Teaching Equivalence with Unlike Denominators - Assignment Example

February 11, 2008 Early Childhood Teaching Teaching Equivalence With Unlike Denominators A. Three Prerequisite Skills One of the skills that a student will take with them into their later years is how to ask why. In so doing, we give the student an understanding of basic mathematical concepts which will sustain them in their later years. If we teach younger students the why of a math problem, they will embrace the how piece of it. By way of example, in teaching place value, it is good to use visual aids to assist in grasping the concept. Place value is something kids understand partially at first, and then that deepens over a few lessons but it must be reviewed regularly. I suggest introducing the concept through counting money, it gives a concrete example which the children will find fun, but because it is part of handling money they are aware the place value is vital to counting change. 2. The concept of "how", accompanies the concept of "why. The "how" something works is teaching the mechanical pieces of the lesson. This is often boring to the child and not very well received, but if combined with an insightful "why" lesson you will have a far simpler task ahead of you. Each child will process the information differently, so you may need to alternate the focus of lessons by using one period going over the how and another going over the why and supplementing with practice sheets. 3. Clarifying the term "Equivalent" and Finding A Common Demoninator: Perhaps the most crucial part of teaching equivalence in fractions is teaching the children how to find a common denominator. The term itself is intimidating, but the task is not impossible. The best way to teach children how to find a common denominator is to use manipulatives. The fact that Students' have misconstrued the equal sign is a topic that has been researched for more than thirty years (Weaver, 1971,1973). It might be beneficial to start off with discussing with the class what the term "equivalent" means to them. At least by doing so we can gage where our students are from a terminology standpoint. This would be beneficial if applied the terms numerator and denominator as well. Because we are dealing with rather large terms it helps to have visual aids. This is where the use of manipulatives comes in handy. Manipulatives are an essential teaching tool which allow children to learn visually. B. The Concept of Finding Equivalent Fractions Using Manipulatives. The problem with textbooks and workbooks is that often the children are distracted by the instructions and fail to use the visual aid. Children move from addition and subtraction (concepts that they have likely been using well before their formal education began on the topic) and are suddenly thrust into an area which is completely foreign. Cursory review of math text and exercise books reveals a great deal of "words" which I think are intimidating. Yes there are pretty pictures with bunnies, pies, balls and whatnot. Yet children still fail to become engaged. Why not turn the lesson into a visual demonstration that you and the children can enjoy Moreover, by watching the children actively participate, we as teachers are able to assess their true comprehension. This is the advantage of using manipulatives. Additionally, it is a wonderful way to insure complete class participation. C. Steps I would teach students in finding Equivalent fractions. I have found that children of all ages are very interested in detective work. There is a sense of power and self confidence that comes with solving a mystery. Television is replete with various shows that show crime scene investigations along with the science behind it. Moreover, both girls and boys seem to have an equal interest in the field. I would suggest to my students that we are CSI detectives. I would suggest that the first thing that we might want to do is to ID (identify) our fraction. Included with that identification would be all of the alias our fraction might use to evade our detection. For example, is also known as 2/4, 3/6, 4/8, 5/10 and so on. So when our fraction wants to hide, he may disguise himself as one of the many aliases he may have and we have to know all of them! Our suspect, the fraction, has two parts to him. The top part of him is the numerator and the bottom half of him is the denominator. In order to properly identify our suspect, we must compare him with the lineup of the aliases. We would use the fraction work sheets or the black board as our CSI notes to compare each suspect and see if through reducing the fraction, they are an equivalent or are they a new suspect. With each new fraction, we begin a new lineup. Thus, it would be a good idea to turn our classroom into a mini investigation lab. Each new set of equivalencies earns its own lineup and as each set of fractions is worked upon using finger prints, or mini DNA samples or whatever mini crime tool is easiest to improvise with, the children are checking their own detective work against the lineup on the board. I think that based upon my own background in law enforcement, I could make this a lesson that is not only interesting, but engaging to the children because they will learn without even realizing it. Naturally, I would match the "evidence" that I use as samples based upon what I perceive to be of interest to the children. I could use fingerprints and other crime scene investigative samples. D. Moving from Concrete Manipulatives to Paper and Pencil Equations Obviously I cannot turn my tests into a CSI laboratory. Accordingly, I would next move to a new manipulative such as cubed strips of paper. I would have the children begin their testing, class work, and homework, for fractions using their manipulatives. For example: I would give each child a strip with ten cubes in the strip. I would allow the children to cut the strip into the amount of cubes they deem appropriate to aid them on the work. The strip of cubes would be stored into a little plastic bag and the children can then count that as part of their class materials. From there I would slowly wean them off of the strips and straight onto paper. E. Examples Our suspects , , 1/3, 2/3, 2/6, and have escaped from custody and is out on the loose. We have dispatched an all points bulletin and need you to provide to the police with three alias for each suspect. In order to catch our suspects as quickly as possible, please write the suspect, and their equivalents or alias next to them. = _______, _______, _______ 2/6= _______, _______, _______ = _______, _______, _______ = _______, _______, _______ 1/3 = _______, _______, _______ 2/3 = _______, _______, _______ Works Cited Weaver, J. F. (1971). Some factors associated with pupils' performance levels on simple open addition and subtraction sentences. The Arithmetic Teacher, 18, 513-519. Weaver. J. F. (1973). The symmetric property of the equality relation and young children's ability to solve open addition and subtraction sentences. Journal for Research in Mathematics Education, 4(1), 45-56. Works Consulted Hernandez, B. (2008). Creative Ideas For Teaching Fractions. Retrieved February 21, 2008, from about.com Web site: http://homeschooling.about.com. Weaver, J. F. (1971). Some factors associated with pupils' performance levels on simple open addition and subtraction sentences. The Arithmetic Teacher, 18, 513-519. Weaver. J. F. (1973). The symmetric property of the equality relation and young children's ability to solve open addition and subtraction sentences. Journal for Research in Mathematics Education, 4(1), 45-56. Read More