According to our approach to mathematics education, the optimal aim of the teaching of mathematics is to assist students in achieving efficient mathematical work. But, what does efficient exactly mean in that case? And how can teachers reach this objective? The model of Mathematical Working Spaces with its three dimensions--semiotic, instrumental,…

In this paper, readers are guided through the design and development of educational programs based on the 4C/ID model. This was illustrated via a practical example in Physics education, to teach the theme "Electrical circuits" to students of the 9th grade of compulsory education. In the article, the followed steps are described, from…

School engagement involves cognitive, emotional, and behavioral components that overlap conceptually. This conceptual ambiguity has led to measures that have either consisted of one general factor or separate correlated factors. However, neither approach can sufficiently account for both the uniqueness and the overlap of the subcomponents. The…

The present study investigates the empirical separability of mathematical (a) content domains, (b) cognitive domains, and (c) content-specific cognitive domains. There were 122 items representing two content domains (linear equations vs. theorem of Pythagoras) combined with two cognitive domains (modeling competence vs. technical competence)…

Learning how to give effective feedback can be a difficult task for teacher leaders. This is especially true for what is called "hard feedback"--that is, feedback that challenges the teacher's practice and therefore may cause some level of professional discomfort. Educators at the University of Pittsburgh's Institute for Learning have…

In this study, the effect of 3 cognitive variables such as logical thinking, field dependence/field independence, and convergent/divergent thinking on some specific students' answers related to the particulate nature of matter was investigated by means of probabilistic models. Besides recording and tabulating the students' responses, a combination…

In recent years, science education has placed increasing importance on learners' mastery of scientific reasoning. This growing emphasis presents a challenge for both developers and users of assessments. We report on our effort around the conceptualization, development, and testing the validity of an assessment of students' ability to reason around…

This work uses the concepts and tools of complexity theory to examine the effect of logical thinking and two cognitive styles, such as, the degree of field dependence/independence and the convergent/divergent thinking on students' understanding of the structure of matter. Students were categorized according to the model they adopted for the…

In the present study, I examine a modelling strategy as employed by a teacher in the context of an algebra lesson. The actions of this teacher suggest that a modelling approach will have a greater impact on enriching student learning if we do not lose sight of the need to manage associated cognitive loads that could either aid or hinder the…

This study reports on our steps toward achieving a conceptually coherent and empirically validated learning progression for carbon cycling in socio-ecological systems. It describes an iterative process of designing and analyzing assessment and interview data from students in upper elementary through high school. The product of our development…