FRACTAL CORRELATIONS ON CONTENT AND COGNITIVE DOMAINS AND MATHEMATICS PERFORMANCE ACROSS COUNTRIES

European Scientific Journal, Jun 2015

Fractal correlations on content and cognitive domains and mathematics performance based on TIMSS 2011 across countries was the focus of this study. Fractal dimensions as reflected by the fractograms and correlations of the variables for each factor were analyzed. Results showed that Mathematics performance is highly influenced by content and cognitive domains if taken jointly. But if variables for each factor are analyzed independently, cognitive domains such as Knowing, Applying, and Reasoning have high positive relationship to Mathematics performance. Content domains like Algebra, Geometry and Number Sense have also high positive relationship except Data and Chances. The findings revealed that Content and Cognitive domains have significant bearings in Math performance of the participating countries.

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FRACTAL CORRELATIONS ON CONTENT AND COGNITIVE DOMAINS AND MATHEMATICS PERFORMANCE ACROSS COUNTRIES

European Scientific Journal June 2015 edition vol.11 FRACTAL CORRELATIONS ON CONTENT AND COGNITIVE DOMAINS AND MATHEMATICS PERFORMANCE ACROSS COUNTRIES Angeline Pogoy Vincent Theodore Balo Geronimo Obaob Jr. Sonny Chiu 0 0 Faculty of College of Teacher Education, Cebu Normal University Fractal correlations on content and cognitive domains and mathematics performance based on TIMSS 2011 across countries was the focus of this study. Fractal dimensions as reflected by the fractograms and correlations of the variables for each factor were analyzed. Results showed that Mathematics performance is highly influenced by content and cognitive domains if taken jointly. But if variables for each factor are analyzed independently, cognitive domains such as Knowing, Applying, and Reasoning have high positive relationship to Mathematics performance. Content domains like Algebra, Geometry and Number Sense have also high positive relationship except Data and Chances. The findings revealed that Content and Cognitive domains have significant bearings in Math performance of the participating countries. Fractal correlations analysis; fractogram; TIMSS mathematics scores; content domain; cognitive domain - Introduction The Trends in International Mathematics and Science Study (TIMSS 2011) is an international study directed by the International Association for the Evaluation of Educational Achievement (IEA) as cited by Thomson, Hillman and Wernert (2012). It summarized the fourth and eighth grade students’ math achievement of the 63 countries and 14 benchmarking countries (Mullis, 2012). The goal of TIMSS is to provide comparative information about educational achievement across countries to improve teaching and learning in mathematics and science. TIMSS (2011) results present the content and cognitive domains across participating counties. The content domains described the content that is intended to be assessed; while the cognitive domain described the cognitive abilities and behaviors as they engage with the mathematics content. The content domains were found in the curricula of the participating countries, and are the subject of the major international and national reports for TIMSS. Grade eight students are assessed in number, algebra, geometry and data and chance. TIMSS 2011 Mathematics Framework identified the three (3) cognitive domains which are; knowing which covers the facts, procedures and concepts students need to know; applying which focuses on the ability of students to apply knowledge and conceptual understanding to solve problems or answer questions; and reasoning – which goes beyond the solution of routine problems to encompass unfamiliar situations, complex contexts and multi-step problems. At the eighth grade, students should have developed number sense and computational fluency, understand the meanings of operations and how they relate to one another, and be able to use numbers and operations to solve problems. It includes whole numbers, fractions and decimals, integers, ratio and proportion and percent, number patterns and relationships (TIMSS, 2011). As noted in TIMSS 2011, in algebra, functional relationships and their uses for modeling and problem solving are of prime interest. The algebra content domain includes recognizing and extending patterns, using algebraic symbols to represent mathematical situations, and developing fluency in producing equivalent expressions and solving linear equations. The major topic areas in algebra are: patterns, algebraic expressions and equations/formulas and functions. Geometric shapes, geometric measurement and location and movement are contained in the content domain in geometry. As presented in TIMSS 2011 Mathematics Framework, this also includes understanding coordinate representations and using spatial visualization skills to move between two- and three-dimensional shapes and their representations. Students are expected to use symmetry and apply transformation to analyze mathematical situations. The cognitive range extends from making drawings and constructions to mathematical reasoning about combinations of shapes and transformations. Students describe, visualize, draw, and construct a variety of geometric figures, including angles, lines, triangles, quadrilaterals, and other polygons. Students are asked to combine, decompose, and analyze compound shapes. The data and chance content domain includes data organization and representation, data interpretation and chance. Students describe and compare characteristics of data (shape, spread, and central tendency), and draw conclusions based on data displays. They have to identify trends in data, make predictions based on data, and evaluate the reasonableness of interpretations. Eighth-grade students’ appreciation of chance (elementary probability) also includes the occurrence of familiar events as certain; as having greater, equal, or less likelihood; or as impossible, and should extend to using data from expe (...truncated)


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Angeline Pogoy, Vincent Theodore Balo, Geronimo Obaob Jr., Sonny Chiu. FRACTAL CORRELATIONS ON CONTENT AND COGNITIVE DOMAINS AND MATHEMATICS PERFORMANCE ACROSS COUNTRIES, European Scientific Journal, 2015, Volume 11, Issue 16,