Just-in-Time Algebra: A Problem Solving Approach Including Multimedia and Animation.
2003; Volume: 37; Issue: 1 Linguagem: Inglês
ISSN
0730-8639
AutoresRoseanne S. Hofmann, Walter R. Hunter,
Tópico(s)Innovative Teaching and Learning Methods
ResumoAbstract A Beginning Algebra course was recently developed which places stronger emphasis on learning to solve problems. Topics are introduced and developed using real world applications, and students learn estimating, graphing, and algebraic algorithms for the purpose of problems. Nearly every problem is an applied problem. Initial results indicate that applications motivate the students by appearing to be a more relevant topic as well as help teach them A textbook and an array of supplementary technology tools focused on this approach were created. The philosophy of the new course is that solving problems requires algebra. In 1997 the authors radically reconstructed the Montgomery County Community College Beginning Algebra curriculum trying to follow the sentiments expressed in the following core reports in our field: Everybody Counts, A Report to the Nation on the Future of Mathematics; Curriculum and Evaluation Standards for School Mathematics; and Standards for Curriculum and Pedagogical Reform in Two-Year College and Lower Division Mathematics. There were two reasons for changing our Beginning Algebra course. First, the course was not working well (Laughbaum, 1992; National Sciences Education Board, 1990; Steen, 1992). Too much emphasis was being placed on symbolic manipulation without context. Topics such as factoring trinomials, simplifying rational expressions, and simplifying radicals were being taught to students who felt they were never going to use these skills again (AMATYC, 1994; Davis, 1989; Kysh, 1991; NCTM, 1989), and students who went on to take Intermediate Algebra treated these topics as if they had never seen them before or, worse, recoiled at the thought of having to use them again. Second, the use of graphing calculators became a requirement in followup courses. Thus, we needed to address the issue of what algebraic topics students would need to know in order to learn higher mathematics. New Curriculum A review of the previous Beginning Algebra course showed that most of the work fell into three categories: simplify, solve, and graph, with most of the time spent on simplifying. A stronger emphasis on problems was suggested so that topics taught would solve a problem, either by estimating, graphing, or applying an algebraic algorithm (AMATYC, 1993; Cauley et al., 1995; Kysh, 1991; National Research Council, 1989). Traditional algebraic courses teach skills first and provide a few word problems if time permits. Our revised curriculum, which uses a just-in-time approach (Bennett, 1999), starts with an applied problem and then looks for the algebraic skills to solve it. Generally, topics are introduced by real world applications. Almost every problem is an applied problem. The applications have been shown not only to motivate the students but also to help teach the material. We require a scientific calculator and encourage students to use it. Estimating and exponents become more meaningful when students use a calculator (AMATYC, 1994; Cauley, 1995; Mercer, 1992; National Science Education Board, 1990). The basic model for the first half of the course is exemplified by the following problem: Selena starts a lawn mowing business for the summer. She spends $300. 00 on a lawn mower and charges $8. 00 an hour. This problem can be used to: Introduce variables Solve simple linear equations Graph lines by plotting points Graph lines by finding intercepts Motivate the equation y = mx + b This model is used to connect the abstract concepts to a concrete example. Students discover the need for variables, introduced by using tables, by attempting to answer the question: How much money will Selena earn if she works the following hours during the summer? IMAGE FORMULA11 From the table students notice that the only part under the calculation heading that changes is the number of hours, hence the need for a variable h. …
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