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Tuesday, December 7, 2010
Friday, November 19, 2010
Sunday, November 14, 2010
Word Problem Analysis
From Mathematics 10 p. 313 # 12
Sharon creates a function in the form f(x) = __ x + __ for her classmates to solve. To figure out the actual equation, students give Sharon input values. She gives them the output from the function. The values are f(1) = 5, f(2) = 8, f(-1) = -1, and f(-2) = -4. What is the equation for Sharon's function?
Create a function of your own. Have someone determine the equation of your function by giving you input values and studying the pattern in your responses.
1. Is it practical?
To me this question does not seem overly practical. When in life are students going to have to create an equation that their peers will have to guess?
2. Is the imagery memorable?
Once again the question is not overly memorable. The question is just another exercise for students to run through, only this time they get to run through it with a partner. They will likely forget this very quickly.
3. Can it be solved with the given information?
Yes, the problem gives you enough information that it can be easily solved.
4. Can it be interpreted in more than one way?
I do not believe that this particular question can be interpreted in more than one way, though the responses to the second part will surely be different across the class.
5. Would students be able to interpret it as intended?
I believe so, yes. It is a very straight forward question.
6. Is there anything strange about it?
Beyond the fact that it has little connection to real life situations that students will find themselves in, there is not anything strange about it.
The question seems to me to be just another drill and kill kind of question that does not require a lot of creative thinking or true problem solving. It is just a practice question disguised in a different costume.
Sharon creates a function in the form f(x) = __ x + __ for her classmates to solve. To figure out the actual equation, students give Sharon input values. She gives them the output from the function. The values are f(1) = 5, f(2) = 8, f(-1) = -1, and f(-2) = -4. What is the equation for Sharon's function?
Create a function of your own. Have someone determine the equation of your function by giving you input values and studying the pattern in your responses.
1. Is it practical?
To me this question does not seem overly practical. When in life are students going to have to create an equation that their peers will have to guess?
2. Is the imagery memorable?
Once again the question is not overly memorable. The question is just another exercise for students to run through, only this time they get to run through it with a partner. They will likely forget this very quickly.
3. Can it be solved with the given information?
Yes, the problem gives you enough information that it can be easily solved.
4. Can it be interpreted in more than one way?
I do not believe that this particular question can be interpreted in more than one way, though the responses to the second part will surely be different across the class.
5. Would students be able to interpret it as intended?
I believe so, yes. It is a very straight forward question.
6. Is there anything strange about it?
Beyond the fact that it has little connection to real life situations that students will find themselves in, there is not anything strange about it.
The question seems to me to be just another drill and kill kind of question that does not require a lot of creative thinking or true problem solving. It is just a practice question disguised in a different costume.
Cycling Digits
Friday, November 12, 2010
Response to Adaptive Article
Ferret's story was very touching. To have that confidence in your own abilities is what we all want for our students, but to know as the teacher that that confidence is leading to missteps is a difficult thing to deal with. Do we step in and point out the error or do we lead the student to see the error for themselves? I feel it is much better to lead the student to see the error for themselves. The other question that comes to mind is if Ferret is using this strategy incorrectly how many other students are also using it incorrectly?
Another aspect of the article that I want to touch on is the idea of correcting a students method based on the efficiency of it. If a student has found a strategy that works for them and they feel comfortable using, in my experience they are less likely to switch to a different method. For example, my grade 10's became comfortable using algebraic methods to find the x and y intercepts of a graph and when they were introduced to how the calculator could aide them they were very resistant to using it, even though it is a tool that speeds up the process. We have to question the purpose behind introducing a method that we feel is more efficient. Is the purpose of mathematics to produce efficient problem solvers? Or is the purpose to produce students who are comfortable solving problems not matter what method they may use? I would prefer the second.
Another aspect of the article that I want to touch on is the idea of correcting a students method based on the efficiency of it. If a student has found a strategy that works for them and they feel comfortable using, in my experience they are less likely to switch to a different method. For example, my grade 10's became comfortable using algebraic methods to find the x and y intercepts of a graph and when they were introduced to how the calculator could aide them they were very resistant to using it, even though it is a tool that speeds up the process. We have to question the purpose behind introducing a method that we feel is more efficient. Is the purpose of mathematics to produce efficient problem solvers? Or is the purpose to produce students who are comfortable solving problems not matter what method they may use? I would prefer the second.
Monday, November 1, 2010
Experiences from the Past Two Weeks
While everyone else was out on their short two week practicum, I spent my time writing a 10 page literature review for EDCP 550 - Math Education: Origins and Issues. My literature review was based on the trend of math anxiety - what are its causes and how can the high school class teacher help students to deal with their anxiety in a positive way. A lot of the reading that I had to do for the paper made me think of my students from the past two years. The last two years I spent at a private Christian school teaching students in the applied stream of mathematics. So they already come into my room with a negative opinion about their abilities as math students. By building relationships with my kids I was able to, I think, help they get past some of their fears and worries. I know that when I told them I would not be returning for September of this year they were less than impressed. I got the comment "Miss L. I'm going to fail Applied 30 if you are not here to help me!" This tells me that the student knows that I was and am on their side, more interested in helping them succeed than simply getting them through. Even this semester I have heard from a few of them asking how I am doing in class and telling me that I need to come back to them. I definitely believe that the relationship you build with the students in your class can and does go a long way in helping students deal with some of their anxiety. I can only hope to continue to build similar relationships with my future students and create an environment where math anxiety is lessened.
Another lesson from the past two weeks is the importance of making connections with colleagues. As we were a small school the high school staff was very close. Thus when they found out I was planning on doing my diploma program I had the grade 12 English and socials teacher offer to be my editor for any papers that I would have to do. Too often at larger schools we can get locked into our department and not necessarily make connections with others. My connection with the English 12 teacher allowed me to email her my 10 page paper and be confident that the editing would be done by someone who may not necessarily understand math, but is awesome with the written word.
Another lesson from the past two weeks is the importance of making connections with colleagues. As we were a small school the high school staff was very close. Thus when they found out I was planning on doing my diploma program I had the grade 12 English and socials teacher offer to be my editor for any papers that I would have to do. Too often at larger schools we can get locked into our department and not necessarily make connections with others. My connection with the English 12 teacher allowed me to email her my 10 page paper and be confident that the editing would be done by someone who may not necessarily understand math, but is awesome with the written word.
Monday, October 18, 2010
Poem
Something from nothing,
Is it really possible?
Not from our human perspective.
Infinite, unending, beyond us
Division, splitting, separation
Why do we have to be divided?
Sometimes pain is necessary for growth.
Still it is painful
Zero to worry about,
Why do we worry about what tomorrow will bring?
There are infinite possibilities
He is in ultimate control
Something from nothing,
It is really possible,
Beyond our human perspective
Infinite, unending, forever
Is it really possible?
Not from our human perspective.
Infinite, unending, beyond us
Division, splitting, separation
Why do we have to be divided?
Sometimes pain is necessary for growth.
Still it is painful
Zero to worry about,
Why do we worry about what tomorrow will bring?
There are infinite possibilities
He is in ultimate control
Something from nothing,
It is really possible,
Beyond our human perspective
Infinite, unending, forever
Saturday, October 16, 2010
Group Microteaching Reflections
Summary of Comments
The comments we received were mostly positive in nature. The majority really liked that we attempted a Jigsaw approach to this topic. One comment I really liked is that the approach made a potentially dry topic more fun. The class felt that we did a great job of organizing the groups and having something different and interesting for each group to do. The biggest critique we had was the lack of time at the end for the original group of three to report back to each other. On a personal note, my voice was too quiet at one point when I was attempting to not talk over my teammates.
Personal Reflection
I really enjoyed doing this micro-teaching lesson with Michelle and Debbie. It was very interesting discovering the different historical applications of the Pythagorean Theorem. I really wanted to be a part of each of their groups to learn more about what they had discovered. I would absolutely use an approach like this with a class of my own to make the learning of the history and modern applications a fun activity. I would probably extend the activities at each station so that they would expand on the information we only briefly touched on. The one thing I would make sure to improve would be the amount of time that the original groups of three had to debrief with each other. I would also include a longer time of class debrief. Overall an enjoyable activity.
The comments we received were mostly positive in nature. The majority really liked that we attempted a Jigsaw approach to this topic. One comment I really liked is that the approach made a potentially dry topic more fun. The class felt that we did a great job of organizing the groups and having something different and interesting for each group to do. The biggest critique we had was the lack of time at the end for the original group of three to report back to each other. On a personal note, my voice was too quiet at one point when I was attempting to not talk over my teammates.
Personal Reflection
I really enjoyed doing this micro-teaching lesson with Michelle and Debbie. It was very interesting discovering the different historical applications of the Pythagorean Theorem. I really wanted to be a part of each of their groups to learn more about what they had discovered. I would absolutely use an approach like this with a class of my own to make the learning of the history and modern applications a fun activity. I would probably extend the activities at each station so that they would expand on the information we only briefly touched on. The one thing I would make sure to improve would be the amount of time that the original groups of three had to debrief with each other. I would also include a longer time of class debrief. Overall an enjoyable activity.
Thinking Mathematically Chatpers 2 & 3
I first started reading these chapters online from the posting and found them difficult to follow for two reasons. First some of the content was cut off by the scanning and second because I felt as if I was missing some important aspect that had been introduced in chapter one. So once I had an actual copy of the book I read chapter one before proceeding to chapters two and three. This was much better and my insights follow.
Phases of Work
I particularly like how the authors set out the three phases in this chapter and spend most of it focused on phase one. Even though we subconsciously realize we often walk through the three aspects of the entry phase it was great to have it put into words. I appreciated how each aspect was expounded on and more ideas and examples were given to help develop them. I think students would benefit from spending some time pursuing this as well. It may formalize it in their understanding better than anything else we could do.
The review phase is something that we often overlook, even as teachers. How often do we ask our students to look back over what they've done and justify their solutions. We rarely spend any time actually teaching them how to critically look back at what they have done. This chapter gives me some ideas of how I could focus less on the answer and more on helping students justify their work.
Responses to Being Stuck
I really identified with this chapter. Recently in the Problem Solving class we were given a set of five problems to solve, of which we had to hand two in. There was only one question that I felt at all capable of doing on my own. It was very difficult to admit that I could not do the rest of them without help. I was hopelessly stuck and felt extremely defeated. It was only through this experience that I could identify with students who may often feel the same way about any math questions. This chapter showed me that it was okay to be stuck and that being stuck is perhaps the best place to be to truly learn something.
Phases of Work
I particularly like how the authors set out the three phases in this chapter and spend most of it focused on phase one. Even though we subconsciously realize we often walk through the three aspects of the entry phase it was great to have it put into words. I appreciated how each aspect was expounded on and more ideas and examples were given to help develop them. I think students would benefit from spending some time pursuing this as well. It may formalize it in their understanding better than anything else we could do.
The review phase is something that we often overlook, even as teachers. How often do we ask our students to look back over what they've done and justify their solutions. We rarely spend any time actually teaching them how to critically look back at what they have done. This chapter gives me some ideas of how I could focus less on the answer and more on helping students justify their work.
Responses to Being Stuck
I really identified with this chapter. Recently in the Problem Solving class we were given a set of five problems to solve, of which we had to hand two in. There was only one question that I felt at all capable of doing on my own. It was very difficult to admit that I could not do the rest of them without help. I was hopelessly stuck and felt extremely defeated. It was only through this experience that I could identify with students who may often feel the same way about any math questions. This chapter showed me that it was okay to be stuck and that being stuck is perhaps the best place to be to truly learn something.
Thursday, October 14, 2010
Group Microteaching
EDCP 342A October 15th, 2010
Group Micro Teaching – Apprenticeship and Workplace 10
Michelle, Deb, Nadine
Bridge: 2 min
Catch interest by having students form groups of three and numbering themselves 1,2,3 for jigsaw activity in which they will become the expert on some aspect of the history or modern use of the Pythagorean Theorem.
Learning Objective:
Students will be able to demonstrate an understanding of the Pythagorean Theorem by describing historical and contemporary applications of it.
Ø To learn a historical use for Pythagorean Theorem and to understand where Pythagoras' inspiration came from.
Ø To understand that this theorem came about from a practical application, not pen and paper theory.
Teaching Objective:
Ø Learn and improve our methods in conducting an engaging and educational lesson that will reach everyone.
Ø To interactively show the motivation for the Pythagoras Theorem, introduced to Pythagoras by the ancient Egyptians.
Ø To try out the Jigsaw strategy.
Pre-test: 1 min
Ø Who can tell me what we already know about the Pythagorean Theorem?
o Looking for formula, triples, and to see if anyone might already know where it comes from.
Participatory Learning: 7 min
Ø Split groups into 1’s, 2’s and 3’s.
o 1’s at Egyptian Station (Deb)
o 2’s at Babylonian Station (Michelle)
o 3’s at Modern Application Station (Nadine)
Station 1 – Egyptians
Ø Explain how ancient Egyptians used a right-triangle to redistribute fields after yearly flooding.
Ø Explain how they made a right triangle using rope and knots
Ø Explain how Pythagoras became involved/interested
Ø Make a right-triangle with a piece of string and ruler. Make a 3, 4, 5 triangle and see if they can find a right angle in the classroom with it.
Station 2 – Babylonians
Ø Explain Babylonian Mathematics and history of Pythagorean Theorem.
Ø Teaching Babylonian numbering system and ancient tablet.
Ø Briefly cover other ancient cultures in which Pythagorean Theorem was known and used
Station 3 – Modern Uses
Ø Talk about how surveyors use their equipment to set up right hand triangles in order to calculate distances etc…
Ø Have students using laptops research other possible modern uses for Pythagoras.
Ø If they cannot find any, have them brainstorm a list of possible fields that they think may use the Pythagorean Theorem.
Materials Needed:
o String and rulers
o White board, diagrams of tablet and Babylonian numbering system
o Laptops, paper to write ideas down on, pens
Post-Test: 3 min
Groups of three re-form and students teach other members about their area of expertise. Only have 1 minute each to share.
Summary: 2 min
Students complete the statement: The one thing I learned today that I didn’t know before was _______________________________________________________________________________. (Orally if time allows.)
Feedback and Reflections on the Jive Mini-lesson
The feedback I received on teaching the Jive was overall positive. My group members appreciated that I was actively involved in correcting their technique as I walked around. They said the pace was good and the instructions were very easy to follow. Finally they appreciated that I used the history and origin of the Jive to create interest in the lesson. A few of the critiques were that I needed to perhaps explain the proper partner position ahead of time and maybe add some extensions that the professional dancers do.
This mini-lesson was very fun to do. I have taught a ballroom dance class before as an option for my students and it brought back good memories. I did adapt the way I have previously taught this type of lesson as experience has taught me that a slower introduction to the basic step is very important, especially for the gentlemen. I needed to have a little bit more prepared for the students I had as we got through it much more quickly than I expected. In the future I would make sure that I have the proper music with me so that the students can try it with a regular tempo Jive song. Unfortunately all of my ballroom music is currently in Prince George.
Wednesday, October 6, 2010
Timed Writing
Division
Take a group of things and split them up into smaller things, a process kids have difficulty with, trying to teach long division with grade tens of polynomials and the difficulty they have with it, what's the point, hard to think of splitting things up, ummmmm, not sure what else to say, fractions, decimals, being separate from my family here in vancouver, divisions in politics, no one can agree, divisions in the church, humans need to be right create divisions, divisions in families when not everyone agrees exactly with each other, this is a very difficult exercise in and of itself, how does it relate to life outside school, how to reconcile deep divisions, have nothing else to say really about this, hate being divided from those I love, gonna happen again on Tuesday...
Zero
Place holder, not a new concept, took a long time to develop a symbol that meant nothing, do we really understand the meaning of nothing, division by zero is impossible because you cannot take something and turn it into nothing unless you are God, there is zero to worry about because He has it under control, is often forgotten about in mathematical context, running out of things to say about zero, had more to say about division, is it an easy concept for kids to truly understand...
Take a group of things and split them up into smaller things, a process kids have difficulty with, trying to teach long division with grade tens of polynomials and the difficulty they have with it, what's the point, hard to think of splitting things up, ummmmm, not sure what else to say, fractions, decimals, being separate from my family here in vancouver, divisions in politics, no one can agree, divisions in the church, humans need to be right create divisions, divisions in families when not everyone agrees exactly with each other, this is a very difficult exercise in and of itself, how does it relate to life outside school, how to reconcile deep divisions, have nothing else to say really about this, hate being divided from those I love, gonna happen again on Tuesday...
Zero
Place holder, not a new concept, took a long time to develop a symbol that meant nothing, do we really understand the meaning of nothing, division by zero is impossible because you cannot take something and turn it into nothing unless you are God, there is zero to worry about because He has it under control, is often forgotten about in mathematical context, running out of things to say about zero, had more to say about division, is it an easy concept for kids to truly understand...
Mathematics and Citizenship
I enjoyed reading this short article about mathematics and its role in developing good citizens. It continues to surprise me how prevasive mathematics is beyond the classroom. I would never think that things we hear on the news on a nightly basis are linked to math concepts. It makes sense now, but I would never think that, we as humans, have assigned numbers or mathematical concepts to most things we come across.
As far as the classroom is concerned, I have found that students find it very difficult to explain how they arrived at their answers. I think this is largely because the climate of mathematics education does not put enough emphasis on expecting students to be able to justify their solutions. Mathematics is considered very black and white; it is right or it is wrong. This article made me think back to the video where the teacher didn't say if their answers were correct or not. Instead he expected them to know that they were correct without any justification from an outside source. This is a great skill for us to be attempting to instill in our students; the ability to make choices for themselves and know that their choice is the best thing for them.
As far as the classroom is concerned, I have found that students find it very difficult to explain how they arrived at their answers. I think this is largely because the climate of mathematics education does not put enough emphasis on expecting students to be able to justify their solutions. Mathematics is considered very black and white; it is right or it is wrong. This article made me think back to the video where the teacher didn't say if their answers were correct or not. Instead he expected them to know that they were correct without any justification from an outside source. This is a great skill for us to be attempting to instill in our students; the ability to make choices for themselves and know that their choice is the best thing for them.
Saturday, October 2, 2010
The Math Wars
Battleground Schools: Mathematics Education
In the article battleground schools there were two differing schools of thought concerning how mathematics should be taught and approximately three different eras of reform that were considered. The two differing schools of thought are considered conservative and progressive. The conservatives prefer a more teacher directed model of math education while the progressivists prefer a teacher as guide and facilitator model. Each of the eras, 1910-1940 Progressivist, 1960's New Math, and 1990"s Math Wars, seems to favour one approach to the exclusion of the other.
What I noticed as I was reading this article was how driven by societies needs are our math classrooms. Math is not necessarily considered a subject to be taught simply for the pleasure that it can bring. It comes across more as a means to an end. We teach math so that our students can be productive members of society, be that members of an independent thinking democratic society, or a highly scientific, space race populace. Math is to be taught for the purpose of preparing kids for the "real world". To me this indicates that we expect all students to leave school and be the top performers in whatever field of study they happen to get into and if they aren't then we have somehow failed them.. What we fail to realize is that not all students are going to be Einsteins. For me it brings to mind the question, "why do we teach math?" I think we should be teaching math for math's sake. It is a disipline full of interesting things that can be explored simply for the fun of it. Yes, it absolutely has value in the high level careers like engineering and should be pursued for that reason as well. However not all of our students are going to be engineers and to teach all of them as if they will be is doing a disservice to our kids. If we can instill in the students, maybe not a love for, but an appreciation for the complexities and intricacies of mathematics then I believe we will have done our job.
Wednesday, September 29, 2010
Letters From the Future
Dear Miss L.
I want to say thank you for being my teacher all those years ago. I came into your class really not enjoying math at all and you helped me see that it is not all bad. I appreciated how much you cared about me beyond how well I could do on a test. You really took the time to see me as not just another face in the crowd. You cared about how I was doing in and outside of class. Even though I was never really great at math and didn't persue it any farther after your class, I left school with a more positive attitude about my strenghts and weaknesses.
Sincerely Student A
Dear Miss L.
I am writing this letter just to let you know how I felt about you as a teacher. You were one of my least favourite teachers and here is why. You were often too focused on the little stuff like how an assignment was to be set up, what kind of pen/pencil I used. That was never that important in the grand scheme of things. I also didn't appreciate how fast you always went. It seemed like as soon as a few people understood you were moving on. I didn't like how it always felt like you were the be all and end all of knowledge. It made it difficult to approach you if I didn't understand something. I also felt like you were never as clear as you could be in your feedback to us. Lastly it seemed to me that you favoured the females in the class and that was not very fair. I hope things have changed over the years for you and that your students now are better off.
Student B
I think I am the most worried about being remember for being picky about the small stuff. How an assignment is laid out isn't as important what they learn through it. I am worried about being seen as favoring certain students over others. I am afraid of losing that personal connection I have now with students when I eventually end up in a larger school. I am also afraid of not having sufficient background knowledge to properly teach the subject matter.
I want to say thank you for being my teacher all those years ago. I came into your class really not enjoying math at all and you helped me see that it is not all bad. I appreciated how much you cared about me beyond how well I could do on a test. You really took the time to see me as not just another face in the crowd. You cared about how I was doing in and outside of class. Even though I was never really great at math and didn't persue it any farther after your class, I left school with a more positive attitude about my strenghts and weaknesses.
Sincerely Student A
Dear Miss L.
I am writing this letter just to let you know how I felt about you as a teacher. You were one of my least favourite teachers and here is why. You were often too focused on the little stuff like how an assignment was to be set up, what kind of pen/pencil I used. That was never that important in the grand scheme of things. I also didn't appreciate how fast you always went. It seemed like as soon as a few people understood you were moving on. I didn't like how it always felt like you were the be all and end all of knowledge. It made it difficult to approach you if I didn't understand something. I also felt like you were never as clear as you could be in your feedback to us. Lastly it seemed to me that you favoured the females in the class and that was not very fair. I hope things have changed over the years for you and that your students now are better off.
Student B
I think I am the most worried about being remember for being picky about the small stuff. How an assignment is laid out isn't as important what they learn through it. I am worried about being seen as favoring certain students over others. I am afraid of losing that personal connection I have now with students when I eventually end up in a larger school. I am also afraid of not having sufficient background knowledge to properly teach the subject matter.
Friday, September 24, 2010
Five Burning Questions - Assignment 1
Questions for Math Student:
1. What memorable method did a current or previous math teacher use that made the learning easier?
2. What memorable method did a current or previous math teacher use that made the learning fun?
3. Why is your favourite math teacher your favourite? What did they do differently than other math teachers?
4. Why do you like (or dislike) math?
5. How do you feel about the amount of math homework that you get?
Questions for Math Teacher:
1. How do you incorporate topics into your math class which show how the math applied to real life outside the classroom?
2. Do you include history of math into your classroom? How?
3. What types of methods do you use to ensure that the student’s homework or assignments are their own?
4. What is the most challenging part about teaching the subject?
5. How do you approach both the students who like math and students who dislike math?
Hong, Michelle & Nadine
1. What memorable method did a current or previous math teacher use that made the learning easier?
2. What memorable method did a current or previous math teacher use that made the learning fun?
3. Why is your favourite math teacher your favourite? What did they do differently than other math teachers?
4. Why do you like (or dislike) math?
5. How do you feel about the amount of math homework that you get?
Questions for Math Teacher:
1. How do you incorporate topics into your math class which show how the math applied to real life outside the classroom?
2. Do you include history of math into your classroom? How?
3. What types of methods do you use to ensure that the student’s homework or assignments are their own?
4. What is the most challenging part about teaching the subject?
5. How do you approach both the students who like math and students who dislike math?
Hong, Michelle & Nadine
Assignment 1 Report
Assignment 1 Report
(Group Members: Michelle Davis, Hong Jiang and Nadine Lundie)
PART 1 – Mathematics Teacher
We chose to ask our five burning questions to two different math teachers with varying experience. The first teacher interviewed had graduated from the UBC four years ago and has been teaching grade 11 and 12 math. The second teacher is the Senior Math Expert and has 30 years of high school teaching experience. We decided to ask two teachers with different levels of teaching experience to compare our results.
We found the answers were quite different in that the responses from the recent UBC grad were responses that we as teacher candidates might have thought of. On the other hand, the responses from the experienced math teacher were quite different and her methods unexpected. For example, we asked both teachers how they approach both the students who like math and dislike math. The newer teacher said that when she has a student who is only there because it’s a requirement to graduate and they are not interested in pursuing anything mathematical after high school then she simply tells them what they need to pass. She explains the requirements for them to get a specific grade and lets the students decide for themselves what grade they want. The experienced math teacher did not bring up the notion of ‘requirement to graduate’ and said that she shows students that math is more than computation. She believes that math is a fine art and compares it to music in saying that playing scales is not all music is. She says that she teaches from the premise that math is creative, efficient, effective and fun. She believes that all students can and should have an appreciation for mathematics even if they never plan to pursue it. She is not content to just let them be.
This premise also relates to how she manages to relate math to concepts beyond the classroom. She describes math as a way of thinking which helps with organizational skills, efficient procedures and problem solving. She goes on to say that this mathematical way of thinking is used even for daily things such as your cell phone plan or relationship issues. She firmly believes that math is more than just procedures to memorize and strives to make this come across to her students.
One thing our group found interesting was how the experienced teacher incorporated topics from the real world into the classroom compared to the newer teacher. Rather than presenting or telling about real world applications, the experienced teacher posed questions or problems for the students to think about. For example, using a parabola to represent a bridge or arch she would ask the students whether they could replicate a famous structure in a different location over another river of different width or to allow for taller boats. We found this very interesting because not only is she relating math to a real problem, she is also having the students try and solve it themselves. This would be a great idea for a group project.
PART 2 – Mathematics Student
We asked our five burning questions to a high school student who likes math and a high school student who dislikes math. When considering math a mere subject, the student said that they like math because there is either a right answer or a wrong answer, and there is no maybe answers. The other student said they dislike math because they feel it is too hard for them to understand and they wait too long to ask for help until right before the unit test. Our group was wondering if perhaps the teacher was not approachable enough for extra help, or if the student already established a sense of defeat about math.
We found it interesting that the students had similar answers as to what about a specific math teacher made them their favourite. Both the students said that the teacher made math fun, used good humor and brought jokes about math into the lesson. For example, one of the students said that their teacher gave the three different forms for the equation of a line names that were funny and non-math related to help students remember. The student who disliked math said their favourite teacher explained things in the simplest and easiest way and the student who liked math said their favourite teacher did things that were hands on and interactive. One of the students also said their favourite teacher let them watch “Finding Nemo” during class. It seems to us that it is much more about the relationship that the teacher built with the kids that made them memorable.
A few of the other comments we found interesting had little to do with the content of mathematics itself. The student who likes math said that her teacher cared, wanted to help, and made sure that the students were doing okay, and not just in math. The student who dislikes math said that their favourite teacher had a positive attitude. We found this intriguing that these characteristics are completely unrelated to the subject. We have been learning that being a teacher is more than knowing and teaching your subject matter. It is also about caring for your students and their success.
Of course the issue of homework came up with both students. They both said they did not much like homework, which is not surprising. The student who dislikes math said that if too many questions were assigned they would dread even getting started on it. It’s an interesting issue; how much homework is too much? How much is not enough? As the teacher how do you treat homework in the evaluation process?
Conclusion
This interview was very eye opening for all the members in our group. We can relate to the answers from the newer math teacher, although we aspire to develop the methods of the experienced teacher. We believe the confidence and creativity this teacher brings to the classroom comes not only with experience but also with constant reflection and adaptation.
We gained a different perspective by interviewing both types of math students. We saw that they had different concerns in areas like what made learning the easiest, but they had the same ideas about homework and why a certain teacher were their favourite. We learned that the teacher having a positive attitude and caring about their personal well being, which are both unrelated to math, are more important than we previously thought.
Wednesday, September 22, 2010
Tuesday, September 21, 2010
Dave Hewitt Video
I have to say, I really enjoyed the video presentation on Monday. It is such a simple way of presenting so many different aspects of math that some students find so difficult to grasp. I really appreciated the fact that the tapping method can illustrate many so things like sequences of numbers, the properties of counting, the number line and its properties, positive and negative numbers, algebra, skip counting, etc...the list can go on and on. It is such a versatile way of reaching students at any level of mathematics, not just grade eight students trying to learn positive and negative numbers. I also really liked how the group dynamic worked with this method. By the end almost all, if not all, of the students were participating and correcting themselves without fear of being laughed at. There was less pressure for them to be perfect right away and if they didn't get something right off the bat that was okay. There were encouraged to work as a team. It was an us versus the math kind of thing and the math wasn't portrayed as something beyond their scope of ability.
One question I have is how can this type of method be moved into to more complicated fields, like geometry or trigonometry? How can we make this type of method work just as well in Calculus?
One question I have is how can this type of method be moved into to more complicated fields, like geometry or trigonometry? How can we make this type of method work just as well in Calculus?
Friday, September 17, 2010
Remembering Math Teachers
I have two different situations that come to mind when considering memorable math teachers. The first was in high school with the three teachers I had for my whole high school experience. The first teacher encouraged me to challenge myself by taking AP math in successive years; he knew I would have been bored and underchallenged had I stayed in the regular route. The second teacher was just a strong teacher who explained things in such a way that I could easily understand them. My final teacher, grade 12 and calculus, was a phenomenal instructor who was also very easy to approach and cared about us beyond simply what we did in his classroom.
The second experience that has had impact on me as a teacher came much more recently. The last two years teaching in Calgary, I shared my classroom with the master math teacher. The first year I was very resistent to her suggestions, especially if I had not asked for advise. The second year I realized that she was just trying to help me become the best math teacher I could possibly be. I enjoyed sitting in on her classes and seeing her at work. Seeing how she inspires the students to do their personal best and not try to live up to anyone elses standard. She is someone I truly wish to become like. I still contact her often when I am need a word of encouragement.
The second experience that has had impact on me as a teacher came much more recently. The last two years teaching in Calgary, I shared my classroom with the master math teacher. The first year I was very resistent to her suggestions, especially if I had not asked for advise. The second year I realized that she was just trying to help me become the best math teacher I could possibly be. I enjoyed sitting in on her classes and seeing her at work. Seeing how she inspires the students to do their personal best and not try to live up to anyone elses standard. She is someone I truly wish to become like. I still contact her often when I am need a word of encouragement.
Tuesday, September 14, 2010
Skemp Article
Relational Understanding and Instrumental Understanding - Richard R. Skemp
Relational versus instrumental understanding is a debate that will continue for a long time. It is an issue to which there is no easy answer. Each approach has value in and of itself, but the reality of the situation is not black and white. The need for relational understanding is apparent and necessary for a true understanding of mathematics, a true love and appreciation for it as a subject matter. However, the reality is that the curricular expectations, student expectations, parental expectations, provincial expectations, etc...don't necessarily allow for the application of a relational approach. There is too much in the curriculum to spend large amounts of time focusing on the connections behind the concepts. Often the students do not want to know the "why"; they are content with the formula and that's it. The best a teacher can do is strive to draw out those connections, whenever and wherever possible, that make math really meaningful without losing sight of the importance of instrumental understanding as well. It is an ongoing challenge in my own career to try and mesh the two as much as is possible given the current environmental restrictions.
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