Overview
This unit is intended to scaffold students in the thinking process of solving word problems that involve percents. Its specific focus is to present a simple template that students can use to translate and solve percent word or story problems of varying dimensions. The goal of this template is to develop a robust understanding of the language used in solving word problems, so that many variations of problems can be correctly read.
While the intent is to alleviate the negative stereotypes and fear about math problems, the unit will assist math teachers to cultivate a tangible trend of thought, in translating and resolving word problems involving the use of percents. I hope to accomplish two things: first, the unit will set out to create a thought process that will respond to questions such as: What makes certain problems alike? Are they alike in mathematical structures, or are there also some differences? How do the problems differ when placed in groups referred to as bins? Second, the unit will utilize general principles to describe the bins by considering which bins have similar or different characteristics. This grouping process will present a structure that categorizes the nature of word problems concerning percents.
From a logical standpoint, word problems are the starting point and ending point since they embody the meaning of operations. The meaning of arithmetic namely, is how to translate real life situations into arithmetic exercises. As a starting point, word problems should be an integral part of mathematics instruction, but instead, many textbooks include word problems as a separate chapter making it appear as if it is one of the arithmetic fields or an application (Aharoni, 2007). The traditional method of teaching mathematics-progressing from computation to word problems- is a pedagogical version of putting the cart before the horse (Burns, 1984, p. 228).
From time immemorial, teaching math in grade school, especially word problems, has been a venture marked by positive challenges. In recent times, these challenges have been so profound that it is now a battle between teachers and students. Experience has shown that misbehavior and poor classroom management are prevalent in math classrooms.
On one hand, every teacher soon becomes aware when students do not understand a topic, their interests diminish, they withdraw, and they become bored and negative behavior sets in. On the other hand, when students are motivated and can relate to the topic being taught, they develop interest, become engaged and participate more.
The concern about withdrawal and lack of interest in math is due not only to poor math foundations that students bring from lower grade schools to high school, but also due to insufficient strategic methods in math. When they reach high school, students' expectations become overwhelming. The coddling that occurs in elementary and middle schools disappear and an unnecessary state of anxiety develops among new students. This state of anxiety is engendered by students' need for self esteem and fear of having their ignorance exposed in front of their peers.
The other concern that affects the teaching of math is the negative groundswell of opinion that "math is hard." As a result, students develop a dislike for numbers and analytical thinking. Although some of the apprehensions students have about numbers are based on poor foundations, much is intrinsic and due to cognitive dissonance; Psychoanalyst Jean Piaget's theory of cognitive dissonance occurs when the schemata or knowledge reservoir of an individual encounters new information that it cannot easily absorb resulting to disequilibrium. (Berger 2006). Parents demoralize their children by reinforcing their cognitive dissonance that math was not a subject for them and their siblings during their own school days and therefore, failing math could be a family trait. While this type of conditioning continues in the core unit of the community, kids continue to get passed on without meeting minimum promotion requirements.
In spite of the belief that math is hard, it still remains the queen of the sciences, and arithmetic the queen of mathematics; hence, for students to acquire appropriate math skills, a study of arithmetic is necessary. In this age and time, students who come to our classrooms face extreme difficulties in algebra and science courses because they lack basic skills in dealing with arithmetic problems to enable a smooth transition to algebra. There are also students who come to our classes with excellent computational skills but have never been taught how to translate and structure story problems into mathematical statements. Because of this situation, as a high school math teacher, I have included in this four-week curriculum unit, simple pedagogical strategies and hands-on activities related to the teaching of percent word problems to 9th graders in my intensive math class. The strategies that will be frequently used are the KWL and T-Charts; the KWC chart which is a modified version of the KWL and more applicable to science topics will be introduced. Cooperative learning and differentiated instruction methodologies of teaching will form the core of my classroom activities.
The word problems that I have included in this unit involve calculating percents of quantities, finding changes such as the decreases and increases of percents, finding missing information in a percent problem, expressing percents in several real life situations such as finding discounts and sales commissions. A more complex application of percent stories involving the calculation of ratios is presented later on in the unit to accommodate advanced students and induce critical thinking.
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