# Project-Based Mathematics

Does any one know of any country, state, school which has adopted PBM as the way to teach and assess mathematics in the final two or three years of secondary school (before sixth form)? I don’t mean the use of projects to enhance the lessons or help children learn and apply concepts, but the whole three years based on projects with, say, 60% of the final assessment based on class-based project work and 40% on a written exam, for the O level.

# Response to “Malta: new Learning Outcomes Framework”

Thank you Alexandre for taking an interest in the curriculum being developed for the Maltese schools. (As a matter of information, this curriculum is being developed by a consortium of foreign “experts” supported by a European Social Fund grant. What is shown on the website is work-in-progress, and one hopes that the final product will be a more coherent curriculum and banalities like the one you pointed out will have been removed.)
So, let me share my answers to the same question you ask, basically why does this draft curriculum contain such a statement: I can use equivalent fractions to discuss issues of equality e.g. gender. I agree with your two responses, namely mis-use of vocabulary and the strictures imposed by an Outcomes Based (OB) curriculum. But allow me to elaborate further.
In my view, the above statement would be banal whether one uses the term “equivalent fractions” or “similar fractions” or any other notion which extrapolates from 1/2=2/4=3/6=etc to anything having to do with gender equality. The problem, in my opinion, is that some people do not realise that, in science, we expropriate a word from everyday vocabulary to use in a context which does have some similarity to the everyday use of the word, but whose meaning becomes something technical which cannot be exported back to the everyday sense of the word.  I sometimes taught classes of Arts students who felt they needed to use some mathematical jargon in their essays (a few years ago the fashionable thing to do was to drop the words “chaos” and “fractal”). One of my usual examples of how wrong this is involved the use of the word “work”, as used in science and in everyday life. Translated into the context of curricula, the analogous banal statement could be something like: I can calculate the work done by a given force moving an object through a given distance and I can use this to discuss the conditions of work in factories and industry.
What surprises me when statements such as the one on gender equality are made is that while the ambiguity of language is appreciated outside science, in fact it can be a wonderful tool in the hands of a good writer, when transporting scientific vocabulary back into the everyday world, this variegated meaning of the same word in different contexts is sometimes forgotten. I have no explanation why this happens.
But another problem with curricula written in OB style and which could have a bearing on such wording is the necessity that the statements should be written in a way that the learning child would write them, for example, by starting the description of each outcome with “I can…” That sentences such as the one you quote about gender issues crop up is not, in itself the main problem, in my opinion. Such sentences can be edited out when reviewing the curriculum. The problem, as I see it, is that this style excludes the possibility that the curriculum contain concepts to guide the teacher but which the student would not likely be able to express. So take your improved statement of how mathematics can help understand social inequalities:
I believe in the power of mathematics and I am convinced  that comparing numbers (for example, salary)  reveals a lot about gender inequality (and other, frequently hidden,  inequalities in the world — just recall the Oaxaca Decomposition and its role in fight against discrimination of any kind).
It might be reasonable to expect a Level 5 student (aged 7-8) to express such a statement up to “gender inequality”, but hardly the rest of the statement, although the writer of the curriculum might very well want to make a reference to the Oaxaca Decomposition to give the teacher an example of a highly non-trivial use of mathematics in this context.
This OB format, I believe, betrays a fallacy about the teaching of mathematics, namely that teaching elementary mathematics to 7-year olds, say, does not involve deep knowledge of mathematics, certainly not deeper than what a 7-year old can express.
I look forward to reading other comments, especially by readers of this blog who are more familiar with OB curricula than I am.

# OBE

No, it is not the Queen’s Honours list. It stands for Outcomes Based Education, the latest pedagogical fad. The EU has practically adopted it as its official educational project. Which probably means that to bid successfully for EU funded projects you’d stand a better chance if you insert the OBE here and there.

But I am writing this because in the Wikipedia page Outcomes-based education

I was somewhat amused to (re)read a paragraph such as this:

In a traditional education system, students are given grades and rankings compared to each other. Content and
performance expectations are based primarily on what was taught in the past to students of a given age. The goal of traditional education was to present the knowledge and skills of an older generation to the new generation of students, and to provide students with an environment in which to learn. The process paid little attention (beyond the classroom teacher) to whether or not students learn any of the material.

and guess what reference they cite at the end of this paragraph? The
Constance Kamii and Ann Dominick 1998 paper on the “harmful effects” of algorithms in Grades 1-4. They also quote this gem from the paper:

“The teaching of algorithms is based on the erroneous assumption that mathematics is a cultural heritage that must be transmitted to the next generation.”

And whole countries build their educational policies on such “findings”.