Investigating the role of spatial thinking in children’s design ideation through an open-ended design-by-analogy challenge

Spatial thinking is ubiquitous in design. Design education across all age groups encompasses a range of spatially challenging activities, such as forming and modifying mental representations of ideas, and visualizing the scenarios of design prototypes being used. While extensive research has examined the cognitive processes of spatial...

Cognitive and embodied mapping of data: an examination of children’s spatial thinking in data physicalization

Understanding and effectively using visual representations is important to learning science, technology, engineering, and mathematics (STEM). Various techniques to visualize information, such as two- and three-dimensional graphs, diagrams, and models, not only expand our capacity to work with different types of information but also actively...

The effectiveness of activation of prior mathematical knowledge during problem-solving in physics

Mathematics is of major importance in science subjects. Unfortunately, students struggle with applying mathematics in science subjects, especially physics. In this qualitative study we demonstrate that transfer of algebraic skills from mathematics in physics class can be improved by using pre-knowledge effectively. We designed shift-problems...

The integral as accumulation function approach: A proposal of a learning sequence for collaborative reasoning

Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about<br/...

Teachers’ core beliefs about improving transfer of algebraic skills from mathematics into physics in senior pre-university education

Students in senior pre-university education face difficulties in the application of mathematics in physics. This paper presents the results of a qualitative study on teachers’ core beliefs about improving the transfer of algebraic skills to physics. Teachers were interviewed about their beliefs regarding a transfer problem from mathematics to...

Teachers’ beliefs systems about improving transfer of algebraic skills from mathematics into physics in senior pre-university education

Senior pre-university education (SPE) students experience difficulties applying mathematics to physics. This paper reports the outcome of an online explorative quantitative study of teachers' belief systems about improving transfer of algebraic skills from mathematics into physics, conducted among 503 mathematics and physics teachers working...

Teachers’ beliefs about improving transfer of algebraic skills from mathematics into physics in senior pre-university education

Students in senior pre-university education encounter difficulties in the application of mathematics into physics. This paper presents the outcome of an explorative qualitative study of teachers’ beliefs about improving the transfer of algebraic skills from mathematics into physics. We interviewed 10 mathematics and 10 physics teachers using...

Hyperelliptic integrals and generalized arithmetic–geometric mean

We show how certain determinants of hyperelliptic periods can be computed using a generalized arithmetic-geometric mean iteration, whose initialisation parameters depend only on the position of the ramification points. Special attention is paid to the explicit form of this dependence and the signs occurring in the real domain.