The purpose of this study is to examine the nature of what students notice about symbols and use as they solve unfamiliar algebra problems based on familiar algebra concepts and involving symbolic inscriptions. The researcher conducted a study of students at three levels of algebra exposure: (a) students enrolled in a high school pre-calculus…

Abstract reasoning is critical for science and mathematics, but is very difficult. In 3 studies, the hypothesis that alternatives generation required for conditional reasoning with false premises facilitates abstract reasoning is examined. Study 1 (n = 372) found that reasoning with false premises improved abstract reasoning in 12- to…

Almost half of the US public rejects the idea that humans originated via evolution rather than by supernatural design. Moreover, studies demonstrate that even biology teachers have difficulty teaching their students about evolution, often including creationist explanations as well. A typical response to such findings is the argument that greater…

This paper reports on a mixed-model case study of designing and implementing a constructivist teaching intervention about reproduction and physical family resemblance for young children. The objective of the study was to explore whether the ways that preschoolers reason about the resemblance between offspring and parents can be improved with a…

The purpose of this study is to examine the kinds of reasoning that African American young men learn and develop when playing Spades, a common cultural practice in African American communities. The qualitative study found that the Spades players routinely consider multiple variables and their mathematical relationships when making decisions. The…

This journal article discusses Advanced Mathematical Thinking (AMT) and how to enhance it. AMT is ability in representing, abstracting, creative thinking, and mathematical proving. The importance of AMT ability development in accord with government expectation who realize about the importance of mathematical competency mastery for student's life.…

Linear functions are an important part of the middle school mathematics curriculum. Students in the middle grades gain fluency by working with linear functions in a variety of representations (NCTM 2001). Presented in this article is an activity that was used with five eighth-grade classes at three different schools. The activity contains 15 cards…

We can now get purposefully directed in the way we assess our learners in light of the emergence of evidence from the field of neuroscience. Why higher-order learning or abstract concepts need to be the focus in assessment is elaborated using the knowledge of semantic and episodic memories. With most of our learning identified to be implicit, why…

In an online graduate-level early childhood education course, the authors sought to playfully disrupt and transform educators' conceptions of children's "dark play," as provoked by contemporary popular culture. Embracing the imaginative potential of darkness and liminality, the course participants problematized and expanded their…

Nationwide, the increasing popularity of e-books is undeniable; sales of e-books increased an astounding 4,456% over a 5-year period. Researchers, Miranda, Johnson, and Rossi-Williams, determined that e-readers have a positive impact on students' desire to read. This study attempted to determine if the use of institution issued e-readers would…

Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…

We examined whether inductive reasoning development is better characterized by accounts assuming an early category bias versus an early perceptual bias. We trained 264 children aged 3 to 9 years to categorize novel insects using a rule that directly pitted category membership against appearance. This was followed by an induction task with…

The Raven's Standard Progressive Matrices (RSPM) is a 60-item test for measuring abstract reasoning, considered a nonverbal estimate of fluid intelligence, and often included in clinical assessment batteries and research on patients with cognitive deficits. The goal was to develop and apply a predictive model approach to reduce the number of items…

This study considers tertiary calculus students' and instructors' conceptualizations of slope. Qualitative techniques were employed to classify responses to 5 items using conceptualizations of slope identified across various research settings. Students' responses suggest that they rely on procedurally based conceptualizations of…

Activity-based instructional strategies promote physical interaction with manipulatives to represent abstract concepts. As a means to improve student achievement in mathematics, educational researchers and practitioners often recommend instructional strategies that capitalize on the assumed benefits of manipulatives. Recent research has indicated…