Determining how to provide good tutoring functions is an important research direction of intelligent tutoring systems. In this study, the authors develop an intelligent tutoring system with good tutoring functions, called "FUDAOWANG." The research domain that FUDAOWANG treats is junior middle school mathematics, which belongs to the objective…

This article presents a lesson that focuses on numeracy. In the lesson, students were tasked to find the best path for a new expressway. The purpose of the activity was for students to gain an appreciation of the complexities associated with designing public infrastructure and to put into practice the mathematical skills. This article also…

Research has shown that students should be given the opportunity to explore mathematical concepts by building on their knowledge and focusing on mathematical reasoning. When students represent ideas, make conjectures, collaborate with others, and give explanations and arguments, they are using mathematical reasoning (NCTM 2000). Certain teaching…

Has technology revolutionised the mathematics classroom, or is it still a device waiting to be exploited for the benefit of the learner? There are applets that will enable the user to solve complex equations at the push of a button. So, does this jeopardise other methods, make other methods redundant, or even diminish other methods in the mind of…

"When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data," notes the Common Core State Standards Initiative (2010, p. 72). This exploration of the recursive process in the Devil and Daniel Webster problem reveals that the symbolic spreadsheet fits this bill.…

Improving the mathematical skills of the next generation of students will require that elementary and middle school teachers are competent and confident in their abilities to perform fraction operations and to solve algebra equations The present study was conducted to (a) quantify relationships between prospective teachers' abilities to perform…

This study examined students' understanding of diagrams and their use of diagrams as tools to solve mathematical word problems. Students with learning disabilities (LD), typically achieving students, and gifted students in Grades 4 through 7 ("N" = 95) participated. Students were presented with novel mathematical word problem-solving…

Math Teachers' Circles have been spreading since their emergence in 2006. These professional development programs, aimed primarily at middle-level mathematics teachers (grades 5-9), focus on developing teachers' mathematical problem solving skills, in line with the Common Core State Standards-Standards of Mathematical Practice. Yet, to date,…

We share results from a quasi-experimental study in which we compared achievement between traditional lecture-based and computer-based sections of college algebra on a common multiple choice exam as well as performance on problem solving items. Students in the computer-based group performed better on the final exam and were also more likely to…

Based on Steiner's fascinating theorem for trapezium, seven geometrical constructions using straight-edge alone are described. These constructions provide an excellent base for teaching theorems and the properties of geometrical shapes, as well as challenging thought and inspiring deeper insight into the world of geometry. In particular, this…

This paper examines the use of contextual problems to support mathematical learning based on current classroom practice. The use of contextual problems offers some potentials to engage and motivate students in learning mathematics but it also presents some challenges for students in classrooms. Examples of the use of contextual problems from…

This study describes the mathematical construction of a real-life model by means of parametric equations, as well as the two- and three-dimensional visualization of the model using the software GeoGebra. The model was initially considered as "determining the parametric equation of the curve formed on a plane by the point of a pen, positioned…

Students' success in solving problems involving proportional reasoning is an indication that they have moved beyond additive thinking to multiplicative thinking. However, classroom work indicates that many students do not reason proportionally in many practical contexts. The authors discuss a particular task that reveals students'…

In this paper a two-stage research study is described focused on problem solving relevant to place-value and on the use of the operations within the calculator environment. The findings show that in this specific environment and via appropriate tasks teachers are provided with a context to better understand what year 5 or 6 pupils know or do not…

The use of manipulatives to teach mathematics is often prescribed as an efficacious teaching strategy. To examine the empirical evidence regarding the use of manipulatives during mathematics instruction, we conducted a systematic search of the literature. This search identified 55 studies that compared instruction with manipulatives to a control…