Introducing an approach to detailed assessment involving videotaping clinical interviews, the authors highlight strengths of this approach for understanding children's thinking, informing instruction, and furthering professional learning. (Contains 4 figures.)

This article describes a tool teachers can use to analyze student work and provides activity suggestions to guide instruction based on their findings. By integrating the voice of the child and the voice of the discipline, teachers can use their inner voice to build a model of the child's understanding. (Contains 8 figures.)

In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts. The data we then present provides evidence of the possibility of learning new concepts through…

This qualitative study examined the relationship between young deaf children's level of mathematics ability ("high" and "low," as defined by test score on the Test of Early Mathematics Ability-3) and opportunities available for the construction of early mathematics knowledge during a problem-solving task implemented by their parents. Findings…

The reactions of students towards mathematics in Bali (in the NW Province of Cameroon) are appalling. This is due to a misconception regarding its uses. The author thinks that these problems derive partly from the influence that the Western curriculum has had in Bali--mathematical contexts are based around train times in Liverpool instead of from…

In the author's second grade maths class, the students were excited and energised after discovering, understanding and learning an advanced mathematical concept. In the class, the second-graders spent a great deal of time discussing how they used the number grid to work out 96 - 7. In this article, the author presents a portion of the class…

It is important for students to have opportunities to experience mathematics in contexts outside of the mathematics classroom. The links between mathematics and other disciplines can help students develop a fuller understanding of mathematics. Problems arising in health, science, and social studies can help students understand ratios, measurement,…

Research suggests that young children's active participation in music supports emergent mathematics knowledge, such as patterning and one-to-one correspondence. The authors define and explain steady beat, rhythm, melody, tempo, dynamics, rhythm, and style. They suggest ways teachers can use these elements of music with infants, toddlers, and young…

We report a case study that explored how three college students mentally represented the knowledge they held of inferential statistics, how this knowledge was connected, and how it was applied in two problem solving situations. A concept map task and two problem categorization tasks were used along with interviews to gather the data. We found that…

Given a 5-peg by 5-peg geoboard, how many different lengths can be made by stretching a rubber band to form an oblique segment between any two pegs? This investigation requires students to make connections to the Pythagorean theorem, congruence, and combinations. With its use of visual representation and a range of mathematical ideas that can be…

A way to present the concept of symmetry to children is presented. (DB)

This article shows how Pythagorean triples can be generated naturally from a class of infinite series whose sums are zero, making surprising and interesting connections between different areas mathematics. This material can be suitable for use by teachers and students at various levels, but the simplest forms of the ideas may be best understood at…

Greek philosopher mathematician, Aristarchus of Samos, in the third century B.C., proposed that the sun held in the central position, casting its light symmetrically outward on the other celestial bodies. He demonstrated the way in which a person could use simple observations and elementary geometry to measure on a cosmic scale.

In this note properties of two sequences generated by the recurrence relation G[subscript n] +2 = 4 G[subscript n] +1 - G[subscript n], are studied. It is shown that one of the sequences leads to a family of diophantine triplets. Some interesting properties of these sequences are also established.

Helping pre-service teachers to feel competent and courageous about the mathematics they will find themselves teaching as elementary school teachers is a critical component of any math methods course. This paper addresses this aim by highlighting a process that involves pre-service teachers in creating original mathematics literature books. This…