in the classroom
How important is maths for students in the future ? A lot of people look at maths quite functionally . They say , ‘ Well , when will I need to be able to solve a quadratic equation in real life ? Why do I need to learn this stuff ?’ It ’ s an interesting argument because you don ’ t . But the same thing goes for so much of what we do at school . Most things that we learn at school , you could do without if you had to .
But education is about much more than that . It ’ s about self-actualization . It ’ s about being able to realise your dreams and do things you might not otherwise have been able to . It ’ s about developing passions . And unless you ’ re exposed to some of these ideas at school , you won ’ t even know whether it ’ s something that you could be interested in the future . There ’ s a human flourishing that education provides .
But when it comes to maths , I think what happens is we try and sell it to students as this functional thing . We say , ‘ Well , you ’ ve got to learn to add up so you know you ’ ve got the correct change at the supermarket .’ Which , of course , is a little bit anachronistic now when everyone uses their card to tap and pay .
As they get into high school , they start to realise that they don ’ t actually need a lot of this stuff in their everyday lives . But we don ’ t seem to apply that standard to everything else in the school curriculum .
Yes , some people will go on to be mathematicians , some will not , but they ’ ll go on to be educated members of society who understand proportion and ratio , relationships between variables and graphs and lots of these other things . It ’ s very useful if you want to be a productive citizen and contribute positively to the society .
Why do you think Year 12 enrolment in mathematics has dropped below 10 % for the first time ? Most people think that you have to motivate students about a subject , and then they will learn it and they will achieve . To me , that at least misses one direction of how the effect works , and it ’ s possibly completely the wrong way around .
There was a study few years ago in Canada that showed motivation didn ’ t predict future achievement , but achievement did predict future motivation . This was for maths for kids in elementary school . This is quite reasonable when you think about it : if you feel that you are achieving in a subject area , then you are going to be more motivated to pursue that area in the future .
If you ’ ve not come across these concepts before , you don ’ t know whether you ’ re going to find them interesting or not . But if you are getting a sense of achievement , then you might find that interesting . If you ’ re getting this regular daily sense of achievement in your maths class , that you are making progress , that you ’ re understanding concepts you didn ’ t understand before , then that is likely to pay forward into future motivation .
If you look at our precipitous decline in math achievement as measured by PISA since about 2006 , I think there is a relationship there between that and the decline in enrolments in Year 12 . If we ’ ve got fewer students who are achieving well in maths at the age of 15 , it makes sense that we ’ d have fewer students who want to take that forward into Years 11 and 12 .
Are we teaching maths the right way ? I don ’ t think we are . I don ’ t think the Australian curriculum should promote a particular teaching style , to an extent that some things are unavoidable .
At my school , we break things down into tiny steps . We demonstrate everything and explain everything fully before we expect the students to do it . Then , they practise it with a similar example . Then , we gradually bring things back together , build them into larger wholes . And eventually , we get students to the point where they can independently solve problems .
But things like problem-based learning , inquiry learning , discovery learning , constructivist learning , the idea behind all of those is that students should be given a problem that they don ’ t necessarily know how to solve , and then with the guidance of the teacher , kind of figure out how to solve the problem and learn math that way .
The problem with that is it ’ s not consistent with our contemporary understanding of how the mind works and how learning happens . It overloads students . It ’ s maybe okay for students who are already quite advanced in their maths , but it ’ s not very good for students who don ’ t have those resources .
Engineers Australia ’ s Chief Engineer said maths should be taught only by qualified
Kids are actually capable of a lot more if taught well , if taught efficiently .
teachers in the field . What are your thoughts on this ? I think it ’ s a case by case basis . I think I understand why big bodies are concerned about out-of-field teaching , but there ’ s a difference between someone who has two methods , PE and Maths , that they ’ ve studied in teacher training and someone that has PE and something else and ends up teaching maths .
I also think that it depends on the level as well . You can have teachers who are very effective at teaching primary school mathematics , who wouldn ’ t be as effective at teaching year 11 and 12 because of their content knowledge .
In most primary schools , students would have one teacher for all of their subjects , and those teachers will be really confident in some areas and maybe less confident in others . Maybe students could have a specialist maths teacher in primary school ? I think that could be one way that we could help .
How can Australian schools become international leaders in maths ? I think we have to cast aside the limitations of things like the Australian curriculum and work together a bit more as a professional community . Unfortunately , the people that have appointed themselves to tell us what to do as a profession don ’ t really , by and large , know what they ’ re on about .
They ’ re beholden to various sociological ideologies and theories and they ’ re politically against things like explicit teaching for reasons that are quite obscure .
We need to instead talk horizontally to each other as members of the profession , share information , share research on things like explicit teaching , Rosenshine ’ s principles of instruction , cognitive load theory , all these things that I was never taught about but that I ’ ve learned through interacting with other professionals via social networks .
I don ’ t see much hopeful change driven from bureaucracies or universities because they seem to be stuck on a certain set of ideas that got us in this situation in the first place . ■ educationreview . com . au | 15