Today we Dave Hewitt demonstrate a alternative method of teaching. A strategy that involve the whole class, one that is dramatic and like an orchestra. In the classroom we saw him tap the walls with his rulers and have the class add and subtract depending on the direction Dave was tapping in. They would all reply by speaking in unison. Clockwise was add, counterclockwise was subtract. His goal was to have the students see that pattern of what is going on.
Dave eventually introduced variables as a starting number. He drew a row of boxes on the chalk board and designated one as x and chose another box as the destination. He then demonstrated that he could do various combinations of left and right taps to get to the desired destination.
Example: x -> x + 2
This could be solved as three taps right and one left or two taps left and four right, etc
On the board he wrote:
x + 2 = x + 3 - 1 = x - 2 + 4 = x + 612 - 610 ...
He did this all without describing what '=' was too. He wanted them to learn by association.
Some good things about it is that it starts simple and goes to complex and it is an introduction to patters. Also, it is interactive and engaged the whole classroom. Also, the classroom was well managed.
However, there are many negatives to this teaching lesson. There would be a good number of children who will be very bored due to the extremely slow pace. There was no note taking involved which could be seen as both good and bad. Bad for some since a few people may get nervous not having anything written down to refer to. I would also like to see this orchestra method used for a more involved topic other than adding and subtracting which is something the students should have already learned.
Certain topics should be taught using traditional style (quadratic equation), some using constructivist style (geometry) and others by using this Orchestra method (counting). I guess the trouble is figuring out which is best suited for each lesson topic.
On a different note, I was talking to Mike after class and we were talking about alternative ways of teaching math. Us both being Physics students too, Mike brought up math labs (ie. Physics). I thought, why not? Especially kinematics, the math involved in physics is very simple and uses math from grades 8 and 9, and a little from grade 10 in the means of trig. I definitely want to explore this more, teaching math but using physics related questions for applications and word problems.
Wednesday, September 30, 2009
Saturday, September 26, 2009
Math Interview Reflections
After listening to the many groups talk about their interviews I have concluded that the most useful and interesting questions were the ones regarding teacher strategies and classroom management. All those questions asking students their feelings about math and such resulted in what I expected. Among students, not much has changed. Well, I am only 5 years removed from high school and that’s not a lot of time to result in large changes. Every school still has a wide range of students with various competencies in math which usually reflects how they grade their teachers. Also, most students don’t know what the purpose of math is other than a requirement for getting by high school or needed for doing taxes. If that was true though, math could be seen as useless since there are computer programs to do our taxes for us now a days. The applications and purposes of math must be better explained to the students during the lessons.
Before I talk about what I found interesting from some of the other groups I’ll go in detail about the responses I got from our own groups interview. The person we interview is a new teacher who just went through the UBC education program last year. He studied math and physics and got a full time job right after graduation at a fairly new school in Surrey.
The first question we asked was about his transition from the practicum to the full time job. He explained how the full time job is a lot more work. Lesson prepping is the most time consuming component of teaching and all of that has to be completed outside of the classroom. I didn’t expect the degree and quantity of work that he made it out to be. The number of different courses he has to teach his first year is amazing, and for all of them, new lesson plans. I didn’t ask, but hopefully he gets lots of help from his fellow educators.
The second question asked about the amount of time the class is devoted to lecture and how much towards seat work. He responded with 20-40 minutes of seat work depending on the lesson. He reinforced the notion that it is very important to vary the class with activities such as math bingo. Many students can’t last the full 75 minutes that a class goes for and need to get up and move around. This is similar to one of the other groups interviews. One teacher said they like to start with a bus driver game, move on to a challenge question, lecture for 25 minutes and end with some time for work. Variety seems to be a common trend among math teachers these days and I think it is a good thing. Another thing was peer tutoring. I like the idea of peer tutoring because lots of times students have different perspectives and methods on how to approach a problem which can be extremely useful. Also, it may be easier for some kids to ask for help from a peer than a teacher. In my old school one of my math teachers was trying to set up a peer tutor system where the tutors would get paid 10 dollars per hour from the school. I believe it got going after the year I graduated.
The third question asked about any visual methods he used in class. To him, algebra tiles are stupid and I’m going to have to agree with him. It depends on the subject. Subjects such as geometry and surface area where kids can physically measure objects are visual methods really useful. Consistencies of notation was the fourth question. His advice, follow the notation in the textbook. Students get lost easily with simple changes such as f(x) = g(x).
The final question asked about special needs students and the alternative teaching strategies used when working with them. As a new teacher he says it is extremely difficult. Be patient and offer time outside of class. Also, use peer tutors!
Keeping students interested is a must as a teacher. I liked one of the responses from one of the other groups. To keep the top students interested, give them challenging problems and have them act as tutors. As for the struggling students, as long as they don’t give up, you’re doing a good job. Keep giving them encouragements as much as possible.
From these interview sessions I have learned a lot of useful information which I should be able to use in my own teaching practices. To end this blog I will mention the secret final question of the interview: What is your favourite pie?
If you answered 3.14… you are on the right track.
Before I talk about what I found interesting from some of the other groups I’ll go in detail about the responses I got from our own groups interview. The person we interview is a new teacher who just went through the UBC education program last year. He studied math and physics and got a full time job right after graduation at a fairly new school in Surrey.
The first question we asked was about his transition from the practicum to the full time job. He explained how the full time job is a lot more work. Lesson prepping is the most time consuming component of teaching and all of that has to be completed outside of the classroom. I didn’t expect the degree and quantity of work that he made it out to be. The number of different courses he has to teach his first year is amazing, and for all of them, new lesson plans. I didn’t ask, but hopefully he gets lots of help from his fellow educators.
The second question asked about the amount of time the class is devoted to lecture and how much towards seat work. He responded with 20-40 minutes of seat work depending on the lesson. He reinforced the notion that it is very important to vary the class with activities such as math bingo. Many students can’t last the full 75 minutes that a class goes for and need to get up and move around. This is similar to one of the other groups interviews. One teacher said they like to start with a bus driver game, move on to a challenge question, lecture for 25 minutes and end with some time for work. Variety seems to be a common trend among math teachers these days and I think it is a good thing. Another thing was peer tutoring. I like the idea of peer tutoring because lots of times students have different perspectives and methods on how to approach a problem which can be extremely useful. Also, it may be easier for some kids to ask for help from a peer than a teacher. In my old school one of my math teachers was trying to set up a peer tutor system where the tutors would get paid 10 dollars per hour from the school. I believe it got going after the year I graduated.
The third question asked about any visual methods he used in class. To him, algebra tiles are stupid and I’m going to have to agree with him. It depends on the subject. Subjects such as geometry and surface area where kids can physically measure objects are visual methods really useful. Consistencies of notation was the fourth question. His advice, follow the notation in the textbook. Students get lost easily with simple changes such as f(x) = g(x).
The final question asked about special needs students and the alternative teaching strategies used when working with them. As a new teacher he says it is extremely difficult. Be patient and offer time outside of class. Also, use peer tutors!
Keeping students interested is a must as a teacher. I liked one of the responses from one of the other groups. To keep the top students interested, give them challenging problems and have them act as tutors. As for the struggling students, as long as they don’t give up, you’re doing a good job. Keep giving them encouragements as much as possible.
From these interview sessions I have learned a lot of useful information which I should be able to use in my own teaching practices. To end this blog I will mention the secret final question of the interview: What is your favourite pie?
If you answered 3.14… you are on the right track.
Battlegrounds School Response
This article talks about the two main stances in Mathematics Education. The two dichotomies are the Conservative approach and the Progressive approach. To keep it short, the Conservative method is what most people know of when they think math class, lectures, homework, memorization, tests and repeat. The Progressive approach is to have the students come to understand math, to see the patterns emerging from lived experiences and to stimulate problem solving skills.
In table M.1, one of the columns is what should drive curriculum design in public schooling. For Conservative it reads: for the masses, the need to do simple, practical calculations. For Progressive it reads: to expand learners’ modes of thought and develop flexible problem-solving abilities.
This article is pushing for the Progressive approach and lists complicating factors which are preventing the switch from Conservative to Progressive. It goes into different times of our history when a change of mathematics teaching was attempted.
I completely agree that people are math phobic in North America. Many people, particularly parents remember math being extremely difficult and meant only for a small elite or the nerds, and mad scientists who are unable to cope with the world of human interactions. Also, these people feel no shame at being incompetent at math. Children become scared of math before they even start and if they find it troubling they are told it’s ok. This fearful approach is the completely wrong approach towards math and has to be fixed.
Who said war wasn’t good for anything... Apparently, because of war, math curriculums were changed to better prepare students in math due to the perceived need of an increasingly scientific and technological populace. Between 1910 and 1940 a Progressivist Reform occurred due to World War I. John “Dewey challenged the Cartesian split between knowing and doing, or abstract and applied knowledge.” Dewey’s progressive education involved that students must form and test hypotheses and perceive patterns and relationships. His ideas only won acclaim in very progressive schools.
In the 1960s due to the USSR beating the US in the space race, “The New Math” was created. This was another progressive teaching method but it didn’t go over very well. Many math teachers themselves did not know this new math and were incapable of teaching. The new math “supported understanding over fluency,” and “inquiry and sense-making over absorbing and applying facts.
In some ways conservative methods of teaching math works. It works for some but not for all and because of that, people have been trying to change the curriculum for the better. But what gets in the way of this change? The math illiterate with their fears. Also, traditionalists who claim that children are being short-changed by teachers experimenting with their education when they use progressive methods.
The traditional methods of teaching works for some students but still too many are being left behind. Progressive methods must be integrated with the Conservative methods to accommodate a larger portion of students.
In table M.1, one of the columns is what should drive curriculum design in public schooling. For Conservative it reads: for the masses, the need to do simple, practical calculations. For Progressive it reads: to expand learners’ modes of thought and develop flexible problem-solving abilities.
This article is pushing for the Progressive approach and lists complicating factors which are preventing the switch from Conservative to Progressive. It goes into different times of our history when a change of mathematics teaching was attempted.
I completely agree that people are math phobic in North America. Many people, particularly parents remember math being extremely difficult and meant only for a small elite or the nerds, and mad scientists who are unable to cope with the world of human interactions. Also, these people feel no shame at being incompetent at math. Children become scared of math before they even start and if they find it troubling they are told it’s ok. This fearful approach is the completely wrong approach towards math and has to be fixed.
Who said war wasn’t good for anything... Apparently, because of war, math curriculums were changed to better prepare students in math due to the perceived need of an increasingly scientific and technological populace. Between 1910 and 1940 a Progressivist Reform occurred due to World War I. John “Dewey challenged the Cartesian split between knowing and doing, or abstract and applied knowledge.” Dewey’s progressive education involved that students must form and test hypotheses and perceive patterns and relationships. His ideas only won acclaim in very progressive schools.
In the 1960s due to the USSR beating the US in the space race, “The New Math” was created. This was another progressive teaching method but it didn’t go over very well. Many math teachers themselves did not know this new math and were incapable of teaching. The new math “supported understanding over fluency,” and “inquiry and sense-making over absorbing and applying facts.
In some ways conservative methods of teaching math works. It works for some but not for all and because of that, people have been trying to change the curriculum for the better. But what gets in the way of this change? The math illiterate with their fears. Also, traditionalists who claim that children are being short-changed by teachers experimenting with their education when they use progressive methods.
The traditional methods of teaching works for some students but still too many are being left behind. Progressive methods must be integrated with the Conservative methods to accommodate a larger portion of students.
Monday, September 21, 2009
Response to Heather J. Robinson Reading
"First Comes Learning," is the motto at Robinson's school and it is a good motto.
Before I begin talking about what I like and dislike about her changes in teaching methods I will first talk about those grades listed on Table 4.1. Am I reading it correctly?! From my understanding, in the final exam 56 out of 64 students failed the exam when she did primarily lecture style lessons. That's 88%. When she changed over to the new instructional method, the semester B failure percentage was 38% and semester A failure rate was 24%. My math teachers all taught similarly to Robinson's original teaching style and I'm positive the failure rate was no where near 88%. Maybe it was due to the demography of the area she taught in?
Robinson really changed from one teaching style to the extreme other end of the spectrum. What I get from this article is that just like how different students require different methods of being taught to learn, some teachers are much better at teaching one way than another. Lecture style teaching has been used for a very long time in high schools and for many teachers I bet they saw success year in and year out. Does this mean they are better at teaching? Who knows!?
The problem with lecture style teaching is that there will always be some, the number of students varying each year, who cannot effectively learn through that method. Robinson's goal is to "leave no child behind." However, I think she's a bit excessive. I'm not sure exactly how many hours a week she teaches for but since it is semester I'm assuming about 5 or 6. Only 1 of those hours she states as using for lectures. Wow, that is an extremely small amount of time. I cannot even conceive of teaching like that since I have never experienced anything like it before. If I go to my practicum it would be awesome if my supervisor taught like that because I would love to see it in action and see how it is possible.
Some things I really liked about her school and teaching methods is the time reserved after school for homework and getting help and the peer tutoring that developed. That 45 minutes reserved for getting help from the teachers would definitely be really useful for many students. But at the same time, for the students that don't need help and have to wait around before club activities begin have it a bit rough. Kind of like punishing them for doing well. Peer tutoring is good. When I teach I would like to set up some form of peer tutoring outside of class under the supervision of teachers.
Time to bring this all to a close. Robinson has some great ideas but I think she's going a bit overboard. She has seen great improvement from changing teaching styles in just one year but is it because she was not a very effective lecturer, the demography of the city or the fact that this new teaching style really suits her and her sample of students? For a math class, less than 20% of the course being lecture format seems a bit small. Especially for grades 11 and 12 I have a hard time seeing all the material being covered by only lecturing for about 10 or 12 minutes a day.
I'll have to wait until I teach a class for the first time and find out for myself. What will work and what will fail miserably. Time will tell.
Before I begin talking about what I like and dislike about her changes in teaching methods I will first talk about those grades listed on Table 4.1. Am I reading it correctly?! From my understanding, in the final exam 56 out of 64 students failed the exam when she did primarily lecture style lessons. That's 88%. When she changed over to the new instructional method, the semester B failure percentage was 38% and semester A failure rate was 24%. My math teachers all taught similarly to Robinson's original teaching style and I'm positive the failure rate was no where near 88%. Maybe it was due to the demography of the area she taught in?
Robinson really changed from one teaching style to the extreme other end of the spectrum. What I get from this article is that just like how different students require different methods of being taught to learn, some teachers are much better at teaching one way than another. Lecture style teaching has been used for a very long time in high schools and for many teachers I bet they saw success year in and year out. Does this mean they are better at teaching? Who knows!?
The problem with lecture style teaching is that there will always be some, the number of students varying each year, who cannot effectively learn through that method. Robinson's goal is to "leave no child behind." However, I think she's a bit excessive. I'm not sure exactly how many hours a week she teaches for but since it is semester I'm assuming about 5 or 6. Only 1 of those hours she states as using for lectures. Wow, that is an extremely small amount of time. I cannot even conceive of teaching like that since I have never experienced anything like it before. If I go to my practicum it would be awesome if my supervisor taught like that because I would love to see it in action and see how it is possible.
Some things I really liked about her school and teaching methods is the time reserved after school for homework and getting help and the peer tutoring that developed. That 45 minutes reserved for getting help from the teachers would definitely be really useful for many students. But at the same time, for the students that don't need help and have to wait around before club activities begin have it a bit rough. Kind of like punishing them for doing well. Peer tutoring is good. When I teach I would like to set up some form of peer tutoring outside of class under the supervision of teachers.
Time to bring this all to a close. Robinson has some great ideas but I think she's going a bit overboard. She has seen great improvement from changing teaching styles in just one year but is it because she was not a very effective lecturer, the demography of the city or the fact that this new teaching style really suits her and her sample of students? For a math class, less than 20% of the course being lecture format seems a bit small. Especially for grades 11 and 12 I have a hard time seeing all the material being covered by only lecturing for about 10 or 12 minutes a day.
I'll have to wait until I teach a class for the first time and find out for myself. What will work and what will fail miserably. Time will tell.
Memorable Math Teachers
Teachers from my past...
Mrs. Law from my high school, how could I ever forget her. I believe she taught me in grade 9, 11, 12 and calculus. 4 out of 6 math courses, there is no way I would not remember her unlike my grade 8 and 10 math teachers. Anyways, as a math teacher, I thought she was good although I didn't have anyone to compare her with. I like math, I was good at math, math was my thing in high school.
Many of my class mates on the other hand thought differently then me. Their complaint was that she just lectured day in and day out. And it's true, that is what she did. For me though, that was all I needed from her, she would lecture I would take it in and work it out in my head and if I knew the stuff I would go ahead and do homework in class. I can understand where my class mates are coming from though. Pure lecture was not enough for many of them and they needed something more or different.
Another teacher that comes to mind is Anmar Khadra from UBC. I think the course was for either 1st or 2nd order PDE's. That guy had so much energy and had such passion when he taught our class. He wanted everyone to get involved and there was no way anyone would be able to get away with sleeping in that class. He did a good job in teaching too, at least for me.
In both cases, a lecture teaching style was used and they both relied on instrumental learning for the subjects. Before I came to the education program I didn't know there was a different way to teach math. I still think instrumental learning and lecture style teaching is necessary in math, but I don't want to be like my past teachers and rely solely on those techniques. I just finished reading the Robinson article and she really went from one extreme of teaching to the other. I'll have to find the correct balance for myself.
Mrs. Law from my high school, how could I ever forget her. I believe she taught me in grade 9, 11, 12 and calculus. 4 out of 6 math courses, there is no way I would not remember her unlike my grade 8 and 10 math teachers. Anyways, as a math teacher, I thought she was good although I didn't have anyone to compare her with. I like math, I was good at math, math was my thing in high school.
Many of my class mates on the other hand thought differently then me. Their complaint was that she just lectured day in and day out. And it's true, that is what she did. For me though, that was all I needed from her, she would lecture I would take it in and work it out in my head and if I knew the stuff I would go ahead and do homework in class. I can understand where my class mates are coming from though. Pure lecture was not enough for many of them and they needed something more or different.
Another teacher that comes to mind is Anmar Khadra from UBC. I think the course was for either 1st or 2nd order PDE's. That guy had so much energy and had such passion when he taught our class. He wanted everyone to get involved and there was no way anyone would be able to get away with sleeping in that class. He did a good job in teaching too, at least for me.
In both cases, a lecture teaching style was used and they both relied on instrumental learning for the subjects. Before I came to the education program I didn't know there was a different way to teach math. I still think instrumental learning and lecture style teaching is necessary in math, but I don't want to be like my past teachers and rely solely on those techniques. I just finished reading the Robinson article and she really went from one extreme of teaching to the other. I'll have to find the correct balance for myself.
Sunday, September 20, 2009
Booppps Lesson Plan - My Reflections
The micro teaching assignment has come to a close and now I must reflect on what I learned. I will begin by giving my impressions on the lesson immediately after presenting.
What I thought went well:
The props were well prepared and I clearly stated the objectives. I discovered that most everyone had had some experience with baseball but none had pitched before. I had everyone participate by giving each person a baseball to hold. As I showed the different grips, I had them follow along, making sure each person had the correct grip before continuing. For each grip, I tried to give a really brief explanation on how they worked, however I did not linger very long on each since I had a lot of grips to get through.
The first grip I showed them was the 4-seam fastball. After showing a total of 3 grips I tested their knowledge by asking them each to again show me the 4-seam fastball. I explained that if you are going to remember anything from today, remember this grip because whenever you throw a ball of around the same size, this is the proper grip to use. One of my students then said "really? That doesn't seem natural to me. When I throw a ball, the natural way I grip it is like this." This actually led into the next grip I was going to show because the grip he displayed was a palm ball, a variation of the change up. I thought it was cool how one students comment/question allowed the flow of the lesson to run more smoothly.
How would I improve the lesson?:
I needed more time. To solve this problem, the best method would be to cut down the number of grips being shown. If I were to do this lesson again, I would not show the 2-seam fastball and the splitter, giving more time to show the curve ball. I felt a bit rushed and with more time (or less grips) this problem would be solved. I would also be able to add a post test at the end of the presentation and have a more flushed out summary.
Reflections based on my peers' feedback:
My peers feedback pretty much coincides with my own evaluation. Time management. They would have liked to have seen more time spent on the curve ball. I agree with them. Now that I think about it, the curve ball is one of the most interesting pitches in baseball. The way I set up my lesson was showing the different grips in the order that I learned them when I was young (except the splitter). My peers would have liked to have seen more closure to the topic and to include a post-test at the end.
One of my favorite comments I received was to provide more info on why each grip/throw is important and how they are used in baseball strategy. I liked that one, explaining a little bit about the strategy of baseball would have been a good edition to the lesson.
What I thought went well:
The props were well prepared and I clearly stated the objectives. I discovered that most everyone had had some experience with baseball but none had pitched before. I had everyone participate by giving each person a baseball to hold. As I showed the different grips, I had them follow along, making sure each person had the correct grip before continuing. For each grip, I tried to give a really brief explanation on how they worked, however I did not linger very long on each since I had a lot of grips to get through.
The first grip I showed them was the 4-seam fastball. After showing a total of 3 grips I tested their knowledge by asking them each to again show me the 4-seam fastball. I explained that if you are going to remember anything from today, remember this grip because whenever you throw a ball of around the same size, this is the proper grip to use. One of my students then said "really? That doesn't seem natural to me. When I throw a ball, the natural way I grip it is like this." This actually led into the next grip I was going to show because the grip he displayed was a palm ball, a variation of the change up. I thought it was cool how one students comment/question allowed the flow of the lesson to run more smoothly.
How would I improve the lesson?:
I needed more time. To solve this problem, the best method would be to cut down the number of grips being shown. If I were to do this lesson again, I would not show the 2-seam fastball and the splitter, giving more time to show the curve ball. I felt a bit rushed and with more time (or less grips) this problem would be solved. I would also be able to add a post test at the end of the presentation and have a more flushed out summary.
Reflections based on my peers' feedback:
My peers feedback pretty much coincides with my own evaluation. Time management. They would have liked to have seen more time spent on the curve ball. I agree with them. Now that I think about it, the curve ball is one of the most interesting pitches in baseball. The way I set up my lesson was showing the different grips in the order that I learned them when I was young (except the splitter). My peers would have liked to have seen more closure to the topic and to include a post-test at the end.
One of my favorite comments I received was to provide more info on why each grip/throw is important and how they are used in baseball strategy. I liked that one, explaining a little bit about the strategy of baseball would have been a good edition to the lesson.
Booppps Lesson Plan - Peer Evaluation
Hello and welcome back to Thiessen's Math Blog. My last blog detailed my lesson plan on how a pitcher grips a baseball. My group consisted of 3 other people. I taught and was evaluated by Erwin, Ralph and Vincent. Below is a summary of what they said:
"The learning objectives were clear. Greg told us that we would be learning some of the various grips that a pitcher would use in a game. He bridged the topic by showing his interest in baseball and asking about our prior knowledge with the topic. We each said we played a little baseball but Greg then asked we if any of us had been pitchers. None of us had. Greg's lesson included a participatory activity by providing us each with a baseball to practice the various grips. In the middle of the lesson he asked us a question testing our memory on the fastball grip. He concluded the presentation by explaining how grips can change the rotation and speed of the ball. Overall it was a smoothly run hands on lesson. He showed enthusiasm for the subject and kept our attention.
"Some things Greg could work on is including more time at the end for a post-test to check in on our learning. He should also provide more info on why different grips are important and how they are used in baseball strategy. He needs a bit more closure to the topic and a little less complicated working with the different types of fastballs. The order of presentation of the grips could have been modified a bit too. More time should have been given to the curve ball."
"The learning objectives were clear. Greg told us that we would be learning some of the various grips that a pitcher would use in a game. He bridged the topic by showing his interest in baseball and asking about our prior knowledge with the topic. We each said we played a little baseball but Greg then asked we if any of us had been pitchers. None of us had. Greg's lesson included a participatory activity by providing us each with a baseball to practice the various grips. In the middle of the lesson he asked us a question testing our memory on the fastball grip. He concluded the presentation by explaining how grips can change the rotation and speed of the ball. Overall it was a smoothly run hands on lesson. He showed enthusiasm for the subject and kept our attention.
"Some things Greg could work on is including more time at the end for a post-test to check in on our learning. He should also provide more info on why different grips are important and how they are used in baseball strategy. He needs a bit more closure to the topic and a little less complicated working with the different types of fastballs. The order of presentation of the grips could have been modified a bit too. More time should have been given to the curve ball."
Wednesday, September 16, 2009
Booppps Lesson Plan - Gripping a Baseball
For this micro teaching assignment I will be instructing the students on how a pitcher grips a baseball. I will be giving each of my students a baseball and they can follow me as I show and explain the various grips. I will tell them why the pitch is used and how it works. I will be drawing lines on each of the baseballs to make it more evident on how to hold the ball.
Pitching Grips for a Baseball - Teaching the Booppps Way
For the players, baseball is the loneliest team sport in North America. Why is that? In sports like hockey, football, and the other football each of the players constantly come in contact with each other. In baseball, when out in the field, rarely do the players get within a foot of each other. Every play begins with the man on the mound, the pitcher.
But even though the pitcher is all alone on that mound, he is dependent and can rely on the catcher calling the pitches and the 7 players supporting him from behind. Also, a pitcher is not without his weapons. A variety of pitches to fool the batters.
Bridge - Baseball is awesome! Particularly pitching.
Teaching Objectives - To get everyone participating. Time permitting I will try and show the students the following pitches: 4-seam fastball, 2-seam fastball, splitter, the 3 change-ups, curve-ball, and slider. The most important ones (in my opinion) are the 4-seam, change-ups and curve so I will get those out of the way first.
Learning Objectives - To have the students remember how to grip a 4-seam fastball and at least 1 other grip I showed them.
Pretest - Ask them about their baseball experience and if any had played baseball in the past.
Participating Activity - I will demonstrate each grip one at a time and have each person follow my lead with their own baseballs.
Post Test - I will ask each of them to demonstrate to me a 4-seam fastball and one other one I randomly select.
Summary - If you ever have to throw a baseball or similar sized ball in the future, hopefully you remember the 4-seam fastball grip. It is the most effective for any type of throwing of a ball around that size.
Pitching Grips for a Baseball - Teaching the Booppps Way
For the players, baseball is the loneliest team sport in North America. Why is that? In sports like hockey, football, and the other football each of the players constantly come in contact with each other. In baseball, when out in the field, rarely do the players get within a foot of each other. Every play begins with the man on the mound, the pitcher.
But even though the pitcher is all alone on that mound, he is dependent and can rely on the catcher calling the pitches and the 7 players supporting him from behind. Also, a pitcher is not without his weapons. A variety of pitches to fool the batters.
Bridge - Baseball is awesome! Particularly pitching.
Teaching Objectives - To get everyone participating. Time permitting I will try and show the students the following pitches: 4-seam fastball, 2-seam fastball, splitter, the 3 change-ups, curve-ball, and slider. The most important ones (in my opinion) are the 4-seam, change-ups and curve so I will get those out of the way first.
Learning Objectives - To have the students remember how to grip a 4-seam fastball and at least 1 other grip I showed them.
Pretest - Ask them about their baseball experience and if any had played baseball in the past.
Participating Activity - I will demonstrate each grip one at a time and have each person follow my lead with their own baseballs.
Post Test - I will ask each of them to demonstrate to me a 4-seam fastball and one other one I randomly select.
Summary - If you ever have to throw a baseball or similar sized ball in the future, hopefully you remember the 4-seam fastball grip. It is the most effective for any type of throwing of a ball around that size.
Relational and Instrumental Understanding - Response to Skemp Article
We were given an article by Richard R. Skemp to read outside of class. The name of the article was: Relational Understanding and Instrumental Understanding. The paper was first published in 'Mathematics Teaching', 77, 20-26, (1976). Wow that is old. When he wrote this, Richard R. Skemp was part of the Department of Education at the University of Warwick.
A quick breakdown, Instrumental Understanding is understanding without knowing the why behind whatever you are learning. You are given a tool or equation to solve a problem and then you use that tool to solve it. Relational Understanding is understanding by relating the topic to things you already know. Using reason and deduction to understand, giving the person a tool box of knowledge to solve a problem.
So, the assignment was to read the 15 page paper, select 5 quotes and respond. Here it is, enjoy thoroughly!
As a student, when it came to math, I would categorize myself into the relational understanding group. But it was not as if I would not do well in a topic if it was taught instrumentally. Whenever that occurred, my brain would just store that information somewhere in my head where it could churn until eventually connections would be made and the ‘why’ behind the topic revealed itself on its own. In high school, those connections rarely took much time. However, I realize that not everyone is math orientated and capable of making rational connections on their own and therefore require a teacher to show them.
“…for many pupils and their teachers the possession of such a rule, and the ability to use it, was what they meant by ‘understanding.’ – page 2, lines 11-13
As Skemp implies, memorizing does not equal understanding. In math, a teacher could give out formulas and rules and if a student managed to memorize the two he would probably do well on an exam. Not great, but well. To many, this result would be satisfactory, but this should not be. Pure memorization rarely becomes long term knowledge with the formulas and rules trickling away from the students minds after the course in question has ended. Little do they expect the hole they are digging for themselves. As math progresses and gets more involved each year, more formulas and rules come into play which overlaps what was learned previously. The result: overwhelmed students who dread math.
“I used to think that math teachers were all teaching the same subject, some doing it better than others.” – page 6, lines 17-19
“…there are two effectively different subjects being taught under the same name, ‘mathematics’.” – page 6, lines 20-21
Skemp’s article impressed me since it really made clear the difference between rational and instrumental understanding and reinforced the importance of rational understanding. He made me take another look at myself and realize that lots of my knowledge remains at “the intuitive level” [page 13, line 5] and the importance of taking that extra time to readdress those topics.
“…if people get satisfaction from relational understanding, they may not only try to understand relationally new material which is put before them, but also actively seek out new material and explore new areas…” – page 10, lines 22-26
Instrumental understanding is very one dimensional. Facts just are and there exists no depth to their meaning. Relational understanding fills that depth and lets the student know that there is indeed a purpose or a reason to what is being taught. Understanding often equals interesting and when something is interesting desires to learn more often arise.
“From the marks he makes on paper, it is very hard to make valid inference about the mental processes by which a pupil has been led to make them; hence the difficulty of sound examining in mathematics.” – page 12, lines 4-8
Skemp makes a good point; it is very challenging to discover all of the learning styles of every student in the classroom. Even if you did discover it, could you accommodate every learning style? From reading this article I would conclude that relational teaching should be used since it accommodates both types of students and hopefully the instrumental students would one day discover there is more to math and desire to know the reasons behind the formulas.
“…learning relational mathematics consists of building up a conceptual structure from which its possessor can produce an unlimited number of plans for getting from any starting point within his schema to any finishing point.” – page 15, line 36-page 16, line 1
Relational teaching best benefits the students. In math, if a student understands the reasons and processes, he can more easily apply his knowledge when problems he has not seen before arise. Also, there may be more than one method to solving a problem and relational understanding would allow the student to possibly find those paths and reach the desired solution.
A quick breakdown, Instrumental Understanding is understanding without knowing the why behind whatever you are learning. You are given a tool or equation to solve a problem and then you use that tool to solve it. Relational Understanding is understanding by relating the topic to things you already know. Using reason and deduction to understand, giving the person a tool box of knowledge to solve a problem.
So, the assignment was to read the 15 page paper, select 5 quotes and respond. Here it is, enjoy thoroughly!
As a student, when it came to math, I would categorize myself into the relational understanding group. But it was not as if I would not do well in a topic if it was taught instrumentally. Whenever that occurred, my brain would just store that information somewhere in my head where it could churn until eventually connections would be made and the ‘why’ behind the topic revealed itself on its own. In high school, those connections rarely took much time. However, I realize that not everyone is math orientated and capable of making rational connections on their own and therefore require a teacher to show them.
“…for many pupils and their teachers the possession of such a rule, and the ability to use it, was what they meant by ‘understanding.’ – page 2, lines 11-13
As Skemp implies, memorizing does not equal understanding. In math, a teacher could give out formulas and rules and if a student managed to memorize the two he would probably do well on an exam. Not great, but well. To many, this result would be satisfactory, but this should not be. Pure memorization rarely becomes long term knowledge with the formulas and rules trickling away from the students minds after the course in question has ended. Little do they expect the hole they are digging for themselves. As math progresses and gets more involved each year, more formulas and rules come into play which overlaps what was learned previously. The result: overwhelmed students who dread math.
“I used to think that math teachers were all teaching the same subject, some doing it better than others.” – page 6, lines 17-19
“…there are two effectively different subjects being taught under the same name, ‘mathematics’.” – page 6, lines 20-21
Skemp’s article impressed me since it really made clear the difference between rational and instrumental understanding and reinforced the importance of rational understanding. He made me take another look at myself and realize that lots of my knowledge remains at “the intuitive level” [page 13, line 5] and the importance of taking that extra time to readdress those topics.
“…if people get satisfaction from relational understanding, they may not only try to understand relationally new material which is put before them, but also actively seek out new material and explore new areas…” – page 10, lines 22-26
Instrumental understanding is very one dimensional. Facts just are and there exists no depth to their meaning. Relational understanding fills that depth and lets the student know that there is indeed a purpose or a reason to what is being taught. Understanding often equals interesting and when something is interesting desires to learn more often arise.
“From the marks he makes on paper, it is very hard to make valid inference about the mental processes by which a pupil has been led to make them; hence the difficulty of sound examining in mathematics.” – page 12, lines 4-8
Skemp makes a good point; it is very challenging to discover all of the learning styles of every student in the classroom. Even if you did discover it, could you accommodate every learning style? From reading this article I would conclude that relational teaching should be used since it accommodates both types of students and hopefully the instrumental students would one day discover there is more to math and desire to know the reasons behind the formulas.
“…learning relational mathematics consists of building up a conceptual structure from which its possessor can produce an unlimited number of plans for getting from any starting point within his schema to any finishing point.” – page 15, line 36-page 16, line 1
Relational teaching best benefits the students. In math, if a student understands the reasons and processes, he can more easily apply his knowledge when problems he has not seen before arise. Also, there may be more than one method to solving a problem and relational understanding would allow the student to possibly find those paths and reach the desired solution.
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