Before we start, if you have not read part 1 in this series, I do recommend you to do so before reading about the results presented in this post, in order to understand them. Here is a quick re-cap anyway:

I have now worked for six months with my new students in grade seven. During this period of time we have not had any standard tests. Instead I have activated my students with presenting problems just beyond their scope of knowledge and during the process of solving these problems, I have continuously offered feedback to my students on how they are doing (the methods for doing this can be read in my previous posts). I want to point out that we have not played any games or tried to do anything “fun”. So far we have only focused on understanding arithmetics and algebra. Anyway, half a year is long enough to start noticing real progress, but how can progress be measured or evaluated?

When thinking about measuring students progress, one immediately think of test results. However, test results do not contain a lot of information. I believe that good results in mathematics, or any subject for that matter, is a direct consequence of students having an interest and motivation to learn. But how can we find out if the students have gained an interest in the subject?

A wise man, Dr. Ingvar Stål, told me many years ago that if a school is successful and catches the students’ interest, they will eagerly go home after the day is over and tell their families all of the exciting things they have learned. So in order to gather information about my students, I turned to their guardians. I asked them if they have noticed any difference in the students’ attitudes towards mathematics. Here are just a few of all the many positive comments I received (the students’ names are of course made up):

“Sophia eagerly works at home and her interest and motivation to learn mathematics have improved. She likes the way math is taught.”

“Josephine has already earlier liked mathematics. However, I think she has become more independent and more interested in calculations and developed more confidence. She does her homework and likes to show me the exercises. The other day she challenged me with a task and I was able to solve it, even though mathematics was not my strongest subject.”

“Martin seems to think that it is fun and interesting with mathematics the way it is done right now, and it is always fun to see that there are subjects in school that students really seem to enjoy.”

“Anna likes mathematics more nowadays and appreciates that there are no standard tests. Her attitude is more positive now than before, even though she has always liked math.”

“Jonas likes the way math is taught. He discusses the exercises more than before at home. He has become more interested in the subject.”

“When Ella started junior high, she did not like math at all. Everything was difficult and the “books were thrown around” when difficulties appeared. But now she is thinking, working with the exercises and does not give up easily. It is still difficult from time to time but her attitude has changed a lot.”

“Mathematics has definitely become a central subject among all the other subjects. Math is a subject that offers many challenges, however, the student is having fun at the same time. Every homework and digital test is a new challenge and a competition against yourself. The bar for allowing yourself to make mistakes is higher now, for better or worse. The results are often good but mistakes can be experienced being greater than they actually are, since they affect the grade. However, it is good that the students continuously have digital tests and not standard tests, as before.”

“Emma’s attitude has changed drastically. She is much more interested and involved in math today than she was before.”

“Thomas has always liked math, but I think he likes it more now than he did before. It is important to him to get everything right at the digital tests, and he gets disappointed if he makes a mistake.”

“It is more fun to use a digital math book. It is good that there are solutions and theory for the exercises. There is no pressure when there are no standard tests, which is a good thing.”

If students are presented with the right problems, have access to good sources and a workplace that supports collaboration; learning will become interesting

From these comments it is obvious that the students have found an interest in mathematics and that they are motivated to learn. If you read the comments carefully, it is even mentioned that not having standard tests is a positive thing and that working with technology has many advantages. The comments about the pressure to get everything right in the digital tests sounds more serious than it really is. These comments arises from the students’ own will of being excellent. The students are aware that they are good at math and that is why a small mistake can be disappointing, even though it does not matter much.

In this post I was going to present and discuss comments of a more negative nature, however, I did not receive any such comments. At the most, there were a few neutral comments saying that “there is no change in attitude, the student has always liked mathematics and there is no change in that”.

I know that many who are reading this series are waiting to see how my students will perform in a standard test, and we will get there, but for me knowing that my students are developing an interest in mathematics is all the results I need.


Would you like to learn more about the digital math book mentioned in the comments? Then please visit (available in English, Swedish and Finnish).

Are tests necessary? Part 7 – Results(1)