Wednesday, March 24, 2010
Correction to the 1st Article's Citation
Guerrero, S. M.. (March 2010). The value of guess and check. Mathematics Teaching in the Middle School, 15(7), 393-398.
Enabling Teachers to Teach
Smith, M. S., Bill, V., & Hughes, E. K.. (October 2008). Thinking through a lesson: Successfully implementing high-level tasks. Mathematics Teaching in the Middle Schools. 14(3), 132-138.
The authors of the article Thinking through a Lesson: Successfully Implementing High-Level Tasks want teachers to know, though it is hard to think of high-level tasks, it is worthwhile to create these tasks using TTLP (Thinking Through a Lesson Protocol). Teachers may complain that it is overwhelming to plan a high-level task for every day, but the authors suggest that TTLP shouldn't be used every day at first. With the help of other teachers to develop more and more cognitive tasks, TTLP should be used periodically to where eventually a teacher will have a task for every day by accumulating them over time. Though planning a high-level lesson takes a lot of time using TTLP, it is possible to use only part of the TTLP method. The goal of using TTLP is to help teachers change the way they think about a lesson. By using TTLP, teachers will be able to further the use of a high-level task, so that students are able to learn more. Using TTLP will also enable a teacher to know how to respond to complications in the task, thus helping the task to go a lot smoother, and for the goals of the task to be met.
I think TTLP is a great way to create lesson plans that will promote cognitive thinking in students. Though there are a lot of things to think about when planning a lesson using TTLP, I think that the outcome is worthwhile. TTLP helps teachers to think about questions to ask students to further their thinking, and also helps the teacher think more about how students might respond to the task. When a teacher has already looked into where students might have trouble or how they can further a child's thinking if students are having a relatively easy time accomplishing the task, a teacher can then be more prepared for these cases. A teacher will already know how to respond. Knowing how to respond before something happen gives an advantage to the teacher, so that the teacher's task will go smoother, and will help the teacher and students stay focused on the goals of the task.
The authors of the article Thinking through a Lesson: Successfully Implementing High-Level Tasks want teachers to know, though it is hard to think of high-level tasks, it is worthwhile to create these tasks using TTLP (Thinking Through a Lesson Protocol). Teachers may complain that it is overwhelming to plan a high-level task for every day, but the authors suggest that TTLP shouldn't be used every day at first. With the help of other teachers to develop more and more cognitive tasks, TTLP should be used periodically to where eventually a teacher will have a task for every day by accumulating them over time. Though planning a high-level lesson takes a lot of time using TTLP, it is possible to use only part of the TTLP method. The goal of using TTLP is to help teachers change the way they think about a lesson. By using TTLP, teachers will be able to further the use of a high-level task, so that students are able to learn more. Using TTLP will also enable a teacher to know how to respond to complications in the task, thus helping the task to go a lot smoother, and for the goals of the task to be met.
I think TTLP is a great way to create lesson plans that will promote cognitive thinking in students. Though there are a lot of things to think about when planning a lesson using TTLP, I think that the outcome is worthwhile. TTLP helps teachers to think about questions to ask students to further their thinking, and also helps the teacher think more about how students might respond to the task. When a teacher has already looked into where students might have trouble or how they can further a child's thinking if students are having a relatively easy time accomplishing the task, a teacher can then be more prepared for these cases. A teacher will already know how to respond. Knowing how to respond before something happen gives an advantage to the teacher, so that the teacher's task will go smoother, and will help the teacher and students stay focused on the goals of the task.
Thursday, March 18, 2010
There is More to it than Guess and Check
Guerrero, Shannon M. (March 2010). The Value of Guess and Check. Mathematics Teaching in the Middle School, 15, 393-398.
Main Idea/author’s thinking: Guess and check is a powerful problem-solving strategy that helps students make connects from conceptual understanding to algebraic representation. From the method Guerrero has described, students are first required to break down the word problem into it’s components by identifying what they know and what they are trying to find. The next step is to guess values for what they are trying to find and see if it fits the information given. If it doesn’t, then another guess is to be made based on the previous guess. They are to guess until they find an answer that fits all the information given. As they guess, they are to use a table format to organize the information given and the guesses they have been making. The final step is to use the guess and check method to make algebraic representations for the information given. Guerrero claims that it is easier once a student has already figured out the answer to then relate the information given to a symbolic representation. She also believes that through the process of guess and check, students will better learn how to decompose words problem. Thus, better understanding what each word problem is asking.
Though guess and check may be helpful in some situations, I think there are better methods that can be used to help students with solving word problems. Guess and check is helpful when you don’t know how to solve a problem, but it’s not very helpful when the problem is more complex and possibly has to do with fractions. Guessing the right fraction between 0 and 1 can be hard because there are an infinite amount of possibilities. The process of guess and check that Guerrero refers to may be helpful to some, but I think there are more concise ways of breaking down a word problem without have to use guess and check. I think organizing the information similar to the way Guerrero has suggested is a great way to break down a word problem, but I do not think it is necessary to use a guess and check system. That could be skipped so that the next step would be to represent the information given in an algebraic expression, and solve for the unknown(s). Through Guerrero says guess and check can be very effective when first learning how to deal with word problems, she admits that it is not very effective later on when dealing with more complex problems. I think that if you start to teach students through guess and check, they will not want to move on from that. Through that process, they get the answer through guessing first, what more is needed… There would not be much need for algebra after that in a child’s eyes. This also would lead to the problem that some students might start to think math is a game of guess and check. There are obviously better mathematical ways of solving a problem than guess and check.
Main Idea/author’s thinking: Guess and check is a powerful problem-solving strategy that helps students make connects from conceptual understanding to algebraic representation. From the method Guerrero has described, students are first required to break down the word problem into it’s components by identifying what they know and what they are trying to find. The next step is to guess values for what they are trying to find and see if it fits the information given. If it doesn’t, then another guess is to be made based on the previous guess. They are to guess until they find an answer that fits all the information given. As they guess, they are to use a table format to organize the information given and the guesses they have been making. The final step is to use the guess and check method to make algebraic representations for the information given. Guerrero claims that it is easier once a student has already figured out the answer to then relate the information given to a symbolic representation. She also believes that through the process of guess and check, students will better learn how to decompose words problem. Thus, better understanding what each word problem is asking.
Though guess and check may be helpful in some situations, I think there are better methods that can be used to help students with solving word problems. Guess and check is helpful when you don’t know how to solve a problem, but it’s not very helpful when the problem is more complex and possibly has to do with fractions. Guessing the right fraction between 0 and 1 can be hard because there are an infinite amount of possibilities. The process of guess and check that Guerrero refers to may be helpful to some, but I think there are more concise ways of breaking down a word problem without have to use guess and check. I think organizing the information similar to the way Guerrero has suggested is a great way to break down a word problem, but I do not think it is necessary to use a guess and check system. That could be skipped so that the next step would be to represent the information given in an algebraic expression, and solve for the unknown(s). Through Guerrero says guess and check can be very effective when first learning how to deal with word problems, she admits that it is not very effective later on when dealing with more complex problems. I think that if you start to teach students through guess and check, they will not want to move on from that. Through that process, they get the answer through guessing first, what more is needed… There would not be much need for algebra after that in a child’s eyes. This also would lead to the problem that some students might start to think math is a game of guess and check. There are obviously better mathematical ways of solving a problem than guess and check.
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