Teaching kids real math with computers/calculators

[Dan]

The idea of teaching kids "real maths" is an old one, the most recent attempt introducing CAS and expecting kids to learn algebra by getting a machine to do it for you. Here is my response to a similar post about a fortnight ago:

Interesting discussion. As a teacher of mathematics for the last 10 years, my 2 cents worth:

Memorization of times tables an absolute must. As someone mentioned, expecting students to fill in the gaps in their knowledge with a calculator does not work. e.g. 99,000/4 student says 396,000 and doesn't bat an eyelid (pressed * instead of /). Or (6+4)/2 = 8 (enters it left to right with no consideration of order of operations). You are laughing but I see this ALL THE TIME.

A 12-year old I am tutoring took over 10 minutes to do his timetables when I started with him. (used a HP50g program to time him). A girl around his age was doing it in under 3 minutes, I've got him now doing it in under 4 minutes. We are doing fractions now and if his timetables skills were still bad if would be impossible to teach. 3/4 + 1/3, "well you find the lcd and find equivalent fractions. How many times does 4 go into 12?" I've had students stare at me blankly. "O.K. use you calculator". 3! "O.K. multiply the numerator by 3" (goes for calculator again). "Now do the same for 1/3". The student keeps going for their calculator, gets lost in the steps, asks "hang-on what are we trying to do?" It's ridiculous. When we get to algebra they are completely lost.

People thought CAS was the answer, focus on problem solving instead of tedious algebraic manipulations but it doesn't work like that.