### Recent postsView all

 Problem: find exact ratio of are…1 Sep 19 Probability - Complement Approac…1 Jun 19 Worked Solutions - HL Paper 1 Ex…21 May 19 Euler's method on the TI-Ns…17 Mar 19 what is path of midpoint of a fa…24 Nov 18 Effective GDC Use #317 Nov 18 P.o.t.D.- 301 problems30 Sep 18 Effective GDC Use #219 Sep 18 Effective GDC Use #111 Sep 18 P.o.t.D.- 250 Problems6 May 18 Some fun with primes ... and Geo…18 Jan 18 primitive Pythagorean triples30 Dec 17

# GDC - visual check ... solution?

Tuesday 7 October 2014

Today I posed a fairly common type of 'quadratic functions' question to my first year Maths HL students. The question is also suitable for SL students although questions like this are less common on SL exams. It is a 'fair' question for both HL and SL students. The reason I'm highlighting it in a blog post came about because the way in which I and some of my students verified our answer to it brings up some interesting questions about how technology might blur the distinction between verification (checking answer) and proof (formal, analytic process of obtaining answer).

The ensuing brief discussion in class was an opportunity to ask an interesting question about knowledge. Are results (knowledge) obtained by means of technology any more or less reliable than that obtained without the use of technology?

OK, below is the question and its solution. But, like I said, what generated an interesting discussion was how some of us decided to use the dynamic features of our TI-Nspire CX handheld device (not 'calculator') to check the answer ... and whether this check could be considered a legitimate way to solve/prove.

Below is a short video of what we did on a TI-Nspire CX to check the answer.  If we skipped the analytic solution (shown above) and obtained the answer from the animated graph shown below, would that be considered a legitimate solution?