[A 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.
De Morgan Gazette 
It is is really like a nightmare. The humanity is under attack and they
are everywhere!
Who are they? Brain-washed believers of the dogma that living beings are
just a complex sort of finite-state automata? Or in most of the cases
worse: just conformists who are ready to go willingly to wherever the
mainstream takes them.
Frankly to speak, I don’t know how to respond. A few weeks ago I
received a similar list of “assessable outcomes” from the university
administration, supposedly meant for the self-evaluation of the
university. They were asking for comments and suggestions. I did not
answer, because objecting to this or that specific item seemed to me
like collaborating with them. The only honest answer I could give (and
obviously didn’t) was that I consider this kind of reductionism as a
crime, which needs to be rejected on principle.
How can we support the Maltesean colleagues? And all others to come?
Can we open a front by writing something like manifesto against
outcome-based education and starting a campaign on the internet?
Frankly, I do not believe much in such methods, but still, one could try.
Outcome-based methods have been adopted in education systems around
the world, at multiple levels. Australia and South Africa adopted OBE
policies in the early 1990s but have since been phased out. The United
States has had an OBE program in place since 1994 that has been adapted
over the years. In 2005 Hong Kong adopted an outcome based approach for
its universities.[6] Malaysia implemented OBE in all of their public
schools systems in 2008. The European Union has proposed an education
shift to focus on outcomes, across the EU. In an international effort to
accept OBE The Washington Accord was created in 1989, it is an agreement
to accept undergraduate engineering degrees that were obtained using OBE
methods. As of 2014 the signatories Australia, Canada, Taiwan, Hong
Kong, India, Ireland, Japan, Korea, Malaysia, New Zealand, Russia,
Singapore, South Africa, Sri Lanka, Turkey, the United Kingdom and the
United States.
As one can immediately recognise from the paragraphs above (Wikipedia:
outcome-based education), it is a highly political issue and it is long
decided for by the powers that be. There are already new economic
sectors feeding from these policies. Just while I was writing this mail
I received a phone call from a friend who came out from a meeting with
an internet platform provider for such purposes. The topic is apparently
very hot and is evolving too fast.
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Also see my post: Outcome Based Education
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It feels like a lifetime’s work to put all the arguments against these Maltese outcomes, and OBE in general, and I only have a few minutes, so will offer a very truncated response. I think the original purpose of an outcomes-based approach was fine – that it gave common expected goals for learning a subject in the school curriculum, rather than allowing some teachers to carry on ploughing through mathematics in their own favourite way, irrespective of whether anyone was learning anything from them. Its introduction in South Africa was to level the playing field so that all students could expect to have access to the same mathematics (unlike during apartheid) because they were all expected to realise similar outcomes. Educating everyone towards some agreed purposeful worthwhile goals justifies education as being a state funded concern, rather than the concern of individuals. In conjunction with a market-place view of education this becomes poisonous because for the market to operate outcomes need to be measurable, and in order to be measured the outcomes have to be easily tested on a large scale and the possible disciplinary and human centred desirable outcomes of an education in mathematics have to either be ignored, or watered-down, or mangled. This is what happened in UK in the late 90s when ‘mathematical investigation’ became ‘find a formula relating variables in a situation by applying inductive reasoning to a table of integer values’. That is when it all goes pear-shaped and turns into little gobbets of procedural performance that, accumulated over time, do not magically turn into mathematics, nor a mathematically-competent populace. (Understanding multiplication to be repeated addition, for example, as well as being mathematically slovenly will not get you very far in mathematical competence). Meanwhile the ‘assessability’ juggernaut tightens a grip on the world via the global companies such as Pearson who, presumably, promulgate the OBE approach because it can be manipulated to be testable. One of the things that amazes me about the Maltese version is the colour coding. Did anyone notice that the colour coding is predominantly red in year 5, i.e. what they call ‘cognitive learning’ but as you progress you apparently do less and less cognitive learning and a higher proportion of other things. So just as the concepts become harder and harder and applicability and transformability becomes more necessary the OBEs turn into ‘managing learning’ and ‘reading and writing’ rather than ‘cognitive’. I don’t know about other people but in my mathematical studies I became more and more cognitively challenged and more and more dependent on changing and developing my mathematical thinking as I met more and more abstract ideas. How have Malta managed to decide that in their world maths becomes less and less cognitive? If you substitute ‘easily testable learning’ for ‘cognitive learning’ I think it is more obvious what is going on here.
I am stumped about what to do about it, since, like in our own government, personal political whim trumps long term development by knowledgeable people, properly trialled and with a supported teaching force.
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You are quite right, we do not need to start from a blank page in 2015. State-funded elementary schooling has been established in Malta since 1798, and education was first made compulsory in 1946. So we have been developing curricula for quite some time, and, I would say, based rather on the British model, so certainly not in some isolated vacuum. But it seems that when EU funds are available what is important is to spend them not what you might get in return. So now, it seems, we are actually starting from scratch with a curriculum drawn up by foreign consultants who might not even dream of proposing this in their home country.
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