Making the Case
What is maths?
The basic process of maths is about problem solving:
- Define questions Think through the scope and details of the problem; define manageable questions to tackle.
- Translate to maths Prepare the questions as maths models ready for computing the answer. Select from standard techniques or formulate algorithms.
- Compute answers Transform the maths models into maths answers with the power of computers or by hand calculating. Identify and resolve operational issues during the computation.
- Interpret results Did the maths answers solve the original problem? Fix mistakes or refine by taking another turn around the Solution Helix.
We have a poster for use in classrooms that shows this in detail; we call it the CBM Solution Helix of Maths.
Why learn maths?
There are three main reasons why we want people to learn maths. First, there are technical jobs. Second, there's everyday living, particularly with the rise in the abundance and use of data. Third, what one might call logical mind training—being able to reason, whether with maths itself or with other things. In practice, these are neither reflected by the subject matter nor tethered to today's prescribed outcomes effectively. Therefore, we've rethought outcomes to target real-world needs, which has involved a much broader view of mathematical understanding and skills, as well as a systematic approach to fitting multiple dimensions of need together coherently. (For example, maths concepts, such as an equation, are split from maths tools, such as solving the quadratic. "Managing computations" and "confidence to tackle new problems" are integral to the outcomes.)
What's wrong with today's maths?
It's 80% a different subject from what is required.
Because computers mechanised computation beyond previous imagination and do calculating really well. Today's maths education spends 80% of the curriculum time gaining expertise in hand–calculation methods and algebraic manipulation. The curriculum is ordered by the difficulty of the skills necessary to complete the calculation, rather than the difficulty of understanding the complexity of the topic.
How can CBM fix this?
The CBM curriculum is unique in assuming computers by default, and so avoiding the need to learn most of the complex hand–calculation skills that were vital to our predecessors. The CBM curriculum has been written from core guiding principles that firmly focus on the needs of learners for jobs and everyday life in the near future.
How does the CBM curriculum differ from today's?
The new curriculum is problem centred versus the traditional mechanics–centred curriculum, so students are taught to solve problems using the tools available to them, rather than learning isolated, out–of–context skills, like completing a long division problem or calculating standard deviation. In today's curriculum, computers are mainly used to assist in the teaching of hand–calculation techniques.
This table shows you how some topics are contained within the problems:
|Traditional curriculum||Example modules within the CBM curriculum|
|Mean, mode, median||"Am I normal?"|
|Probability||"Do I know what I do not know?"|
|Averages, range and percentiles||"Are girls better at maths?"|
|Representing & selecting data||"How can I convince you?"|
|Distribution fitting||"How tall is the tallest woman in Estonia?"|
|Hypothesis testing||"Can I spot a cheat?"|
Is CBM a Computational Thinking curriculum?
CBM is the start of today's best structured program for engendering computational thinking—one that's principally around maths but applied to problems and projects from all subjects. Ultimately our aim is to build the anchor Computational Thinking school subject as we broaden CBM beyond being solely based in maths. Read more »
Why hasn't a CBM curriculum already happened?
It's a matter of an interactive process, an understanding of what needs to change on the ground and at the top, pressure from universities and industry, the ability to follow and change high-stakes assessments. It will happen differently in each country; the first countries to make the change will gain enormously.
"Get the basics first"
The key question is, the basics of what? Are the basics of photography loading film, or for that matter coating a glass plate with chemicals? No, in essence they are a creative way of representing the world, alongside learning about today's mechanics to execute that (which will change).
The essence of maths is the four steps of problem solving, and today's mechanics are calculating with a computer. It's understandable how the mechanics of calculating got confused with the essence of maths, because for centuries those mechanics were the main stumbling block that usually critically stopped its application. Now they're not, and it's fundamental to understand this difference between "mechanics of the moment" and "essence of the subject."
"Computers dumb maths down"
As with all tools, it depends upon how the computer is used. If the computer replaced the understanding of number, mental arithmetic or proportion, then the objection would be valid. However, if the computer is used to create processes, investigate parameters and solve problems, then this demands a skill set far more advanced than is currently being taught during the hand–calculation curriculum.
"Hand–calculating procedures teach understanding"
So why don't we teach students how to find square roots accurately by hand? Using a hand–drawn representation in the classroom is key to communicating the flow and logic of mathematical operations to younger learners. The foundation mental imagery constructed should be simple and efficient and allow the concept to be built upon securely. The extension to hand–calculation procedure—areas like long division, solving quadratic equations and statistics—was necessary due to the lack of an alternative method. Now there is an alternative.
Why take action now?
A number of factors have combined to make a powerful case for change.
While maths education has changed rapidly and improved in recent times, the real world has changed rapidly too, just along a different track, resulting in students who are prepared with skills that are no longer needed.
Access to computation is now so widespread, even in poorer countries, that students should not be discouraged from using it in their education. Coding can be done on a smartphone, online or even on a £25 Raspberry Pi.
In order to access the huge available computational power, even advanced professionals need the right interface to predict options, interpret meaning and offer suggestions about what to do. All of this can now be done for any student who wants to solve problems.
Download the Computer-Based Maths brochure today
Download the brochure now.