Stop the math war
How do you teach children to count? This question has resulted in trench warfare. Time for balance in the arithmetic discussion.
image: Nanne Meulendijks
At my primary school (eighties) I was one of the two best in my class in math. I easily scored an 8 or higher, because automation was easy for me. Do sums and say the tables? You could wake me up for it. But in high school it became a different story, and it kept me awake. Apart from the Pythagorean theorem and some basic algebra, I got completely lost. Instead of understanding, I developed a fear of grades, which led to a relieved drop in a number of subjects in fourth grade.
Although this n = 1 only says something about me, and leaves all kinds of circumstances out of consideration, my case still focuses on the question that is central to the arithmetic discussion: how do you teach children a solidly founded calculation concept?
The image that the situation is dramatic with the level of calculation is not correct
In recent years, the discussion in the media has split into two camps: proponents of 'traditional' arithmetic, and proponents of 'realistic' arithmetic. Proponents of traditional math advocate an emphasis on skill, practice and intensive repetition with direct instruction from the teacher. Proponents of 'realistic' arithmetic emphasize insight into numbers and relationships, practice with realistic situations and understanding. The teacher has a more coaching role in this.
Proponents of traditional methods argue that the math skills of Dutch children have declined in the last twenty years. This is due to the fact that almost all calculation methods in the Netherlands are based on the didactics of realistic arithmetic. In his new book Effective math education in primary school writes 'traditional' proponent Marcel Schmeier, for example: 'In the past four years, the math achievements of Dutch students on the Timss test have dropped from 540 to 530. It is the lowest score that the Netherlands has achieved in the past twenty years.'
“Students need clear explanations from the teacher instead of having to figure out for themselves how to add unnamed fractions, for example,” says Schmeier. "Practicing and checking understanding together with direct feedback are powerful didactic principles." Schmeier thinks it is important that after fifteen years there is a traditional calculation method again (which he himself contributed to). "For teachers it is important that there is something to choose again."
Douwe Sikkes agrees, a teacher with a 'passion' for arithmetic and 33 years of experience in special primary education. He is an advocate of explanation, practice and automation. "Good students can come up with a solution themselves, but for children who have difficulty with language comprehension or are less smart, that is difficult." According to Sikkes and Schmeier, the dominance of realistic calculation methods leads to a gap between children from socially strong and children from socially weak backgrounds.
Mix
That makes sense. Yet the numbers do not support that fear. Kees Hoogland, associate professor of didactics of arithmetic and mathematics in vocational education at the Hogeschool Utrecht: “The same Timss study shows that 99 percent of the students achieve the basic level. The average is depressed by the lagging results of our best students. ” This year, the Education Inspectorate will investigate how it is possible for the best students to lag behind.
'Stomping endless sums was wise when there were no calculators yet'
Yes, realistic calculation methods are dominant in didactics, Hoogland acknowledges. "But schools are constitutionally free to choose their own didactics. In practice, you always see a mixture of working methods and approaches to content at schools that are more or less focused on automation, understanding and connecting math with reality." In the report Automation in arithmetic mathematics The Education Inspectorate writes that 98 percent of the schools use extra materials in addition to the calculation method to automate calculations.
The difficult thing about arithmetic mathematics education is that there is a tension between two goals: on the one hand the development of basic skills, on the other hand the development of higher-order skills and insight. 'In current educational practice, higher-order skills and insight usually take second place,' notes the Dutch Association for the Development of Mathematics and Mathematics Education (NVORWO) in a vision document published at the end of December last year. However, research and worldwide experience indicate that too much focus on mere operations and procedures ultimately stands in the way of good arithmetic and mathematical results; the pupils then acquire skills that have only a limited scope and are not very flexible and durable. '
Hoogland is co-author of this document. "In the XNUMXs, it was extremely wise to endlessly stamp sums because of the simple fact that there were no calculators."
He continues: “The nostalgia-oriented discussion in the media has a paralyzing effect on the development of good math education that is appropriate for our time. We are now being overtaken left and right by other countries and have lost our top position in terms of didactic developments and student results. Pity."
Grab the best and don't categorically reject something because you've figured out in advance that it's not good
“I don't see an end to the discussion any time soon,” says Marian Hickendorff, assistant professor of educational sciences at Leiden University. The supporters and opponents will never find each other, because in essence they have a different idea about what arithmetic is. “The traditional paradigm mainly revolves around basic skills and the execution of procedures. Within the realistic paradigm it is mainly about understanding, insight and application. The interpretation of the figures depends on the paradigm from which you are looking. ”
Hickendorff, who insists on being neutral in the discussion, lined up the facts and presented them at the 36th Panama Conference (on arithmetic and math education) last January. Since 1987, the performance in estimating arithmetic, numbers and number relationships, mental arithmetic (addition and subtraction) and arithmetic has improved by percentages. Performance on the more 'traditional' components (sums with larger numbers where it is convenient to calculate on paper) deteriorated. "Both developments are in line with the shifts in the importance of these components in the methods."
In addition, the performance in fourteen parts has remained roughly the same in recent years, she emphasizes. This applies to the basic operations (automating the tables), calculating with proportions, calculating with fractions, calculating with tables and graphs, measuring (length, area, volume, weight) and geometry. “The dramatic picture of the calculation level is incorrect. In the final tests, the performance in arithmetic has remained roughly the same for years and has increased rather than decreased. The performance of the best students is lagging behind compared to other countries, but that is not as dramatic as is sometimes suggested. ”
What she wants to make very clear?
“Direct instruction works, especially with weak calculators. But there is no compelling evidence that it works better than more accompanying instruction. It also works. ” The researcher therefore hopes that in the remainder of the discussion the teacher will be central, and not the method. “All the literature shows that teachers play the most crucial role in the learning process. Make sure that they have sufficient baggage to be able to transfer the material properly, and to be able to make their own assessment in didactics. ”
In order to do what suits them, it is important that there are calculation methods with different approaches. Meanwhile, the realistic methods contain sequences of sums and the long division is back, she notices. And the latest traditional method also contains realistic elements, such as 'gapping'. “That is a good development. Take the best with it and do not categorically reject something, because you have thought in advance that it is not good. It's time to stop the trench warfare. ”
