Drawing on her research into students' evidential reasoning, Elisabeth Pickles explores the possibilities for how such reasoning might be assessed. Existing exam mark schemes focus too heavily on generic processes involved in the analysis of source material and insufficiently on the historical validity of reasoning and conclusions produced.…

Classically, geometry has been the subject in which students encounter mathematical proof based on formal deduction. Attention to proof in the geometry curriculum is strengthened by a focus on reasoning and sense making. This book examines the four key elements (conjecturing about geometric objects, construction and evaluation of geometric…

To support 11th-grade students' informal inferential reasoning, a teaching and learning strategy was designed based on authentic practices in which professionals use correlation or linear regression. These practices included identifying suitable physical training programmes, dyke monitoring, and the calibration of measurement instruments. The…

Explanations are considered to be key aids to understanding the study of mathematics, science, and other complex disciplines. This paper discusses the role of students' explanations in making sense of data and learning to reason informally about statistical inference. We closely follow students' explanations in which they utilize their experiences…

In April, the "New England Journal of Higher Education" ("NEJHE") launched its "New Directions for Higher Education" series to examine emerging issues, trends, and ideas that have an impact on higher education policies, programs, and practices. In this installment of the series, DiSalvio speaks with Richard Arum,…

Given minimal evidence about novel objects, children might learn only relationships among the specific entities, or they might make a more abstract inference, positing classes of entities and the relations that hold among those classes. Here we show that preschoolers (mean: 57 months) can use sparse data about perceptually unique objects to infer…

A common approach used for introducing algebra to young adolescents is an exploration of visual growth patterns and expressing these patterns as functions and algebraic expressions. Past research has indicated that many adolescents experience difficulties with this approach. This paper explores teaching actions and thinking that begins to bridge…

A game is a set of activities involving one or more players. It has goals, constraints, payoffs, and consequences. A game is rule-guided and artificial in some respects. (Richard Wilson, 2010). According to Garris et al. (2002), define educational game play as "voluntary, nonproductive, and separate from the real world"; and they found…

The present studies investigated children's and adults' intuitive beliefs about the physical nature of essences. Adults and children (ranging in age from 6 to 10 years old) were asked to reason about 2 different ways of determining an unknown object's category: taking a tiny internal sample from any part of the object (distributed view of essence)…

Differential gender performance in standardized mathematics assessment has long been a heated topic. Gender gaps of varied magnitude have been identified on large-scale assessments in the United States. To continue the investigation, this study examined male and female performance on the Programme for International Student Assessment (PISA) 2003…

Reduction is a problem-solving strategy, relevant to various areas of computer science, and strongly connected to abstraction: a reductive solution necessitates establishing a connection among problems that may seem totally disconnected at first sight, and abstracts the solution to the reduced-to problem by encapsulating it as a black box. The…

In this theoretical essay, the author addresses the existence of divergent evidence, portraying both competence and lack of competence in a fundamental realm of higher order thinking--causal and scientific reasoning--and explores the educational implications. Evidence indicates that these higher order reasoning skills are not ones that can be…

Many under-prepared university students do not know how to study (Martin and Arendale 1993) because they have not yet developed the abstract reasoning skills that allow them to learn new ideas simply by reading a text or listening to a lecture. This article draws from selected findings from a PhD study currently being undertaken at a university in…

This study examined whether college students are better able to apply knowledge of simple mathematical concepts when they are taught the concepts using abstract symbols or concrete examples. The research described in this article is consistent with What Works Clearinghouse (WWC) evidence standards. Strengths: The study is a well implemented…

We explored the effects of task-related factors on reasoning processes in geometry focusing on a comparison-of-perimeters task in which the irrelevant feature area interferes with the reasoning process. We studied the effects of congruity, salience, and complexity on participants' accuracy of responses and reaction times. The study shows that…