# Experiences with Structured Derivations

### Teaching Experiences

A large number of students in more than 30 schools in Finland, Sweden and Estonia have participated in high school courses based on structured derivations. We have collected experience data related to the method, and below are some comments from our users.

### Comments from our Student users

"Here you really learn what you have to do at each step, you can’t just skip something without knowing what to do, you really do understand each step."
–Boy, Finland

"I would recommend this method to those who are weak in maths. I wasn’t good, my grade was 3 (scale 1-5) but now it’s 5. Structured derivations helped me."
–Boy, Estonia

"It was like something unnatural happened. But I mean I even understood something. With that I’m quite satisfied."
– Girl, Finland

"At least you prepare more for the tests as you actually have to write down everything thoroughly, including those derivations. If you’d be calculating in the usual way on paper, you wouldn’t be as concerned with what the calculations look like or what the derivations are like."
–Boy, Finland

"Now I think about what I’m supposed to do next as opposed to just calculating."
–Girl, Finland

### Comments from our Teacher users

"I have always dreamt about the students being able to explain their solutions verbally, now they have to write the explanations, it’s even better!"
–Teacher, Estonia

"In my opinion with the structured derivations students can be aware of what they are doing – that’s different. Otherwise they maybe just wrote down all material in one day and the next day wondered, what it was what I did. Structured derivations are helping me understand what I am doing."
–Teacher, Estonia

"It is the clarity in it, absolutely. When a student's mind is wandering and she is looking around casually, then she can catch up by reading the comments written there in between. It is good for the students, in particular, that what the teacher is saying is now written down there in the solution too."
–Teacher, Finland

"Firstly, it is a good pedagogic tool because it is a way, I have noticed, to write derivations I am showing to the students, that makes them see what I have done. And if they write down what I am writing, then they understand how it goes. And in the other way around, it is the same thing for me, too. That is good to see..."
–Teacher, Sweden

### Empirical Studies

Teachers' Experience from Using Interactive E-books in the Classroom (Hägerstedt, E., Mannila, L., Salakoski, T. and Back, R-J., The Seventh Nordic Conference on Mathematics Education, NORMA14. Turku, Finland, June 2014)

"It Takes Me Longer, but I Understand Better" – Student Feedback on Structured Derivations (Back, R-J., Mannila, L. and Wallin, S., International Journal of Mathematical Education in Science and Technology, Vol. 41, No. 5, pp. 575-593)

An Empirical Evaluation of Structured Derivations in High School Mathematics (Peltomäki, M., and Back, R-J., ICMI 19: 19th ICMI Study Conference on Proof and Proving in Mathematics Education. Taipei, Taiwan, May 2009)

Promoting Students’ Justification Skills Using Structured Derivations (Mannila, L. and Wallin, S., ICMI 19: 19th ICMI Study Conference on Proof and Proving in Mathematics Education. Taipei, Taiwan, May 2009)