Book Review: The Math(s) Fix - Part 2 of 2
In the last instalment, I reviewed Conrad Wolfram's diagnosis of what is wrong, or outdated, about Maths education today. In this second part, I will review his "Math(s) Fix".
Context is King!
A concept that recurs throughout this part of the book is that of "context-based learning". In fact, the program Wolfram proposes presents all materials in one of two kinds of contexts:
- Primary Contexts: These are key areas that will remain applicable for students even after leaving school. E.g. "When to take up insurance".
- Secondary Contexts: These are contexts that are useful to engage students in learning mathematical tools but that are not likely to be of use to them beyond their schooling.
The benefits of this context-based learning are many, but here are two:
- when the contexts are as real as possible, the data will be messy. This provides an incentive to use, in the classroom, the tools that are used in the real world, namely computers and software.
- It teaches the student to choose the tools that are most appropriate for the problem. In the current, tool-centric approach, exercises are designed to practice the skill that has just been taught. Students know this and don't develop the ability to look at a problem and then reach for their toolset for help.
How do you assess it?
I am sitting by myself with the room door closed. Yet, I can hear the voice of a notional objector asking: "But how would you assess this?" Wolfram's answer is that, given the use of good tools, assessments can be richer. E.g.: "Adjust the dynamic parameters of a model". Furthermore, different students can be allocated different data sets. I wholeheartedly agree.
The 5 groups
In the Victorian curriculum, Maths is broken up into three content areas: Number and Algebra, Measurement and Geometry, Statistics and Probability.
Wolfram's computer-based maths is broken into five "groups":
- Data Science
- Information Theory
- Architecture of computation
You can see how modern applications of mathematics are highlighted here.
Instead of our "Achievement Standards", Wolfram proposes a list of outcomes, summarised on page 104 of the book and also here. Some of these outcomes fulfil the purposes of the 4-part process discussed in part 1: Define, Abstract, Compute, Interpret.
Below are the outcomes that correspond to the second part, Abstract:
Best test of understanding
The proposed computer-based core computational subject (Say this 10 times before bed for a week!) equips the students with the ultimate test of understanding: Program your solution! We all know that a great way to test that you understand something is to try to explain it to someone who doesn't have prior knowledge of the concept. The act of writing a computer program is precisely the act of writing explicit instructions for the computer to carry out.
This reminds me of a time that I took 3 of my year 10 students to a teacher conference where they presented some of their work in a computing course. When asked about the benefits of learning computer programming, one of them said something like:
"When you have to write a computer program, you need to make sure that you understand every step of your solution to the problem because you have to teach that step to the computer."
Will we get there?
Some places probably will. Estonia seems to have committed to trialling the specific program laid out by Wolfram. I am doubtful about this happening in Australia any time soon. We have been trying to incorporate algorithms and coding within maths and, anecdotally, the results are not so encouraging. The trouble is that it is still possible to have a B.S. with a major in Mathematics without much exposure to programming. If I were standing on a soap box right now, I would shout: "Introduce a freshman year in our universities". Luckily, I am sitting down and feeling quite relaxed so I won't shout anything!
Wolfram's solution is to have the program specified to the extent that activities are fully scripted. He envisages live coding sessions being run online with a teacher who is competent in this skill. I am not convinced that a teacher of the existing mathematics subject will be OK with delivering a considerably different course, one with which they are not comfortable. The fact that they will be supported with resources, training and online help will not compensate for their current status of mastery. People's identity as a highly competent and senior teacher will be under threat.
I hope that I am wrong but I fear that it will take a considerable shock to shift us towards a modern, computer-based mathematics subject.