Sun Xuhua Suanna

DOI: Vol.16(No.3) 155-176, 2012

It is an important issue to explore classroom environments which are conducive to developing students` mathematical performance. This study explores the effects of different classroom environments (solution-demand and corresponding-time setting) on mathematical performances. Fourteen and eighteen prospective teachers were required to prove a task under different conditions respectively: a) Cognitive demand of multiple-solution corresponding time of three hours, and b) Cognitive demand of a right solution corresponding time of 20 minutes. We used SOLO as the assessment tool for mathematical performance from quality perspective. Significant differences were found in the quantity and quality of mathematical performance. The regular environment focusing on speed and accuracy were found to be directly linked to low levels of performance. The findings above provide implications to the cognitive benefits of multiple-solution demand and corresponding time setting.

classroom environments, multiple-solution task, proving, trapezoid, cognitive demands

Huang Xingfeng , Li Shiqi , An Shuhua

DOI: Vol.16(No.3) 177-194, 2012

What strategies are used to help students understand quadratic functions in mathematics classroom? In specific, how does Chinese teacher highlight a connection between algebraic representation and graphic representation? From October to November 2009, an experienced teacher classroom was observed. It was found that when students started learning a new type of quadratic function in lessons, the teacher used two different teaching strategies for their learning: (1) Eliciting students to plot the graphs of quadratic functions with pointwise approaches, and then construct the function image in their minds with global approaches; and (2) presenting a specific mathematical problem, or introducing conception to elicit students to conjecture, and then encouraging them to verify it with appoint approaches.

Quadratic function, classroom teaching, pointwise approach, Global approach, Chinese mathematics classrooms

Seong A Kim , Jong Sool Choi

DOI: Vol.16(No.3) 195-206, 2012

We adopt a spirit of problem based learning to the class of Multivariable Calculus in a school of scientifically talented students and observed effects of our teaching-learning method in the Spring Semester of 2010. Twelve students and observed effects of our teaching-learning method with usual traditional one in the subject of multivariable calculus. Especially, we investigated changes in the learning attitude and cognitive development of the students toward definition and theorem of mathematics. Each group of 4 students worked on a sheet of our well-designed structured problems of several steps in each class and presented how they understood the way of constructing new definition and related theorems. Instructor`s role in this research was to guide students` activities as questioner so that students could attain the clear meanings of definitions and theorems by themselves. We firstly analyzed students` process of mathematization of definition through observing their discussions and presentations as well as their achievements in the quizzes and final exams. Secondly, we analyzed students` class-diaries collected at the end of each class in addition to pre/post surveys.

mathematization, Learning, cognitive development, small group discussions, definition, theorems, problem based Learning