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I am looking for studies which compare students who did not receive mathematical education beyond basic mthematics and those that learned maths upto introductory calculus, with the assumption that both groups recieved similar education in other subjects such as social sciences and natural sciences uptil average high school standards. Has it been found that there is a quantifiable difference in understanding, analytical ability etc between the two groups? In other words, what evidence is there that learning maths beyond the basics has benefited them at the stage of just having completed high school?

I understand a basic science curriculum in this case to include a little mathematics, which both groups should know, and for this purpose a notion of solving linear equations (and hence elementary algebra) besides arithmetic is included in basic mathematics. However, there is no trigonometry or geometry in a basic mathematics course, and in general a person learning basic mathematics knows no more then is the essential to understand basic science.

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Considering that majors in fields where higher math is a prerequisite (CS, EE, Physics, Math etc.) earn significantly larger salaries, I don't think there's any doubt that it benefited them. – nbubis Sep 1 '13 at 5:45
That is not what I meant. I mean whether there is a benefit uptil the stage of end of their high school? Have they been found to have better understanding, better analytical abilities etc at that stage? Also, I am really looking for empirical studies. – Shahab Sep 1 '13 at 5:52
@Potato: Not only quantitative ability, but also qualitative abilities such as decision making, critical thinking etc. In general what does mathematical training give exclusively (other then a knowledge of the subject), which a non mathematical trained person doesn't have? – Shahab Sep 1 '13 at 6:19
Now with Math Educators active, perhaps you should ask the moderators to migrate this question there. – Asaf Karagila Apr 20 '14 at 7:30
Shahab, since this is not an option, perhaps you can cross-post it to the other site. – Asaf Karagila Apr 23 '14 at 4:41

This has been studied in Sweden, but the answer sort of begs the question, and I'll try to simplify the problem:

There appears to be a strong correlation between gradelevel in math and grades in all other subjects, especially for students in the earlier years of their education. Some have used this to support the argument that math somehow creates capacity within areas, in the sense that math somehow increases a students ability to complete assignments everywhere.

Now, the counterargument to this is that, students with a high grade in math have practically always had high grades in math, and math serves more as an indicator of how well a student is able to adapt to the social institution of "Schools". Studying is a skill in itself, and knowing how to study will infer math. Also, socioeconomic background play a huge role in this as well.

In a nutshell, the problem can be concluded with the following: noone (to my knowledge) have succesfully separated "math" as the single distinguishing factor in the sense you ask for. It begs the question in the sense that, does math make you smarter, or are you already smart since you know math? (Note: I use the word "smart" idiomatically here, I'm not trying to spark a debate).

You are however wrong in assuming that social science doesn't require math. I've got 2 degrees, in philosophy, a teaching degree in math as well as philosophy and currently working on my economics degree. If you ask me, the number one mistake social scientists make is somehow related to math. Most of the time, statistical data is missrepresented or missunderstood, even on elementary level, such as percentage.

I can give several examples out of the top of my head; is there a way to measure "justice"? Or "equality"? What about "influence"? Most mathematicians stay clear of it since it's not quantifiable, but many papers on the subject actually try to quantify it, and make broad assessments based on these quantifications.

PS. Yes, this is probably the wrong forum to discuss this.

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