The Sun and the Moon are our most visible neighbors in space, yet their distance and size relative to the Earth are often misunderstood. Science textbooks fuel this misconception because they regularly depict linear images of Moon phases without respect to the actual sizes of the Sun, Earth, and Moon, nor their correlated distances from one…

This paper uses a partial differential equation which occurs in a reduced model of large scale circulation in an ocean basin as an educational vehicle through which to demonstrate the usefulness of a set of mathematical techniques in analysing the equation. A parameter occurring in the equation does in reality vary from very small through…

This study addressed a twofold problem--the soundness of a theoretical stage-distinction regarding the process of constructing a new (to the learner) mathematical conception and how such distinction contributes to fine grain assessment of students' mathematical understandings. As a context for the study served the difficult-to-grasp concept of…

Gender differences in speed of perceptual comparison, of picture-plane mental rotation, and in switching costs between trials that do and do not require mental rotation, were investigated as a function of stimulus material with a total sample size of N=360. Alphanumeric characters, PMA symbols, animal drawings, polygons and 3D cube figures were…

This article presents a story of Robert Andrew's mental engagement with mathematics. It has been jointly written by Robert, who is a Y8 student, and his father, Paul Andrews, who is a mathematics educator. It starts with Robert who presents the context for the story and is followed by Paul's commentary which draws on what Robert has written.…

"Geomlab" is a functional programming language used to describe pictures that are made up of tiles. The beauty of "Geomlab" is that it introduces students to recursion, a very powerful mathematical concept, through a very simple and enticing graphical environment. Alongside the software is a series of eight worksheets which lead into producing…

In the middle years of primary schooling, the teaching of common fractions frequently involves written activities that use abstract representations of numbers, symbols, and images. Many students, however, still need the benefit of concrete materials and sensory motor experiences to enhance their understanding of the concepts associated with common…

As a teacher's aide this author is often asked to help children who have difficulty with mathematics. Recently she was asked to help children from three different grades with their understanding of time. Although each grade had a different activity to undertake, all of the children struggled to grasp time-concepts that adults often take for…

A sample (n=48) of eight-year-olds with specific language impairments is compared with age-matched (n=55) and language matched controls (n=55) on a range of tasks designed to test the interdependence of language and mathematical development. Performance across tasks varies substantially in the SLI group, showing profound deficits in production of…

I identify and discuss ways in which different types of connections are described in the South African mathematics National Curriculum Statement and its related documents, particularly at the Further Education and Training (FET) level. I argue that connections are central to the way the discipline of mathematics, its learning outcomes, and…

New Mexico Mathematics Content Standards, Benchmarks, and Performance Standards identify what students should know and be able to do across all grade levels, forming a spiraling framework in the sense that many skills, once introduced, develop over time. While the Performance Standards are set forth at grade-specific levels, they do not exist as…

In 12 audio taped sessions, three kindergarten children engaged algebra in a teaching for understanding, thematic project. Toni, Asa, and Cornel had one-on-one lessons dealing with simple natural numbers, patterns, and relationships. Along the way, each child studied one of Toni Morrison's Who's got game books to explore repetition patterns in…

Users of logistic regression models often need to describe the overall predictive strength, or effect size, of the model's predictors. Analogs of R[superscript 2] have been developed, but none of these measures are interpretable on the same scale as effects of individual predictors. Furthermore, R[superscript 2] analogs are not invariant to the…

With the current focus in mathematics education on the importance of developing students' conceptual understanding, fluency with the language of mathematics, critical thinking, and working mathematically, teachers are constantly expected to design challenging and investigative tasks that can engage and motivate students in their learning of…

There are many classroom activities that can be implemented with primary students that introduce and immerse them in ratio investigations. Some enjoyable tasks include finding the ratio of tongue rollers to non-tongue rollers in the classroom; left-hand dominant to right-hand dominant; right-thumb over left-thumb when clasping the hands to…