Providing adequate proof is one essential mathematical method, but it is a difficult task for many school-age students. While previous studies have revealed the cognitive factors of proving the proof, the function of affective factors and learning engagement has been largely unexplored. This study examined the effects and processes associated with…

Many students are not good at geometric proofs. One reason for this is that it is possible to memorize the proof procedure explained by the teacher without understanding the structure of a geometric proof. So far, we have developed a web-based application that supports the understanding of the "structure of geometric proofs" in junior…

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…

Recent research on the scaffolding of instruction has widened the use of the term to include forms of support for learners provided by, amongst other things, artefacts and computer-based learning environments. This paper tackles the important and under-researched issue of how mathematics lessons in junior high schools can be designed to scaffold…

Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…

Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…

This research is a descriptive research with scanning method. It aims to define the relationship between the gender and academic success of secondary school students and their play preferences. The population of the research is composed of the secondary schools of Burdur city centrum and the sample group is composed of the students who are…

In this study, students' views were taken about history of Pythagoras theorem that contains improved activity which in the history people was thrilled at and there are a lot of their proofs. The study was conducted with 15 students 8th grade at a public elementary school in Trabzon during the spring term of 2009-2010 school year. Case study method…

Prior research on students' uses of technology has suggested it can be used to support students' development of formal justifications and proofs. The ways in which these technologies influence the construction of arguments and proofs remain uncertain. Furthermore, research has not been conducted that compares the arguments students develop while…

An online interactive geometry item was developed to explore students' abilities to create prototypical and "tilted" rectangles out of line segments. The item was administered to 1,002 students. The responses to the item were hand-coded as correct, incorrect, or incorrect with possible evidence of a misconception. A variation of the nearest…

Learning about the area formulas provides many opportunities for students even at the beginning of junior secondary school to experience mathematical deduction. For example, in easy cases, students can put two triangles together to make a rectangle, and so deduce that the area of a triangle is half the area of a corresponding rectangle. They can…

This study examines the mediating role of homework in the daily practice of a middle-school mathematics teacher and her colleagues in Shanghai. It aims to explore how a system of homework activities mediates and engenders a cultural pedagogy characterized by transforming errors into resources for teaching and learning. The transformation itself…

This paper presents key findings of my research on the approaches to justification by investigating how a sample of teachers in Hong Kong and Shanghai taught the topic Pythagoras theorem. In this study, 8 Hong Kong videos taken from TIMSS 1999 Video Study and 11 Shanghai videos videotaped by the researcher comprised the database. It was found that…