Utilizing an Algorithmic Instructional Technique in the Developmental Mathematics Classrooms
Selina Vasquez · Mathematics and computer education · 2003
Developmental mathematics students need to gain both fundamental and problem-solving skills. They need a strong mathematical foundation for obtaining their educational goals since most degree plans require at least one non-developmental mathematics course. And, in some states, such as Texas, state-mandated problem-solving tests must be mastered in order to graduate from college. purpose of this paper is to discuss an Algorithmic Instructional Technique [AIT] that addresses both fundamental and problemsolving skills bv using non-traditional instructional methods. AIT consists of a steady progression through four phases: modeling, practice, transition, and independence. progression begins with teacher-directed instruction of fundamental topics and continues towards a student-directed learning environment for complex topics in a problem-solving context. ultimate goal is to provide a student-centered learning environment where students gain understanding of mathematical concepts by creating pertinent to successfully guide them to efficient non-rote systems to accomplish mathematical tasks. This approach uses problem-solving techniques that are solidified through carefully developed including those based on real-world situations. A complete set of unpublished lesson plans/activities have been developed and a copy will be sent to interested readers who e-mail the author. essence of the AIT centers on natural mathematical tendencies. That is, the instructional method enhances students' likely ability to find patterns, make conjectures, and validate their hypotheses with proof. Yet, the AIT expands on this by incorporating group work such as cooperative learning, whole-class discussion, and peer-tutoring in order to provide the students with an experience that allows them to formalize their thoughts through discussion and demonstration. In this respect, the AIT accommodates various learning styles. This instructional technique is also based on the creation of algorithms. essence of an algorithm is to ... formulate mathematical definitions and generalizations discovered through investigations (National Council of Teachers of Mathematics [NCTM], 1989, p. 140). According to NCTM's Curriculum and Evaluation Standards for School Mathematics, Many of the topics in the secondary school mathematics curriculum can and should be investigated and developed by students from an algorithmic perspective (p. 178). This is primarily because The development and analysis of lie at the heart of computer methods of solving problems (NCTM, . 178). An algorithmic approach may help diminish academic difficulties. First, individualize the learning experience. Typically, there are several ways to solve a problem and, consequently, there are various appropriate for any given problem. Hence, each student can develop and use that he/she is more likely to grasp. Second, provide for a means of simplifying mathematics. However, this is not to propose that become recipes for -solving mathematics since ... such knowledge [of computational algorithms] should grow out of the problem situations that have given rise to the need for such algorithms (NCTM, 1989, p. 8). With the use of algorithms, students can reflect upon and clarify their thinking about mathematical ideas and relationships (NCTM, p. 8). Third, the ability to construct and apply provides the students with the ability to do other important skills such as effectively read a mathematics textbook, develop outlines, and follow directions. Each of these requires logical thinking skills that the student practices each time he/she uses algorithms. Finally, assist with the communication of mathematics; they can express mathematical ideas orally and in writing (NCTM, p. 140). In general, can foster mathematical understanding that in turn, helps to decrease the underachievement that developmental mathematics students typically exhibit. …