General Education Mathematics Research Articles

교양수학 교과목에 대한 효율적 교수-학습지도 방안

There are serious difficulties with management of general mathematics education courses because of enormous gap between freshman's ability of mathematics and lack of problem solving ability. In this paper, we try to find methods so we can reduce the difficulties. By utilizing students survey, manage...

Novice Special Educators’ Instructional Practices, Communication Patterns, and Content Knowledge for Teaching Mathematics

In this study, the authors examine the influence of teacher and student communication patterns, instructional practices, and teacher pedagogical content knowledge on students’ mathematics learning in both general and special education mathematics classrooms. Five pre-service special education teachers in field placements and 43 students with varying disabilities participated in this study. Observations of teachers during mathematics lessons and follow-up interviews were conducted. Students in these settings completed a pretest and posttest of mathematics content taught over 6 weeks of instruction. Results reveal two sets of instructional practices, communication patterns, and teacher understandings of mathematics for teaching that differentially affected student performance. Implications are discussed for teacher education and further research.

Review of Quantitative Reasoning: Tools for Today's Informed Citizen by A. Sevilla and K. Somers

Alicia Sevilla and Kay Somers, Quantitative Reasoning: Tools for Today’s Informed Citizen. (Emeryville CA: Key College Publishing, 2007). 626 pp. Softcover with Student CD. $79.95 (USA) ISBN 1-931914-90-1. http://www.keycollege.com/catalog/titles/quantitative_reasoning.html From charts and graphs (Topic 1) to decision making (Topic 21), Quantitative Reasoning offers a good selection of topics that students in a general education mathematics course and other individuals in our society should understand. Organizing the 21 chapters (topics) under the headings of numerical reasoning, logical reasoning, and statistical reasoning, Sevilla and Somers focus their chapters on examples and devote the last 224 pages to 21 Excel activities. Parallel graphic-calculator activities are on the Student CD, together with the data bank for the Excel activities. The strong orientation toward exercises and activities will assist instructors in making their course an engaging numeracy experience for their students; however, it also likely means that some instructors will find that some explanations are not as fully developed as they would like. With the selection, structure, exercises and activities provided by Sevilla and Somers, instructors can easily add supplemental material according to their own interests and priorities.

A Critical Examination of Learning Disabilities in Mathematics: Applying the Lens of Ableism

Introduction Background and Rationale Over half of the students who receive special education services are labeled as learning disabled (LD); they comprise approximately five to six percent of the entire K-12 student population (Hehir, 2005). Most students are labeled LD in reading; however, approximately twenty percent are either labeled as LD in mathematics or LD in both reading and mathematics (G. Williamson, personal communication on March 9, 2006). Therefore, it is likely that one in every one hundred students in American public schools carries the label of LD in mathematics. Many may perceive one percent to be a small and insignificant slice of the K-12 population and may wonder why I would choose to focus my on such a small group of students. My response is three-fold. First, federal legislation such as the No Child Left Behind Act (NCLB, 2001) and the Individuals with Disabilities in Education Act (IDEA, 2004) require us to pay attention to the quality of all students' education and (probably more so) their academic performance. Second, not much literature exists in mathematics education on this topic. As a field, we have published mathematics education work relating to race, gender, and socioeconomic status, but on the subgroup of special education, particularly students carrying the label of LD in mathematics, we remain largely silent. Lastly, the social, emotional, educational and political realities for those involved--the labeled student him/herself, his/her parents, the labeled student's general education mathematics teacher as well as his/her special education teacher, the administrators and in fact the labeled student's entire school--are extremely significant. I am deeply concerned with issues of equity and the power differentials inherent in our society, and I want our schools to seek ways to eradicate practices in mathematics education that privilege some at the expense of others. Theoretical Perspective In this article, I apply a critical pedagogy (Kincheloe & McLaren, 1994; Freire, 1997) perspective looking through the lens of ableism (Rauscher & McClintock, 1977; Hehir, 2005) to examine current educational policy, research and practice regarding the identification of and labeling of students as LD in mathematics. Kincheloe and McLaren (1994, p. 453) state, inquiry that aspires to the name critical must be connected to an to confront the injustice of a particular society or public sphere within the society. A critical pedagogy perspective, then, seeks to uncover hegemonic (power) relations, ideologies, and inequities in education, critique instrumental rationality, and inspire a movement for toward social justice. The following are assumptions from a critical pedagogy perspective that are pertinent to this article: 1. Acknowledging schooling as a form of cultural politics that endorses only particular forms of knowledge, thus creating a dominant group of successful knowers and others (Brantlinger, 1997, 2001); 2. Challenging the traditional view of education as a neutral and just process, and instead, recognizing it serves as an oppressive social structure (Freire, 1997) for some students; 3. Believing that self and social empowerment should precede mastery of technical skills tied to the marketplace and that educators should attempt to see and experience education from the perspective of those who are not dominant and work towards positive social change (Pasco, 2003, p. 5). Hehir (2005) discusses how the ideology of ableism negatively affects the education of children labeled with disabilities and urges educators and policymakers to focus on making just and equitable decisions about the policies and practices that support the educational, emotional and social progress of individual children. In his book on eliminating ableism, he utilizes (and in this paper I adopt) the following definition for ableism: Ableism is a pervasive system of discrimination and exclusion that oppresses people who are perceived to have cognitive, emotional, and/or physical disabilities. …

CAS as a didactical challenge

The paper starts with the discussion of a concept of general mathematics education (mathematics education for everyone). This concept views the focus of teaching mathematics in the reduction of the demands in the field of operative knowledge and skills as well as in an increase of the demands in the fields of basic knowledge and reflection. The consequences of this concept are didactically challenging for the use of Computer Algebra Systems (CAS) in the teaching of mathematics. By reducing the operative work we reduce exactly that field in which the original potential of CAS lies. It is shown that in such maths classes the main focus of CAS is on their use as a pedagogical tool, namely as support for the development of basic knowledge and reflection as well as a model of communication with mathematical experts.

Issues and Challenges for Middle School Mathematics Teachers in Inclusion Classrooms

The purpose of this qualitative study was to investigate typical middle school general education mathematics teachers' beliefs and knowledge of students with learning disabilities and inclusive instruction and to gain an understanding of the process of inclusion as it is implemented in middle school classrooms. In‐depth interviews, surveys, and classroom observations were conducted with seven teachers. The constant comparative method was used to analyze all interview and observation data. The findings reveal that even teachers who believe that inclusion is being successfully implemented are unclear about their responsibilities towards included students and the learning characteristics and specific mathematics teaching approaches that would be effective. The general educators feel that they were grossly under‐prepared during preservice and inservice for the realities of inclusion teaching. The study provides insights that can be used to enhance preservice and inservice programs for teachers and underscores the necessity for building teamwork and collaboration among general and special education middle school teachers.

Middle School Mathematics Teachers' Beliefs About Inclusion of Students with Learning Disabilities

The purpose of this descriptive study was to investigate middle school general education mathematics teachers' beliefs and self-perceived knowledge regarding teaching students with learning disabilities (LD) in inclusive classrooms. Teacher beliefs regarding administrative support and higher education teacher preparation were also examined. The Survey on Teaching Mathematics to Students With Learning Disabilities in Middle School was completed by 228 sixth-, seventh-, and eighth-grade general education mathematics inclusion teachers from 19 states. In addition, telephone interviews were conducted with a subset of 26 survey respondents. Frequency analyses were performed on the survey data, with χ2 tests comparing teachers on demographic variables. Follow-up interview responses were summarized to elaborate on the major research questions. The findings revealed three central issues: (1) teachers had a limited understanding of the mathematics learning needs of students with LD, (2) teacher collaboration was judged to be the most beneficial and available resource by general educators teaching students with LD in inclusive mathematics classrooms, and (3) teachers did not feel that teacher education programs at the preservice level and professional development at the inservice level were adequate in preparing them for teaching students with LD in inclusive mathematics classrooms. Implications and recommendations for teacher preparation and program implementation are provided.

Teaching Mathematics to College Students with Mathematics-Related Learning Disabilities: Report from the Classroom

This article reports on action research that took place in one section of a college general education mathematics course in which all three students who were enrolled had diagnosed learning disabilities related to mathematics. The project emerged in response to a question about performance in a mathematics course in which making sense of mathematics would be a primary focus, explaining one's work would be expected, and discourse among members would be a routine occurrence. Implications for teaching similar courses to students who have a mathematics-related learning disability are discussed.

Mathematische Bildung im Klagenfurter Doktorand(inn)enkolleg

In 2003 we set up a programme for PhD-studies (,,Doktorand(inn)enkolleg”) at the University of Klagenfurt which should promote and support PhD-studies in the field of mathematics education. Within this programme it is worked on the topic “general mathematics education” from different perspectives. In the first part of this paper intentions, the fields of work and the form of organisation are briefly demonstrated. The second and main part considers in detail the work in one of the four fields of work, and finally, the third and last part presents some experiences with regard to the contents as well as general ones.

An Assessment of General Education Mathematics Courses via Examination of Student Expectations and Performance

This paper discusses the method and results of an evaluation of general education mathematics courses. Students at the University of Louisville were surveyed in the first week of the Fall 2000 semester to determine their expectations for their mathematics course. Student grades were examined to determine how student expectations related to student outcomes. The workload expected by students is substantially different from that expected by faculty, and this difference is reflected in final course grades.

Apportionment and the 2000 Election

Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsMichael G. NeubauerMichael Neubauer (michael.neubauer@csun.edu) received his Ph.D. from the University of Southern California under the direction of Robert Guralnick in 1989 and is now at California State University, Northridge. He became interested in apportionment theory while teaching the topic and after many conversations on the topic in between swimming laps he and Joel Zeitlin finally got the idea for this article. He very much enjoys the company of his wife and his two kids.Joel ZeitlinJoel Zeitlin (joel.zeitlin@csun.edu) received his degrees from UCLA and is now at California State University, Northridge. After a thesis in Lie Groups and Algebras in 1969, he has followed his interests, usually relating to geometry or computing, but this time arising from conversations about general education mathematics courses. He enjoys the usual math nerd stuff: family, friends, food, books, exercise, and television.

CAS in general mathematics education

A rational discussion of the use of Computer algebra systems (CAS) in mathematics teaching in general education needs an explicit image of (general) mathematics education, an explication of global perspectives and goals on mathematics teaching focusing on general education (chapter 1). The conception of general education according to the «ability of communication with experts» described in chapter 2 can be such an orientation for analysing, considering, classifying and assessing the didactical possibilities of using CAS. CAS are materialised mathematics allowing for more or less exhaustive outsourcing of operative (also symbolically) knowledge and skills to the machine. This frees up space of time as well as mental space for the development of those competences being in our view relevant for general mathematics education. In chapter 3 the idea of outsourcing and the role of CAS for it is discussed more detailed as well as consequences being possible for the CAS-supported teaching of mathematics. Beyond, CAS can be didactically used and reflected as a model of communication between (mathematical) experts and lay-persons (chapter 4). Chapter 5 outlines some research perspectives.

Functions of Number Theory in Music

Connecting mathematics with other disciplines is one of the major goals of many general-education mathematics courses taught at universities and colleges across the nation. Of course, from kindergarten to calculus, good teachers demonstrate and explore these connections as a means of making clear the relevance and importance of mathematics to every person. In particular, I have cheerfully noticed a renewed interest in the relationships between mathematics and music. This article examines several fundamental notions of number theory as they arise in music theory, and in the process, develops several music-related functions. I see an added pedagogical benefit in emphasizing the importance of functions in mathematics with examples from a different arena than the usual function pool. Middle school and high school teachers might find that a subset of these topics are handy nuggets of material that can show examples of applications of mathematics outside the mainstream uses in science and engineering. I created this article as notes for the liberal-arts mathematics course that I teach at my college and have consistently found this topic to be one of the students' favorites.

Increasing mathematical problem-solving performance through relaxation training

Two intact classes of 30 undergraduate students enrolled in the same general education mathematics course were each administered the IPSP Mathematics Problem Solving Test and the Mathematics Anxiety Rating Scale at the beginning and end of the semester. Both groups experienced the same syllabus, lectures, course requirements, and assessment techniques; however, one group received relaxation training during an initial class meeting and during the first 5 to 7 minutes of each subsequent class. The group which had received relaxation training had significantly lower mathematics anxiety and significantly higher mathematics performance at the end of the course. The results suggest that relaxation training may be a useful tool for treating anxiety in undergraduate general education mathematics students.

Weaving Mathematical Instructional Strategies Into Inclusive Settings

In order to facilitate the successful inclusion of students with disabilities into general education mathematics classes, efforts must be made to explicitly examine how the needs of these students can be reconciled with the direction of mathematics reform. This article describes a framework that allows teachers in inclusive settings to interweave together instructional strategies from a variety of paradigms in order to meet individual learning needs in an environment that embraces current reform initiatives. Factors to be considered in the instructional decision-making process are highlighted, and an instructional continuum from more teacher-centered strategies to more student-centered strategies is described.

Returns to General, Technical and Vocational Education in Developing Countries:recent evidence from Suriname

We employ a new data set from Suriname to estimate private and social returns to technical, vocational and two tracks of general education (mathematics and language). Return estimates are based on gender-specific wage equations, corrected for sample selection bias and adjusted for unemployment. We find that, for both genders, returns to either general track exceed returns to technical or vocational education. Female returns to the language track exceed those to the mathematics track from the social and private perspective, while for males, both social and private returns in the mathematics track exceed those in the language track.

A MULTIMEDIA STATISTICAL UNIT FOR GENERAL EDUCATION

ABSTRACT This paper describes the development and evaluation of a multimedia statistical unit for a college general education mathematics course. The findings indicate that students in the multimedia instructional program showed significantly higher statistical performance than students in a control group. The multimedia instruction seemed especially well suited to female students who, although initially apprehensive, adapted quickly and effectively to the use of videos, data displays and computer applications incorporated in the program.

Classwide Curriculum-Based Measurement: Helping General Educators Meet the Challenge of Student Diversity

This study examined the effectiveness of innovative curriculum-based measurement (CBM) classwide decision-making structures within general education mathematics instruction, with and without recommendations for how to incorporate CBM feedback into instructional planning. Forty general educators, each of whom had at least one student with an identified learning disability for math instruction, were randomly assigned to three groups: CBM with classwide reports that summarized information and provided instructional recommendations, CBM with reports but without recommendations, and contrast (no CBM). Results indicated that only the CBM teachers who received instructional recommendations designed better instructional programs and effected greater achievement for their students.

APPLICATIONS ÜBER ALLES: MATHEMATICS FOR THE LIBERAL ARTS

ABSTRACT This paper presents a fresh approach to a general education mathematics course. The basic idea is to turn the customary mathematics class on its head by focusing on applications first, through a reading of articles from magazines and newspapers, and then turning to the technical mathematical details. A description of the topics that were covered in my course, along with references to various publications, is given. A course such as this one is important because it conveys how mathematics is serving the goals of society.

Reviews

Because mathematics has always been an important part of elementary and secondary curricula, it has been a frequent target of critical commentary and proposals for reform in content or pedagogy. Few teachers today could describe the content or impact of such landmark events as the Committee of Ten, the Perry Movement, the 1923 National Committee on Mathematical Requirements, the 1940 Progressive Education Association report, Mathematics in General Education, or even the 1961 Royaumont report, New Thinking in School Mathematics. However, everyone in education and many in the general public have ideas about and (more likely) opinions on the “new math” era in school mathematics that dominated the decades from 1955 to 1975.