This article focuses on exploring students' understanding of the concept of function concerning three main aspects: secondary students' ability to (1) define the concept of function and present examples of functions, (2) solve tasks which asked them to recognize and interpret the concept of function presented in different forms of representation,…

Beliefs and problem solving are connected and have been studied in different contexts. One of the common results of previous research is that students tend to prefer algorithmic approaches to mathematical tasks. This study explores Swedish upper secondary school students' beliefs and reasoning when solving non-routine tasks. The results regarding…

Supporters of K-12 arts education often make the case that when students study music, dance, theatrical performance, and the visual arts, they tend to improve in the academic subjects as well. But, as Lois Hetland explains, that's not the best way to advocate for greater investments in arts instruction. In fact, a careful analysis of a vast amount…

We are in an era that calls for increasing "training" in educational research methodologies. When the National Research Council (2004) calls for training in educational research that is "rigorous" and "relevant," the focus strongly emphasizes WHAT should be taught instead of WHO is being engaged in the learning.…

Cognitive aspects of children's executive function (EF) were examined as moderators of the effectiveness of parental guidance on children's learning. Thirty-two 5-year-old children and their parents were observed during joint problem-solving. Forms of guidance geared towards cognitive assistance were coded as directive or elaborative, and…

The use of medical metaphors of different types of language tests such as diagnostic test, a screening test, a remedial test have misled many language teachers and educators into believing that such tests are panacea for all L2 learning difficulties and ensure successful language learning. They seem to put an overemphasis on learning product…

Computer scientists are working on reproducing all human skills using artificial intelligence, machine learning and robotics. Unsurprisingly then, many people worry that these advances will dramatically change work skills in the years ahead and perhaps leave many workers unemployable. This report develops a new approach to understanding these…

Solving unfamiliar problems on one's own is important, but in today's increasingly interconnected world, people are often required to collaborate in order to achieve their goals. Teamwork has numerous benefits, from a diverse range of opinions to synergies among team members, and assigning tasks to those who are best suited to them. Collaboration…

A cadre of school inspectors with different backgrounds visit thousands of schools annually in Sweden as is also the case in several other European and other nations. Do these inspectors believe that they 'make a difference'? In this chapter we elaborate on inspection effects as they are perceived by Swedish inspectors and inspection managers at…

The goal of educating for creativity must be active understanding rather than passive knowing. To understand is to have the capability to re-create, which trains the ability also to create. The ability to create requires problem-finding as well as problem-solving. It requires practice. Best practice involves the emulation of creative people and…

Computational fluency is composed of three components: efficiency, mathematical flexibility, and conceptual understanding. Although research highlights the importance of all three of these components in mathematical understanding, a majority of assessments primarily focus on efficiency. In this paper, we propose a novel way of measuring and…

We reflect upon a paper we wrote that was published in 1995 (20 years ago). We outline the motivation for the work and situate it in the state of the art at that time. We suggest that a key contribution was to highlight the need to provide support for learners who reason with external representations. The support must be flexible enough to…

Although counting problems are easy to state and provide rich, accessible problem-solving situations, there is much evidence that students struggle with solving counting problems correctly. With combinatorics (and the study of counting problems) becoming increasingly prevalent in K-12 and undergraduate curricula, there is a need for researchers to…

I think most physics teachers would agree that two important components of a proper solution to a numerical physics problem are to first figure out a final symbolic solution and to only plug in numbers in the end. However, in spite of our best efforts, this is not what the majority of students is actually doing. Instead, they tend to plug numbers…

Previous research indicates that sensori-motor experience with physical systems can have a positive effect on learning. However, it is not clear whether this effect is caused by mere bodily engagement or the intrinsically meaningful information that such interaction affords in performing the learning task. We investigated (N = 74), through the use…