The Principles Of Knowledge For Manipulating Fractions And Decimals

Algebra is a critical aspect of mathematics which provides the means to calculate unknown values. According to Bednarz, Kieran and Lee (as cited in Chick & Harris, 2007), there are three basic concepts of simple algebra: the generalisation of patterns, the understanding of numerical laws and functional situations. The understanding of these concepts by children will have an enormous bearing on their future mathematical capacity. However, conveying these algebraic concepts to children can be difficult due to the abstract symbolic nature of the math that will initially be foreign to the children. Furthermore, each child’s ability to recall learned numerical laws is vital to their proficiency in problem solving and mathematical confidence. It is obvious that teaching algebra is not a simple task. Therefore, the importance of quality early exposure to fundamental algebraic concepts is of significant importance to allow all

Numeracy development is important for all children as maths is an important part of everyday life. The way in which maths is taught has changed greatly over the years. When I was at school we were taught one method to reach one answer. Now, particularly in early primary phase, children are taught different methods to reach an answer, which includes different methods of working out and which also develops their investigation skills. For example, by the time children reach year six, the different methods they would have been taught for addition would be number lines,

Van de Walle, J, Karp, K. S. & Bay-Williams, J. M. (2015). Elementary and Middle School Mathematics Teaching Developmentally. (9th ed.). England: Pearson Education Limited.

Students had previously covered the topic of developing fluency in multiplication by 2-digit numbers. After that topic students moved on to cover number sense, dividing by 1-digit divisors using mental math to prepare them for the following topic of my learning segment. The topic of my learning segment consists of developing fluency, dividing by 1-digit divisors. I designed my lesson as a three-day unit focusing on long division by modeling division with place-value blocks, dividing 2-digit by 1-digit numbers, and dividing 3-digit by 1-digit numbers. Students were introduced to division prior to my learning segment but the struggled to understand and comprehend division because students were only introduced to the division algorithm and were not provided with a mnemonic to help them recall the steps. Students also weren’t introduced to division with manipulatives or drawings. Therefore, I

As a student, I always enjoyed math. In high school I took all of the offered math classes, including Calculus. The first math class I took in college was a breeze, and I thought that this one would be no different. What could I learn about elementary school math that I did not already know? Contrary to my expectation, the first day of class, I learned things about math that had never been brought to my attention. This paper will discuss what I have learned about subtraction, about students, about the Common Core State Standards, and how my concept map has changed since my first draft.

Sarama, J., & Clements, D. H. (2006). Mathematics in kindergarten. (61 ed., Vol. 5, p. 38). YC Young Children. Retrieved from http://media.proquest.com.ezproxy.apollolibrary.com/media/pq/classic/doc/1129349361/fmt/pi/rep/NONE?hl=&cit:auth=Sarama, Julie;Clements, Douglas

It is important to teach children numeracy to suit their age and use appropriate techniques to suit their age and ability because sometimes too much emphasis on formal recording of 'sum' if introduced to early to children could make it difficult for them to understand. The learning style of numeracy is given more emphasis today to make them understand it much better. In the early years emphasis is made on how to make children understand different methods of working out to be able to arrive to an answer. Working with children the aim is to give children solid ground on

Answer- To demonstrate ability to solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, students will complete 5 addition problems with like denominators and 3 word problems, when asked to do so with the rest of the class, on a paper-pencil teacher-made fractions quiz, with 80% accuracy, at the end of the unit.

In the chapter, “Equal Sharing Problems and Children’s Strategies for Solving them” the authors recommend fractions be introduced to students through equal sharing problems that use countable quantities because they can be shared by people or other groupings. In other words, quantities can be split, cut, or divided. Additionally, equal sharing problems assist children to create “rich mental models “for fractions (p.10).

In the article, “Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities,” the authors believe that number sense is as foundational to learning mathematical concepts as phonemic awareness is to reading. Gersten and Chard’s theory is based on “conceptualization of constructivism as a joint approach” where students learn conceptually with a focus on terminology and explore operations using a variety of methodologies. Furthermore, the authors support the merging of number sense activities with fact families’ automaticity activities.

“He knew this informal experience with the distributive property would be important in subsequent lessons and the student writing would provide him with some insight into whether his students understood that quantities could be decomposed as a strategy in solving multiplication problems.” (Ex. Lines 81-83 provides evidence of Elicit and use evidence of student thinking).

Multiplicative thinking, fractions and decimals are important aspects of mathematics required for a deep conceptual understanding. The following portfolio will discuss the key ideas of each and the strategies to enable positive teaching. It will highlight certain difficulties and misconceptions that children face and discuss resources and activities to help alleviate these. It will also acknowledge the connections between the areas of mathematics and discuss the need for succinct teaching instead of an isolated approach.

Teaching students effectively in areas of multiplicative thinking, fractions and decimals requires teachers to have a true understanding of the concepts and best ways to develop students understanding. It is also vital that teachers understand the importance of conceptual understanding and the success this often provides for many students opposed to just being taught the procedures (Reys et al., ch. 12.1). It will be further looked at the important factors to remember when developing a solid conceptual understanding and connection to multiplicative thinking, fractions and decimals.

Maths is ubiquitous in our lives, but depending on the learning received as a child it could inspire or frighten. If a child has a negative experience in mathematics, that experience has the ability to affect his/her attitude toward mathematics as an adult. Solso (2009) explains that math has the ability to confuse, frighten, and frustrate learners of all ages; Math also has the ability to inspire, encourage and achieve. Almost all daily activities include some form of mathematical procedure, whether people are aware of it or not. Possessing a solid learning foundation for math is vital to ensure a lifelong understanding of math. This essay will discuss why it is crucial to develop in children the ability to tackle problems with initiative and confidence (Anghileri, 2006, p. 2) and why mathematics has changed from careful rehearsal of standard procedures to a focus on mathematical thinking and communication to prepare them for the world of tomorrow (Anghileri).

Mathematics, like every creation of man, have evolved without really knowing how far you can get with them: the scope of the computer, physics, chemistry, algebra, all are evidence of this. Every aspect of our culture is based in some way or another in Mathematics: language, music, dance, art, sculpture, architecture, biology, daily life. All these areas of measurements and calculations are accurate. Even in nature, everything follows a precise pattern and a precise order: a flower, a shell, a butterfly, day and night, the seasons. All this makes mathematics essential for human life and they can not be limited only to a matter within the school curriculum; here lies the importance of teaching math in a pleasure, enjoyable and understandable way. Mathematics is an aid to the development of the child and should be seen as an aid to life and not as an obstacle in their lifes.