Mathematics is important. As teachers, we want to know the most effective methods are for maximising the maths performance of students. Ideally, we might create a virtuous cycle where increased maths achievement boosts students’ self concept, leading to greater motivation for the subject and further improvements in performance.
A new study sheds some light on how we might approach this. David Geary and colleagues analysed a rare longitudinal data set. 167 students were followed from Kindergarten through to Grade 8, undergoing a battery of assessments each year. Some of these were generic such as IQ and working memory tests, as well as reading assessments. Others were specific to mathematics and included tests of arithmetic and fraction knowledge.
The researchers found a correlation between all of these tests and maths performance. However, they found that the maths specific skills seemed to become more important as students aged. Fraction knowledge became particularly important in later grades.
This makes a lot of sense. Mathematics is not a general skill. You don’t improve at it by practising problem solving, you improve at it amassing knowledge specific to the subject.
There are some limitations to the study. The researchers had to decide what tests to run and so they picked factors they thought might be relevant. There could be other factors associated with mathematics performance – for instance, non-cognitive traits such as resilience – that the researchers did not test for.
However, I think that this demonstrates the importance of early maths teaching. If students do not learn basic maths skills and number facts at primary school then this will degrade their later ability in mathematics. The idea that we can then motivate these students into persisting with maths seems implausible.
Filling the pail 
I must confess to being a bit befuddled by the way my daughter (now in Year 2) is being taught maths. From the little I can judge, it is being taught very inductively (no bad thing in itself, but it can be taken to extremes) and with a strange grab-bag of concepts. She has no idea about the 4x times table, but can tell me the difference between a vertex and an apex. Confusing.
Greg is onto something here,
In 2014 NAPLAN revealed 30% of Year 5’s and 20% of Australian Year 7’s could not do a simple subtraction of the form “A bike costs $132 and John has saved up $45 how much more money does he need to save?” This is Year 2 level and it was in multiple choice format.
I think the main reason kids turn off maths so much is they do not have the cognitive tools to do it. If a child cannot do something, and this is reinforced a multitude of times, it is best to do in-order to preserve a semblance of self-esteem is to withdraw from maths and say it is boring.
I actually wrote an article about this:
Norton, S. (2016). Mathematics engagement in an Australian Lower Secondary School. Journal of Curriculum Studies Available from http://dx.doi.org/10.1080/00220272.2016.1141995
How do so many Australian children get to early secondary with so little mathematics? There are a number of factors including culture and not valuing education and not being prepared to work hard. But a big factor is the poverty of mathematics knowledge among graduating primary school teachers. I have written three articles on this recently and a few earlier:
1) Norton, S. (2017). Primary mathematics teacher confidence and its relationship to mathematical knowledge. Australian Journal of Teacher Education. 42(2), 47-61. Available from: http://ro.ecu.edu.au/ajte/vol42/iss2/4/
2) Norton, S. & Zhang, Q. (2016). Primary mathematics teacher education in Australia and China: What might we learn from each other? Journal of Mathematics Teacher Education. Available online from: http://link.springer.com/article/10.1007/s10857-016-9359-6
3) Norton. S. (2016). Primary mathematics teacher education encountering difficult terrain: A personal perspective. International Journal of Mathematics Teaching and Learning. Available from: http:/www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/3/8
I think a major factor that explains why we are graduating so many primary teachers who struggle with upper primary mathematics relates to the changing role of universities. There has been a retreat from a role in nation building and a refocus on universities seeing themselves as enterprises. This is coupled with almost complete lack of accountability with respect to knowing the discipline. The whole social constructivist theory has been conveniently high jacked and twisted to suit the notion that depth of discipline is not necessary since the graduating teachers can account for any deficit over a life time of teaching and learn along with the children. But a big consideration is money. Western universities are falling over themselves to offer increasingly simple, convenient courses and very reluctant to fail anyone in teaching. The social constructivist “child centred” argument is a convenient theoretical support for minimal demands on knowledge. I am trying to publish in this area as well, but so far there is a little reluctance on the part of journals to publish the stuff. I wonder why.
I think Greg’s activism is what is needed to turn around a culture of apathy, exploitation and short term thinking. There need to be more of it.
Stephen
Reblogged this on The Echo Chamber.