Examining and analysing students’ feedback to explore which design elements could be relevant when learning basic logical competencies in a learning environment where real-world objects and technologies are combined, demonstrated that A) Using open tasks with multiple solutions, B) Just-in-time feedback and C) Novelty effects in the learning process are central to students in our exploratory educational case study.
In developing the design elements of the learning environment that are central to students in our study, we did not focus on the feedback related to learning environments per se – i.e. combining technologies, using Logifaces and the intended learning of mathematics. Instead, we focused on the design elements that are central to students in such a learning environment. As the design elements central to students, we qualified those student feedbacks which could be central to students’ learning or motivation, and which could support or hinder learning processes.
Using open tasks with multiple solutions
A key design element for students in our exploratory educational case study was that students were able to take their learning paths in solving the problem, using their strategies. The students described the associated thinking and experimenting with their strategies or solutions as very motivating.
[F] It was good that you were able to work at your own pace and that you could work on your own idea and not just have to meet specifications.
[I, b-b-b] The fact that you can or have to think for yourself before working is really good.
In this process of learning, students described the task as a brainteaser rather than a classical mathematics task. According to the teacher’s feedback, working on this brainteaser activated students much more during lessons than usual. In this context, the teacher mentioned that a high involvement could be observed in mathematical high-achievers as well as in mathematical low-achievers. An increase in activity and motivation of otherwise mathematically below average successful students is reflected in the following quote.
[I, b-b] It is really cool that we can learn and do brainteasers at the same time.
[F] I liked the fact that we were able to do more tinkering and puzzling around in the classroom than just learning normally in class.
When working on open-tasks with multiple solutions, it was positive for students that new mathematical or technological knowledge or competencies could be associated with achieving a concrete goal. Students emphasised that it was positive that only those new concepts were learned that could be used immediately when utilising a new solution strategy.
[I, g-g] We learn exactly just the things we need to solve the problem – we would not have learned these things otherwise, would we?
A key design element for students in our exploratory educational case study was that tasks were open-ended and there were several possible solutions. Achieving these open tasks was described by students as a brainteaser rather than an everyday mathematics lesson. When processing these brainteasers, it was crucial for the students that only those new concepts were introduced that were needed in the specific case.
Just-in-time feedback
When experimenting with Logifaces stones and Excel, it was vital for students of our study that they received immediate feedback or knew that they could get feedback at any time. Students emphasised that they found it enjoyable that a teacher and another person they could ask were present in all lessons.
[F] A good thing about the lessons was that you could always ask the teacher or the other person if your concept is right and what the commands are to realise your concept.
In addition to teachers’ feedback, students also pointed out in their feedback that classmates as feedback providers were an essential element of our case study. In connection to classmates as feedback providers, it was emphasised that classmates were consulted both when problems were acute and when feedback on new strategies or ideas for solving the problem was needed.
[I, b-b] Working or learning in a group is really great. We only argue from time to time how we will implement our ideas. Do not think about it, it is quite normal for us.
[F] It was good that in a first step you could immediately ask your seat neighbour if you did not understand something.
In addition to feedback on concrete strategies or ideas for solving the mathematical-logical problem of our case study, it was vital to students that the learning goal and task communication were clear and that questions concerning learning goal or task could be asked at any time.
[I, g-g-g] It was really good that you explained at the beginning exactly what we should do – and thank you that we can ask you again because we do not know all the details.
[F] If the task and the images related to the task would have remained visible on the beamer for the whole lesson, that would have helped. But as we could always ask you, it was not that bad.
However, not only the teacher or classmates were described by the students as feedback instruments. Also Logifaces-stones and Excel could be used to test developed strategies for solving the mathematical-logical problem was described by the students as a means of feedback.
[I, b-b] Experimenting with the stones and the program is cool – and you can immediately check if the program is correct.
In summary, feedback for students is a key design element in our exploratory educational study. The decisive aspect for the students in our study was, on the one hand, that they could choose from a variety of feedback options. On the other hand, the feedback from the students made it evident that regardless of the type of feedback, it was important for the students that the desired feedback medium was available immediately when questions or problems arose. Thus, not only just-in-time learning but also just-in-time feedback was a central design element for the students of our exploratory educational study.
Novelty effects in the learning process
Students’ feedback made it clear that what was new or different in our exploratory educational study was a key design element for the students in our study. Students often described the new or different in our study in an undifferentiated way, merely contrasting the new or different with everyday teaching.
[I, b-b] Today it is a real change compared to normal lessons – that is exciting.
[F] What I liked about working with Logifaces was that it was really creative and different learning than usual.
However, much of students’ feedback also related to concrete design elements of our study. An essential aspect for the students was combining mathematics learning as well as using Logifaces-stones and technologies. The surprise associated with this combination had a positive effect on the students’ motivation, which can be found in the teaching notes as well as in the written feedback from the students:
[F] I found working with the building blocks really interesting and I would not have thought at first that the building blocks could have anything to do with mathematics or information.
In addition to combining mathematics, Logifaces-stones and technologies, new insights into the potential uses of Excel were a design element of our study that was remarkable for students.
[I, b-b-b] These lessons reveal just how powerful Excel actually is ... I would not have thought that you can almost do coding with Excel.
The feedback revealed that learning in our case study was always exciting and therefore motivating for students when something new or unexpected occurred during the learning process. This new or unexpected could refer to the design as a whole or very specific elements of our exploratory educational case study.