consider a case of multi-digit multiplication: ‘49885320 x 12534959 = 625310440901880’. When one uses a pencil, paper and a long-multiplication algorithm to compute the answer to that sum, writing plays a constitutive role in the process of figuring out the answer, since the position of the numerals that one writes on the paper are part of how one arrives at the solution to the sum (p. 6).
So, indeed, using pencil and paper constitute part of the process of figuring out the answer. But, figuring out the answer is a kind of performance or behavior. It is a kind of performance that involves both cognitive and non-cognitive components. There are the brainy cognitive processes, such as multiplying together the rightmost elements, and the non-brainy, non-cognitive processes, such as making marks on the paper.
For a couple of years now, I have been thinking that extended cognition is more appealing as the 20th Centenary cognition/behavior divide that, e.g. Skinner and Chomsky agreed to draw, has faded away.
I first talked about this breakdown with respect to Rob Rupert's book back in 2009, but I've also got it as part of the talk I gave at Groningen workshop on the need for a mark of the cognitive. I'll also be talking about it again at the "Interfaces of the Mind" workshop in Bochum next month.