Object-Spatial Visualization And Verbal Cognitive Styles, And Their Relation To Cognitive Abilities And Mathematical Performance

The present study investigated the object-spatial visualization and verbal cognitive styles among high school students and related differences in spatial ability, verbal-logical reasoning ability, and mathematical performance of those students. Data were collected from 348 students enrolled in Advanced Placement calculus courses at six high schools. Correlational analysis revealed that spatial ability, verbal-logical reasoning ability, and mathematical performance were significantly correlated with each other. High spatial visualizers had significantly higher spatial ability and mathematical performance scores than high object visualizers. No significant differences were found between verbalizers and high spatial visualizers in their verbal-logical reasoning ability and mathematical performance scores. Results provide support for the existence of two contrasting groups of visualizers with respect to their spatial ability

The Role Of Cognitive Ability And Preferred Mode Of Processing In Students\u27 Calculus Performance

The present study sought to design calculus tasks to determine students\u27 preference for visual or analytic processing as well as examine the role of preferred mode of processing in calculus performance and its relationship to spatial ability and verbal-logical reasoning ability. Data were collected from 150 high school students who were enrolled in Advanced Placement calculus courses. The measures of preferred mode of processing did not correlate with the measures of spatial ability and verbal-logical reasoning ability, suggesting that cognitive abilities did not predict the students\u27 preference for visual or analytic processing. Multiple regression analysis revealed that spatial visualization ability, verbal-logical reasoning ability, preference for visual processing contributed significantly to the variance in calculus performance. Correlations between calculus performance and the measures of preferred mode processing suggest that the nature and complexity of mathematical tasks might have influenced the students\u27 degree of preference for using visual processing

Object-Spatial Imagery And Verbal Cognitive Styles In High School Students

The present study investigated object-spatial imagery and verbal cognitive styles in high school students. We analyzed the relationships between cognitive styles, object imagery ability, spatial visualization ability, verbal-logical reasoning ability, and preferred modes of processing math information. Data were collected from 348 students at six high schools in two school districts. Spatial imagery style was not correlated with object imagery style and was negatively correlated with verbal style. Object imagery style did not correlate significantly with any cognitive ability measure, whereas spatial imagery style significantly correlated with object imagery ability, spatial visualization ability, and verbal-logical reasoning ability. Lastly, spatial imagery style and verbal-logical reasoning ability significantly predicted students’ preference for efficient visual methods. The results support the cognitive style model, in which visualizers are characterized as two distinct groups who process visual-spatial information and graphic tasks in different ways

Visual Thinking And Gender Differences In High School Calculus

In a previous paper the authors defined symplectic Local Gromov-Witten invariants associated to spin curves and showed that the GW invariants of a Kähler surface X with p g \u3e 0 are a sum of such local GW invariants. This paper describes how the local GW invariants arise from an obstruction bundle (in the sense of Taubes) over the space of stable maps into curves. Together with the results of our earlier paper, this reduces the calculation of the GW invariants of elliptic and generaltype complex surfaces to computations in the GW theory of curves with additional classes: the Euler classes of the (real) obstruction bundles. © 2012 by The Johns Hopkins University Press

Completing the Incomplete: Making Sense of Completing the Square Using Manipulatives

Participants will use algebra tiles to make sense of completing the square. This workshop will focus on collaboration to build a deeper understanding of the topic. Participants will also discuss student misconceptions, possible errors when completing the square, and how manipulatives can help students make sense of the process

Exploring Euclidean and Taxicab Geometry with GeoGebra

Technology has changed the nature of mathematics learning and instructional practices (Andreasen and Haciomeroglu, 2013; Edwards, 2015; Haciomeroglu, Bu, Schoen, and Hohenwarter, 2011). Dynamic and interactive technology enriches students' learning opportunities and shifts the focus of instruction to understanding and student-centered learning by providing a means of modeling mathematical relationships (Bu and Henson, 2016; Haciomeroglu, Bu, Schoen, and Hohenwarter, 2011). The authors connect Euclidean and non-Euclidean geometries through an exploration of rich tasks of Taxicab geometry, sharing methods for organizing and presenting tasks to enhance students' understanding of geometry concepts

Making Sense of Quadratic Equations

This session will engage participants in exploring quadratic equations using a variety of tools. Connections to the Standards for Mathematical Practices will be made, and mathematical tasks, which are designed to provide opportunities for rich discourse and student engagement will be shared. Participants will also discuss student misconceptions and possible errors as they solve quadratic equations

Conceptual and Procedural Understanding: Prospective Teachers’ Interpretations and Applications

The preparation of prospective secondary mathematics teachers often revolves around working to improve knowledge of mathematics for teaching and understanding the conceptual development and trajectories of mathematics. “Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems” (NCTM, 2014, p. 42). Prospective teachers need to be prepared to teach concepts along with procedures (Ball, Thames, & Phelps, 2008) particularly with the implementation of the Common Core State Standards (CCSS). In their own experience as a learner of mathematics, however, many prospective teachers come with procedural understandings of mathematics and many struggle to understand the underlying concepts and why those procedures work. Challenging prospective teachers to examine their own understandings of mathematical concepts and their preconceived ideas of good mathematics instruction becomes an important aspect of mathematics teacher preparation. In this study, prospective secondary mathematics teachers were asked to read Principles to Actions’ section on Conceptual Understanding and Procedural Fluency (NCTM, 2014). Having individually defined conceptual and procedural understanding in their own words, they were asked to apply those understandings to determine how a student might solve a percentage problem with a conceptual and with a procedural understanding. Prospective teachers’ definitions and student solutions were examined to answer the question: In what ways do prospective secondary mathematics teachers define conceptual understanding and procedural understanding and subsequently apply those definitions to solve a percent problem? Using the prospective teachers’ own definitions of these two terms, the researchers compared the definitions with how each prospective teacher distinguished between the types of understandings when applied to the given percent problem. Data showed some disconnect between definitions and applications. Additionally, responses of prospective teachers to the percentage problem could have been either conceptual or procedural based upon varying aspects of student solutions

Exposing Calculus Students To Advanced Mathematics

To ensure the competitiveness of the USA in the global economy, and its role as a leader in science and engineering, it is important to cultivate the next generation of home grown mathematicians. However, while universities across the USA offer calculus classes to thousands of undergraduate students each year, very few of them go on to major in mathematics. This paper posits that one of the main reasons is that the mathematical community does not expose calculus students to the beauty and complexity of upper-level mathematics, and that by doing so before they fully commit to their programme of study, the number of students with a qualification in mathematics can be increased. The results show a significant increase in the number of students planning to add a minor in mathematics, and an increased likelihood among freshmen and sophomores to change their major. © 2013 © 2013 Taylor & Francis