# Good teaching methods fueling students' enthusiasm for maths in school

**Study shows that working independently in small groups is much more motivating**

Students are having much more fun learning maths if they can work independently in small groups to find solution strategies. This is the result of a recent study published in the Educational Studies in Mathematics journal. The authors of the study, including Prof. Dominik Leiss from Leuphana University of Lüneburg, recommend that students are encouraged even more strongly to work independently in maths classes than they were before.

A total of 224 ninth grade students participated in the so-called DISUM study (www.disum.de). Half of them were taught using a teacher-centered approach. The teacher gave the students a task, then gathered their ideas about how the task could be solved, and finally developed the correct solution on the blackboard jointly with all students in class. After that, the students had to perform similar exercises with the teacher helping them where necessary.

The other half of students tried to perform the relevant task independently in groups of four. First, each of them read through the instructions and tried to develop ideas about how the problem could be possibly solved. Then each student could discuss and further develop his or her ideas with the other students in the group. In this case, too, the teacher helped them individually ("Once again read through the instructions carefully" or "Simply draw a sketch"), but he avoided giving any direct clue to the right solution, wherever possible.

After ten lessons, the students should say how much they enjoyed working on the maths problems. Finding: The students who had worked in small groups were much more enthusiastic about tackling the given problem than those students from the controlled group taught in a teacher-centered manner. Even more important: "They also were much more able to solve the given problem independently," explained Professor Leiss, a co-author of the study.

Better performance with modeling tasks

According to Leiss, however, the study was focused on a specific type of task, namely the so-called modeling tasks. These tasks refer to everyday problems that need to be translated into a mathematical model before they can be solved. Example: Mr. Stein lives in Trier and always crosses the Luxembourg border to fill his VW Golf car with cheaper Luxembourg gasoline. Is this worthwhile?

Such tasks often do not contain all the information required to solve them. This is why they allow for broad discussions. How empty does the tank need to be so that it is worthwhile driving to Luxembourg, and what price difference does there need to be? Is it sufficient to take into account gasoline consumption and distance for making a detour to the gas station? Or should I also take into account additional operating costs?

"Modeling tasks are much more open by nature than just having students search a mathematical formula," says Leiss. "And this openness should also be reflected in the learning environment." In other words: Working independently in small groups is much more suitable for solving modeling tasks than it is for doing so-called calculation tasks, in the case of which students simply have to enter values in a formula.

Principally, Leiss makes a plea for strengthening the mathematical understanding of students by using modeling tasks. "Our study has made clear that modeling tasks also fuel the students' enthusiasm for calculation tasks. So this way, you can kill two birds with one stone."

Contact details:

Prof. Dominik Leiss

Institute of Mathematics and its Didactics

Leuphana University of Lüneburg

Phone: 04131/677-2242

Email: leiss@leuphana.de