Multiplication and Division Essay Example

Multiplication and Division Paper Teachers should distinguish between these classes of problems. Also, they should be able to give examples using themes and children’s literature. Research shows that students who are exposed to problem solving on a daily (or almost daily) basis score better on measures of both problem solving and computation (Carpenter, Fennema, Peterson, Chiang, Loef, 1989). Today, elementary math textbooks are gradually incorporating more classes of problems into their series (Smith, 2006). However, the teacher must still be resourceful in writing examples as needed. In his study, Bebout (1990) found that first-grade children learned to write number sentences with the box in the correct place for many of the problem types. After five weeks of direct instruction using this method, it was found that the students were more successful in solving problems regardless of their pretest scores. Some children even learned to generalize the instruction and were able to solve more difficult problems in which the box begins the number sentence. However, not all of the problem types are easy to solve. Teachers recognize that comparison problems are difficult to solve. But the most difficult problems are the number sentences that begin with the box (e. g. Join-Start Unknown and Separate-Start Unknown). To assess the children’s understanding of problem solving, the teachers may chart the kinds of problems the children can solve and the methods they used to solve the problems. Smith (2006) stresses that the best way to determine the strategy the child used in solving the problems is to ask the child how he thought and solved the problem. We will write a custom essay sample on Multiplication and Division specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Multiplication and Division specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Multiplication and Division specifically for you FOR ONLY $16.38 $13.9/page Hire Writer Smith further emphasizes that â€Å"Looking at both the problem types and the level of sophistication in strategy gives primary teachers a powerful assessment guide for future planning†. As with addition and subtraction, there is a wide range of problem types for multiplication or division which teachers can benefit from. Most researchers classify multiplication and division problems into two general categories — asymmetrical and symmetrical (Kouba Franklin, 1993). Asymmetrical problems are problems in which numbers are not interchangeable. Each element of the story problem plays its own role and cannot be interchanged with the other. These elements can be modeled very clearly to children in different situations — grouping situation (2 boxes of 6 cans, not 6 boxes of 2 cans), rate situations (5 pencils at 3 cents, not 3 pencils at 5 cents), and comparison situations (mother rabbit 4 lbs. ) weighs 3 times as much as the baby, not the baby rabbit weighs 3 times as much as the mother) (examples from Smith, 2006). In symmetrical problems, the numbers can be interchanged. It doesn’t matter which one is the multiplier. These problems often make use of charts, arrays, and area models as illustrations. One illustration is area problems. although we define length as the longer side and the width the shorter side, the sides play similar roles: length ? width = width ? length. Another example is selection problem, also called combination or Cartesian product problems. For example, when calculating sandwich combinations: 3 kinds of bread and 4 fillings, each kind of bread can be matcher to one of 4 fillings or each kind of filling to one of 3 kinds of bread. Problem types can also be classified through considering what happens in the problem and observing the strategy students use in solving them. This analysis is just an extension of the work on addition and subtraction in the preceding section. Hendrickson (1986) classified these problems into four general categories — change problems, comparison problems, rate problems, and selection problems. As with the categories in addition and subtraction problems, these categories have subtypes depending on which variable is unknown. To be able to teach children in solving multiplication and division problems, teachers must be familiar with each of these types, their level of difficulty and the strategy used by the children to find a solution. Some are easier than others. As with solving addition and subtraction problems, teachers should evaluate the types of problems their students are able to solve and the strategies they used to solve them. In this paper, we will use the different problem types to find out the level of understanding the children has on the discussion. Each problem will represent one of each type.

Comparing Hinduism and Buddhism

Comparing Hinduism and BuddhismThe comparative study of Hinduism and Buddhism through its historical periods, its relationship with the philosophical traditions, as well as from an exegetical perspective. A central theme of this comparative study is to reveal the history of the Christianized forms of both these religions.Historically, both Hinduism and Buddhism were inspired by their founder, Siddhartha Gautama (also known as Buddha). In addition, both, in their Indian context, inspired their followers by proclaiming a set of enlightened principles. It is also important to note that each originated as monotheistic religions and as truly did not believe in the deity of another.The different elements of the belief that each religion promotes are manifested in the various forms of worship. Both Hinduism and Buddhism have equally traditional forms of worship. However, the elements of each differ, as do the sects within these religions. These differences influence the beliefs that each of fers to its followers.Not only do the westernized forms of these religions differ in their worship practices, but also in their doctrines. With both Hinduism and Buddhism, the central doctrine is the existence of a supreme Being, known as God. God is worshipped in both the names Hinduism and Buddhism. In both cases, the deities are believed to represent and protect the supreme Being.Within the tenets of these two religions, some of the fundamentals of both are similar. For example, both believe in the oneness of the Gods and the sacredness of their respective teachings. One example of this is the belief that the teachings and philosophy of one can be accepted without question by all the other aspects of Hinduism and Buddhism.Within both Hinduism and Buddhism, the chief deities of each religion are believed to embody the deities and works of God. However, it is important to understand that the right to accept or reject a deity is determined by each individual believer. As with other concepts of religion, there are those who prefer to exclude the concept of God, while others who choose to accept it. This is seen in the fact that Hinduism and Buddhism have sometimes been polarized along this line.There are many similarities between the beliefs that are held by Hinduism and Buddhism. For example, both sects believe in human reincarnation. It is important to note that the history of reincarnation in both Hinduism and Buddhism is deeply entwined with these two religions. The underlying foundation of both is essentially the belief that at some point, the soul will be reborn into a new life, which will provide for the fulfillment of its purpose.From the above, it can be concluded that both Hinduism and Buddhism are concepts that have evolved over the years. It is also important to acknowledge that within the past few centuries, several movements have emerged that have either split the religion, or at least disturbed the central doctrine of both Hinduism and Buddhism. Therefore, if the study of these two religious sects is going to advance and continue to thrive, it is imperative that we study the history of these religions and try to determine the main fundamentals of both, which have led them to where they are today.