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.

Malta: new “Learning Outcomes Framework”

Malta published the new Learning Outcomes Framework for school mathematics

http://www.schoolslearningoutcomes.edu.mt/en/subjects/mathematics

In my opinion, it is representative of current trends in mathematics education around the world and deserves a wider open discussion.

A random bit from Level 5:

COGNITIVE LEARNING
31. I can use equivalent fractions to discuss issues of equality e.g. gender.

I believe in 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 Oxaca Decomposition and its role in fight against discrimination of any kind). But equivalent fractions? 1/2 = 2/4 = 3/6? How are they related to gender issues?

I am a teacher of mathematics; when I hear a strange statement from my student, my first duty is to try to analyse my student’s way of thinking.

I found that the  “Learning Outcomes Framework” triggers in me the same Pavlovian reflex of trying to figure what the authors of the “Framework” have meant.   In this particular case, I cannot come up with anything better than a conjecture that perhaps the authors of  “Learning Outcomes Framework” associate the words “equivalent” and “equality” a bit too closely. Every teacher of mathematics  knows that mixing similary sounding terms is one of more common stumbling blocks for weaker students. The standard pedagogical remedy is to help the student to separate the concepts by asking him/her a splitting (or separating) question, for example

Equivalent fractions are also known under the name “similar fractions”. Why does the learning outcome

31. I can use similar fractions to discuss issues of equality e.g. gender.

appear to be less coherent and less convincing?

My main concern about “Learning Outcomes Framework” is that an official governmental document of a souverign nation of proud historic past has to be analysed using didactical tools (such as “separating questions”) reserved for work with struggling students.

Malta is a small country, and contributions to the debate from mathematics education experts from around the world might happen to be useful to our Maltesean colleagues. Please post your comments here.

Alexandre Borovik