Sixth grade students with lower mathematical ability perform better on complex arithmetic problems if they write down their calculations. This discovery was made by psychologist Marije Fagginger Auer, a specialist in Methodology and Statistics. Her outlook is optimistic: 'After training, these students are more likely to choose this solution strategy.' She will defend her PhD dissertation on 15 June.
The importance of writing down calculations
In recent decades, there has been a sharp decline in the performance of sixth graders (11 to 12-year-olds) on certain aspects of mathematics, especially multidigit multiplication and division (such as 23×56 and 544÷34). At the same time, changes have taken place in the strategies used by students to solve these arithmetic problems: they are more likely to answer them without writing down their calculations, and they often make mistakes. PhD candidate Fagginger Auer: 'We wanted to learn more about these developments and to find possible solutions. Our research shows how important it is to look at children's solution strategies. It also shows that children can benefit from writing down their calculations, especially the more vulnerable group with lower ability.'
Choosing between solution strategies
Children solve arithmetic problems using many different solution strategies, for instance digit-based algorithms such as 'long division' or a whole-number method . Developments in maths teaching have resulted in greater emphasis on informal strategies, such as mental arithmetic. However, some students with lower mathematical ability may not be able to choose wisely between strategies. These students often opt for a risky approach to answering, without writing down their calculations. Boys are more likely to do this than girls. It appears that teachers have only limited influence on this choice, but there is something that can be done about it. If lower ability students have to write down their calculations, their performance is better. After training, these students are more likely to choose written calculations.
Assessment data and experiments
'In our study we combined two approaches in order to find out more about how sixth graders choose a multiplication or division strategy, and about the performance resulting from their choice. For the first approach we used a national assessment of the mathematical abilities of Dutch students at the end of primary school (Cito). We analysed the correlations in this assessment between the teachers' reports of their mathematics instruction and the strategy use and performance of their students. For this, we used new applications of latent variable models. The second approach consisted of experiments in primary schools, where we looked at the spontaneously used strategies and performance (accuracy and speed) of students, and how these can be favourably influenced. Writing down calculations was more likely to result in a correct answer, but it did take more time.'
Fagginger Auer will apply the expertise she has gained in Leiden at the Netherlands Association of Universities of Applied Sciences (Vereniging Hogescholen) in The Hague. 'As a psychometric specialist, I'm going to be working on national knowledge assessments for teacher training, within the '10 for the teacher' (10voordeleraar) project (see text box).'
10 for the teacher (10voordeleraar)
There's no doubt about it: teachers need to know their job and their subject matter. The initiative was therefore taken a few years ago to strengthen the knowledge component in teacher training. In 2008 it was decided, in consultation with the teacher training programmes and the Ministry of Education, to develop knowledge databases, national knowledge assessments and peer review. All these activities are organised within the 10voordeleraar (10 for the teacher) programme.
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