pros and cons of factoring quadratic equations

Notice that the constant term is the product and the coefficient of x is the sum If the sides are not equal, then it is a rectangle, say, of sides and where. In Figure 2, geometrically, the area of the larger square is the sum of the individual areas. The Quadratic Equation Concept The quadratic equation concept can be introduced geometrically by referring to the squares shown in Figures 1 and 2. From this literature review, it is clear that there is a need for further research into the sources of students’ difficulties with quadratic equations.

Research suggests that teachers tend to avoid teaching alternative methods due to high instances of process skill errors with techniques such as the quadratic formula and completing the square (Zakaria et al., 2010). Barnes (1991) suggests using graphing calculators to plot quadratics with no roots, one root, or two roots and linking this to the discriminate values. Geometric models are useful tools that may ensure students are able to understand, manipulate, and apply the quadratic formula via completing the square procedure (Norton, 2015). For example, factorization with algebra tiles link quadratics with basic multiplication and division concepts via the area model of rectangles and squares (Howden 2001). Further, other methods that are more efficient or that develop conceptualization may be neglected in teaching (Bosse & Nandakumar, 2005). Over-emphasis on relatively simple factorization is concerning since many quadratic equations cannot be factorized. Research has shown that students and teachers shy away from some techniques and favor factorization, generally using coefficients that are easy to factorize since students’ ability to perform fractional and radical arithmetic has been reported as low (Bosse & Nandakumar, 2005). Each of these techniques has its own advantages and disadvantages when it comes to teaching, learning, and applying. In most curricula this involves factorization, the square root method, completing the square, and the use of the quadratic formula. A key process in working with quadratics is solving or finding the 𝑥 intercepts, should there be any. Hattie (2009) notes “fluency with prerequisite knowledge, even at a very early stage, is highly predictive of latter success”. The cognitive load work by Kirschner, Sweller, and Clark (2006) gives an explanation for the necessity of fluency with prerequisite knowledge. The Australian Academy of Science (AAS) also recognizes the intertwined relationship between conceptual understanding, procedural fluency, and problem solving and reasoning due to the hierarchical nature of mathematics (AAS, 2015, p. Kotsopoulos (2007) reports that students need to develop procedural and conceptual knowledge through various learning experiences in an integrated manner. It is important to consider the impact and current evidence relating to teaching methods and the learning of quadratic equations. Students have been found to struggle particularly solving for 𝑥 in the form 𝑥 2 = 𝑘 (k>0) and (𝑥 − 𝑟)(𝑥 − 𝑠) = 0 where 𝑟 and 𝑠 are any real numbers (Vaiyavutjamai et al., 2005). Literature Review The resounding theme in mathematics education research is that students’ performance in the domain of quadratic equations is exceptionally poor and does not significantly increase even after instruction (Chaysuwan, 1996 Vaiyavutjamai et al., 2005). However, the quadratic formula is advantageous in the fact that it is applicable to all quadratics and will always yield the correct solution. Depending on the quadratic in questions, there is an appropriate time for each method. The quadratic formula is as follows: There are other methods used for solving quadratics, such as graphing, factoring, and completing the square. The degree also describes the number of possible solutions to the equation (therefore, the number of possible solutions for a quadratic is two). A quadratic is an equation in which the degree, of highest exponent, is a square.

Introduction The quadratic equation is a formula that is used to solve equations in the form of quadratics.

Pros and cons of factoring quadratic equations