Computer Based Math Redux

I’ve posted before about Conrad Wolfram’s efforts to remove calculation from the curriculum and make everything computer based. There is now a website devoted to the initiative ( and Conrad Wolfram’s blog recently announced their first country interested in taking up the curriculum: Estonia.

Estonia isn’t too surprising a choice; they recently put programming in the standard curriculum starting at first grade.

However, they’re not diving into axing algebraic manipulation from the curriculum yet; rather Computer Based Math (abbreviated CBM) is planning to “rewrite key years of school probability and statistics from scratch”. This is a reasonable first step given statistics is often taught computer based or at least calculator based these days (my colleague who teaches AP Statistics next door does so) and it does feel very silly to work through a passel of “figure out the standard deviation” problems by hand.

However, I’m going to play devil’s advocate again with a thought experiment. Since algebraic manipulation is not being removed at this time, these questions aren’t going to be applicable to Estonia yet, but presuming Computer Based Math continues working with them it should come up soon.

Suppose you are in a curriculum where you are used to algebraic manipulations being done by a CAS system. You are learning about statistics and come across these formulas:

Mean for a probability distribution
\mu = \Sigma[x \cdot P(x)]

Variance for a probability distribution (easier to understand)
\sigma^2=\Sigma[(x-\mu)^2 \cdot P(x)]

Variance for a probability distribution (easier computations)
\sigma^2=\Sigma[x^2 \cdot P(x)] - \mu^2

Standard deviation for a probability distribution
\sigma=\sqrt{\Sigma[x^2 \cdot P(x)] - \mu^2}

[These are incidentally off page 208 of Triola’s Elementary Statistics, 11th Edition.]

What is necessary to use the formulas conceptually? What understandings might someone lack by not having experienced the algebra directly? Is it possible to understand the progressive nature and relations with these formulas just by looking at them? Is it necessary (to be well-educated in statistics) to do so? If it is necessary, what specific errors could somebody potentially make in a statistics calculation? Could this be mitigated by the text? Could this be mitigated by steps taking during the CAS portion of the education that while not leading to lengthy practice in “manipulate the algebra” problems will still allow understanding of the text above?

3 Responses

  1. Reblogged this on evangelizing the [digital] natives and commented:
    I go back and forth on the importance of calculation in my instruction. It only bugs me when kids don’t even know their basic multiplication.

  2. Hi, Jason,

    I’m a proponent of the movement to make everything computer based. I could write a thesis on why, but let’s just say my personal experience as a statistics instructor made me realize that 99% of students just want to be able to get the answer, not understand why. The TI-83 is a Godsend to these students…its wonderful to see the light in their eyes when they realize they don’t actually have to calculate anything! Now, if they were to be statisticians (I have yet to come across a prospective statistician in my community college classes), then the answer is yes — they should know the reasoning and the conceptualization behind the “answer.”

    I came across your blog via David Wees, and as a fellow mathematics educator I thought you might be able to help in spreading the word about an educational TV show for preteens about math that we’re putting together. “The Number Hunter” is a cross between Bill Nye The Science Guy and The Crocodile Hunter — bringing math to children in an innovative, adventurous way. I’d really appreciate your help in getting the word out about the project.

    I studied math education at Jacksonville University and the University of Florida. It became clear to me during my studies why we’re failing at teaching kids math. We’re teaching it all wrong! Bill Nye taught kids that science is FUN. He showed them the EXPLOSIONS first and then the kids went to school to learn WHY things exploded. Kids learn about dinosaurs and amoeba and weird ocean life to make them go “wow”. But what about math? You probably remember the dreaded worksheets. Ugh.

    I’m sure you know math is much more exciting than people think. Fractal Geometry was used to create “Star Wars” backdrops, binary code was invented in Africa, The Great Pyramids and The Mona Lisa, wouldn’t exist without geometry.
    Our concept is to create an exciting, web-based TV show that’s both fun and educational.

    If you could consider posting about the project on your blog, I’d very much appreciate it. Also, if you’d be interested in link exchanging (either on The Number Hunter site, which is in development, or on which is a well-established site with 300,000 page views a month) please shoot me an email. We’re also always looking for input and ideas from other math educators!

    Thanks in advance for your help,


  3. I also use Triola’s 11th. I ask my students to do one standard deviation calculation without technology (the sample SD of three numbers) so that hopefully they see the process, but then afterwards they get to use technology. By the way, I think Triola has the best sense of humor among math textbook authors I have ever seen – I can’t find the page reference right now, but he does an experiment that he says is “more fun than humans should be allowed to have.”

    Jerry Tuttle

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