Since I began teaching Physics in a University I've observed several patterns in our students far background that reflect how did some of them acquire certain skills and concepts, specially in the mathematical domain. As a father of two children that are now building up their background knowledge, I recognise the origins of some of these patterns.
A lot has been written about the hierarchical structure of mathematics knowledge, the impact of a missing link in its concept chain, and the not always successful relationship between teenagers and abstract thinking.
We are used to see how students in elementary school are told to calculate a huge number of arithmetic operations. After years of memorizing multiplication tables and doing long divisions, they are introduced actual math, starting with algebra and geometry.
There's a point in the chain where the use of calculators takes place in the curriculum. For some students this event constitutes a kind of liberation because of their lack of computational skills. The role of calculators in the classroom has always been a source of some controversy and in fact there is little correspondence between the use of this tool in different countries or even between different educational centres in the same region. The root causes of disagreement are however unclear.
Although there is no doubt that technologic tools must play a determinant role in children education, in my opinion, not enough efforts have been done to address the challenges of integrating technology for teaching and learning in the schools. School policies, rigid time-constrained evaluation strategies and the shortage of economic resources barely contribute to the development of assessment techniques that focus on student thinking through an appropriate use of modern tools.
Math teachers face the noticeable difficulty to engage teens in approaching and experiencing the world through an entirely different way of thinking. But obvious barriers should not be, nowadays, an excuse to make a difference between "math" and "non-math" persons. It's striking how a society where most decisions tend to be made based on quantitative facts still gives support to innumeracy.
Calculators, in all its modern forms, are by far the first tool children encounter that extends their computational horizon. A calculator can be used as a gadget for putting away tedious numerical operations or it could serve as a bridge to other more powerful analytical tools.
It's common that children begin using calculators in the school as they are introduced in applied sciences like physics or chemistry. The problem could come around if the calculator is only the way to quickly reach a numerical solution of a problem, allowing children to be given a lot more of homework and apply repeatedly more and more memorised formulae avoiding any type of analysis of the calculations in the way.
In academic training math is always ahead. When children meet physics for the first time, the math involved has been acquired years ago; this time gap remains in fact until higher education. Little arithmetic is needed for introductory physics at the first level. But the fact that a teen has acquired multiplication and division long ago doesn't imply at all that it is easy for a teen to perceive the difference between 1 meter × 2 and 1 meter × 2 meter, or between 1 meter ÷ 2 meter and 1 meter ÷ 2 second, if no one guides the abstraction process.
It's important not to deprive math of its capacity to look at near reality from an open point of view, what we call abstract thinking, specially in the compulsory stages of education. The ability of filtering great amounts of information, selecting only the aspects which are relevant for a particular purpose and deriving general rules and relationships should not be a gift restricted to a specific population group. Therefore, it's interesting to explore different approaches to the magnitude quantification and operation in basic applied sciences, when exposed to the children, further than the merely verification of the result of using a formulae pack.
With this motive in mind, I spent a couple of summer holidays in developing a mobile tool my kids could work with, first as a pocket calculador, and progressively as a training bench for more sophisticated software. Thinking of helping them to master the app, I realised a blog could be a good idea just to begin with.