# Why meaningful math problems are defined out of online assessments

Dan Meyer said:

at this moment in history, computers are not a natural working medium for mathematics.

For instance: think of a fraction in your head.

Say it out loud. That’s simple.

Write it on paper. Still simple.

Now communicate that fraction so a computer can understand and grade it. Click open the tools palette. Click the fraction button. Click in the numerator. Press the “4″ key. Click in the denominator. Press the “9″ key.

That’s bad, but if you aren’t convinced the difference is important, try to communicate the square root of that fraction. If it were this hard to post a tweet or update your status, Twitter and Facebook would be empty office space on Folsom Street and Page Mill Road.

It gets worse when you ask students to do anything meaningful with fractions. Like: “Explain whether 4/3 or 3/4 is closer to 1, and how you know.”

It’s simple enough to write down an explanation. It’s also simple to speak that explanation out loud so that somebody can assess its meaning. In 2012, it is impossible for a computer to assess that argument at anywhere near the same level of meaning. Those meaningful problems are then defined out of “mathematics.”

via http://blog.mrmeyer.com/2012/what-silicon-valley-gets-wrong-about-math-education-again-and-again

I am sure there is a perfectly good reason for using fractions instead of decimals, but I can’t think of one. I don’t remember the last time I tried solving a problem using 3/4 instead of .75.

Like cursive writing and alphabetization, using fractions is a skill nobody needs.

Doug

Fractions and fractional representations are used constantly in algebra and other maths. There are countless instances when one might find a fractional division or ratio representation far easier to work with and think with than a strict base-10 redux into decimals… not to mention those times when you just don’t know a numerical value for part of the fraction. How would 1/a get expressed as a decimal?

Now back to the posts point, there are a few things that can make some things on twitter less awkward… But it’s not a universal solution. One could, for example, express 1/x as x^-1… Or the square root of one half as (1/2)^1/2… But for number lines or sets and such, there’s just no way to do it in ASCII naturally.

Come on Brian….when is the last time you called 1/2 a ration instead of a fraction….when in fact it is a ratio…..kids hate fractions because of all of the silly number exercises that you have to go through to do anything with them…. 1/a is a ration every bit as good 1/2. if you need to know what a is…solve for it….and that is where the computers strength shows through…lets do math which is about ideas and relationships….not 6th grade arithmetic…..and we should start exploring algebra as soon as possible!

I shared this article with one of our math writers. We disagree that meaningful math items are necessarily separate from online assessments. She wrote to me:

I would say from a SOLARO perspective that our interface is much easier in terms of how fractions are entered. As far as “defining meaningful problems out of math”, I’m not sure I agree. Any curriculum anywhere has always had aspects of the curriculum that are not assessable on standard tests. For example, any kind of outcome about understanding why a formula works must be assessed by teachers, in the classroom. It is an assessable concept, it is just not assessable on standard tests. It is the job of the teacher to teach and assess these outcomes. The rising prevalence of machine scored tests should not be an excuse to stop teaching students to solve rich problems like the kind discussed in the article. Standardized tests are a part of assessment, but they are not the be-all end-all. Students spend a whole year in their classrooms being assessed by their teachers; this is when this kind of assessment can be done.

Doug, you are partially correct. Fractions/ratios are needed for exact answers whereas decimals occasionally have to be rounded. For example, ask a middle school student to multiply 2/3 * 18. Turning 2/3 to a decimal students answers will produce an answer similar to 11.9999 when the answer is 12. I realize the answers are reasonably close but just trying to give you a situation where computation with fractions make more sense.

I think there are trade offs with every medium. I’ve worked with online high school courses that allow the student to rewind and repeat the lesson as often as they need to; and if a student gets a practice problem wrong, the computer provides an explanation of how to correctly solve the problem before the student tries another problem.

For at-risk learners, these are HUGE game changers compared to the traditional math classroom where students are reliant on their own poorly taken notes when completing homework; and where the student can conceivably complete a dozen homework problems incorrectly because feedback isn’t provided until the next day’s class. It takes 5-6 repetitions to learn a math concept but 12-15 repetitions to unlearn the wrong approach and relearn the correct approach.

As long as math classes continue to teach to the middle, and use archaic methods of instruction and feedback, the question of what to teach becomes almost irrelevant, IMHO.