Under what conditions can a true "science of mental life" arise from psychological investigations? Can psychology formulate scientific laws of a general nature, comparable in soundness to the laws of physics? I argue that the search for such laws must return to the forefront of psychological and developmental research, an enterprise that requires…

In this article, the author offers two well-known mathematical images--that of a dot moving around a circle; and that of the tens chart--and considers their power for developing mathematical thinking. In his opinion, these images each contain the essence of a particular topic of mathematics. They are contrasting images in the sense that they deal…

A majority of studies on learning disabilities have focused on elementary grades. Although problems with learning disabilities are life-affecting only a few studies focus on deficits in adults. In this study adults with isolated mathematical disabilities (n = 101) and adults with combined mathematical and reading disabilities (n = 130) solved…

Useful for small groups or one-on-one instruction, this book offers successful math interventions and response to intervention (RTI) connections. Teachers will learn to target math instruction to struggling students by: (1) Diagnosing weaknesses; (2) Providing specific, differentiated instruction; (3) Using formative assessments; (4) Offering…

This article concludes the serialization of the Royal Statistical Society's Schools Lecture for 2004, on "Lies and statistics".

In some elementary courses, it is shown that square root of 2 is irrational. It is also shown that the roots like square root of 3, cube root of 2, etc., are irrational. Much less often, it is shown that the number "e," the base of the natural logarithm, is irrational, even though a proof is available that uses only elementary calculus. In this…

This book contains mathematics activities based upon the concepts of Fibonacci numbers and the Golden Ratio. The activities include higher order thinking skills, calculation practice, integration with different subject areas, mathematics history, extensions and home tasks, teaching notes, and questions for thought and comprehension. A visual map…

Examines questions about reported findings that the natural number concept derives from a prior understanding of ordination rather than a prior understanding of cardination. (GO)

An elementary arithmetic workbook in whole numbers for speakers of Hmong has an introductory section and a variety of exercises in conceptualizing, writing, spelling, and sequencing numbers from 0 to 999. (MSE)

The history of the two numbers e and pi is traced, and the relationship of thesetwo numbers to the history and development of mathematics is indicated. (DT)

The representation of a binary number by a row of people sitting or standing by their chairs is reviewed. The representation is extended into a counting activity and then directions are given for combining the counters into an automatic "machine" which will add, subtract, multiply, and divide. (DT)

Not all of mathematics can be taught in formal textbooks. Just as an English course can be enlivened by selections from literature, a mathematics course can gain depth and interest from special readings. This volume can be read in conjunction with the SMSG First Course in Algebra or Intermediate Mathematics. It introduces the subject of number…

This supplement was written for students who are especially good in mathematics and who have a lively interest in the subject. It is suggested that the supplement be read with pencil and paper in hand. All questions should be considered and answered, if possible, when they occur. A casual reading of the supplement is, in most cases, unprofitable.…

A brief biography of Pythagoras, including discussions of his contributions to philosophy and mathematics, is presented. (CR)