This paper looks at an activity that breaks the normal classroom teaching pattern (where students are often content to be reluctant, inactive participants in the learning process) with an activity that is likely a new experience for most students--letting the students create and solve their own problems. This is done within a problem structure…

The purpose of this research is to know how Naïve Geometry method can support students' understanding about the concept of solving quadratic equations. In this article we will discuss one activities of the four activities we developed. This activity focused on how students linking the Naïve Geometry method with the solving of the quadratic…

Gain a new perspective on the sharing of erroneous solutions in classroom discussions. Based on their research in grades four and six, the authors reveal how student-to-student correction of errors promotes mathematical reasoning and understanding. Tips for teachers include strategies for using students' errors to encourage reasoning during…

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth…

I propose an approach to service-learning that encourages and enables students to engage with human rights and social justice in ways that are democratic and effective. I describe a teaching process in which civic action can be critically reflected on not just to promote engagement and build knowledge but ultimately to encourage and equip students…

We have designed a unique guided-inquiry-inspired course for entry-level graduate students using chemical research as a mechanism to teach research-oriented problem-solving skills. The course has been designed for flexibility around a shared research experience. The curriculum can be modified each year by incorporating a new research project into…

Today's students require educators who will guide them to think critically, grow in character, and value relationships. These students become empowered to change their world and overcome social and racial oppression and marginalization. Empowered students are those who attain skills and knowledge with their teachers, and become equipped and…

The goal of the study was to reconstruct and dismantle a sequence of events that preceded an insight solution to a challenging problem by a ninth-grade student. A three-week long solution process was analysed by means of the theory of shifts of attention. We argue that concurrent focusing on what, how and why the student attends to when working on…

This paper reports on the role of the graphing calculator (GC) in the learning of derivatives and instantaneous rate of change. In a longitudinal study, we administered task based interviews before and after the introduction of calculus. We analyzed students' use of the GC in these interviews. This paper reports on the case of one student, Andy,…

An English teacher and a math teacher collaborating to improve practices in classroom discussion develop a problem-solving method that steers students away from seeking simple solutions and into an understanding of the complexity and nature of problems.

The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…

The Spider and the Fly puzzle, originally attributed to the great puzzler Henry Ernest Dudeney, and now over 100 years old, asks for the shortest path between two points on a particular square prism. We explore a generalization, find that the original solution only holds in certain cases, and suggest how this discovery might be used in the…

Word problem solving involves the construction of two different mental representations, namely, mathematical and situational. Although educational research in word problem solving has documented different kinds of instruction at these levels, less is known about how both representational levels are evoked during word problem solving in day-to-day…

Creativity, which is concerned with problem solving, is essential if we are to generate new solutions to the massive and complex problems in the unknown future. Our next generation needs an educational platform where they can be taught to possess creativity. Design education is such a way to foster students' creativity. Therefore, it is essential…

The purpose of the study is to examine and evaluate the impact the the multimedia textbook-based interactive, based on ICT model learning environment provides for the learning styles of the university students majoring in Philology. The study sought to identify tangible (seemingly measurable) and intangible (difficult to measure) gains this…