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 (http://computerbasedmath.org) 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
Variance for a probability distribution (easier to understand)
Variance for a probability distribution (easier computations)
Standard deviation for a probability distribution
[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?