This study examines how third-graders' conceptions about the origin of species are affected by formal instruction and whether children can learn not only about evolution but also about natural selection. We interviewed the same group of third-grade children (8-9 years old) twice, before and after following a curriculum about these topics.…

The purpose of this article is to describe the process of a proof construction. It is more specific on the failure of the process. Piaget's frameworks, assimilation and accommodation, were used to analyze it. Method of this research was qualitative method. Data were collected by asking five students working on problems of proof using think aloud…

The memorial costs and benefits of trial-and-error learning have clear pedagogical implications for students, and increasing evidence shows that generating errors during episodic learning can improve memory among younger adults. Conversely, the aging literature has found that errors impair memory among healthy older adults and has advocated for…

Inequalities are one of the foundational subjects in high school math curricula, but there is a lack of academic research into how students learn certain types of inequalities. This article fills part of the research gap by presenting the findings of a study that examined high school students' methods of approaching absolute value inequalities,…

In 2 studies, children ages 3 to 7 years were asked to recall a series of touches that occurred during a previous staged event. The recall interview took place 1 week after the event in Study 1 and immediately after the event in Study 2. Each recall interview had 2 sections: In 1 section, children were given human figure drawings (HFDs) and were…

Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…

Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…

The need to provide understandable problems and ways to help children understand problems are explored. An interview with a sixth grader depicts his incorrect strategies and leads to suggestions for teaching problem solving using a range of mathematical models for each operation. (MNS)

Investigated was how easily pupils aged 12 and 13 who were initially unaware of the invariance of an operation (with decimals) modeling a situation could be led to such awareness. Results from clinical interviews are reviewed and a protocol presented. It appeared difficult to induce conservation. (MNS)

The projection of shadows task developed by Inhelder and Piaget was used to identify error patterns and solution strategies used by diverse populations in a sequence of proportion tasks. In Study A, two group tests were administered to 607 students from science and mathematics classes in grades 9 and 10. A sub-sample of 69 students was involved in…

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…