{"id":4878,"date":"2010-07-23T09:49:31","date_gmt":"2010-07-23T09:49:31","guid":{"rendered":"http:\/\/scienceblogs.com\/principles\/2010\/07\/23\/real-math-doesnt-use-calculato\/"},"modified":"2010-07-23T09:49:31","modified_gmt":"2010-07-23T09:49:31","slug":"real-math-doesnt-use-calculato","status":"publish","type":"post","link":"https:\/\/chadorzel.com\/principles\/2010\/07\/23\/real-math-doesnt-use-calculato\/","title":{"rendered":"Real Math Doesn’t Use Calculators"},"content":{"rendered":"

The Dean Dad is worried about remedial math<\/a>:<\/p>\n

\n

In a discussion this week with someone who spends most of her time working with students who are struggling mightily in developmental math, I heard an argument I hadn’t given much thought previously: students who have passed algebra and even pre-calc in high school frequently crash and burn when they hit our developmental math, because the high schools let them use calculators and we don’t.<\/p>\n

[…][P]art of me wonders if we’re sacrificing too much on the altar of pencil and paper. It’s great to be able to do addition in your head and long division on paper — yes, I know, I’m old — but is it worth flunking out huge cohorts of students because their high schools let them use calculators and we don’t? <\/p>\n<\/blockquote>\n

(The ellipses replace a bit where he expresses “uninformed sympathy” with professors who don’t allow calculators. The cut is for length, not to distort his argument)<\/p>\n

The reason why many math departments– including the one where I work– either do not allow calculators or greatly restrict their use is very simple: Real math doesn’t use calculators. If you are going to do math or science at a college level, you need to be comfortable with problems that can not be solved by punching numbers into a calculator.<\/p>\n

<\/p>\n

I’m trying to think of a good analogue from the humanities or social sciences. I think it’s reasonably accurate to say that the notion that math at the college level involves calculators is rather like the belief that history at the college level is about memorizing the names of the kings of England, or that English at the college level is about parts of speech and metrical forms, or that economics at the college level is about learning to balance your checkbook.<\/p>\n

The ability to do numerical operations is an important background skill for math or science, but it is not by any means the core of the discipline. Most of the time, people in the mathematical sciences are working with equations as abstract objects; the numbers are secondary. <\/p>\n

The reason for restricting the use of calculators in introductory math and science classes is that calculators will be no help in higher math classes, and can be an active impediment to learning. The sooner you can start breaking students of their fixation on numerical manipulation and move them toward being comfortable with algebra and other more abstract representations, the better.<\/p>\n

If that’s true, why do high schools math classes allow calculators? For the same reason that high school English classes continue to have vocabulary tests– high school is about establishing the minimum level of competence needed to function as a citizen in modern society. The ability to do math with a calculator is the absolute rock-bottom minimum skill required for modern society– I think it would be good to have students come out of high school being familiar with algebra (algebra is like sunscreen<\/a>), but I’ll settle for them being able to do math on a calculator.<\/p>\n

College level work is supposed to be different. It’s preparing students to be able to function at more than the minimum level of competence in a subject. Accordingly, college-level classes will force students to develop the skills they would need to move up to higher level classes, or at least allow them to determine that they are not sufficiently interested in the subject to develop the necessary skills, and major in something else.<\/p>\n

That’s why introductory college math classes often restrict the use of calculators, and why I have on occasion done the same with intro physics classes. If you’re going to do physics beyond the level of Giancoli<\/a>, or math beyond the level of introductory calculus, you will absolutely need to be able to do abstract operations that a calculator will not help with.<\/p>\n

Now, you can ask whether what’s appropriate for introductory classes is really appropriate for remedial<\/em> classes, which is the real context. If the goal is only to bring those students up to the minimum level of competence they should’ve had coming out of high school, then I suppose not. But to the extent that those classes are supposed to be catching students up to the point where they’re prepared to do college-level math, I think it is appropriate– it’s the equivalent of having a really good high school class that gives students a leg up on their first year of math, only, you know, a year late. My own inclination is to say that classes at the college level– even remedial classes at the college level– should aim higher than the minimum acceptable level, so I’m on board with calculator bans, even at the remedial level.<\/p>\n","protected":false},"excerpt":{"rendered":"

The Dean Dad is worried about remedial math: In a discussion this week with someone who spends most of her time working with students who are struggling mightily in developmental math, I heard an argument I hadn’t given much thought previously: students who have passed algebra and even pre-calc in high school frequently crash and… Continue reading Real Math Doesn’t Use Calculators<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,13,9,7,11],"tags":[],"class_list":["post-4878","post","type-post","status-publish","format-standard","hentry","category-academia","category-education","category-math","category-physics","category-science","entry"],"_links":{"self":[{"href":"https:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/4878","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=4878"}],"version-history":[{"count":0,"href":"https:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/4878\/revisions"}],"wp:attachment":[{"href":"https:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=4878"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=4878"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=4878"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}