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Debunking myths concerning teaching arithmetic

One often sees gloomy Dutch newspaper headlines about pupils’ arithmetic skills in elementary schools. But is the situation really so bad? Marian Hickendorff is conducting intricate research on performance in and the teaching of arithmetic. The conclusions she draws beg to differ.

‘In The Netherlands, there are a lot of negative feelings out there concerning arithmetic education and children’s standards in arithmetic in elementary schools: “education used to be better” or “children can’t do arithmetic any more.” But there is no good research behind claims like these. With my research, I want the figures speak for themselves and to substantiate claims about arithmetic education empirically,’ says Marian Hickendorff.

Performance in arithmetic: better or worse?

Over the past 14 years she has conducted research on Dutch arithmetic education in all sorts of intricate ways. Work she has done in this area includes detailed analyses of pupils’ answer books from the so-called periodic assessments. These periodic assessments demonstrate that pupils’ performance in arithmetic in the past 30 years is actually rather constant. In certain things they have gotten better, in other things they’ve gotten worse. For example, working with estimates and the concept of number has improved, while performing more complex operations (addition, subtraction, multiplication, and division) has actually gotten worse.

Hickendorff looked closely at the results by examining the way that pupils solve arithmetic problems. This entailed analysing the notes and calculations that pupils make when solving problems. Hickendorff explains: ‘Here we see that children tend to do things in their head instead of working out a calculation on paper, and that results in wrong answers.’

It is hard to say why pupils are more likely to do something in their head than to follow a calculation procedure, such as writing out a long division problem on paper. ‘It fits well with the changes in arithmetic education in the past few years, where the emphasis has shifted to learning higher-order skills (“Do you understand what you are doing? Can you also make an approximate calculation, without using precise figures?”). However, we do see from the periodic assessment that, on average, boys are more likely to use their own strategy in solving an arithmetic problem than girls do.’

‘Dutch children have gotten worse at arithmetic’: is this claim true?

Debunking prevailing ideas

Hickendorff’s empirical research provides hard evidence on all sorts of hot issues in education. For example, in the case of a discussion that has been raging for some time now: should pupils be doing ‘bare’ arithmetic problems or so-called context problems? Those are problems with a story or an image. ‘Experts don’t agree on the effectiveness of context problems, opponents think that this type of problem has more to do with reading comprehension than with arithmetic. This would have the consequence that pupils who don’t read well are immediately disadvantaged.’

Hickendorff is examining whether this is true. She presented two versions of the same arithmetic problem to 685 8th-grade pupils: a classic arithmetic problem and a context problem. ‘It turned out not to make any difference, including for children who are weaker in reading or who don’t speak Dutch at home. So, this result contradicts prevailing ideas.’

New periodic assessment

In the coming period, Hickendorff will conduct the periodic assessment together with Cito, the Kohnstamm Instituut, and the KPC Group. She will be specifically looking at the learning process: What occurs in arithmetic class? How do teachers use data about their pupils’ learning progress to choose their teaching strategies? How much time does the teacher spend standing in front of the class and how much time is spent working in small groups?

The report for that study should be completed in 2020. The examination team will use this report to determine the current quality of arithmetic education.

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