This study explored factors that contribute to students' concepts of magnification and scale. Spatial visualization, logical thinking, and concepts of magnification and scale were measured for 46 middle school students. Scores on the "Zoom Assessment" (an assessment of knowledge of magnification and scale) were correlated with the "Test of Logical…

In an effort to assess models of inductive reasoning and deductive reasoning, the authors, in 3 experiments, examined the effects of argument length and logical validity on evaluation of arguments. In Experiments 1a and 1b, participants were given either induction or deduction instructions for a common set of stimuli. Two distinct effects were…

This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…

We start by visiting the maths section of the web site answers.yahoo.com. Here, anybody can ask a question from anywhere in the world at every possible level. Answers are given by anyone who wants to contribute and then askers/readers rate the responses. A brief look here and it is starkly clear that our young people are struggling and their…

In this study subjects are presented with sequences of heads and tails, derived from flipping a fair coin, and asked to consider their chances of occurrence. In this new iteration of the comparative likelihood task, the ratio of heads to tails in all of the sequences is maintained. In order to help situate participants' responses within…

Multiplicative reasoning is required in different contexts in mathematics: it is necessary to understand the concept of multipart units, involved in learning place value and measurement, and also to solve multiplication and division problems. Measures of hearing children's multiplicative reasoning at school entry are reliable and specific…

Quantitative literacy has been recognized as an important skill in the higher education and workforce communities, focusing on problem solving, reasoning, and real-world application. As a result, there is a need by various stakeholders in higher education and workforce communities to evaluate whether college students receive sufficient training on…

The purpose of this study was to examine the extent to which teacher ratings of behavioral attention predicted responsiveness to word reading instruction in first-grade and third-grade reading comprehension performance. Participants were 110 first-grade students identified as at risk for reading difficulties who received 20 weeks of intensive…

Project Clarion, a Jacob K. Javits-funded project, focused on the scale-up of primary-grade science curricula. Curriculum units, based on an Integrated Curriculum Model (ICM), were developed for high-ability learners, but tried out with all students in Title I settings to study the efficacy of the units with all learners. The units focus on the…

Engaging students in classroom discourse offers opportunities for students to participate in the construction of joint understandings, to negotiate relationships between different types of evidence, and to practice making evidence-based claims about science content. However, close attention to social aspects of learning is critical to creating…

Considerable literature has documented both the pros and cons of students' use of empirical evidence during proving activities. This article presents an analysis of a classroom episode involving in-service middle school, high school, and college teachers that demonstrates that learners need not be steered away from empirical investigations during…

Achieving success takes hard work and perseverance, but another crucial ingredient is the ability to learn from failure. Instructors must encourage students to make mistakes within the classroom so they will attempt great things outside it. This is where the freedom of trial and error should be championed, to be able to hone students' skills so…

Despite the importance of writing analytically in response to texts, there are few assessments measuring students' mastery of this skill. This manuscript describes the development of a response-to-text assessment (RTA) intended for use in research. In a subsequent validity investigation we examined whether the RTA distinguished among classrooms in…

This paper explores the proposition that teaching of critical thinking (CT) should include: (1) identifying and addressing the many environmental variables acting as barriers to our human thinking, i.e., an open system approach, and (2) utilizing the interrelatedness of the CT building blocks, i.e., creative thinking techniques, levels of…

This study has been carried out in order to determine the status of the analogy drawn with the capital and lower letters in vertical and italic handwriting by teachers working in the first grade classes of primary schools. The research has been conducted on 151 first grade teachers working in Turkey. The data was acquired by means of a…