Since Bruner's introduction of discovery learning in the 1960s, there has been an ongoing and intensive debate on the value of inductive teaching methods (e.g., problem-solving followed by instruction, such as in problem-based learning and productive failure) compared to deductive teaching methods (instruction followed by problem-solving, such as…

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…

Historically, police educators delivering academy programs have overused traditional or teacher-centred methods as part of an authority driven command and control culture. In addition to being educationally unsound, this teaching approach has limited the development of the critical thinking skills needed for effective reform in the community…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the…

This study focuses on the problem of 'teachers' teaching' and 'students' learning' in college education courses. It aims to introduce the Deep Learning theory into the teaching of ideological and political theory courses in universities; deepen the theoretical framework of education courses and the associated learning, maintenance, promotion, and…

Transformative learning theory has provided a sound theoretical base for adult education's Western and Eastern academic field. This article aims to introduce the mandala model of transformative learning by transferring Mezirow's theory of perspective transformation onto a mandala map. In the mandala model, the learning agent exercises two…

Worked examples are effective learning tools for algebraic equation solving. However, they are typically presented in a static concise format, which only displays the major derivation steps in one static image. The current work explores how worked examples that vary in their extensiveness (i.e., detail) and degree of dynamic presentation (i.e.,…

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…

We report here on an intervention implementing a structural approach to arithmetic problem-solving in relation to learning outcomes among preschoolers. Using the fundamental principles of the variation theory of learning for developing the intervention and as an analytical framework, we discuss teaching and learning in commensurable terms. The…

This article presents a review of literature exploring five different perspectives on mathematical modeling in mathematics education. Because there is not a single agreed-on definition of what mathematical modeling is or how it should be done, a focused and extensive review of mathematical modeling is essential. The five broad classifications…

Recently, Gauthier introduced a method to construct solutions to the equations of motion associated with oscillating systems into the mathematics education research literature. In particular, Gauthier's approach involved certain manipulations of the differential equations; and drew on the theory of complex variables.Motivated by the work of…

This paper presents a model for mastery learning. The framework for this model overlays the cognitive and knowledge dimensions from Krathwohl's revision of Bloom's Taxonomy, the Revised Taxonomy, with Polanyi's theory of personal knowledge. A simplified framework integrates Polanyi's concepts of subsidiary and focal awareness with the Revised…

This paper examines current views and definitions of learning transfer as well as their dominant characteristics. An alterior way to view learning transfer as preparation for future learning (PFL) is presented along with its defining features. This paper is divided into five sections: (a) what comprises learning transfer, (b) the conventional…

Research shows that teachers and educators struggle to act when conflict appears in the classroom. This article argues that (political) conflict should not be avoided or eradicated. Teachers should enable conflict and attend to their pupils in the process, in order to enable further understanding of each other and their differences, as part of…