The term Letting Go has been used by Van de Walle and in our classrooms to represent how teachers teach THROUGH problems. Where are you on this at this point? Examing the teaching stations, and your own ideas. Key- When should the mathematics teacher let go and when do you believe it is best to do otherwise?
I think going through the experience of being the teacher in the teaching stations helped me see what it means to let go. I was so tempted to help a couple of my 'students', but remembered to direct them back to their group to talk it through and discuss the issues they were having. I wish I had gotten further along in the 'After' process, but I was able to see other teachers go through that. I think a teacher should always be able to let go. The only time when it Letting Go is not the best option would be when students are having a difficult time with the problem, are getting frustrated, withdrawn, and quit working. It is okay to let students struggle, but when my students simply can't figure it out, you must give hints or help them or they get frustrated and quit. This definitely doesn't help the learning process. Once they quit, it's hard to get them motivated again. So letting go works as long as you're monitoring well and can sense when it is time to try something different.
Friday, June 29, 2007
Friday, June 22, 2007
Blog 4 - Math all around us
How is mathematics used by those in the pubic domain? To address this question, explore the news or print media in the next few days to get an idea of its power to decide. What does this imply for the teaching of mathematics, constructivism, and who can do mathematics?
Mathematics is used in nearly everything. This means that we must prepare every child to do mathematics. Service, business, public, etc...all sectors rely heavily on math. From simple things like making correct change at the grocery store to making complex public and private sector budgets - math is all around us. This has serious implications for the teaching of mathematics. We must ensure that it is being taught in a way that the students learn best. Mathematics must be comprised of meaningful learning. Students have to be able to make connections with events in their everyday lives to make math relevant. Constructivism must be employed. Student-centered classrooms are necessary to foster the deeper understandings required today. Math is no longer teacher-centered with rules and procedures. Students have to be able to construct their own knowledge and make connections among mathematical ideas. Everyone can, and must, do mathematics.
Mathematics is used in nearly everything. This means that we must prepare every child to do mathematics. Service, business, public, etc...all sectors rely heavily on math. From simple things like making correct change at the grocery store to making complex public and private sector budgets - math is all around us. This has serious implications for the teaching of mathematics. We must ensure that it is being taught in a way that the students learn best. Mathematics must be comprised of meaningful learning. Students have to be able to make connections with events in their everyday lives to make math relevant. Constructivism must be employed. Student-centered classrooms are necessary to foster the deeper understandings required today. Math is no longer teacher-centered with rules and procedures. Students have to be able to construct their own knowledge and make connections among mathematical ideas. Everyone can, and must, do mathematics.
Wednesday, June 20, 2007
Blog 3 - Limitations to Constraints
What have you and your colleagues seen in the past as "limitations" to the student-centered teaching of mathematics? What is the status of your current thinking regarding these "limitations"? How do you envision "engineering" as a way of shifting thinking from "limitations" to "constraints"?
Limitations of the past included such things as the inability to "let go", insufficient time, parents who aren't involved, students who seem bored or disinterested, insufficient technology, etc. I now see that these don't have to be limitations. They don't have to prevent the student-centered teaching of mathematics. Rather than being limitations, we can design (or engineer) a curriculum where these are only the constraints that we must plan for and overcome. They can no longer be excuses for why we can't teach student-centered mathematics, but lessons must be planned in a way as to overcome these constraints
Limitations of the past included such things as the inability to "let go", insufficient time, parents who aren't involved, students who seem bored or disinterested, insufficient technology, etc. I now see that these don't have to be limitations. They don't have to prevent the student-centered teaching of mathematics. Rather than being limitations, we can design (or engineer) a curriculum where these are only the constraints that we must plan for and overcome. They can no longer be excuses for why we can't teach student-centered mathematics, but lessons must be planned in a way as to overcome these constraints
Saturday, June 16, 2007
Blog 2 - Constructivism
Having considered the question, how students learn mathematics through terms like constructivism and understanding, how do these theories and perspectives compare with what you have thought prior to this course? What do you think are the implications for constructivism in the classroom -- what would it look like?
Prior to this course, I thought that an effective way of learning was by using the 'show-and-tell: teacher-directed approach'. This way, the students were shown how the teacher wants the problem solved, and are guided in this manner. The students aren't able to construct their own ideas. No reasons are offered as to why you approach a problem in this manner, rules are assumed to be obvious, and the teacher receives no input on the ideas students have. The teacher can only find out if students are able to follow directions. However, many students who solve the problems correctly really don't understand and will be reinforced that math is a collection of rules to be learned.
Constructivism is much different; it is a student-centered approach. Students are free to develop their own ideas by using prior knowledge to give meaning to the problem solving strategy they develop. Once students have been given time to work on the problem and connect ideas to construct new ideas and develop an understanding, there is a discussion phase where ideas continue to grow. Students may hear new ideas that they hadn't thought of. Teachers begin where the students are - with their ideas. Students are allowed to solve problems in ways that make sense to them by using their own ideas.
Prior to this course, I thought that an effective way of learning was by using the 'show-and-tell: teacher-directed approach'. This way, the students were shown how the teacher wants the problem solved, and are guided in this manner. The students aren't able to construct their own ideas. No reasons are offered as to why you approach a problem in this manner, rules are assumed to be obvious, and the teacher receives no input on the ideas students have. The teacher can only find out if students are able to follow directions. However, many students who solve the problems correctly really don't understand and will be reinforced that math is a collection of rules to be learned.
Constructivism is much different; it is a student-centered approach. Students are free to develop their own ideas by using prior knowledge to give meaning to the problem solving strategy they develop. Once students have been given time to work on the problem and connect ideas to construct new ideas and develop an understanding, there is a discussion phase where ideas continue to grow. Students may hear new ideas that they hadn't thought of. Teachers begin where the students are - with their ideas. Students are allowed to solve problems in ways that make sense to them by using their own ideas.
Wednesday, June 13, 2007
Blog 1 - Influence of Past Experiences
What have been your past experiences learning or teaching mathematics and how have they influenced what you said about mathematics teaching and learning in class?
In my group, we defined math as: reasoning, logic, problem solving, and strategy. We came up with this based on past experiences both learning and teaching math. I always viewed learning math as following certain rules, formulas and strategies to come up with the correct answer. But once I began teaching, I relaized the reasoning, logic and problem solving strategies were very important. Math is no longer guided by strict rules. It is much more about relating it to the students in order to engage them so they can be effective problem solvers. The CRCT has very few straight-foward problems. Most of the problems force students to read, think, use reasoning and logic, and effectively choose the correct strategy to solve the problem. Getting away from the "teacher show" allows students to collaborate and solve problems on their own. Students learn by doing.
In my group, we defined math as: reasoning, logic, problem solving, and strategy. We came up with this based on past experiences both learning and teaching math. I always viewed learning math as following certain rules, formulas and strategies to come up with the correct answer. But once I began teaching, I relaized the reasoning, logic and problem solving strategies were very important. Math is no longer guided by strict rules. It is much more about relating it to the students in order to engage them so they can be effective problem solvers. The CRCT has very few straight-foward problems. Most of the problems force students to read, think, use reasoning and logic, and effectively choose the correct strategy to solve the problem. Getting away from the "teacher show" allows students to collaborate and solve problems on their own. Students learn by doing.
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