Background/purpose: It is an urgent necessity to identify geometric conceptual errors among students at different levels. These errors cannot be ignored, as they hinder the learning of related concepts. Teachers need to be aware of these errors, which are often embedded in students' cognitive structures, so that they can work on eliminating them…

Teachers need to address global climate change with students in their classrooms as evidence for consequences from these environmental changes mounts. One way to approach global climate change is through examination of authentic data. Mathematics and science may be integrated by interpreting graphs from the professional literature. This study…

This proceedings volume of InCoTEPD 2018 covers many ideas for handling a wide variety of challenging issues in the field of education. The outstanding ideas dealing with these issues result in innovation of the system. There are many innovation strategies resulting from recent research that are discussed in this book. These strategies will become…

Using Logo to work through a maze is described. Suggested programs to help students learn to debug programs are also included, along with the story of the original "computer bug." (MNS)

This paper is concerned with the role of meaning and understanding in the acquisition of computational skill in subtraction. Evidence on the syntactic nature of subtraction errors is reviewed, with common "bugs" described. Then, data collected from interviews with four children are summarized in terms of their semantics of concrete…

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…

Diagnostic teaching is described and discussed. Different types of errors are explained and examples of errors and their possible diagnoses are given. (MK)

A study to determine if "random" or "careless" errors in multiplication made by individual students take on discernible patterns is described. Implications for teaching are discussed. (MK)

A computer program is given which will generate a list of descriptions of the items to which a student has responded incorrectly on the Keymath Diagnostic Arithmetic Test. It is designed for the TRS-80, Model III, with two disk drives. The documentation lists all required materials, describes the six options and how to use them, indicates the…

Research recurrently indicates that children who have difficulty with arithmetic often use systematic routines that yield wrong answers. Recent research has focused less on identifying the most common errors among groups of children and more on analyzing individual children's errors. This paper considers the source of systematic errors in…

The informal subtraction strategies that children develop are discussed in detail, with the role of the counting-down strategy described. Problems and remedies for difficulties caused by counting backward and the double count are also presented. (MNS)

Interviews were used to find the frequency of different types of errors made by 95 sixth-year Papua New Guinea students on a mathematics test. The general trend was the same as for western students, but the Papua New Guinea students made far fewer careless errors. (MNS)

Diagnostic evaluation is a major way to help students overcome errors. How such evaluation can be done is discussed, with comments on what should be checked and recorded by the teacher. (MNS)

What two teachers found when they took a close look at the results of a sentence-solving test given in grades four and five is reported. Error patterns appeared less frequently after instruction but recurred on retention tests. How students can be helped is suggested. (MNS)

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