5th graders (n=527) were randomly assigned to self-explain worked examples (WE) or solve problems during a yearlong study. WE students learned more algebra skills when given algebra worked examples on an end-of-year transfer measure. Comparing attempts, conceptual, and mechanical correctness by condition, results demonstrated that the condition…

Results of the last thirty years in mathematics education have shown the importance of an operational concept development. One of the geometrical concepts that has been researched for years already, however, not with the particular focus on its systematic teaching in school mathematics, is the concept of angle. In this paper we focus on children's…

In this study we explored to what extent middle school teachers were able to appropriately identify proportional situations when presented with various mathematical structures and if there were relationships between attributes of the teachers and their ability to identify proportional situations. Interestingly, there were no strong relationships…

Upper primary school students' difficulties with decimal place value are widely recognised due largely to the availability of assessment tools that accurately identify students' misconceptions in this domain. Yet, many students' decimal difficulties seem to stem from a lack of understanding of whole number place value for which there are few, if…

The teaching of mathematics involves problem solving skills which prove to be difficult on the part of the pupils due to misrepresentation of the word problems. Oftentimes, pupils tend to represent the phrase "more than" as addition and the word difference as "- ". This paper aims to address the problem solving skills of grade…

Two related studies are reported about the (lack of) activation of real-world knowledge in elementary school students' understanding and solution of school arithmetic word problems. In the first study a set of word problems was collectively administered to 75 fifth-graders during a typical mathematics lesson. Half of the problems were standard…

A study investigated whether presenting scientific information about seasonal change in a narrative which is also a refutation text will promote learning of the information more than presenting it in an expository text which is either a considerate refutation text or an inconsiderate non-refutation text. Subjects, 123 seventh grade students and…

With consistently low levels of academic performance and high rates of absenteeism (Bourke & Rigby, 2000), the students in this study are the most educationally disadvantaged group in Australia with respect to mathematics. This paper reports on a study undertaken with Years 5-7 students in a Queensland aboriginal community to determine their…

This study probed children's reasoning about both correct and incorrect but plausible statements of hypothetical children concerning the concepts of subtraction, with the intention of examining misconceptions in greater depth. Eight third graders, 14 fourth graders, and 14 fifth graders were interviewed individually to assess their understanding…

This study tested the effectiveness of having fifth-grade students generate their own examples of selected concepts on energy. Hypotheses were that subjects would perform better on sections of a test related to definitions and recognition of exemplars of the concepts for which they found their own examples than on sections related to comparible…

Some pre-instructional misconceptions held by children can persist through scientific instruction and resist changes. Identifying these misconceptions would be beneficial for science instruction. In this preliminary study, scores on a 60-item true-false test of knowledge and misconceptions about earthquakes were compared with previous interview…

"Becoming Successful Problem Solvers" is a 12-episode video series designed for use with middle school students. The materials are intended to create new assessment tools for teachers, to develop instructional devices that are useful in promoting problem solving in middle school classrooms, and to promote classroom discourse about…

Over a period of about 3 years, 3204 students in Grades 4 to 10 completed 9862 tests to identify and track their interpretation of decimal notation. Analysis of the longitudinal data demonstrates that different misconceptions persist among students to different degrees and in different patterns across the grades. Estimating the prevalence of…