Go to the Learning Theories Website , find a theory that would be useful in supporting your approach/philosophy of teaching mathematics, describe it briefly, and explain why/how it is specifically useful.
Before you can find a theory that relates to your teaching, you must first first a paradigm that relates to you as a person. If I had to choose one, I would choose Humanism - focuses on human freedom, dignity and potential. The reason why I felt so connected to to this is because of my mentality of how one should learn Math - not through reading a textbook and doing repetitive questions, but rather feeling it out, playing around with what you have and discovering what you can do. Math was an art-form well before our time, as people were still discovering it. Mathematicians first had examples, then proved those examples in general. Why can't it be approached the same way today?
In terms of a theory, I chose the ARCS Model of Motivational Design - Attention, Relevance, Connection, Satisfaction. I chose this mainly because of its first aspect - Attention, and how it's obtained. The first step in it is gaining perceptual and/or inquiry arousal. Most things in math weren't solved because a book asked a problem, but instead there were problems around them that they were curious about solving, and that curiously stemmed into the knowledge of math we have today. Students should have a chance at that same curiousity. From there, they can formulate their own results.
Now, the issue that can arise is that not every student is a future mathematician, thus certain topics might take some students a very long time (if ever) to reach through discovery. So I guess there's a bit of metaphorical "bumper lanes" you have to set to nudge them in the right direction. But I still feel learning should be... Learning. Not retaining. You learn through going through experiences yourself and reflecting on said experiences.
Social Development Theory by Vygotsky argues that the role of social interaction plays an important role in development. This theory has a strong emphasis on group or partnered learning, where the More Knowledgeable Other, which could be a teacher, coach or peer (anyone with greater understanding of the subject working with the other student/child. This theory uses the Zone of Proximal Development which is a range between a student completing a task under guidance (teacher or peer) and the student completing the task independently. There is a shift from teacher directed to student and teacher collaboration in lessons.
I believe this theory is exceptionally useful in the intermediate senior level. Students at this age are extremely social beings and they will be social in your class whether you let them or not. Therefore, including peer/group activities would be very valuable.
In my last placement in an Advanced Functions class this theory was clearly being used. I would explain a concept or example and then stop and have students discuss the concept/idea/problem with their partner. I would also present a problem and give them time to work on this with their partner or in small groups. I would put a student’s answer to a problem on the document camera and have them or another student explain the process. I would also give student time to work on a set of problems and then help them in small groups. I would then have students take up a few select problems using the document camera or SmartBoard. Through discussions with my AT and my own lessons I have come to believe that students retain more when they are discussing it between themselves, including the social aspect, and minimizing the role of the teacher and increasing the role of the students.
I believe that one of the most useful learning theories for teaching mathematics is the theory of Cognitive Apprenticeship (Collins et al.). As an example, we can look at a mathematics problem that requires several steps to solve.
Sample Problem: Expand and simplify the following expression: (x + 2)(x + 1)
Modelling: The teacher outlines the steps required to solve the problem. The teacher explains the FOIL Method (First, Outside, Inside, Last).
Coaching: The teacher writes an example problem on the board with the same level of difficulty and asks students to solve this problem, using the same method. The teacher offers hints as students proceed.
Scaffolding: Some students may require additional support during the solution process. For example, if a student is struggling with multiplying polynomials, the teacher may need to clarify that x*x is x^2, rather than 2x.
Articulation: The homework may include a series of quadratic expressions in root form for students and a set of corresponding expanded expressions, some of which are incorrect. Students can be asked to expand and simplify the expressions in root form and compare them to the expanded expressions, explaining why the expression is expanded correctly or incorrectly. Students should be able to pinpoint the errors in the solution process.
Reflection: Students can compare their solutions with the solutions of their peers, and they can learn strategies that can enhance their understanding of the solution process.
Exploration. The teacher can ask students to factor an expanded quadratic expression (factoring hasn't been taught yet). The only hint that students are given is that the coefficient of the linear term and the constant are formed by two different mathematical operations with the same two numbers.
Students should ask the following questions: 1. What are the two numbers? 2. What are the mathematical operations? 3. Develop a step-by-step process for factoring a quadratic expression.
Bandura's Social Learning Theory is useful to me as a math teacher because I believe in the importance of ollaborative learning, especially when considering a challenging subject like mathematics. Social learning theory depends on the learner's ability to learn from other's behaviors and the outcomes of those behaviors. People learn by observing others, drawing conclusions, and retaining them.
I think that Social Learning Theory is useful because I have incorporated it into teaching strategies, and have seen how effective it can be. During my second placement (teaching grade 10 academic and applied science), I put students into groups of 4/5 and gave them a topic, as well as 10 related words. I gave them half an hour to come up with a five minute overview of the topic, and had them present their findings to the class. I found this strategy very effective. Students were able to complete the task at hand without any assistance from the internet. It was quite impressive to see the success that they experienced solely from collaborative discussion.
I would employ a similar strategy when teaching mathematics. I would perhaps give groups a challenging question rather than a topic and associated words.
I really like the fact that this theory provides students an opportunity to work collaboratively, and teachers with an opportunity to challenge their students. I've really enjoyed challenging my students on my placements and have found that they often surprise me when i do so!
Before you can find a theory that relates to your teaching, you must first first a paradigm that relates to you as a person. If I had to choose one, I would choose Humanism - focuses on human freedom, dignity and potential. The reason why I felt so connected to to this is because of my mentality of how one should learn Math - not through reading a textbook and doing repetitive questions, but rather feeling it out, playing around with what you have and discovering what you can do. Math was an art-form well before our time, as people were still discovering it. Mathematicians first had examples, then proved those examples in general. Why can't it be approached the same way today?
ReplyDeleteIn terms of a theory, I chose the ARCS Model of Motivational Design - Attention, Relevance, Connection, Satisfaction. I chose this mainly because of its first aspect - Attention, and how it's obtained. The first step in it is gaining perceptual and/or inquiry arousal. Most things in math weren't solved because a book asked a problem, but instead there were problems around them that they were curious about solving, and that curiously stemmed into the knowledge of math we have today. Students should have a chance at that same curiousity. From there, they can formulate their own results.
Now, the issue that can arise is that not every student is a future mathematician, thus certain topics might take some students a very long time (if ever) to reach through discovery. So I guess there's a bit of metaphorical "bumper lanes" you have to set to nudge them in the right direction. But I still feel learning should be... Learning. Not retaining. You learn through going through experiences yourself and reflecting on said experiences.
Social Development Theory by Vygotsky argues that the role of social interaction plays an important role in development. This theory has a strong emphasis on group or partnered learning, where the More Knowledgeable Other, which could be a teacher, coach or peer (anyone with greater understanding of the subject working with the other student/child. This theory uses the Zone of Proximal Development which is a range between a student completing a task under guidance (teacher or peer) and the student completing the task independently. There is a shift from teacher directed to student and teacher collaboration in lessons.
ReplyDeleteI believe this theory is exceptionally useful in the intermediate senior level. Students at this age are extremely social beings and they will be social in your class whether you let them or not. Therefore, including peer/group activities would be very valuable.
In my last placement in an Advanced Functions class this theory was clearly being used. I would explain a concept or example and then stop and have students discuss the concept/idea/problem with their partner. I would also present a problem and give them time to work on this with their partner or in small groups. I would put a student’s answer to a problem on the document camera and have them or another student explain the process. I would also give student time to work on a set of problems and then help them in small groups. I would then have students take up a few select problems using the document camera or SmartBoard. Through discussions with my AT and my own lessons I have come to believe that students retain more when they are discussing it between themselves, including the social aspect, and minimizing the role of the teacher and increasing the role of the students.
I believe that one of the most useful learning theories for teaching mathematics is the theory of Cognitive Apprenticeship (Collins et al.). As an example, we can look at a mathematics problem that requires several steps to solve.
ReplyDeleteSample Problem:
Expand and simplify the following expression:
(x + 2)(x + 1)
Modelling:
The teacher outlines the steps required to solve the problem.
The teacher explains the FOIL Method (First, Outside, Inside, Last).
Coaching:
The teacher writes an example problem on the board with the same level of difficulty and asks students to solve this problem, using the same method. The teacher offers hints as students proceed.
Scaffolding:
Some students may require additional support during the solution process. For example, if a student is struggling with multiplying polynomials, the teacher may need to clarify that x*x is x^2, rather than 2x.
Articulation:
The homework may include a series of quadratic expressions in root form for students and a set of corresponding expanded expressions, some of which are incorrect. Students can be asked to expand and simplify the expressions in root form and compare them to the expanded expressions, explaining why the expression is expanded correctly or incorrectly. Students should be able to pinpoint the errors in the solution process.
Reflection:
Students can compare their solutions with the solutions of their peers, and they can learn strategies that can enhance their understanding of the solution process.
Exploration.
The teacher can ask students to factor an expanded quadratic expression (factoring hasn't been taught yet). The only hint that students are given is that the coefficient of the linear term and the constant are formed by two different mathematical operations with the same two numbers.
Students should ask the following questions:
1. What are the two numbers?
2. What are the mathematical operations?
3. Develop a step-by-step process for factoring a quadratic expression.
Bandura's Social Learning Theory is useful to me as a math teacher because I believe in the importance of ollaborative learning, especially when considering a challenging subject like mathematics. Social learning theory depends on the learner's ability to learn from other's behaviors and the outcomes of those behaviors. People learn by observing others, drawing conclusions, and retaining them.
ReplyDeleteI think that Social Learning Theory is useful because I have incorporated it into teaching strategies, and have seen how effective it can be. During my second placement (teaching grade 10 academic and applied science), I put students into groups of 4/5 and gave them a topic, as well as 10 related words. I gave them half an hour to come up with a five minute overview of the topic, and had them present their findings to the class. I found this strategy very effective. Students were able to complete the task at hand without any assistance from the internet. It was quite impressive to see the success that they experienced solely from collaborative discussion.
I would employ a similar strategy when teaching mathematics. I would perhaps give groups a challenging question rather than a topic and associated words.
I really like the fact that this theory provides students an opportunity to work collaboratively, and teachers with an opportunity to challenge their students. I've really enjoyed challenging my students on my placements and have found that they often surprise me when i do so!