Do people whose native languages are read right-to-left experience mathematical statements differently?

Question

When I see the equation

$$A = B$$

the first idea to occur to me is that $A$ can be transformed into $B$. Although of course

$$B = A$$

has the same content, to me it connotes rather that $B$ can be transformed into $A$. I imagine that this is because English is my native language and I read left-to-right.

Native speakers of Arabic or Hebrew, do you find that the opposite is true for you? Do you find that you experience written mathematics differently at all?

This is a psychology question, it is interesting though. Although, by definition equations are left-right symmetrical so there can't be any 'logical' difference. — Zach466920, Aug 12 '15 at 23:41
I also read L-to-R and do not interpret the expression $A = B$ asymmetrical in any way? — Krijn, Aug 12 '15 at 23:43
@Eli Rose, Since $=$ is almost always considered to be an equivalence relation, maybe you should use ~ instead. — Rocket Man, Aug 13 '15 at 00:02
In programming and in algorithms papers, a = b and b = a mean opposite things (because = is used to assign, rather than define, a variable). Additionally, in CS courses you'll often see notation like $2x^2 = O(x^2)$, while the reverse statement is meaningless. The latter example is really an abuse of notation, though (a more precise notation would be $2x^2 \in O(x^2)$) — BlueRaja - Danny Pflughoeft, Aug 13 '15 at 04:22
The notion of asymmetric interpretation of the = symbol is discussed in Issues with “equals”, where does this come from and how do I combat it? and How to cure students from the idea that root and squaring are identity operators? (on Mathematics Educators Stack Exchange). E.g., "A surprisingly large number of students don't know what the equals sign means. … they think it means "the next step" … or is an instruction to perform some operation." — Scott - Слава Україні, Aug 13 '15 at 06:30

BruceET · Accepted Answer · 2015-08-16T04:08:29.690

My native language is English, but I have taught many international students from countries that read right to left. My observation is that in very simple examples such as your $A = B$, it makes no difference at all, roughly for the reasons mentioned in Comments.

However for long displayed equations, it does seem to me that these international students are more likely to look at the end first. Sometimes this gives them valuable orientation as to motivation. I often suggest that all students browse through the whole equation to get an idea what is going on before plunging into the details of justifying each equal sign, inequality, or implication (from left to right).

On a related matter, many students in north Asia are taught to deal with the denominator of a fraction before the numerator. This has more to do with training and habits than with language differences. However, there sometimes seems to be a real advantage to looking at the denominator first. One example of this is in probability problems with combinatorial solutions: if both numerator and denominator count ordered arrangements, this is often more quickly seen by looking at the denominator first. Also, looking at denominators first is sometimes an advantage in something as simple as adding fractions that need a common denominator.

This is indeed more a psychology question than a mathematical one, but there may be important implications for math education. The relatively strong advantage of looking at denominators first, may give added credence to my claim that there is a (somewhat weaker) advantage in looking at the end of an equation first.

For everyone, I think the lesson is to 'size up' a math problem from several 'angles' before plunging in.

score 5 · Answer 2 · answered Aug 13 '15 at 00:25

Another point: Sometimes when you write $A=B$, it does have a different content from writing $B=A$. This is not emphasized in algebra classes, AFAIK.

For instance, $$(x+1)(x-1)=x^2-1$$ is "expanding", and $$x^2-1 = (x+1)(x-1)$$ is "factoring". However, they're the same equation. (Or they're isomorphic. Or something like that.)

score 3 · Answer 3 · answered Aug 13 '15 at 00:20

3

In the end, I think it's all isomorphic.

An example where the right-to-left reading is more natural than left-to-right is with the function notation $fg(x)$, where $g$ is applied first, despite being written after $f$. But we Westerners got used to that, right? 8-)

BTW, 2000 years ago, Chinese mathematicians did Gaussian Elimination, but they wrote the equations in columns, not rows (because Chinese is read top-to-bottom).

answered Aug 13 '15 at 00:20

Christopher Carl Heckman

4,458

Function composition -- very good example! – Eli Rose Aug 14 '15 at 15:05

score 2 · Answer 4 · answered Aug 13 '15 at 00:09

This may be of interest to you, maybe not so much for written language differences rather than more fundamental "thinking" differences that probably transcend language, but maybe not entirely transcending language. I've seen it first hand, sometimes in physics, multiplication of operators in group actions, and composition of functions, is sometimes thought in a way that gives expressions reversed compared to the way that more "traditional mathematics" would do it. Maybe someone can post an example, it's been a long time since I've seen those very strange physics notations so I can't give a concrete example off the top of my head, I just know they exist. =)

Do people whose native languages are read right-to-left experience mathematical statements differently?

4 Answers4