2085 Words9 Pages

Title: Developing learners` understanding of quadratic functions and solving quadratic equation. Research problem
During teaching practice learners had problems in solving quadratic equations, when learners were taught how to solve problems they don`t care about understanding the nature of the problem and steps to solve the problem. They tempt to memorize how the problems are solved without understanding them.
Mathematical pedagogical content knowledge
Pedagogical content knowledge refers to the ability of the teacher to transform content into forms that are pedagogically powerful and yet adaptive to the variations in ability and background presented by the students (Shulman, 1987).It is the particular form of content knowledge that embodies*…show more content…*

Big ideas are statements of concepts that are central to the mathematical topic. These big ideas link together essential understandings, which are smaller, more concrete ideas. For this exploration of quadratic functions, I have used Developing Essential Understanding of Functions (Cooney, Beckman, & Lloyd, 2010) as a starting point in identifying the big ideas and essential understandings in the study of quadratic functions. I propose that the overarching idea that acts as an umbrella for the big ideas and essential understandings about quadratic functions is that quadratics are functions that underlying multiplicative relationship such as the area of rectangles (Lappan, et al., 2009), and their equations can be written as the product of two linear binomials. Due to this multiplicative nature of quadratic functions, they have different patterns of change than linear and other functions. These patterns in symmetry and rate of change can be seen in the equations, graphs and tables of quadratic functions and in the connections among those representations. can be used to model particular kinds of phenomena. All quadratic functions share common characteristics with the parent functionf(x)=x^2, such as symmetry about a vertical line passing through the vertex of the corresponding parabola. This symmetry,*…show more content…*

In an analysis of textbooks in Sweden, Sonnerhed (2009) found that the curricular materials provided students with the opportunity to learn to use factoring to solve quadratic equations quickly without paying attention to their structure and conceptual meaning. When students learn to solve quadratic equations, they are taught to memorize and enact rules and procedures with little understanding of the meaning of the quadratic equations or what the solutions they find might mean. Sonnerhed’s finding fits well with Skemp’s (1976) categorization of being able to memorize and apply rules as instrumental understanding, and knowing what to do and why as relational understanding. When students only memorize procedures, they may develop instrumental understanding while their relational understanding lags behind. In their analysis of student work on quadratic equations, Didis et al. (2011) found that students incorrectly tried to transfer rules from one form of an equation to

Big ideas are statements of concepts that are central to the mathematical topic. These big ideas link together essential understandings, which are smaller, more concrete ideas. For this exploration of quadratic functions, I have used Developing Essential Understanding of Functions (Cooney, Beckman, & Lloyd, 2010) as a starting point in identifying the big ideas and essential understandings in the study of quadratic functions. I propose that the overarching idea that acts as an umbrella for the big ideas and essential understandings about quadratic functions is that quadratics are functions that underlying multiplicative relationship such as the area of rectangles (Lappan, et al., 2009), and their equations can be written as the product of two linear binomials. Due to this multiplicative nature of quadratic functions, they have different patterns of change than linear and other functions. These patterns in symmetry and rate of change can be seen in the equations, graphs and tables of quadratic functions and in the connections among those representations. can be used to model particular kinds of phenomena. All quadratic functions share common characteristics with the parent functionf(x)=x^2, such as symmetry about a vertical line passing through the vertex of the corresponding parabola. This symmetry,

In an analysis of textbooks in Sweden, Sonnerhed (2009) found that the curricular materials provided students with the opportunity to learn to use factoring to solve quadratic equations quickly without paying attention to their structure and conceptual meaning. When students learn to solve quadratic equations, they are taught to memorize and enact rules and procedures with little understanding of the meaning of the quadratic equations or what the solutions they find might mean. Sonnerhed’s finding fits well with Skemp’s (1976) categorization of being able to memorize and apply rules as instrumental understanding, and knowing what to do and why as relational understanding. When students only memorize procedures, they may develop instrumental understanding while their relational understanding lags behind. In their analysis of student work on quadratic equations, Didis et al. (2011) found that students incorrectly tried to transfer rules from one form of an equation to

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