In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students' intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are…

Understanding how students translate between mathematical representations is of both practical and theoretical importance. This study examined students' processes in their generation of symbolic and graphic representations of given polynomial functions. The purpose was to investigate how students perform these translations. The result of the…

Much research has been conducted on how elementary students develop mathematical understanding and subsequently how teachers might use this information. This article builds on this type of work by investigating how one high-school algebra teacher designs and conducts a lesson on exponential functions. Through a lesson study format she studies with…

The National Council of Teachers of Mathematics [NCTM] noted that middle and high school students are expected to be able to both explain inequalities by using mathematical symbols and understand meanings by interpreting the solutions of inequalities. Unfortunately, research has revealed that not only do middle and high school students hold…

Recent mathematics education reform calls for efforts to create collaborative and student-centered environments, where students have opportunities to reason and construct their understanding as part of a community of learners. Mathematics instruction should provide students opportunities to engage in mathematical inquiry and meaning making through…

In this study we explored the effects of providing ninth-grade students with the chance to take part in decision making concerning the mathematics level they would be assigned to in high school. Decisions concerned their self-competence regarding their mathematical abilities, their learning goals and the class atmosphere. The students were taught…

Parental involvement in the form of "at-home" interest and support has a major influence on pupils' educational outcomes and attitudes. Many parents, however, feel uninformed about current educational practices and how they can be more involved with their child's learning. A number of initiatives have been implemented internationally to encourage…

This paper integrates technology, in the form of a physics simulation; science concepts, via image formation by lenses; and a mathematics apparatus, in the form of rational functions. All constituents merge into an instructional unit that can be embedded into a high school or undergraduate mathematics or physics course. The cognitive purpose of…

Proofs were introduced to high school students by a college mathematician. Student interest and knowledge level were assessed through pre and post tests. There was a significant gain in student knowledge but not in interest. Student learning of proof concepts was clearly displayed, while common errors were often related to lack of algebra skills.…

Student ability, teacher expectations, respective degrees of difficulty, and curriculum and instructional practices all work together to provide students experiences leading to differing levels of success in respect to mathematical translations. Herein, we discuss teacher beliefs and instructional practices, investigate why some translations seem…