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

Related

## Quadratic Equation Research Paper

1026 Words | 5 PagesQuadratic Equations: Introduction: Quadratic equation is a polynomial equation of the 2nd degree. The word ‘quadratic’ comes from the Latin word quadratus which represent the word ‘square’. Quadratic equation is an equation which can be written in the form of ax2 + bx + c = 0, where a and b are coefficients of x2 and x respectively and c is a constant. The coefficient of x2 cannot be zero and the expression ax2 + bx + c is called as ‘quadratic expression’. For example, 4x2 + 5x + 2 = 0 is a quadratic

## The Importance Of Community Policing

1170 Words | 5 Pagesgeographic areas by carefully studying characteristics of problems in the area and then applying the appropriate resources. More generally, problem solving is community participation in the identification and resolution of a problem. According to Rosenbaum et al. (2011), it is the notion that the police and community must work together to identify and solve neighbourhood problem. Police mostly need to identify the root causes of problems and respond to them. As Oliver (2008), in commu-nity policing

## Privacy Characteristics Of Big Data

1520 Words | 7 Pagesinsights and competitive advantage. Big data refers to two conditions, the technological challenge which is about dealing with data intensive domains such as high energy physics, astronomy or internet search. The second condition is dealing with social problems with the main focus being on cultural and environmental factors, when data about people is collected and obtained by organizations such as Facebook, twitter, Google to mention a few. Privacy

## Challenges And Challenges In Counselling

2000 Words | 8 Pagesfrom a counsellor to talk their problems out and also to find solutions to their problem or the crisis that their facing because in some point of everybody’s life, they will face a problem that is beyond their control or that they did not predict of and this is where counselling comes in place to help their needs and give them other solutions. Counselling is also like guidance to the individual that is in need of them or that does not know how to solve the problem their facing. Counselling also involves

## Negative Effects Of Sugar Products

829 Words | 4 PagesHow long will sugar products advertising affect our life? That question should be in people’s minds because sugar products advertising are strong problem. A few years ago companies around the world started to think about how to pull people into sugar products by many ways such as boards in the street, radio stations and the television. They thought about using these advertisements to move their economy and increase their profits. Sugar products advertising may be the source they are looking for to

## Granular Computing Research Paper

2770 Words | 12 PagesAbstract: Granular Computing is an emerging computing model of problem solving and information processing. The main concept behind the development of ‘Granular Computing’ is to develop machine-oriented studies based on the ‘way of human thinking’. With multiple levels of granularity, it is possible to identify, examine and formalize a collection of principles, strategies and methods that are commonly used by humans in daily problem solving. Then this is used to human-oriented solutions development

## Alternativ Alternatives Case Study

747 Words | 3 Pages1. (B) Why is it so important to consider them when making decisions? Good solutions are not possible without good alternatives. Therefore, is it important to consider alternatives because they reflect substantially different approaches to the problem or different priorities across objectives; present us with real options and choices. 2. Explain in one paragraph why it is so important NOT to "Box Yourself in With Limited

## How Does Technology Improve America Essay

706 Words | 3 PagesAmerica is such a stereotypical country. Really, America judges all other countries and how they do things. America, honestly, has no room to even give an opinion. America is one of the worst countries to exist. Has anyone ever really thought about what America has really done as a whole? Really, think about it, has America given everyone the best of the best? More than once, there has been times where America has let the whole country down. However, there are much bigger things to get over. What

## Problem Solving Skills In Customer Service

1774 Words | 8 Pagesservice representative who are confident, has the capability of resolving issues with customers and also satisfying customers’ need. Some steps to problem solving include listening which is often overlooked by service employees. However, listening is the key in understanding the customer, so that a solution may be arrived at. In trying to solve customers’ problem employees must show empathy when dealing with customers by apologizing, if the company product or service is faulty. This is good for customer

## Midterm Reflection

732 Words | 3 Pageswith several conclusions about what I need to change for my upcoming two midterms. I know that one of my main problems was time management when taking the exam, I spent too much time on certain problems and consequently I ran out of time. I didn’t even get to brainstorm an approach for some problems, and left several sections blank. I need to learn how to set time limits for each problem, since I sometimes just spent a lot of time trying to figure

### Quadratic Equation Research Paper

1026 Words | 5 Pages### The Importance Of Community Policing

1170 Words | 5 Pages### Privacy Characteristics Of Big Data

1520 Words | 7 Pages### Challenges And Challenges In Counselling

2000 Words | 8 Pages### Negative Effects Of Sugar Products

829 Words | 4 Pages### Granular Computing Research Paper

2770 Words | 12 Pages### Alternativ Alternatives Case Study

747 Words | 3 Pages### How Does Technology Improve America Essay

706 Words | 3 Pages### Problem Solving Skills In Customer Service

1774 Words | 8 Pages### Midterm Reflection

732 Words | 3 Pages