College Algebra Course Research Articles

Looking at Both Sides of the Equation: Do Student Background Variables Explain Math Performance?

Consistently high failure rates in the college algebra course in a predominantly Hispanic university prompted this study. A cohort of 1,362 students completed a survey addressing students’ entry-level knowledge, educational expectation and motivation indicators, attitudes toward math, and family support for education. The lack of significant differences between ethnic groups in the variables measured may indicate a need to shift researchers’ attention from student background variables toward the teaching component of the teaching-learning equation.

The effect of an interdisciplinary algebra/science course on students' problem solving skills, critical thinking skills and attitudes towards mathematics

This paper briefly describes a newly designed interdisciplinary course called ‘Algebra for the Sciences’ that is currently taught at Southeastern Oklahoma State University. The effects that the course had on students' critical thinking skills, problem-solving skills, and attitudes towards mathematics were studied. The traditional college algebra course was used as a control group. The first semester that the new course was taught, students were randomly placed into one of Algebra for the Sciences or College Algebra. The study lasted for two semesters and a total of eight course sections were used — four sections of the experimental course and four sections of the college algebra course. No significant difference was found in problem-solving skills between students in the interdisciplinary course and students in the college algebra course. Students in the interdisciplinary course had slightly larger gains in critical thinking and significantly more positive attitudes at the end of the course than the students in college algebra.

Factors Influencing Success in Intermediate Algebra

Summary The purpose of this study was to investigate the following factors with respect to their influence on success in an intermediate college algebra course: short weekly quizzes, computer algebra software projects, and a practice comprehensive final exam. The results suggest that all three factors significantly influence success in an intermediate algebra course. Success was measured by achievement on an independent final exam.

The use of computer algebra software in teaching intermediate and college algebra

Two groups of students in an intermediate algebra course as well as two groups of students in acollege algebracourse were compared with respect tothe use/non-use of computer algebra software in the courses. In both courses, the students using the software outperformed the students not using the software on a common final exam. For the intermediate algebracourse, the experimental group (the one using the software) had a mean equal to 80.8, the control group had a mean equal to 76.1, and the p-value was 0.13. For the college algebra course, the experimental group had amean equal to 75.1, the control group had amean equal to 69.4, and the p-value was 0.22. Furthermore, the experimental groups expressed very positive feelings about the use of the software in the course. In addition, the instructors in the experimental groups received their best student evaluations ever when teaching algebra courses.

Some Dimensions of Mathematics Anxiety: A Factor Analysis Across Instruments

The factor structure of the items of three commonly used measures of mathematics anxiety was examined using a sample of 323 undergraduates enrolled in a required college algebra course. Six oblique factors were identified: Mathematics Test Anxiety, Numerical Anxiety, Negative Affect Toward Mathematics, Worry, Positive Affect Toward Mathematics, and Mathematics Course Anxiety. In general, the factors tended to be specific to the particular mathematics anxiety scales with few items from one scale combining with items from another scale to define a given factor. Of particular interest was the identification of the dimensions of positive and negative affect toward mathematics. Additionally, the inter correlations among the factors were subjected to structural equation modeling to see if the factors measured a common dimension. The results did not support the existence of a single common dimension of mathematics anxiety as represented by the six factors.

Validity of Scores on Alternative Predictors of Success in a College Algebra Course

For a sample of 59 male and 26 female students in continuing education at a private university, analyses indicated that (a) scores on a basic algebra test (either in a traditional multiple-choice format in which each item is accompanied by a reinforcing illustrative example) employed for placement of students in an intermediate algebra course were promising predictors of success in this course ( rs = .67 and .66, respectively, p < .05) and (b) affective measures representing the constructs of mathematics anxiety and locus of control appeared to have little, if any, predictive validity.

Assessing the Use of Graphing Calculators in College Algebra: Reflecting on Dimensions of Teaching and Learning

This article considers various aspects of teaching and learning stemming from the integration of graphing calculator use in a semester-long college algebra course. The project examined four class sections, in which two instructors each taught one section using graphing calculators and one section using a traditional approach. Achievement and attitude data showed no significant differences for treatment or instructor; a significant difference in achievement was found for gender. Students in the calculator sections responded to an open-ended questionnaire about their use of the calculator and were generally supportive of the technology. Students were in agreement about specific topics for which the technology was most useful. Overall, findings indicated that the technology use had a positive impact on various dimensions of student learning.

TECHNOLOGY MAKES A DIFFERENCE IN COMMUNITY COLLEGE MATHEMATICS TEACHING

This study examines the influence of graphing calculators on a teacher's assessment practices in a college algebra course. The researcher focused on three techniques of alternative assessment: oral discourse, teacher observations, and problem‐solving investigations. The teacher's assessment practices were revealed during 6 weeks of classroom observations. The researcher examined the teacher's assessment practices before and after the teacher used graphing calculators as tools for teaching and learning mathematics. The use of the graphing calculators enhanced the teacher's assessment practices as related to oral discourse, classroom observations, and problem‐solving investigations. The results of the study indicate the potential for technological tools to influence teachers’ practices of alternative assessment in the mathematics classroom.

FAT MEN IN PINK LEOTARDS OR STUDENTS WRITING TO LEARN ALGEBRA

ABSTRACT This paper presents the findings from a study of the learning experiences of a group of undergraduates enrolled in a writing intensive college algebra course. The curriculum of the course included the usual algebra content; however, the daily teaching and learning practices in this course involved extensive writing to learn activities and journal writing. Many of the writing activities were successful in terms of facilitating student comprehension of mathematical content and could easily be incorporated into any math course. Overall the study revealed that the use of words allowed the student writers to gain ownership of the algebraic content.

The Application of a Computer Algebra System as a Tool in College Algebra

This study compared a traditional lecture‐based college algebra course to an experimental algebra course. The experimental course stressed active student involvement and the use of the computer as a tool to explore mathematics. One hundred thirty‐seven subjects were divided into an experimental group and a control group. Subjects in the experimental group scored significantly higher than the control group on a final measure of inductive reasoning, visualization, and problem solving while maintaining an equivalent level of manipulation and computation skills. However, the attitude of subjects in the experimental group towards the use of the computer in learning mathematics declined significantly.

Applying effective instructional strategies for teaching dyslexic students in a remedial college algebra course

For many secondary and postsecondary students with dyslexia, passing required algebra courses presents a formidable challenge. Although dyslexic students do have specific and sometimes severe learning deficits that can affect their chances of success in algebra, they can succeed if given appropriate and effective instruction that meets their special and individual needs. This article briefly describes the application of effective instructional practices to the teaching of remedial algebra that have been used with dyslexic students in the University of Wisconsin Oshkosh Project Success program.

Statistical Methods for the Social and Behavioral Sciences

Statistical Methods for the Social and Behavioral Sciences consists of 50 chapters organized into 9 parts. In Parts III-VII, statistical procedures are presented by distribution: methods based on exact distributions (Part III), normal distribution (Part IV), chi-square distribution (Part V), t distribu- tion (Part VI), and F distribution (Part VII). Exercises are included at the end of each chapter; answers selected problems are presented at the back of the book. A list of additional readings, arranged by parts, appears near the end of the book. Definitions are indicated in the index by boldface numbers; procedures are marked by italic numbers. The book was for the second statistics course in psychology, education, and other social science disciplines.., .and is well-suited both one- and two-semester courses.... The book progresses through an exten- sive of two-factor designs and a preview of higher designs analy- sis of covariance, regression analysis, and log-linear analysis (book jacket). Multiple sample tests are addressed prior of variance. Para- metric and nonparametric methods are presented on an equal basis, and concepts are developed as they are needed. The purpose of and assump- tions underlying each statistical technique are emphasized. A step-by-step how to summary of statistical procedures is given in boxes in each chap- ter. Examples stress application and interpretation. Simple algebraic developments are included in the body of each chapter; more advanced developments appear in a technical appendix at the end of the chapter. The book has several strengths. It is well written and easy understand. Mathematical skill demand is minimal; a one-semester high school or un- dergraduate college algebra course will enable the reader work through the book. Concepts are presented simply and are built on throughout suc- cessive chapters. Many presentations are intuitively appealing and elegant in their simplicity. The text is remarkably free of spelling and formula errors. (The odds-ratio formula on p. 711 is incorrect; see Kleinbaum, Kupper, & Morgenstern, 1982; Knoke & Burke, 1980.) Boxes are used present an easy-to-understand, step-by-step summary of statistical proce- dures. Parallel treatment of parametric and nonparametric methods is well

Combining Individualized Instruction with the Traditional Lecture Method in a College Algebra Course

In recent years many colleges have noticed an increase in the number of student applicants who are underprepared in the basic skills of reading, writing, and mathematics. At Chapman College, a large percentage of freshmen have been required to take remedial courses in these subjects. Furthermore, many students were not performing well in the remedial course in Intermediate Algebra. To improve the success rate for students in this course, a method for teaching it was developed that combined individualized instruction with the traditional lecture approach. The method was easy and inexpensive to implement, and it required a minimum of reorganization.

A computer-aided vector algebra system for use in high schools

A computer program has been developed to be used in conjunction with college algebra and geometry courses when introducing complex numbers and vector algebra. The input and output form of complex numbers looks like this: a=1+3i. It is possible to define functions, for example, f(z) = a*z + z/(z-a), by just writing the definition, and evaluate their values: f(3+4i) = -7+14i. Similarly, the input-output form for vectors is the usual 5i-3j+7k or then a form applicable also in higher dimensions 5<1-3<2+7<3. The system can be used to evaluate numerically expressions containing vector formulas, like several cross-products, and so students can benefit from this program while doing their homework in vector algebra. The system can also be used to demonstrate subgroups, commutators, idempotents, zero factors, etc., in elementary courses on group theory and ring theory. This program is written in PASCAL and it is called CLICAL.

Test mode anticipation and performance: A classroom experiment

The study investigated the effect of test mode anticipation on performance in the anticipated and the unanticipated mode in four sections (same instructor) of a first-year college algebra course. To build up anticipation, students in two sections received recall tests, and students in the other two sections received recognition tests over 6 successive weeks. Following this, the test mode was changed without warning for half the students in each section. Results showed that performance suffered when the test mode was changed for students anticipating a recognition test. Students anticipating a recall test did equally well in both test modes.

Computer-aided design of graphical review lessons for audio-tutorial college algebra and trigonometry

An audio-tutorial minicourse system of instruction is being developed for the college algebra and trigonometry courses offered at Indiana University-Purdue University at Fort Wayne. This system of instruction is patterned after the one developed by S. Postlethwait. At present a college algebra course, MA 153, is being taught using audio-tutorial minicourses. In the spring semester two trigonometry courses, MA 112 and MA 154, are planned to be taught using this system of instruction. Also, a fourth course, MA 111, will be taught using this system in the spring, 1980, semester. Much mathematics is more easily understood by using graphs. In many minicourses students are required to draw graphs. It is difficult to convey how one graph is “shifted” to obtain another graph using printed materials. As a result, a computer program was developed to create audio-visual review lessons of graphing concepts covered by the audio-tutorial minicourses. A review lesson may contain not only simple concepts such as point plotting, but also dynamic displays of graphs and their transformations. Creation of a review lesson is divided into four steps: (1) coordinate system definition, (2) function definition,(3) example definition, and (4) example viewing. The user is guided through each step via a series of menus. A sophisticated ten minute review lesson may take only 15 to 30 minutes to create. The program is written in TUTOR and runs on the University of Illinois PLATO system.

Student Placement Utilizing Incomplete Data Records

A method is proposed for the construction of a classification rule based on both complete and incomplete data records. This method incorporates the Hocking-Smith estimation procedure to find estimates of the mean vectors and variance-covariance matrices from samples which may contain incomplete data vectors. The resulting estimates are used to construct a discriminant function. We will demonstrate that these incomplete observation vectors contain information relevant to classification and should not be discarded. The proposed method is applied to the placement of students into one of two college algebra courses at Tarleton State University. The standard procedure that ignores incomplete observation vectors in the construction of a classification rule is also applied to the same data, and comparisons are made between the two methods. The proposed method that utilizes the incomplete observation vectors correctly classifies a higher percentage of students than does the standard method.

A Search for Trends among Mathematics Programs in Small Colleges

In order to gather background data for a panel discussion* of the topic Teaching Mathematics to the Beginning Undergraduate, a questionnaire was distributed to the chairmen of 67 four-year colleges and universities in the Midwest. Returns were obtained from 35 colleges with enrollments from 500 to 3,000 and from nine universities. This report focuses primarily on the four-year colleges but will identify those situations uncovered among the universities which appear to be different from those in the colleges. In response to a question about the preparation of students, sixteen chairmen reported that students are less well-prepared now than they were ten years ago, ten thought students are better prepared, and nine thought that there is no appreciable change. An open-ended question was asked of chairmen: What topics from precalculus mathematics are not sufficiently well understood by students when they begin their calculus course? Almost half the responses included trigonometry. Lack of ability to perform important algebraic manipulations was a close second with several specific algebraic topics mentioned on numerous occasions: inequalities (9), absolute values (6), and graphing (6). Denison's admissions staff indicates that trigonometry appears much less frequently on transcripts of prospective students today than it did ten years ago. Trigonometry, when it is studied at all in high school, is more commonly a part of a senior mathematics course. The message from college departmental chairmen seems to be that the time spent on trigonometry has decreased with. the integration of the subject into a one-year course. Each college's enrollment in college algebra was expressed as a percentage of its first-semester calculus enrollment. For the small colleges, these percentages varied tremendously-several colleges still do not give a precalculus college algebra course while others have a very heavy enrollment in algebra. The range was from 0 to 300 per cent and the small-school median was 56 per cent. The state institutions reported ranges from 80 to 300 per cent with

Mathematical Induction: If Student k Understands It, Will Student k + 1?

Of all the topics taught in the usual college algebra course, mathematical induction seems to be viewed with the highest level of suspicion by the greatest number of students. I am always amazed that, when it comes to induction, even my better students tend to feel that they have somehow been hoodwinked. Many students never recognize the end of a proof by induction; they either think that nothing has been proved, or that you (the teacher) assumed what you wanted to prove in the beginning anyway. I generally try two approaches before I give a standard presentation on mathematical induction in an effort to help the student understand the reasoning involved in an induction proof. These approaches are outlined below.