation/symbols. Quite often you will have to stop and think about what it means, and translate it to plain English before reading further. But, like the poster above said, it becomes visual given enough study. A vague picture should emerge once you've seen an idea expressed enough times.

Read slowly, and reread, then reread again. If the idea doesn't register fully, ask yourself, "what does this mean?". Translate it to plain English if you need to.

 

[jtbell]

Given enough study, one can read the symbolic expressions or statements without translation.

I'm a native English speaker, but I can read simple to moderately complex German without thinking about it. Beyond a certain level of complexity, I have to stop and "translate" it in my head. Similarly, I can simply read most math associated with introductory to intermediate-level undergraduate physics. Beyond that, especially with more abstract or concise notations that I don't use regularly, I have to stop and think about it, or expand it into something more "verbose", e.g. writing out a matrix product term by term.

 

[Daverz]

Yes, I try to read math as spoken language, though not any more precisely than needed by context (I don't try to read it ala Victor Borge). That's why it annoys me when an author introduces a symbol without giving it a speakable name.

 

[Overt]

Starting out I think you should absolutely convert it to English in your head. It slows you down and makes you notice every detail in the equation. It also makes it easier to communicate mathematical ideas to someone in a conversation! Rarely the ideal way to do it but sometimes you have to.

For me, writing out all the steps and speaking it in my head at the same pace works well. More laborious but much easier than opening up the book again later.