Probability - A Whale of a Tale by Young - Article Example

Summary of the article, application for educators, reasonable connection to the text reading, what would you like to know more about and the relevance of your question Section I: Summary: Elaine Young, the author of the article, using two different case studies showed that it was possible to relate the mathematical theory of probability to third grade students by using vocabulary and games known to them. In one study, the teacher of a third grade class, composed of mostly students from minority and disadvantageous social group, was able to convey the probability concept by using basic statements, which described events of their daily lives. Children were able to distinguish differences of those statements describing which events are likely, unlikely, impossible and certain to happen. The same children perfectly conveyed probability concepts thru their own drawings, in which they described certain events that were impossible, likely and unlikely to happen. In other study, a teacher used an ordinary game with rolling dices, known to children of third grades, to convey the idea of experimental and theoretical probability. Children clearly understood how to use a fraction to represent theoretical probability of events, in this case, sum of the rolling dices. The author in her work described the methodology about how to teach a complex mathematical concept to students of third of graders. Section II: Education Application: Probability – is a philosophical category, indicating the quantitative extent of the possible emergence of random events with fixed monitoring conditions, characterizing the stability of their relative frequencies. An elementary grade school teacher needs to convey this complex message to the small children. This is a difficult task, but has to be done. Educators task is to build strong foundations in the minds of those small children for future learning of mathematics. How to do it? This is where we need NCTM content and process standards. NCTM content and process standards describe in detail about how to accomplish this task. According to NCTM, educators need to build a curriculum focal point, to relate ideas, concepts, skills, and procedures that will serve the purpose of building foundation in children’s mind. To help the educators, NCTM has created a set of curriculum focal points. According to NCTM, it helps the educators to design and organize the next revisions of their expectations, standards, curriculum, and assessment programs. NCTM process standards emphasize on three things, (1) Problem Solving, (2) Reasoning and Proof, (3) Communication. I am now going to provide an analysis of Elaine Young’s article to demonstrate if it corresponds to NCTM content and process standards. The name of the article is “Probability: a whale of a tale”. Any teacher, who will read this article to the children and ask if they think it is true that Emily can find a whale in her backyard. The teacher will hear children are giggling and discover answers are unlikely or impossible. The children communicated to the teacher thru their reasoning. Belief and facts establish reasoning. The same is here. The article studied two different cases with third grade students. Mrs. Alvarodo and Mrs. Taylor conducted these tests. The case with Mrs. Alvarodo’s students demonstrated reasoning and communication. The third grade students clearly understood how to distinguish events according to likely and unlikely. They also understood, if the event is likely, what is the degree of being likely. A good example in the article is the event; “The principal will visit our class today”. Students’ answers were certain. These little children were still unable to provide proof of their conjecture. After, Mrs. Alvarado’s explanation, their answers changed to likely. In this example, the teacher implied what NCTM process standard names “Reasoning and proof”. Students’ description of their own drawings to show likely, unlikely, and impossible events is another example of reasoning and proof. It is the development and evaluation of mathematical arguments and proofs. The case study of Mrs. Taylor with her students is a step forward towards learning the concept probability. Mathematic is a concept with numbers, reasoning with numbers. Mrs. Taylor with her students entered into the area, which is called, according to NCTM Process Standards, building of new mathematical knowledge through problem solving. Mrs. Taylor conveyed perception of difference between experimental and theoretical probability thru a well-known game of dice rolling. She used a method to explain experimental and theoretical probability to her students. First, she used game board to carry out experimental probability, and then she calculated a table to discuss theoretical probability of rolling a pair of number cubes; finally she showed how to develop a fraction to illustrate the theoretical probability. This whole process corresponds to building of a cohesive cluster of knowledge, skills, and concepts to investigate mathematical conjectures as proposed in NCTM content and process standard. This article contributes an enormous value to professional educators. Section IV: Questions: The article is about teaching a complex mathematical concept to the 3rd grade school students. The author picked up two cases to illustrate how to teach the mathematical concept probability to minor students. The author described two different cases. In one case, the teacher used literature, and in the other case, the teacher used a game procedure. The author showed that the teacher in the first case taught probability by using statements and applying vocabulary to the statements. Students used familiar to them vocabulary - impossible, unlikely, likely, equally likely and certain to the statements to determine the probability of happening different events stated in the statements. The result was excellent. In another example, teacher asked the students to draw pictures to illustrate likely, impossible, unlikely events that may occur. Again the results were excellent. However, the author does not explain how the teacher explained to her students that what they learned was called probability, a branch of mathematics. I think this is a negative side. Educators task is to plant seeds in the minor children’s brains. In the method of measure of likelihood, teacher used numbers to illustrate the difference between experimental and theoretical probability. Methods and explanations used were appropriate. Students explained presented to them statements and their own drawings thru their understanding of words about how to describe a situation, but they did not realize that their descriptions of drawings, interpretations of statements and sum of rolling two number cubes related to a complex concept which is called probability, and which they would learn later on. In both cases, students left the classes without knowing that what they learned either thru vocabulary or thru rolling dices was called probability, and it is a concept of mathematics. This is what is missing in the case studies. References Curriculum Focal Points. (n.d.). National Council of Teachers Mathematics. Retrieved from http://www.nctm.org/standards/focalpoints.aspx?id=274 Young, E. (2010). Probability: a whale of a tale. Teaching children mathematics, 106 – 112. Read More