Recounts a classroom experience which investigated whether any integral solutions for the law of cosines would be analogous to "Pythagorean triples." Several interesting relationships were discovered. (PK)

Two major ways to view the numbers to 100 are counting by ones and grouping by tens and ones. Research suggests that early understanding of numbers comes from counting and that place value instruction cannot be hurried. (PK)

One method (attributed to Archimedes) of approximating pi offers a simple yet interesting introduction to one of the basic ideas of numerical analysis, an iteration sequence. The method is described and elaborated. (PK)

College students were asked to write equations using one of two sets of notational systems. Results indicate that the use of more explicit notation did not help problem-solving performance. (Author/PK)

Discusses the nature and importance of iconic learning (image-related) and a medium to facilitate assessment at the iconic level of knowing. The medium consists of a series of self-inking rubber stamps made with iconic representations of numeration blocks and sticks in denominations of 1, 10, and 100. (JN)

Presents research on cognitive skills demanded by elementary and secondary school mathematics textbooks, based on an original 10-level classification of thinking activities; reports a general decline both in the amount of material demanding student involvement and in the percentage of that material requiring higher-order thinking. (MCG)

Discusses how children's knowledge can be measured/described, knowledge patterns across diverse concepts, interaction of knowledge/learning, and ways children construct more advanced problem-solving rules to replace less adequate ones. Evidence, drawn from studies on children's acquisition of knowledge about balance beams, suggests that knowledge…

This book offers classroom-tested activities designed to make even the most reluctant learners crazy about math. Appealing to everyone from sports fans to readers, future fashion designers to budding musicians, the activities presented in this book offer ways to develop a deep-rooted love and appreciation of math in every student. Teachers are…

We examine a prospective high school teacher's instructional representations of rate of change and right triangle trigonometry to investigate his interpretation and understanding in relation to the development of proportional reasoning. Despite a constant effort by the subject to resort to "real life" examples in order to give meaning to his…

Building on previous research on the tendency in students of diverse ages to overrely on proportionality in different domains of mathematics (e.g., geometry, probability), this study shows that--when confronted with missing-value word problems--Flemish primary school pupils strongly tend to apply proportional solution strategies, also in cases…

Two of the greatest problems of research on affective factors, and in particular, research on beliefs, is "what" and "how" we observe. The first difficulty is due to the lack of a clear terminology; but even once it has been clearly decided what to observe, it is not easy to put this into practice. This report describes from a…

Measure Up is a research and development project that uses findings from Davydov (1975) and others to introduce mathematics through measurement and algebra in grades 1-3. This paper illustrates the use of generalized diagrams and symbols in solving word problems for a group of 10 children selected from a grade 3 Measure Up classroom. Students use…

The Building Blocks to Colorado's Content Standards were developed to connect early childhood education to the K-12 content standards, to advocate for appropriate teaching strategies for preschool children, and to support awareness and understanding of early childhood foundational skills among parents and teachers. Five sets of building blocks are…

The report describes a mathematical modelling activity of a natural phenomenon (transmission of hereditary characters in a codominance case) using the concept of model as a theoretical instrument. The chosen tool enables us to show how the construction of a link between reality and a model is related to the evolution of the graphical…

We are studying two groups of preservice teachers' conceptions, progression and especially the concept of function in connection to y=x+5 when they are taking a course in algebra or one in calculus in their third and sixth term, respectively, in a teacher preparation program. There is a similar development in that they use to a higher degree a…