There was geometry too, of course. By the Intermediate years we were tackling algebra and trigonometry.
But a brave new era is dawning in mathematics education. We no longer need all that so-called ‘objective’ arithmetic. And who says a triangle must have three sides?
The way ahead, according to the Ministry of Education, is to “use maths to develop critical awareness about wider social, environmental, political, ideological, and economic issues.”
According to the Ministry’s new Common Practice Model (CPM), what will help children learn this new kind of mathematical thinking, is something called ‘critical maths pedagogy’. The CPM tells us that children should be “encouraged to interrogate dominant discourses, including that maths is benign, neutral and culture-free”.
Teachers must no longer take for granted that arithmetic works the same for everyone. For example, whether two plus two equals four depends on a student’s cultural background. According to Jason To, President of the Ontario Mathematics Coordinators Association, if you insist that the statement, ‘two plus two equals four’ is an objective fact, you are guilty of "covert white supremacy."
Mr To is right to call out mathematics for its racism. The Arab mathematicians who gave us the concept of algorithms were heinous white supremacists. And the Indian mathematician Aryabhatta, who came up with the number zero, is known to have had a penchant for white hoods and burning crosses.
As always, the Ministry is right too. Critical pedagogy will make mathematics much easier for children to learn. If there are no ‘correct’ or ‘incorrect’ solutions to mathematical problems, it follows that any solution is as good as any other.
Even better, when young people leave school, getting into careers that require mathematical skills will be straightforward. Gone will be all the heavy mathematical lifting currently required to become an economist or engineer.
Having dispensed with the, frankly racist, idea that mathematical problems have ‘correct’ answers, designing a bridge will be a doddle. If mathematics is subjective, then so, by extension, are the so-called ‘laws’ of physics. And critical maths will come as a huge relief to those struggling to pay their mortgages in these days of rising interest rates.
All we need now is for reality to get with the new ‘critical maths’ programme.
Dr Michael Johnston has held academic positions at Victoria University of Wellington for the past ten years. He holds a PhD in Cognitive Psychology from the University of Melbourne. This article was published HERE
According to the Ministry’s new Common Practice Model (CPM), what will help children learn this new kind of mathematical thinking, is something called ‘critical maths pedagogy’. The CPM tells us that children should be “encouraged to interrogate dominant discourses, including that maths is benign, neutral and culture-free”.
Teachers must no longer take for granted that arithmetic works the same for everyone. For example, whether two plus two equals four depends on a student’s cultural background. According to Jason To, President of the Ontario Mathematics Coordinators Association, if you insist that the statement, ‘two plus two equals four’ is an objective fact, you are guilty of "covert white supremacy."
Mr To is right to call out mathematics for its racism. The Arab mathematicians who gave us the concept of algorithms were heinous white supremacists. And the Indian mathematician Aryabhatta, who came up with the number zero, is known to have had a penchant for white hoods and burning crosses.
As always, the Ministry is right too. Critical pedagogy will make mathematics much easier for children to learn. If there are no ‘correct’ or ‘incorrect’ solutions to mathematical problems, it follows that any solution is as good as any other.
Even better, when young people leave school, getting into careers that require mathematical skills will be straightforward. Gone will be all the heavy mathematical lifting currently required to become an economist or engineer.
Having dispensed with the, frankly racist, idea that mathematical problems have ‘correct’ answers, designing a bridge will be a doddle. If mathematics is subjective, then so, by extension, are the so-called ‘laws’ of physics. And critical maths will come as a huge relief to those struggling to pay their mortgages in these days of rising interest rates.
All we need now is for reality to get with the new ‘critical maths’ programme.
Dr Michael Johnston has held academic positions at Victoria University of Wellington for the past ten years. He holds a PhD in Cognitive Psychology from the University of Melbourne. This article was published HERE
12 comments:
I'm sure the idea of postmodernism started as a silly take on the craziest concept that a bunch of philosophy professors could come up with in some French university lunch room way back in the last century some time. Even they new it was silly.
That is until the Marxist got hold of it.
This has already been illustrated in George Orwell's highly respected text book, 1984.
Two plus Two equals Five. !!
Big Brother says so !!
When I started primary school as a child immigrant in 1962, there was no such thing as primary school maths. It was called 'arithmetic'. The first time we did maths was in Year 7 when algebra was introduced.
The term 'mathematics' implies an abstract element not present in arithmetic. '2+2=4' is not a mathematical statement whereas 'x+2=4' is. Even more abstract is 'x+2=y' as we have multiple solutions. But blow me down if I can find a way of making x's and y's stand for 'social justice' or stuff like that.
With the Americanisation of English, people like me have to start living with expressions such as 'primary school maths' (well, they say 'math', don't they). But that's as far as my concessions will go.
Lols. Arithmetic was easy the abstract stuff was well not tricky but tedious. Drawing rainbows now that was cool. 😏 Perfect for introducing children to new ideas.
If anyone was ever to wonder why the standard of our children's understanding of the basics is at an all time low and will only get worse, the statement that our children should be “encouraged to interrogate dominant discourses, including that maths is benign, neutral and culture-free” sums it up in a nutshell.
I can just imagine those 4000-odd MoE wonks being so pleased with themselves, coming out with that little gem. The fact that it is complete nonsense and entirely inappropriate as a model for pedagogy at an elementary school arithmetic/maths level obviously is completely beyond them. Until that kind of woke, pedantic claptrap that has nothing to do with the subject is firmly routed out of the Ministry, we will continue to have a problem and what a bleak future that looks for us all.
Brilliant, Michael. It reminded me of the humourous Math homework example:
"Write an essay on how 8 feels when 5 is taken away from it"
It seems that what used to be humourous and hypothetical is rapidly becoming reality.
Well good bye physics and chemistry from the school curriculum. And NZ. But I guess we have matauranga to save us and the world.
The Minister of Education under the next government will be faced with no mean task. Those staff who have devoted their time to embracing and devising obscure topics and ways of teaching, and spent hours producing complex indirect communications about same, will have to either go or knuckle down to promoting old style teacher methods with information all disseminated in plain understandable Churchillian English. Then there is the problem of the Teaching Council which requires similar urgent attention. The govt attempted to limit their excesses by restricting funds but it had little effect.
I have maths to university level but do not carry a phone or calculator all the time. I regularly find myself faced with basic arithmetic exercises. Whilst some of the alternative methods are often obvious to me, most of the time for reliable consistencey I revert to the columns method learned in the 1940s. And occassionally I chant part of a Times Table to recall some combination.
I recall storekeepers in the 1950s mentally totting up at great speed pencilled price lists, and without the great simplification of decimals
Hopefully, Michael is wrong in his assumption that it will challenge the very nature of arithmetic and physics. He’s being reactionary for the sake of debate surely?
I stand to be corrected but I assume that the revised curriculum only seeks to modify how these fundamental concepts are introduced to children, by asking teachers to consider whether the examples used to present them are appropriate and approachable given the demographics of the students.
For example, if we see two waka with 12 paddlers in each waka, how many paddlers are on the moana? But first, we must define that the accepted convention for modern arithmetic is an expectation that we agree to calculate the answer using base 10 numeracy, i.e. 24 paddlers.
The numeracy base is simply an ‘agreement’, but in order for different cultures and communities to strive towards a common goal, of say, building a bridge, an accepted convention needs to be applied. It doesn’t matter which convention applies, only that all parties accept it.
It could be argued that Michael is being too rigid by defending that 2+2=4 as an incontrovertible “law”. If the numerical convention is base 10 then he is correct but if he is presenting that concept to a group of programmers who are familiar with binary concepts they may challenge his thinking by providing the answer as 20 in base 2.
I’m all for modifying the message so that the student has the best chance of absorbing the material, but you can’t change accepted conventions unless everyone agrees. Mathematics, just like everything else in human thinking, is nothing more than an “agreement”. Language is an even more obvious human construct. Music is a wonderful example of how creative we can be, even within clearly defined boundaries. Take a moment to reflect on how diverse the realm of music is and then remember that the basis of musical sound is simply applied mathematics in base 8!
People don’t realise how narrow the definition of reality actually is. So much of what we humans consider to be reality is in fact merely an agreement, convention, habit or even wishful thinking based on unreliable memories.
Arithmetic is NOT a racially biased discipline but the imparting of this knowledge to students could perhaps be rendered more palatable if it is filtered through a lens that is culturally appropriate to the environment. Social and political will is required to bring about such a change and it looks as though this is where we find ourselves now.
The use of terms such as waka and moana just adds confusion and may not necessarilly lure maori or pacifica students to attend. I suspect the token use of maori and pacifica names and words everywhere turns off just as many students as it does their parents. In my day there was much emphasis on logs. Although as proficent as most at applying, I did not fully appreciate the theory until well into secondary school. But I could use to resolve complex calculations. Now the emphasis is reversed. Pupils may or may not grasp the theory but either way many are not necessarily competent is utilising it. The introduction of base other than 10 at an early stage just adds further confusion. Whoever uses except advanced computer nerds and some electronics persons? How many teachers grasp?
The reality of course is that duodecimal base is in fact way more useful than decimal base. And of course binary is fundamental to many of our systems (except gender). But at the end of the day if you do not understand how to use numbers ( irrespective of base) then how can one use numbers to represent and develop other ideas.
A bit like language. If you can’t string a sentence together how can you carry on a conversation? This analogy is patently obvious when trying to communicate with some one where you have very few words in common.
Who or what can save this country from the fiasco of the MoE' and its maths curriculum? Actually all its curriculum are infested with the same nonsense.
Has the madness of constructivism , got to run to some ridiculous extreme before it is seen for what it is and crashes and burns ? How long can a society go on believing there are no objective facts? As a philosopher said "Constructivism attacks the immune system that saves society from silliness".
The constructivism behind Reading Recovery has been exposed by a longitudinal research study which just reinforced many other studies showing in the long run children who were subjected to it are actually worse off than those who had no intervention.
Why can't these findings carry over to other areas of learning including maths?
I have been a private maths tutor for almost 45 years and could hardly believe the results I got from direct instruction at all school levels. Direct , systematic, sequential learning with an abundance of consolidation and revision is diametrically opposed to constructivism. My students who were sometimes failing very badly thrived and actually enjoyed doing maths. I was embarrassed often that I had at times secretly thought,to begin with, that these students were quite hopeless and 'thick' until they blossomed.
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