Assessment data and other research findings on fractions are briefly reviewed. These indicate that students are able to add and subtract fractions but have substantial difficulty finding and using common denominators. Selected results for nine-year-olds from the first and second national assessments of mathematics are used to portray what students…

The author discusses the use of calculators in calculus classes and difficulties caused by roundoff errors. References for advanced follow-up topics are given. (Author/MK)

Several common errors reflecting difficulties in probabilistic reasoning are identified, relating to ambiguity, previous outcomes, sampling, unusual events, and estimating. Knowledge of these mistakes and interpretations may help mathematics teachers understand the thought processes of their students. (MNS)

Difficulties experienced by algebra students are listed, with comments on what can be done and some implications for teaching. (MNS)

Nearly 48 percent of the students in Developmental Studies Mathematics courses at a major southern university during the fall of 1983 had taken college preparatory mathematics courses in high school. Some had even taken trigonometry, pre-calculus, or calculus. Yet, they were placed in university developmental studies mathematics courses because…

A brief overview is given of a research project funded to investigate the cause and cure of errors in ratio and proportion, algebra, and fractions. Choosing pertinent information, interviewing students, listing significant features, developing lessons, and testing the materials are considered. (MNS)

Data from 32 state assessments in mathematics (conducted in 1984 and earlier) are analyzed in this document. The high degree of variability across the states is stressed, with some of the points of variation in the test development, administration, and analysis process noted. Information is then presented on topics on which students are doing well…

Diagnostic/prescriptive mathematics was examined to ask whether a sufficient body of professional knowledge and practices exist to warrant its inclusion in teacher preparation. Argues that diagnostic/prescriptive mathematics does constitute an appropriate topic for consideration as content in revised teacher preparation programs. (PK)