Conceptualizing essay

Education 315
Dr. Saran
12/12/13
Conceptualizing Essay

“The study of mathematics, like the Nile, begins in minuteness and ends magnificence.” Charles Caleb Colton. Taking that notion into consideration I decided to design my lesson plan which would begin in minuteness and end in magnificence. I wanted to use a topic in mathematics that the children could relate to. So I chose to design my unit plan was based on fractions. My intention was to use what would seem as minute concepts seen in fractions and show how these minute concepts are applied to everyday life. After teaching this lesson I wanted my students to be able to recognize and understand fractions when they came in contact with them whether in school or out of school. Learning about fractions is important because they will encounter fractions in all walks of life. Based on Jean Piaget’s theory of students in the concrete operational stage, which is the age range of 7 years to 11 years develop the ability to organize objects hierarchically, which is known as classification. Each lesson is designed for students to engage and explore the association, relationship and interrelationship encompassed within fractions through various forms of class work. Each lesson is designed to meet the common core standard of 4.NF.
Lesson one which is the introduction lesson students will design and use a set of fractional parts to represent the length model, students will be introduced and will discover fractional relationships, and students will also work with equal fractions. In lesson two students continue working with fractional parts to evaluate, compare and arrange or order fractions. This lesson is an extension of the work explored with fractional relationships in the prior lesson. Students will develop skills and approaches in problem solving, rationality and reasoning while they notice and make connection and association amongst varying fractions. In lesson three the students will use math rods to explore and examine fractional relationships. This work with relationships builds the foundation for advance that comprises more challenging fraction concepts and materials. The math rods are plastic rods in ten different colors. The range of length in each rod varies from one to ten centimeters. The length of each math rod is a different color. In lesson four students will explore and examine the length model by using math rods to find equivalent fractions. Students will build skills in reasoning, rationalizing and problem solving as they explain how and why two fractions are the same length. In lesson five students will use an inch ruler to represent various fractions as lengths. This lesson expands on prior work done in previous lessons with an inch ruler used by the students to measure various items, including items that can be measured to the nearest quarter and half of an inch.
I decided to incorporate math rod manipulatives in this lesson. Dr. Saran taught us that mathematical manipulatives are items and objects which are specifically designed to simplify difficult mathematical problems and concepts and makes them easier for to understand. Research has proven that children learn math more efficiently when they use manipulatives to assist them. Manipulative serves as and aid which helps students to visualize the material being taught. According to Vygotsky “The Zone of Proximal Development (ZPD) is the distance between a student’s ability to perform a task under adult guidance and/or with peer collaboration and the student’s ability solving the problem independently, learning occurred in this zone”. Taking that theory into consideration also, I will also use the differentiate instruction approach when necessary because some students are not on the same level in mathematics as others. Differentiating instruction is an innovative approach for teaching and learning which presents students with various options to absorb content and process content. So some students will receive a more simplified work sheet and instructions while others will receive a more complex worksheet and instructions.
I was not able to teach the whole class but I was assigned three students to teach my lesson. Each student where of different ethnicities so I had to accommodate to the different learning styles of these students. Since my lesson plan incorporated the use of manipulatives these children were able to understand the work more clearly. After teaching some of the lessons I designed an activity sheet to assess how much students had learned and to gauge how effective my teaching was. Each activity sheet was made up of questions that relate to the material that was taught.