Shannon, M.G. (March 2010). The value of guess and check. Mathematics Teaching in the Middle School, 15(7), 392-398.
This article had a large main idea of keeping the method of guessing and checking for different problems, specifically story or word problems. By having students use this method in class, they will come up with a better understanding for the answer they find and will also find their "own way for applying this strategy" (as the author puts it). The author points out different steps the student needs to take in order to use guess and check properly. One needs to ask themselves "What information is given? What am I trying to find? and What do I need to know before I do anything else?" These questions help the student build up their own understanding before creating a table to guess and check the closest answer to the problem (or the answer). Besides the students using the steps and the guess and check method, they are also able to apply it to other places besides story problems, and moreover, create an equation for the specific problem. This equation helps the students fully understand what they were just guessing and checking in order to find the correct answer.
Through guess and check the students are able to find the answer through much work. And though it may help them understand the problem itself once they create an equation, I think another method would be more helpful for the students. I do believe the students should have a complete understanding of what the problem is asking for before finding the answer to the word problem (as described in the guess and check method). But by guessing and checking, the student is just trying different answers to see which is "closest." Then, by the end, the student hopefully has an understanding of the method applied to that specific problem. This is where the student now has an equation to use. But by understanding how or why exactly they are getting "closer" to the answer is a better choice than waiting for the students to understand what they are doing at the end. Many students may not even get that far.
Friday, March 26, 2010
Thursday, March 18, 2010
Assignment #6: NCTM Article #1
Switzer, J. M. (2010). Bridging the math gap. Mathematical Teaching in the Middle School, 15 (7), 400-405.
Through this article Switzer is describing the different algorithms used in elementary school in preparing children for middle school (junior high). Yet, the main idea throughout this paper is the importance of teaching the middle school and high school teachers these different algorithms used in the classrooms at earlier ages. Switzer says that in order for teachers to be effective, they need to be able to build on a child's prior knowledge. Therefore in knowing the algorithms used, they can see where the children are coming from. Also, the teacher will be able to see the connection the algorithms learned have to ones they will learn later on. This will help the teacher know how exactly to teach future algorithms. Therefore, through the different algorithms Switzer described in his journal, teachers will overall be able to help children make the connection to previous knowledge.
Teaching middle school and high school teachers different algorithms used in elementary school classrooms is a very good idea and will over all help school systems, mathematics programs and teachers. In showing teachers what is being taught in younger-aged classrooms, teachers will be able to make connections to the teaching of future algorithms. One example of this is when teachers were taught about the partial products algorithm taught in schools. Skewer then talks about the connection the teachers made to the distributive property. Another important reason for teaching teachers these algorithms used is that it will make it easier for children later in school. By teachers understanding what is being taught to the children before they come into their own classrooms, they will know what they need to build on in order to teach them other algorithms. This will help the children learn easier by building off their prior knowledge. Also, it is important to connect the different schools in their teaching because, like stated earlier, children will have their prior knowledge build upon. But this will then help the children build their confidence as they are able to make connections to ideas/algorithms they already know. From my own experience, I always found it easier to learn when a teacher in mathematics taught me knew ideas, procedures, algorithms, etc. by showing me how they connected to things I had already learned. Thus, the teacher knew what I had learned before coming into their classroom. Therefore, by showing the teachers the algorithms being used in elementary school, teachers will be able to build on prior knowledge, help the kids raise their self-esteem, and also be able to see the connection to future algorithms being taught.
Through this article Switzer is describing the different algorithms used in elementary school in preparing children for middle school (junior high). Yet, the main idea throughout this paper is the importance of teaching the middle school and high school teachers these different algorithms used in the classrooms at earlier ages. Switzer says that in order for teachers to be effective, they need to be able to build on a child's prior knowledge. Therefore in knowing the algorithms used, they can see where the children are coming from. Also, the teacher will be able to see the connection the algorithms learned have to ones they will learn later on. This will help the teacher know how exactly to teach future algorithms. Therefore, through the different algorithms Switzer described in his journal, teachers will overall be able to help children make the connection to previous knowledge.
Teaching middle school and high school teachers different algorithms used in elementary school classrooms is a very good idea and will over all help school systems, mathematics programs and teachers. In showing teachers what is being taught in younger-aged classrooms, teachers will be able to make connections to the teaching of future algorithms. One example of this is when teachers were taught about the partial products algorithm taught in schools. Skewer then talks about the connection the teachers made to the distributive property. Another important reason for teaching teachers these algorithms used is that it will make it easier for children later in school. By teachers understanding what is being taught to the children before they come into their own classrooms, they will know what they need to build on in order to teach them other algorithms. This will help the children learn easier by building off their prior knowledge. Also, it is important to connect the different schools in their teaching because, like stated earlier, children will have their prior knowledge build upon. But this will then help the children build their confidence as they are able to make connections to ideas/algorithms they already know. From my own experience, I always found it easier to learn when a teacher in mathematics taught me knew ideas, procedures, algorithms, etc. by showing me how they connected to things I had already learned. Thus, the teacher knew what I had learned before coming into their classroom. Therefore, by showing the teachers the algorithms being used in elementary school, teachers will be able to build on prior knowledge, help the kids raise their self-esteem, and also be able to see the connection to future algorithms being taught.
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