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
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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)