The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…

In this paper I analyze a problem solving event in a secondary mathematics classroom. As the event unfolds, the teachers, including me, understand the event as involving interactions that were not related to learning. By adopting an expansive view of learning, I advance a different interpretation, that the interactions tell a story of student…

The aim of this study is to measure the effects of teaching problem-solving strategies as an integrated part of the mathematical content prescribed by the curriculum. By implementing the designs principles developed in the previous study, we carry out a one-year-long teaching intervention in a Swedish upper secondary school. Pre- and post-tests…

In this study, I explored how (a) a team-based instructional method rather than a one-teacher-one-classroom, traditional teaching model and (b) an inquiry-based learning approach affected teachers attitudes and self-efficacy for teaching and students attitudes, self-efficacy, engagement, and connections to school. The study was conducted within…

Learners underperform in stoichiometry as they lack conceptual reasoning of the underlying concepts and the ability to solve stoichiometric problems. Therefore, it was necessary to determine if there is a statistical correlation between problem-solving skills and conceptual reasoning in stoichiometry and if so, whether one can significantly…

This article discusses how the key players' multilayered collaboration may be enacted by the Change Laboratory methodology in the footsteps of Virkkunen and Newnham (2013) to address a complex issue for the benefit of adolescents. It can be defined as a group processing approach used by a group to solve a problem of its own defining. Over six…

This research aims to produce a Learning Trajectory Based Instruction (LTBI) that can help the ninth grade students understand the concept of congruence of the two-dimensional shape by examining Lawang Sewu as one of Central Java historical buildings. LTBI is defined as a teaching and learning trajectory that uses Hypothetical Learning Trajectory…

This study aims to determine the ability of algebra students who have 3 levels van Hiele levels. Follow its framework Dindyal framework (2007). Students are required to do 10 algebra shaped multiple choice, then students work 15 about the geometry of the van Hiele level in the form of multiple choice questions. The question has been tested levels…

The research has shown a model of learning activities that can be used to stimulate reflective abstraction in students. Reflective abstraction as a method of constructing knowledge in the Action-Process-Object-Schema theory, and is expected to occur when students are in learning activities, will be able to encourage students to make the process of…

This study explores the effects of the "presence of external representations of a mathematical object" (ERs) on problem solving performance associated with short double-choice problems. The problems were borrowed from secondary school algebra and geometry, and the ERs were either formulas, graphs of functions, or drawings of geometric…

The objective of this paper was to develop a four dimensions dynamic model for designing instructional activities appropriate to electronic and virtual learning environments. The suggested model is guided by learning principles of cognitivism, constructivism, and connectivism learning theories in order to help online learners to build and acquire…

How does learning about scientists' struggles during their scientific knowledge building affect students' science learning? Two hundred and seventy-one high school students were randomly assigned to 1 of 3 conditions: (a) the struggle-oriented background information (n = 90) condition, which presented students with stories about 3 scientists'…

For middle and high school teachers of social studies and English, this book is filled with examples of instructional strategies that address students' readiness levels, interests, and learning preferences. It shows teachers how to formatively assess their students by addressing differentiated learning targets. Included are detailed examples of…

The focus is on the metacognitive awareness of ten high-achieving high school pupils from Denmark and England and their cognitive learning process. Un-structured interviews in smaller groups investigates how they say they learn a mathematical concept that is new to them. I develop the "CULTIS model for analysis" (Consciousness,…

It has been observed that students react in similar ways to mathematics and science tasks that differ with regard either to their content area and/or to the type of reasoning required, but share some common, external features. Based on these observations, the Intuitive Rules Theory was proposed. In this present study the framework of this theory…