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…

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)

This article, a reprint from 1930, offers an interesting perspective on the importance of diagnostic and prescriptive teaching as well as the role of drill and the use of objectives in mathematics. (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)

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)

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

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)

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.…

An overview is presented of information processing analyses of knowledge and performance in three areas of the elementary mathematics curriculum: basic addition and subtraction facts, complex procedures such as multicolumn subtraction, and the solution of word problems. Theories of the knowledge associated with "expert" performance are discussed.…