The purpose of this study was to determine if the use of a graphical teaching and learning approach via the graphing calculator enhances students' understanding of the formal definition of limit. College students in six sections of Calculus I participated by completing a test prior to the introduction of the definition, and completing a second…

This article examines a classroom discussion of multiple interpretations of the scales on two distance versus time graphs. The analysis describes how two students and a teacher used multiple meanings for phrases of the form "I went by" and coordinated these meanings with different views of the scales. Students' ambiguous and shifting meanings did…

Students mainly perceive the transition to secondary school as an opportunity to start their school career anew. Reality often proves them wrong, especially in the case of mathematics. In our paper, we briefly discuss children's transition to secondary school as both an opportunity and a problem, with reference to the Greek context. In discussions…

In 2006, as a beginning teacher in a Western Sydney school, the author explored slow motion animation ("slowmation") as a strategy for teaching Year 4 students about equivalent fractions. She taught at this school five days a week, teaching Kindergarten, Year 4, and Year 5. Slowmation can be defined as a simplified version of claymation…

The National Council of Teachers of Mathematics (NCTM)'s Process Standards support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every primary teacher the opportunity to explore each standard in depth. With language and examples that don't require…

Simple nongraphing calculators can be powerful tools to enhance students' conceptual understanding of mathematics concepts. Students have opportunities to develop (1) a broad repertoire of problem-solving strategies by observing multiple solution strategies; (2) respect for other students' abilities and ways of thinking about mathematics; (3) the…

Using cognitive ethnography as a guiding framework, we investigated US and Japanese fourth-grade teachers' domain knowledge of key fraction representations in individual interviews. The framework focused on revealing cultural trends in participants' organization of knowledge and their interpretations of that organization. Our analyses of the…

The purpose of this study is to design a constructivist learning environment that helps learning the limit concept. The study is a pretest-posttest quasi-experimental research. The control and the experimental groups were chosen from the students attending a calculus course. Worksheets were used to assess students' learning of the limit concept.…

Amy Biehl High School (ABHS) is a charter high school located in downtown Albuquerque that serves students from Albuquerque and the surrounding communities. Despite its population's differences in skills, special needs, socioeconomic class, race, culture, and English proficiency, it has one common goal for all its students: that they are able to…

In this study the effectiveness of an arrow diagram which can help students apply the Chain Rule was investigated. Different variations of this diagram were used as mnemonic devices for applying the Chain Rule. For the investigation two instruments were developed, diagnostic test and post-test. The diagnostic test was developed to determine the…

For over a decade it has been a common observation that a "fog" passes over the course in linear algebra once abstract vector spaces are presented. See [2, 3]. We show how this fog may be cleared by having the students translate "abstract" vector-space problems to isomorphic "concrete" settings, solve the "concrete" problem either by hand or with…

Today's method of teaching the concept of falling bodies in French physics classes is ineffective, not only because it ignores the physical aspect of the phenomenon by addressing only its mathematical aspect, but also because it does not take into account students' initial conceptions, which are often incompatible with scientific knowledge. The…

Mathematics achievement is important in its own right, and is increasingly recognized as crucial to the nation's economy [National Mathematics Panel, 2006. "National Mathematics Advisory Panel: Strengthening Math Education Through Research." Accessed September 29, 2006 from http://www.ed.gov/about/bdscomm/list/mathpanel/factsheet.html.; National…

Research has found that teachers of mathematics are more effective when they have a profound understanding of the content that is being taught and the content to which students have previously been exposed. It is clear that professional programs must enable preservice teachers to develop the knowledge and skills they need to teach elementary…

In the renewed "Primary Framework for Mathematics" for England, great emphasis is given to calculation and its prerequisites (DfES, 2006). Expectations are increased for calculations and the recall of number facts, with mental calculation owning a higher profile, while progression in written calculation is clarified. The greater focus on…