Mathematical Content Areas Research Articles

수학교과서 연구 동향 분석 - 2006년부터 2011년에 게재된 국내 학술지 논문을 중심으로 -

The purpose of this study was to analyze recent research trends of mathematics textbooks to provide implications for textbook research and development. For this purpose, 90 out of 1121 research papers published between 2006 and 2011 in seven prestigious domestic journals were selected. The papers dealing with only Korean mathematics textbooks were analyzed by school levels (i.e., elementary or secondary), mathematics content areas, analytic methods, and implications. The papers comparing our mathematics textbooks with foreign counterparts were analyzed by reasons for the comparison, school levels, subjects for analysis, and implications. The results of this study urge us to pay more attention to secondary mathematics textbooks, least studied content areas, and various but inconsistent analytic methods. This paper also suggests close connections between textbook analysis and textbook development.

Making Instruction and Assessment Responsive to Diverse Students’ Progress: Group-Administered Dynamic Assessment in Teaching Mathematics

This study entailed a 3 (instructional intervention) × 2 (assessment-type) between-subjects experimental design employing a pretest—intervention—posttest methodology. The instructional interventions were administered between subjects in three conditions: (a) dynamic instruction, (b) triarchic or theory of successful intelligence-control instruction, and (c) standard-control instruction. The assessment-type consisted between subjects of either (a) a group-administered dynamic posttest or (b) the same group-administered posttest interspersed with a control filler activity. Performance in different mathematics content areas taught in fourth grade was investigated. In total, 1,332 students and 63 classroom teachers in 24 schools across six school districts participated in the study. The results indicate the advantages of using dynamic instruction and assessment in regular classrooms while teaching mathematics, especially when the student body is highly ethnically diverse.

A Review of the Literature: Fraction Instruction for Struggling Learners in Mathematics

Fractions are an essential foundational skill for future mathematics success (NMAP, 2008). The purpose of this article was to review current instructional practices for teaching fractions to struggling learners and to examine the quality and effectiveness of contemporary research with a view to indicating directions for future research. A comprehensive search of literature published between 1990 and 2008 resulted in the identification of 10 empirical studies that targeted fraction skills for struggling learners. Results indicated that three interventions, found to be effective for improving outcomes in mathematics for struggling learners, were also effective for teaching fractions: graduated sequence, strategy instruction, and direct instruction. In addition, explicit instruction was identified as necessary for improving students’ performance in fractions. Overall, this review highlighted the paucity of research in this critical mathematical content area.

Content Analysis of Children’s Mathematics Proficiency

In this study, 244 children (average age: 61 months) and their parents from the Dallas and Fort Worth metroplex area in Texas were surveyed to investigate children’s proficiency in mathematics content on numbering, sizes, comparisons, and shapes. The researchers investigated children’s proficiency in mathematics associated with children’s gender, ethnic background, and prekindergarten experience. Major findings of this study were as follows: (a) no gender differences were found in mathematics proficiency in all content areas; (b) among four major ethnic groups of children, White children showed higher proficiency in all mathematics content areas than other racial/ethnic groups including African American, Hispanic, and Asian children; (c) children without prekindergarten experiences outperformed children who had prekindergarten experiences in all mathematics content areas except “numbering.” No significant mean differences were found in “numbering” between these two groups.

Using Evidence–Based Practices to Build Mathematics Competence Related to Conceptual, Procedural, and Declarative Knowledge

Mathematics continues to be one of the most difficult components of the school curriculum for students with learning disabilities (LD). The National Council for Teachers of Mathematics, in conjunction with current educational legislation, challenges teachers to maintain high standards for student performance in mathematics. Fortunately, over the past two decades, researchers have identified and validated a number of instructional practices that help students with LD understand and use mathematics in meaningful ways. The purpose of this article is to discuss instructional guidelines and evidence–based practices for building conceptual, procedural, and declarative knowledge within a comprehensive mathematics curriculum. The importance of balancing these three knowledge areas across mathematics content areas is noted.

Making Mathematical Connections by Constructing Tetrahedra

Part of the beauty of mathematics is that seemingly isolated branches of the subject can often be used together to produce solutions to problems. High school students need to engage in activities that help them see how the various branches of mathematics work together in problem-solving situations. NCTM (2000) underscores the importance of such activities, stating, “When students can see the connections across different mathematical content areas, they develop a view of mathematics as an integrated whole” (NCTM 2000, p. 354).

Lithuanian basic school students achievements in mathematics

Lithuanian National Student Achievement Studies have been carried out for already two years. In 2002 Grade 6 students were tested, and in 2003, Grade 4 and Grade 8 students. Some of the main findings from their results in Mathematics are presented in the article, illustrated by several simple examples. It is noticed that a big number of students have problems in relation to understanding the fundamental concepts and having main skills in all the content areas of Mathematics.

WHAT IS QUANTITATIVE REASONING? DEFINING THE CONSTRUCT FOR ASSESSMENT PURPOSES

ABSTRACTIn order to create fair and valid assessments, it is necessary to be clear about what is to be measured and how the resulting data should be interpreted. For a number of historical and practical reasons described in this paper, adequately detailed statements with both a theoretical and empirical base do not currently exist for the construct of quantitative reasoning for use in assessments. There is also no adequate explanation of the important differences between assessments that measure quantitative reasoning constructs and those that are intended to measure achievement in related mathematical content areas.The literature in psychology, psychometrics, philosophy, and education, while containing much that is relevant to the construct of quantitative reasoning, unfortunately does not provide materials that can be used in research and development to address such practical issues or to explain the basic nature of quantitative reasoning assessments. This paper briefly discusses the importance and use of constructs and the quantitative reasoning and standards literature. It then presents a statement about the construct of quantitative reasoning for assessment purposes within a construct validity framework that includes both a definition of the construct and threats to valid score interpretation. These threats are based on related but distinguishable constructs and other types of construct‐irrelevant variance in the assessments.

Predicting Student Growth in Mathematical Content Knowledge

Using national longitudinal data, the authors investigated factors related to student learning or growth in statistics, algebra, and geometry in middle school and high school. The authors used hierarchical linear models to model variation in student rate of growth with factors associated with student characteristics and instructional and environmental factors. In addition, the authors designed the study to identify factors that differentially affect student growth at different levels of secondary school (middle school vs. high school) and for different mathematical content areas (statistics, algebra, geometry). Results indicated substantial growth in all 3 content areas in both middle school and high school. Factors related to student learning were identified and found to differ by level of secondary school and content area.

The Virtual Classroom to Rural Alaska: Web-Based Professional Development For Teachers

Delivering course content to students in rural Alaska has historically been problematic. This paper will discuss the development of a web-based course designed for licensed teachers in rural Alaska. The graduate course was offered fall of 2000 by the University of Alaska Fairbanks’ Center for Distance Education. As recently as two years ago, the primary means of teaching a distance education course at the university was by correspondence or by audio conferencing. The objective of the new course was to provide professional development to practicing classroom teachers in rural Alaska schools. The academic focus was on the integration of technology into the content areas of mathematics, science, social studies, and language arts. Two University of Alaska Fairbanks education professors co-taught the course-using Blackboard, the university’s web-based, instructional program. The researchers concluded that adding a visual component in a web-based format, in addition to real-time interaction with the instructor can greatly enhance the delivery and effectiveness of distance education courses. For licensed teachers taking the web-based course in fall of 2000, this was the first time that they had used so many technologies while taking a distance education course. In a post survey given by their teachers, they uniformly reported a positive learning experience.

Results of an analysis of the TIMS study from a gender perspective

The results of gender analyses of the Third International Mathamatics and Science Study with students of the lower secondary school level—exactly on Year 8—are described. The analyses have been carried out and restricted to twelve selected nations. These TIMSS data were analysed following various categories, as there are mathematical content areas of the items, required mathematical qualification, type of answer, real world context and level of difficulty. The analyses do not show definite and consistent gender patterns for each category, and the apparent tendencies often are even contradictory. On the whole the analyses demonstrate that differences between countries are distinctly bigger than gender differences.

Can Instructional Reform in Urban Middle Schools Help Students Narrow the Mathematics Performance Gap? Some Evidence from the QUASAR Project

AbstractThe mathematical performance of students attending middle schools in economically impoverished communities involved in the QUASAR project was compared to that of a sample of students attending demographically similar (i.e., disadvantaged urban) schools, as well as to the performance of a nationally representative sample of students. Tasks from the 1992 National Assessment of Educational Progress (NAEP) at grade 8 were administered to approximately 600 QUASAR students on each of two occasions during the 1992–1993 school year. QUASAR students outperformed NAEP's disadvantaged urban sample in all mathematics content areas, especially on those tasks assessing conceptual understanding or problem solving and on tasks requiring students to produce their own answers rather than to choose from a set of answer options. On tasks assessing conceptual understanding or problem solving, and on tasks assessing less traditional areas of the middle grades mathematics curriculum (e.g., statistics & probability, alge...

Degree performance as a function of discipline studied, parental occupation and gender

Degree performance in England and Wales was investigated as a function of social class and gender for several disciplines of study. Three performance criteria were considered: FIRST class; GOOD, and COMPETENT. The findings are complex, and some of them conflict with widely held class and gender stereotypes. Women performed better than men at the FIRST class and/or GOOD criteria, in all professional disciplines and in biological sciences. At the FIRST and GOOD criteria women performed best relative to men in biological content areas, next best in physical and mathematical content areas and worst in humanities content areas. A similar ordering of content areas was obtained when comparing students of lower class origins with those of upper and middle class origins. At the COMPETENT criterion, women performed better than men; and students of lower social class origins performed better than students of upper and middle social class origins. There was a trend, particularly marked in the humanities, for women to perform less well at the FIRST class criterion than would have been predicted by their achievements at the GOOD criterion. The implications of these patterns for theories of group differences in excellent academic performance and for educational policy are discussed.

Interaction between Structure of Intellect Factors and Two Methods of Presenting Concepts of Logic

The study reported is directly related to the work of Eastman (1975), which was a continuation of work begun by Carry (1968) and Webb (1971). Eastman obtained a significant interaction when the criterion measure of transfer was regressed on factors of general reasoning and spatial visualization. The Necessary Arithmetic Operations test and the Abstract Reasoning test of the Differential Aptitude Test Battery were used to measure these aptitudes, respectively. Two treatments, one graphical and the other analytical, were used to present methods for finding solution sets of quadratic inequalities. In the graphical treatment, concepts were presented in a symbolic-deductive mode. Eastman observed that factor analytic studies indicated that the measure for spatial visualization used by Carry and Webb (paper folding) had factor loadings on deduction. Conjecturing that the problem of deductive versus inductive presentation of the learning material might have been a confounding variable in the studies by Carry and by Webb, Eastman selected a different measure for spatial visualization, revised the instructional treatments to reflect a figural-inductive mode and a symbolic-deductive mode of presentation, and was successful in isolating an interaction. The present study was an attempt to generalize the results of Eastman to another mathematical content area. Two instructional treatments were written by the authors to present basic logical inference patterns and common logical fallacies. Three inference patterns were presented-modus ponens, modus tollens, and the law of hypothetical syllogism. The two treatments can be characterized as symbolic-deductive and figural-inductive. In the figural-inductive treatment the concept of Euler diagrams was introduced and used to determine whether a conclusion was possible according to one of the three inference patterns. The use of Euler diagrams reflects the figural nature of the treatment. The inductive nature of the treatment was reflected by the fact that the subjects learned to analyze premises by numerous examples without being given-either symbolically or verbally-a statement of the inference patterns. By contrast, the deductive nature of the other treatment was reflected by the fact that the inference patterns were given to subjects as rules prior to any exemplification of the rules, and were given in symbolic form. The symbolic nature of the treat