College Algebra Research Paper

Even though college algebra is considered to be an obstacle for many students in terms of degree completion, as teachers we must teach useful strategies to motivate our students to find interest in mathematics. Recently, there is a psychological problem that we as teachers will face in the future, which is that some students believe they were born incompetent in math. However, “effort is key to their success and failure is a result of a lack of effort” (Cortes-Suarez, 2004). As teachers, we must motivate students that are in denial to improve their mathematical skills to prevent poor academic performance. For that reason, attempts to reshape the educational system could help break the cycle of self-blame that several students possess in order
to prevent failure in the future. Students might believe that algebra is only necessary for school purposes. However, algebra attributions can positively influence problem solving skills, whether it may be in a classroom or work setting. Cortes-Suarez’s research states that college algebra has been identified as a “high-risk course due to its low success rates” with a passing rate less than 60% (2004). This study indicates that “attribution theory” is an important “cognitive method” to approach academic achievement (2004). According to Dweck’s research, “students that blame their academic difficulties on internal factors are likely to experience anxiety and thus have difficulty learning” new material; however, Dweck indicates that by “encouraging students to attribute their poor performance to unstable causes… both improved effort and performance” result in the students (1975). For that reason, being able to use abstract reasoning to solve for unknown variables will enhance students’ problem solving skills in the future. These critical skills will help the students in their future career because they will find possible outcomes for problems they thought were impossible.
According to Andrew Hacker, a professor at Queens College in the University of New York, algebra should not be required for all students.
The reason behind this is due to “untold numbers of students failing algebra” (2012). He claimed that “requiring algebra tends for students to hate mathematics” due to the numerous times retaking this class until they eventually dropout (2012). Society tends to dislike concepts they do not understand and if the students are not well prepared to take algebra, they might even quit college. Nevertheless, Hacker’s research indicates that “our society would collapse without mathematics” (2012). There is a vital need for improvement in our frontiers by using proper “algebraic algorithms” found in movies, investments, and airline tickets prices, which need to be solved (Hacker, 2012). Hacker’s research also states that “mathematics sharpens our minds” and improves our intellectual capacities. However, from his point of view, instead of requiring algebra courses, colleges must consider “quantitative reasoning” classes instead
(2012).
On the other hand, according to NCTM members, college algebra needs to be implemented in the school system.
NCTM Standards show that “mathematical power” is required in order for students to perform effectively in a “variety of authentic settings,” such as in science, technology, engineering and mathematics degrees that require critical thinking skills (Steen, 1992). Algebra viewed from a student’s perspective grants effective problem solving skills, meaning it allows students to seek a correct process and find the precise solution. In order to understand the concept behind algebra, we must first analyze the problem given, understand what the problem seeks to find, reflect on the information given, and take into account the conditions that are presented. Through this thought process, we can then plan our strategy to solve a problem. This approach is useful not only in mathematics, but in other concepts as well. In algebra, logical thinking skills are used to make sense or make connections within a problem in order to find a
solution.
Mathematicians create universal analogies to certain topics. For instance, while students might use numbers as mere tools, they ultimately seek to discover countless information about this world. Even the simplest observations one might make about mathematics might even turn to be directly analogous to at least some aspects of the real world. According to the Mathematical Association of America, algebra is considered to be the “first subject where students develop logical thinking” during their educational careers (2012). For mathematicians, algebra is considered the basis or prerequisite for future courses such as pre-calculus, geometry, calculus, linear algebra, statistics, and advance mathematical courses. Moreover, algebra is known to be a part of mathematics that includes general letters and symbols to represent numbers that can be formulated and found by solving equations. Some students fail to build a solid foundation in mathematics, which is why they are unprepared for college and for work. As students, they are often unable to connect abstract mathematical ideas to properly solve a problem, which is a dilemma that often extends to their future careers. As future math teachers, we must encourage students to understand the concept behind college algebra, which will help them excel in their future.