Pedagogical content knowledge (PCK) begins to develop during teacher education and the teaching practicum reinforces its development. This study is an interpretive inquiry into pre-service mathematics teachers' practicum classrooms. The study explored four pre-service mathematics teachers' PCK through observations and interviews. The pre-service…

This study offers a comprehensive investigation of 14-15-year-old students' comprehension of non-Euclidean geometries, with a specific focus on the assessment of their understanding through a 15-itemed test. The primary objective of this research is to assess the current state of students' knowledge and proficiency in non-Euclidean geometries and…

Students with learning disabilities struggle with word problems in mathematics classes. Understanding the type of errors students make when working through such mathematical problems can further describe student performance and highlight student difficulties. Through the use of error codes, researchers analyzed the type of errors made by 14 sixth…

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…

This report discusses students' understanding of the algebraic concepts of gradient and intercept with respect to simple graphs. A pilot study is described which attempts to identify the difficulties students encounter and determine the number of students who have these difficulties. (MK)

This is a preliminary report on research into computational errors made by six- and seven-year-olds. (Author/MK)

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…

The investigation reported is primarily a description of how college students solve or fail to solve algebra equations. Protocols were collected from two groups of college students; one group was expected to be good solvers, the other group contained many poor solvers. The investigators sought to identify and classify the difficulties students…

Results from an English assessment of achievement on two geometric topics, line symmetry and angles, are reported. Contrasts in the patterns of responses to related items, and to the same items by pupils aged 11 or 15, are highlighted. (MNS)

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)

Findings on ratio and on fractions from a research project on strategies and errors in secondary mathematics are discussed, with typical errors described. Pupils seemed to learn rules without understanding. (MNS)

Results obtained from 11- and 15-year-olds on tests of understanding of decimal place value and its influence on addition and subtraction skills are reported and discussed. (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…

Documented are major categories of errors that appear as children learn decimal fractions. Then the conceptual sources of these errors are established. Different curriculum sequences influence the probability that these classes of errors will appear. They can be used as diagnostic tools to detect children's understanding of mathematics topics.…

Knowledge about the structure of arithmetic expressions enables people to reason effectively about such expressions, including an ability to judge equivalence under transformations. This paper reports an empirical study of six middle-school children who judged the equivalence of three sets of three-term arithmetic expressions with an addition and…