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Studies have shown that learning mathematics through programming can be complex and that the programming itself might even hamper students’ learning. However, few studies have focused on the role of the teacher and the teacher-student interaction that aims to support students’ learning when using programming. The present study examines a didactic design in which a teacher uses well-prepared questions and suggestions that focus on students’ reasoning to solve mathematical problems using Scratch, a block-based programming environment. Forty students, 10-11 years old, solved a geometry problem using Scratch supported by their teacher. The students’ screen activities and teacher-student interactions were recorded. The results indicate that well-prepared general and task-specific questions targeting students’ creative reasoning can help to overcome some of the complexities of learning mathematics while programming. The study furthermore shows that when students have sufficient programming skills, Scratch could even have the potential to support their reasoning and at the same time guide the teacher to give timely feedback.

The present study investigates how to support students’ creative reasoning when they need assistance in solving non-routine tasks. Two groups of 11–12-year-old students solved the same tasks, one group receiving feedback directed at the task solution and the other feedback directed at their thinking processes. The results showed that stu- dents who received feedback directed at their thinking processes expressed reason- ing based on their attempts to solve tasks while the other group often repeated the researcher’s suggestions for solutions. However, there were some instances in which feedback on task level entailed students engaging in creative reasoning.

Rapporter och studier visar att elever som får traditionell matematikundervisning har ytliga kunskaper som snabbt glöms bort och att de ofta är oengagerade inför skolmatematiken. Kreativa resonemang i matematikundervisningen handlar om hur lärare kan planera och genomföra en mer elevaktiv undervisning, som leder till mer bestående och djupgående matematikkunskaper hos eleverna. Boken visar hur undervisning som bygger på problemlösning och kreativa resonemang ger läraren goda möjligheter att genom feedback och frågor stödja elever att utveckla alla de matematiska förmågor som nuvarande läroplan tar upp. Boken inleds med en teoretisk bakgrund med illustrerande exempel. Därefter presenteras ett ramverk för planering och genomförande av undervisning genom kreativa resonemang. Avslutningsvis diskuteras olika aspekter av hur undervisning som planerats enligt ramverket har fungerat i praktiken.Kreativa resonemang i matematikundervisningen vänder sig till lärare, skolledare och lärarstuderande som vill utveckla matematikundervisningen enligt aktuell forskning om lärande i matematik.

The present study contributes to knowledge about how to design tasks that benefit from dynamic software in math education, comparing practice performance and learning outcomes among 129 students practicing on two different task designs using GeoGebra. The task designs differed with respect to the presence or absence of guidelines on how to solve the task. One student group practiced on the guided task while the other student group practiced on the unguided task, and 1 week later a posttest was conducted. Data were statistically analyzed and showed significant differences with regard to success during practice for students solving the guided task. Among the students who succeeded in solving the task (guided or unguided) during practice, however, the analysis showed significant differences in the posttest performance in favor of the unguided students.

This study contributes insights into how task design with different elements of guidancemay influence students’ utilization of dynamic software for problem solving andreasoning. It compared students’ solving of two tasks with different designs supportedby the dynamic software GeoGebra. Data analysed examined students’ approaches toutilizing GeoGebra, the characteristics of their reasoning and their ability to prove thevalidity of their solutions after solving the problems. The results showed that studentswho solved the task with less guidance (without instructions about a specific solvingmethod) were better able to utilize GeoGebra’s potential to support their reasoning andproblem solving. These students reasoned more creatively and presented more advanced proofs for their solutions than the more guided ones.

This paper presents the way pilot studies underpin a design for a future project investigating how formative feedback can be designed in order to support students’ creative reasoning when constructing solutions to mathematical tasks. It builds on the idea that creative reasoning is beneficial to students’ mathematical learning. Four pilot studies have been performed with the purpose of creating an empirical base for the preparation of formative feedback to students in mathematics classrooms. The results represent a development of general theoretical guidelines for formative feedback. Our specific and empirically based guidelines will act as a starting point for further intervention studies investigating the design of formative feedback aimed at supporting students’ creative reasoning.

This study investigates how students’ reasoning contributes to their utilization of computer-generated feedback. Sixteen 16-year-old students solved a linear function task designed to present a challenge to them using dynamic software, GeoGebra, for assistance. The data were analysed with respect both to character of reasoning and to the use of feedback generated through activities in GeoGebra. The results showed that students who successfully solved the task were engaged in creative reasoning and used feedback extensively.