According to the Dutch Inspectorate of Education, many primary school pupils do not learn mathematics as well as they could. In the coalition agreement, the new cabinet expresses the wish that every child should learn mathematics. At the moment, mathematics education is insufficiently attuned to the possibilities and needs of pupils. For her PhD research, Jorine Vermeulen investigated how teachers can better meet the educational needs of pupils in third grade ('groep 5'). "With the right diagnostic questions, you discover how your student thinks".
A teacher could of course have a conversation with his or her student. But according to Jorine Vermeulen that is not ideal. "If you let the student tell you how he or she thinks, then you are dependent on the student's language skills," Vermeulen says. Apart from that obstacle, a teacher can also influence the process. The interaction of a conversation can make a learner think differently. "A pupil may wonder why the teacher asks that very question and then perhaps adjust the solution strategy," Vermeulen says.
To prevent this Vermeulen worked on different diagnostic methods. One of those methods is a type of exercise that should uncover a specific type of calculation errors. "Errors are still often associated by teachers with pupils who are less able to do maths. While some errors are actually made by pupils who are already at a higher level." An example of such an error is the bridging error. A student wants to solve 83 - 57 by first solving 80 - 50 = 30 and then 3 - 7 = -4. In the latter step, the student swaps the numbers to solve the unit shortage and does 7 - 3 which equals 4. Instead of the correct answer (30 - 4 = 26), this produces an error (30 + 4 = 34).
The bridging error is made mainly by students who are already further along in mathematics and are developing a greater number sense. The teacher can now take a step back and ask the pupil to work with a number line. But most pupils do not like this, because it is associated with a lower level of mathematics. "They have the idea that good mathematics means doing as much from memory as possible," says Vermeulen. According to her, it is better for the teacher to support the pupil on his way to a higher level of number understanding instead of taking a step back.
Jorine is a teacher trainer for mathematics at the teacher training college for primary education at Inholland University. She did her PhD research in the department Cognition, Data and Education (CODE; faculty of BMS). She investigated how to effectively find out how a pupil in group 5 thinks when solving addition and subtraction tasks. Her dissertation, titled "Diagnostic Mathematics Assessment in the Third Grade", is available online.