Should we go back to the old days and start long division again? No, says this outgoing professor of mathematics didactics

Paul Drijvers (1958), retiring professor in the didactics of mathematics, actually wants to talk as little as possible about the conflict of directions in Dutch arithmetic and mathematics education in this interview. The one between 'traditional arithmetic' (think: practicing bare sums) and 'realistic arithmetic' (think: story sums). Yet it is always discussed.

The title of his farewell speech at Utrecht University (UU) – he is retiring – refers to it: 'Ten handles for balanced mathematics education'. With that "balanced" he turns against the battle of directions. Drijvers believes that this does not benefit education; the differences are exaggerated and that has a "paralyzing effect", he says via a video connection. As a background he has set a photo of the Academy Building, the ceremonial heart of the UU where he will give his farewell lecture this Monday afternoon and present his book Didactics of mathematics, handbook for teachers in training and practice .

This conflict of directions between traditional and realistic arithmetic has been going on for decades. In traditional arithmetic, the emphasis is on direct instruction by the teacher and the automation of fixed arithmetic procedures. Since the 1980s, realistic arithmetic has gained influence. The emphasis is on discovery learning, insight and arithmetic in 'meaningful contexts'. Since the beginning of this century, mainly realistic arithmetic methods have been available, especially in primary education.

The battle is not always fought with the same intensity, but has a wave movement. In recent years, the debate has flared up again, especially in politics and in the media. The realistic calculators seem to be losing out. Things are not going well with the basic skills, so we have to go back to traditional arithmetic, is the current trend. Some schools have already switched from realistic arithmetic to traditional arithmetic.

You could count Drijvers among the realistic calculators, because he is affiliated with the Freudenthal Institute of the UU, named after the founder of realistic arithmetic. But he criticizes that sharp distinction, as if they were two different religions. "I am not a follower of realistic mathematics education. I have always felt free to be critical of that too."

What message do you have when you say goodbye as a professor?

"First of all, I want to correct the image that there is a 'math disaster'. Three new studies were published last December and the Netherlands comes out quite well in them. For example, research by the Education Inspectorate into children in group eight showed that the math level is about the same as twenty years ago. The PISA study from a year and a half ago [triennial international study into the reading and math skills of fifteen-year-olds] did indeed show that the results have dropped slightly, but that applies to all countries. The Netherlands is still in 10th place out of 81.

"That doesn't mean we shouldn't take such a decline seriously. But to immediately say: we should go back to the past and start long division again, for example? No. My message is: the goal of our mathematics education should be that students can cope in an increasingly complex society. Think of technological developments and also of the enormous amount of information that comes our way every day."

Do you have an example?

“My lecture includes a graph I found on a patient website. It is about the average height of adult men and shows that the Dutch are the tallest and the Indonesians the shortest. According to the graph, with figures instead of a line, an Indonesian would reach just above my knee. Of course that is not possible! It is because the vertical axis does not start at zero, while the feet of the figures are all on the horizontal axis. You want students to learn to understand something like that quickly. That they understand: this cannot be right. Also think of the corona period when an enormous amount of graphs, diagrams and probability calculations came our way. Or of medical interventions and risks. It is important that you can weigh up risks.”

This sounds like realistic arithmetic. Isn't it also important to be able to do sums?

“Yes, that is also important. I advocate balanced education. Because for those applications you need procedural skills. In the world of realistic mathematics education it has been said from the beginning that practice is also important. But then preferably exercises that are somewhat intelligent, that occasionally contain something surprising or playful.”

Last year you criticized the realistic calculation methods of today in NRC. You said: "I see story sums that make no sense."

"Yes, you can come up with a nice story, but if it does not correspond to reality, you miss your target. I think that in recent years there has been too little attention for the didactic quality of arithmetic and mathematics books.

“There is also an example of such a story problem in my new book [see box]. It is about a lawn in a garden. The owner decides to enlarge it and then you have to calculate how wide the new strips are based on the new surface area. That is of course nonsense, because if you are going to extend your lawn, you do have a plan for the dimensions of the new strips in advance, don't you? And if you just did something, you don't measure afterwards what the dimensions of the strips actually are, do you?”