Teachers’ FAQ: What is BrainQuake’s Primary Goal?
From time to time, I use this blog to provide answers to various questions we get from math teachers.
Our primary goal (“a primary goal” would arguably be more accurate, but read on) is to provide supplementary math education materials that Break the Symbol Barrier ™.
“Symbol barrier” is a term I introduced in my 2011 book Mathematics Education for a New Era. It refers to the research finding reported in the landmark 1993 book Street Mathematics and School Mathematics, by Nunes, Carraher, and Schliemann
In the Nunes et al book, the authors reported a field study conducted in a street market in Recife, Brazil. The researchers (posing as shoppers) presented teenagers working on their parents’ stall with purchases designed to require complicated mental arithmetic to work out the total cost and the change. To many people’s surprise, the kids averaged 98% accuracy calculating in their heads at the noisy stall, but scored a dismal 37% when later presented with the same math problem written on paper in the familiar symbolic form, in the quiet comfort of their home. Their dificulty was not that they could not “do the math”; it was having to do it using traditional notation. In other words, they failed the linguistic aspect to the problem.
BrainQuake’s puzzles are designed to present problems as (digital renderings of) “physical” ones, to be solved by “physical” manipulation, so they can master the mathematical thinking separately from (and indeed prior to) mastering the formal notation and the symbol-manipulations required to solve the problem that way. So we split the task of mastering the mathematical problem solving into two parts. Divide and conquer.
We also build tools to help students link their solution in the “physical” mode to the solution using traditional notation. But that’s a story for another post.
The puzzles we create are complex performance tasks, presented as digital puzzle games, with the game structure being a “concrete” presentation of a particular mathematical construct. The puzzles are based on the napkin-sketches mathematicians tends to produce when asked to illustrate how they themselves solve those problems in their head. In other words, they are (enhanced) depictions of how mathematicians do math.
These puzzles are a mathematical equivalent of musical instruments: a student learning music can make progress by sitting in front of a piano and “playing” or exploring, either on their own or with a teacher on hand; our puzzles provide mathematical instruments. As such, they can be used in a wide variety of ways.
An alternative analogy to musical instruments is that our product provides a more user-friendly interface to mathematical thinking than the traditional formalisms (much as the Mac interface transformed computers from technical tools for experts to a consumer product used by all). So our product functions like the Brazilian market stalls in those famous Street Mathematics studies.
BrainQuake began with a simple question: could we design and create “instruments on which you can play math” that, if used as supplements to traditional teaching, would result in significant learning gains? An independent university study led by Stanford University Professor Jo Boaler, published in 2015, showed that we succeeded.
[For a less detailed summary of the Boaler study, but which provides some background, see here.]
