As mathematics educators we want our students to develop a natural curiosity that will lead them on the path toward solving problems in a changing world, in fields that perhaps do not even exist today. Here we present student projects, adaptable for several mid- and upper-level mathematics courses, that require students to formulate their own…

In that current study, pattern conversion ability of 25 pre-service mathematics teachers (producing figural patterns following number patterns) was investigated. During the study participants were asked to generate figural patterns based on those number patterns. The results of the study indicate that many participants could generate different…

The analytical scheme used in the project The Evolution of the Discourse of School Mathematics (EDSM) was developed to analyse the change over time in examination texts. An adapted version of the EDSM scheme has been deployed to analyse the nature of mathematics construed in Palestinian schools' textbooks and the mathematical activity expected of…

Many school systems are adopting new curricula in response to more rigorous standards that require higher-order thinking skills. This chapter presents implementation findings from a randomized, controlled trial of the Cognitive Tutor Geometry curriculum. We found a significant negative effect on student achievement despite the curriculum's focus…

In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and…

An engaging activity which prompts students to listen, talk, reason and write about geometrical properties. The "Bag of Tricks" encourages students to clarify their thoughts and communicate precisely using accurate mathematical language.

This study aimed to reveal the effects of teaching with concrete learning objects taken from the history of mathematics on student achievement. Being a quasi-experimental study, it was conducted with two grade 8 classes in a secondary school located in Trabzon. The experimental group consisted of 27 students and the control group consisted of 25.…

Between 2003 and 2013, the proportion of California 8th graders enrolled in Algebra or a more advanced course nearly doubled to 65 percent. In this paper, we consider the organizational processes that accompanied this curricular intensification. Facing a complex set of accountability, institutional, technical/functional, and internal political…

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

For students who have difficulty envisioning how the mathematics that they are learning is used outside the classroom, an adventure as field mathematicians can be enlightening. Measuring stream discharge is a field experience that allows students to engage in a hands-on (and boots-on) real-world, problem-solving activity and that integrates…

NCTM (2000) described geometry as "a means of describing, analyzing, and understanding the world and seeing beauty in its structures" (p. 309). Dossey et al. (2002) captured the essence of this aspect of visualization by stating that geometry fosters in students an ability to "visualize and mentally manipulate geometric objects." (p. 200).…

"I CAN Learn"[R] is a computer software system that provides math instruction through a series of interactive lessons. These lessons are delivered with a one-to-one student-to-computer ratio. Students determine the pace of each lesson and must demonstrate mastery of the lesson before progressing to the next one. Teachers provide…

Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…

Whereas origami is said to have pedagogical benefits in geometry education, research is inclusive about its effect on spatial ability and geometric knowledge among preservice teachers. The study investigated the effect of origami instruction on these aspects using pretest posttest quasi-experiment design. The experimental group consisted of 52…

The uptake of technology and specifically, GeoGebra software, in teaching mathematics has had mixed success in spite of its documented benefits. This study investigated teachers' perspective towards training and eventual use of GeoGebra as a tool to enhance learning of mathematics. In this article we share findings from a larger study that was…