The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

This paper justifies the need for, and offers some suggestions on, the selection and implementation of mathematical problems known as dynamic solution exercises (DSEs). The intent of this article is to help provide insight into how mathematics teachers can go about making "vertical articulation" a cooperative and tangible part of the…

The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…

This article presents results of a case study of a math circle designed for low income, minority students from an inner city middle school. The students were 6th, 7th and 8th grade African American and Hispanic males enrolled in a science, technology, engineering and mathematics focused charter school. The study focused on the impact of…

We define a differential operator for analytic functions of fractional power. A class of analytic functions containing this operator is studied. Finally, we determine conditions under which the partial sums of the linear operator of bounded turning are also of bounded turning.

Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their…

In this article we consider, via a specific modelling example, the educational benefits to be gained from running mathematical activities with our sixth-form and undergraduate students that, in modern parlance, might be termed "rich tasks". The idea for this modelling activity arose while the author was reading a popular-science book on cosmology…

We unpack the notion of mathematics teacher educators modeling teaching in mathematics teacher education courses. Specifically, we investigated what practicing teachers gained from mathematics teacher educators' modeling by examining: (1) What do mathematics teacher educators believe they model about effective instructional practice? (2) What do…

This article reports on the findings of a research project whose aim was to support and enhance the teaching of risk at Key Stage 4. An innovative and cross-curricular approach has been used, based on modelling socio-scientific issues using new technological tools, designed specifically to enable the consideration of ethical and social issues,…

Communicating and collaborating online are becoming common requirements in education. The specialized notations and symbols necessary for some content areas where mathematical expressions are part of the conversation require that users select appropriate communication tools. The purpose of this article is to describe tools that can be used for…

The butterfly curve was introduced by Temple H. Fay in 1989 and defined by the polar curve r = e[superscript cos theta] minus 2 cos 4 theta plus sin[superscript 5] (theta divided by 12). In this article, we develop the mathematical model of the butterfly curve and analyse its geometric properties. In addition, we draw the butterfly curve and…

Infinity and infinitely small numbers pique the curiosity of middle school students. From a very young age, many students are intrigued, interested, and even fascinated by extremely large or extremely small numbers or quantities. This article describes an activity that takes this curiosity about infinity into the domain of adding the numbers of an…

The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The materials are centered on the fictional town of Happy Shores, a coastal community which is at risk for hurricanes. Actuaries at an insurance company figure out the risks and…

Many students have some difficulty with calculations. Simple dimensional analysis provides a systematic means of checking for errors and inconsistencies and for developing both new insight and new relationships between variables. Teaching dimensional analysis at even the most basic level strengthens the insight and confidence of students, and…