Disclaimer: I haven't written poetry in over 13 years, and I wasn't any good at it back then either.
Division by Zero
I have a proof that two equals one.
It's mathematical.
No, it's mathtastical.
I use it to challenge the students.
They'll check the algebra,
and question the logic.
But the secret should be obvious,
Division by zero.
Reflections
Timed writing and poetry as a pedagogical exercise helped me to reflect on how difficult mathematics may be for some children, since poetry and "free writing" are some of my weakest skills. Aside from putting me outside of my comfort zone, I do not see this as an effective tool for teaching mathematics or sciences, but I am open to further interpretation of this exercise by others.
Thursday, October 22, 2009
Wednesday, October 14, 2009
Reflection on Kinemalgebratics!
MAED 314a-301 INTRODUCTION TO ALGEBRA THOUGH KINEMATICS (aka "KINEMALGEBRATICS")
I would initially like to take a moment and thank Amelia and Erwin for supervising the ball-rolling activity. Although I was managing the other group in their derivations of the kinematics equations and building their concept of algebra, I could hear how much fun university students were having with a simple activity, and it was overwhelmingly reflected in their reviews and comments. I take great pride in knowing that this mathematics activity could easily be the highlight of any grade 8 students day.
Also, many thanks to Erwin for his fantastic sign. That small detail was the highlight of my day. Not that today was a bad day... just otherwise uneventful. :P
As a mathematician, it would hurt me not to include a statistical analysis of my peer feedback, so I'll just get that out of the way now. Each topic is listed by category (Clarity, Active learning, and Connected mathematical ideas) and simply the assessment item number, to save space. I've included the average (AVG) and the standard deviation (STDEV), as well as my own personal assessment (MIKE).
CLARITY 1 >> AVG 4.36 >> STDEV 0.48 >> MIKE 4.00
CLARITY 2 >> AVG 4.68 >> STDEV 0.44 >> MIKE 4.00
CLARITY 3 >> AVG 4.80 >> STDEV 0.40 >> MIKE 4.00
ACTIVE 1 >> AVG 4.82 >> STDEV 0.39 >> MIKE 5.00
ACTIVE 2 >> AVG 4.73 >> STDEV 0.45 >> MIKE 5.00
ACTIVE 3 >> AVG 4.50 >> STDEV 0.67 >> MIKE 4.00
CONNECT 1 >> AVG 4.36 >> STDEV 0.48 >> MIKE 1.00
CONNECT 2 >> AVG 4.45 >> STDEV 0.66 >> MIKE 3.00
My personal assessment reflects how well I think our group did on planning and executing this activity. I believe that every group member really helped to make this a fantastic group project and a great learning experience for the "students" in the classroom.
There should be two items that stand out immediately to the casual observer. First, I scored our group 1/5 for CONNECT 1 (The instructors offered activities that connected to other areas of math). I would like to explicitly state that although this is a "low" mark, I do not believe it represents a failure of any sort, but simply a narrow focus on a specific 15 minute lesson.
Second, I scored our group 3/5 for CONNECT 2 (The lesson connected to other areas of life & culture). I believe that given the 15 minutes, this is a sufficient undertaking. However, if we had been given 30 minutes, I would have liked to introduce more complicated algebra using kinematics (d = d0 + v*t). Simply put, these low scores are not a failure on the part of the group, but instead a reflection of the time constraint.
Next, I would like to address some of the more prevalent "constructive criticism" comments that were listed on the peer reviews. The first comment deals with coordination of the two groups. Unfortunately I ran a half minute behind on the first group, and the second group had to wait until we finished. Although this does not seem like very long, I'm sure it would be an eternity for a grade 8 student. If we were doing an activity like this in a class with multiple instructors, I think having an official "time keeper" to give 2min and 1min warnings would help everyone (read: Mike B.) to pace their lessons appropriately.
The second "constructive criticism" was that we should have better outlined our objectives to the class before beginning. I am still on the fence about this comment, since although I know that many students, myself included, prefer an ordered and clearly laid out lesson structure, I do believe that the world "Algebra" might invoke terror in young students, and I really do like the idea of teaching it implicitly without actually naming the technique until the students are comfortable with the material. Any thoughts on this matter?
I would initially like to take a moment and thank Amelia and Erwin for supervising the ball-rolling activity. Although I was managing the other group in their derivations of the kinematics equations and building their concept of algebra, I could hear how much fun university students were having with a simple activity, and it was overwhelmingly reflected in their reviews and comments. I take great pride in knowing that this mathematics activity could easily be the highlight of any grade 8 students day.
Also, many thanks to Erwin for his fantastic sign. That small detail was the highlight of my day. Not that today was a bad day... just otherwise uneventful. :P
As a mathematician, it would hurt me not to include a statistical analysis of my peer feedback, so I'll just get that out of the way now. Each topic is listed by category (Clarity, Active learning, and Connected mathematical ideas) and simply the assessment item number, to save space. I've included the average (AVG) and the standard deviation (STDEV), as well as my own personal assessment (MIKE).
CLARITY 1 >> AVG 4.36 >> STDEV 0.48 >> MIKE 4.00
CLARITY 2 >> AVG 4.68 >> STDEV 0.44 >> MIKE 4.00
CLARITY 3 >> AVG 4.80 >> STDEV 0.40 >> MIKE 4.00
ACTIVE 1 >> AVG 4.82 >> STDEV 0.39 >> MIKE 5.00
ACTIVE 2 >> AVG 4.73 >> STDEV 0.45 >> MIKE 5.00
ACTIVE 3 >> AVG 4.50 >> STDEV 0.67 >> MIKE 4.00
CONNECT 1 >> AVG 4.36 >> STDEV 0.48 >> MIKE 1.00
CONNECT 2 >> AVG 4.45 >> STDEV 0.66 >> MIKE 3.00
My personal assessment reflects how well I think our group did on planning and executing this activity. I believe that every group member really helped to make this a fantastic group project and a great learning experience for the "students" in the classroom.
There should be two items that stand out immediately to the casual observer. First, I scored our group 1/5 for CONNECT 1 (The instructors offered activities that connected to other areas of math). I would like to explicitly state that although this is a "low" mark, I do not believe it represents a failure of any sort, but simply a narrow focus on a specific 15 minute lesson.
Second, I scored our group 3/5 for CONNECT 2 (The lesson connected to other areas of life & culture). I believe that given the 15 minutes, this is a sufficient undertaking. However, if we had been given 30 minutes, I would have liked to introduce more complicated algebra using kinematics (d = d0 + v*t). Simply put, these low scores are not a failure on the part of the group, but instead a reflection of the time constraint.
Next, I would like to address some of the more prevalent "constructive criticism" comments that were listed on the peer reviews. The first comment deals with coordination of the two groups. Unfortunately I ran a half minute behind on the first group, and the second group had to wait until we finished. Although this does not seem like very long, I'm sure it would be an eternity for a grade 8 student. If we were doing an activity like this in a class with multiple instructors, I think having an official "time keeper" to give 2min and 1min warnings would help everyone (read: Mike B.) to pace their lessons appropriately.
The second "constructive criticism" was that we should have better outlined our objectives to the class before beginning. I am still on the fence about this comment, since although I know that many students, myself included, prefer an ordered and clearly laid out lesson structure, I do believe that the world "Algebra" might invoke terror in young students, and I really do like the idea of teaching it implicitly without actually naming the technique until the students are comfortable with the material. Any thoughts on this matter?
Tuesday, October 13, 2009
Introduction to Algebra using Kinematics
MAED 314a-301
INTRODUCTION TO ALGEBRA
BRIDGE: Today in Math we are going to be doing an activity involving a ball and measurements!
TEACHER OBJECTIVES: To teach algebra implicitly using a Kinematics Lab.
STUDENT OBJECTIVES: Basic understanding of algebra and the ability to apply it to real world situations involving simple kinematics (v=d/t).
PRE-TEST: Intentionally none done, as we don't want to "tip our hat".
PARTICIPATION: Two tables.
1)The first table is a "Kinematics Shout-Out", where the students derive the basic Kinematics equations and put them in algebraic notation. We will be using the equation v=d/t and solving for the variables v, d, t using repetition.
2)The second table is a "Mini-Lab" with a ball rolling a set distance against a wall. The students will measure the distance from a line to the wall, and measure the time it takes the ball to get to the wall. This will then later be applied to the equation learned previously.
Required Materials:
* Masking tape
* Measuring tape
* Stop watches
* Balls
POST-TEST: Students will use their measurements and their new equations to calculate the speeds that the balls were rolling using v=d/t
SUMMARY: Surprise... you just learned algebra!
Write down the equation you learned and how you could apply this to another real life situation for next class.
INTRODUCTION TO ALGEBRA
BRIDGE: Today in Math we are going to be doing an activity involving a ball and measurements!
TEACHER OBJECTIVES: To teach algebra implicitly using a Kinematics Lab.
STUDENT OBJECTIVES: Basic understanding of algebra and the ability to apply it to real world situations involving simple kinematics (v=d/t).
PRE-TEST: Intentionally none done, as we don't want to "tip our hat".
PARTICIPATION: Two tables.
1)The first table is a "Kinematics Shout-Out", where the students derive the basic Kinematics equations and put them in algebraic notation. We will be using the equation v=d/t and solving for the variables v, d, t using repetition.
2)The second table is a "Mini-Lab" with a ball rolling a set distance against a wall. The students will measure the distance from a line to the wall, and measure the time it takes the ball to get to the wall. This will then later be applied to the equation learned previously.
Required Materials:
* Masking tape
* Measuring tape
* Stop watches
* Balls
POST-TEST: Students will use their measurements and their new equations to calculate the speeds that the balls were rolling using v=d/t
SUMMARY: Surprise... you just learned algebra!
Write down the equation you learned and how you could apply this to another real life situation for next class.
Sunday, October 11, 2009
MAED314
CITIZENSHIP EDUCATION
MICHAEL BAYER
"If we think about it, we begin to realize that there is much in our society which has been quantified - the gross national product, the DOW index, unemployment rates, the weather forecast, the smog index, the quality of a hockey player's game performance, a student's understanding of literature, and intelligence itself, with the Intelligence Quotient."
I think this is a really important statement. I believe that teachers should encourage students interest in mathematics by relating new concepts to familiar uses of those concepts, whether they be basic kinematics or statistical analysis. Every new concept should immediately have an application presented. I believe that by making mathematics more "friendly" to the general student, I will foster interest in the subject.
"Mathematics is one of the greatest cultural and intellectual achievements of humankind." - NCTM, 2000
Unfortunately the preceding statement makes mathematics seem to be out of the grasp of the general student, and implies that only the most adept student will ever progress in mathematics, which will in turn make them the elite of humankind. I feel this is a very dangerous statement to make, which may lead to students becoming discouraged in even attempting to learn the subject.
"Teaching students to identify and pose problems, to explain themselves in terms others can understand and to question the invisible structures of mathematics is key to developing informed, active and critical citizens."
I agree completely with this statement. As a mathematics teacher, I believe an interesting form of assessment would be to have students work together in groups to develop a list of questions based on the material already covered, submit this list to the teacher for approval, and in turn have the questions returned to the students in the form of a group homework assignment. Groups would work together to create questions difficult enough that other groups were unable to answer them, which in turn would foster deeper understanding from the problem posers and develop their social "professional" interactions and problem-solving skills.
CITIZENSHIP EDUCATION
MICHAEL BAYER
"If we think about it, we begin to realize that there is much in our society which has been quantified - the gross national product, the DOW index, unemployment rates, the weather forecast, the smog index, the quality of a hockey player's game performance, a student's understanding of literature, and intelligence itself, with the Intelligence Quotient."
I think this is a really important statement. I believe that teachers should encourage students interest in mathematics by relating new concepts to familiar uses of those concepts, whether they be basic kinematics or statistical analysis. Every new concept should immediately have an application presented. I believe that by making mathematics more "friendly" to the general student, I will foster interest in the subject.
"Mathematics is one of the greatest cultural and intellectual achievements of humankind." - NCTM, 2000
Unfortunately the preceding statement makes mathematics seem to be out of the grasp of the general student, and implies that only the most adept student will ever progress in mathematics, which will in turn make them the elite of humankind. I feel this is a very dangerous statement to make, which may lead to students becoming discouraged in even attempting to learn the subject.
"Teaching students to identify and pose problems, to explain themselves in terms others can understand and to question the invisible structures of mathematics is key to developing informed, active and critical citizens."
I agree completely with this statement. As a mathematics teacher, I believe an interesting form of assessment would be to have students work together in groups to develop a list of questions based on the material already covered, submit this list to the teacher for approval, and in turn have the questions returned to the students in the form of a group homework assignment. Groups would work together to create questions difficult enough that other groups were unable to answer them, which in turn would foster deeper understanding from the problem posers and develop their social "professional" interactions and problem-solving skills.
Thursday, October 8, 2009
"What If Not..."
The "What If Not..." or "WIN" approach is an excellent tool that can be used to test the understanding of both the person creating the problem, which would typically be the teacher, and the person solving the problem, which would typically be the student. The reason I say "typically" is because students with a natural curiosity in mathematics will be tempted to push the boundaries of their knowledge and are likely to pose very similar questions to the teacher, so it is always helpful if the teacher has already reflected on similar questions themselves and are prepared to answer higher order questions from the students.
The strength of the WIN approach is the potential it has in identifying students that are adept in mathematics and seeking more of a challenge than the typical classroom environment offers. I believe the best application of the WIN approach would be as bonus questions on homework assignments and tests, where gifted students will be able to entertain themselves while the rest of the class catches up.
The weakness of the WIN approach is its ability to terrify students with a weak or moderate understanding in mathematics. A student that has a tentative understanding of a new concept may find that they are unable to grasp higher order questions until they have affirmed their own knowledge, which may not happen until after a unit is complete.
Unfortunately the WIN approach does not have any application in our micro teaching lesson on "Introduction to Algebra", since we only have 15 minutes to introduce the topic, and I believe the WIN approach is better left for a second or third class on the subject, when students are more comfortable with the material.
The strength of the WIN approach is the potential it has in identifying students that are adept in mathematics and seeking more of a challenge than the typical classroom environment offers. I believe the best application of the WIN approach would be as bonus questions on homework assignments and tests, where gifted students will be able to entertain themselves while the rest of the class catches up.
The weakness of the WIN approach is its ability to terrify students with a weak or moderate understanding in mathematics. A student that has a tentative understanding of a new concept may find that they are unable to grasp higher order questions until they have affirmed their own knowledge, which may not happen until after a unit is complete.
Unfortunately the WIN approach does not have any application in our micro teaching lesson on "Introduction to Algebra", since we only have 15 minutes to introduce the topic, and I believe the WIN approach is better left for a second or third class on the subject, when students are more comfortable with the material.
Sunday, October 4, 2009
Art of Problem Posing - Questions and Comments on Pgs 1-32.
Goal: Write 10 questions or comments to the author regarding pages 1-32.
(1) "We believe that is is necessary first to get "caught up in" (and sometimes even 'caught,' in the sense of 'trapped by') the activity in order to appreciate where we are headed." - Pg 2
I believe this is a fantastic idea for capturing the attention and imagination of the curious learner, but should we be concerned that we may frustrate the less interested students as well?
(2) "Coming to know something is not a 'spectator sport'... As Dewey asserted many years ago, and the constructivist school of thought has vigorously argued more recently, to claim that 'coming to know' is a participant sport is to require that we operate on and even modify the things we are trying to understand." - Pg 2
Thank you very much for clearly writing this statement. After reading this, I am finally beginning to understand the Brent Davis lectures, and I feel less stressed out over the first assignment.
(3) "It is worth appreciating, however, that not everything we experience comes as a problem. Imagine being given a situation in which no problem has been posed at all. One possibility of course is that we merely appreciate the situation, and do not attempt to act on it in any way... Another reasonable response for some situations, however,might be to generate a problem or to ask a question, not for the purpose of solving the original situation, but in order to uncover or to create a problem or problems that derive from the situation." - Pg 4-5
I find this statement acts as a reflection of my own life. There was a time when I questioned and thought critically about everything I experienced. From my questioning came a thirst for knowledge, but more questions arose than answers. Although I have already trained my mind to think critically and question everything, I found it wasn't until years later that I was simply able to appreciate the simplicity of certain situations, and let my mind relax. While I believe it is important to train the minds of students to question, it is equally important to train them how to be at peace. As for how to accomplish this second part, I am still unsure.
(4) "For example, exploration of the perimeters of various rectangles with area 24cm^2 by means of models and drawings, with data as recorded in [the table below], could lead to student recognition and formulation of such problems as the following: Is there a rectangle of minimum perimeter with the specified area? What are it's dimensions?" - Pg 9
This would also make a great launching activity for discussing which three-dimensional geometric shapes have the least surface area to volume ratio, and tie this into nature where soap bubbles minimize their surface area (and surface tension) by choosing a spherical shape. The student wouldn't need to know the complex mathematics and physics of the principle, just understand why this works.
(5) "x^2 + y^2 = z^2; What are some answers?" - Pg 12
Perhaps because of my physics background, I mentally solved for the f(x), f(y), and f(z) algebraically. Although I like the idea of an open ended mathematics question, I feel that further constraints are required before posing such a problem to the students... Half a page later, and I realize that this example was meant to illustrate that exact point. :P
(6) "x^2 + y^2 = z^2; What are some questions?" - Pg 14
My questions:
How do you solve for each individual variable?
Where is this formula used in mathematics?
When is this formula used in real life?
Again, I notice that my answers are different from those in the book. Because I view this formula as a tool, my first thought is "when do I use this tool?" I feel that if students can also see the relevance of this knowledge, they are more likely to be encouraged to learn it.
(7) "[Pythagorean Theorem] has to do with squares on the sides of a right triangle" - Pg 16
I am completely lost on this one. Is it a paper folding exercise?
(8) "Does the [Supreme Court Judges] handshake have an effect on subsequent cordiality? - Pg 20
I think this is a fantastic question to ask the students, but how can it be graded, since I do not know the answer myself?
(9) "If one angle of an isosceles triangle is twice another, is the shape of the triangle determined?" - Pg 21
From this question I immediately thought "Can you solve for every angle in the triangle?" Additionally, when I saw the figures below, I thought "If a triangle is made up of four identical isosceles triangles, what is the relationship between the angles of the larger triangle and the smaller ones?" This is a pretty self-evident question, but may help to make the struggling students in the class feel that they are developing a deeper understanding, and therefore open them up to further exploration in the subject.
(10) The geoboard has an appeal to the uninitiated student as well as to the sophisticated one... What would you do with it? - Pg 22
I would love to ask students how many squares can be made using the board. I recall a fellow that I did my physics undergrad with that had trouble with traditional homework questions, but excelled at puzzles like this. I think this would be a great opportunity to "level the playing field" in the classroom between the mathematically-inclined students and those that struggle with the subject.
(1) "We believe that is is necessary first to get "caught up in" (and sometimes even 'caught,' in the sense of 'trapped by') the activity in order to appreciate where we are headed." - Pg 2
I believe this is a fantastic idea for capturing the attention and imagination of the curious learner, but should we be concerned that we may frustrate the less interested students as well?
(2) "Coming to know something is not a 'spectator sport'... As Dewey asserted many years ago, and the constructivist school of thought has vigorously argued more recently, to claim that 'coming to know' is a participant sport is to require that we operate on and even modify the things we are trying to understand." - Pg 2
Thank you very much for clearly writing this statement. After reading this, I am finally beginning to understand the Brent Davis lectures, and I feel less stressed out over the first assignment.
(3) "It is worth appreciating, however, that not everything we experience comes as a problem. Imagine being given a situation in which no problem has been posed at all. One possibility of course is that we merely appreciate the situation, and do not attempt to act on it in any way... Another reasonable response for some situations, however,might be to generate a problem or to ask a question, not for the purpose of solving the original situation, but in order to uncover or to create a problem or problems that derive from the situation." - Pg 4-5
I find this statement acts as a reflection of my own life. There was a time when I questioned and thought critically about everything I experienced. From my questioning came a thirst for knowledge, but more questions arose than answers. Although I have already trained my mind to think critically and question everything, I found it wasn't until years later that I was simply able to appreciate the simplicity of certain situations, and let my mind relax. While I believe it is important to train the minds of students to question, it is equally important to train them how to be at peace. As for how to accomplish this second part, I am still unsure.
(4) "For example, exploration of the perimeters of various rectangles with area 24cm^2 by means of models and drawings, with data as recorded in [the table below], could lead to student recognition and formulation of such problems as the following: Is there a rectangle of minimum perimeter with the specified area? What are it's dimensions?" - Pg 9
This would also make a great launching activity for discussing which three-dimensional geometric shapes have the least surface area to volume ratio, and tie this into nature where soap bubbles minimize their surface area (and surface tension) by choosing a spherical shape. The student wouldn't need to know the complex mathematics and physics of the principle, just understand why this works.
(5) "x^2 + y^2 = z^2; What are some answers?" - Pg 12
Perhaps because of my physics background, I mentally solved for the f(x), f(y), and f(z) algebraically. Although I like the idea of an open ended mathematics question, I feel that further constraints are required before posing such a problem to the students... Half a page later, and I realize that this example was meant to illustrate that exact point. :P
(6) "x^2 + y^2 = z^2; What are some questions?" - Pg 14
My questions:
How do you solve for each individual variable?
Where is this formula used in mathematics?
When is this formula used in real life?
Again, I notice that my answers are different from those in the book. Because I view this formula as a tool, my first thought is "when do I use this tool?" I feel that if students can also see the relevance of this knowledge, they are more likely to be encouraged to learn it.
(7) "[Pythagorean Theorem] has to do with squares on the sides of a right triangle" - Pg 16
I am completely lost on this one. Is it a paper folding exercise?
(8) "Does the [Supreme Court Judges] handshake have an effect on subsequent cordiality? - Pg 20
I think this is a fantastic question to ask the students, but how can it be graded, since I do not know the answer myself?
(9) "If one angle of an isosceles triangle is twice another, is the shape of the triangle determined?" - Pg 21
From this question I immediately thought "Can you solve for every angle in the triangle?" Additionally, when I saw the figures below, I thought "If a triangle is made up of four identical isosceles triangles, what is the relationship between the angles of the larger triangle and the smaller ones?" This is a pretty self-evident question, but may help to make the struggling students in the class feel that they are developing a deeper understanding, and therefore open them up to further exploration in the subject.
(10) The geoboard has an appeal to the uninitiated student as well as to the sophisticated one... What would you do with it? - Pg 22
I would love to ask students how many squares can be made using the board. I recall a fellow that I did my physics undergrad with that had trouble with traditional homework questions, but excelled at puzzles like this. I think this would be a great opportunity to "level the playing field" in the classroom between the mathematically-inclined students and those that struggle with the subject.
Friday, October 2, 2009
Hypothetical Student Responses - 2019
Dear Mr. Bayer,
I would like to thank you for making mathematics fun for me. Although I decided not to continue on in math, I did find that your course was my favorite because of the laboratory "experiments" you included in the course. It really helped me to understand the concepts being taught, particularly algebra and trigonometry. I wasn't a fan of the word problems, but at least I could see how I could actually apply all the materials that I learned in class.
You really helped to make the subject "exciting" by being excited about teaching. I had a tendency to fall asleep in some of my other classes, but I was always able to stay awake in your class.
Mr. Bayer,
I wanted to let you know that I really did not enjoy your class. First, I thought that your "pop quizzes" were an extremely unfair form of punishment against the class for acting up and not focusing on work. Second, since when does Math need labs? If I wanted labs, I would take a science class. If I wanted a "sanity check", I would see a psychiatrist. You teach math... you shouldn't be doing anything other than punching numbers into a calculator. You suck.
Oh, and "Think-Pair-Share"? Why couldn't we do this on tests?
SUMMARY: My hopes and worries.
From my written work, I hope that I can convince most students that mathematics does not have to be dry, and I hope to accomplish this by incorporating simple physics concepts as a tool to teach mathematics, such as throwing a ball against a wall to measure velocity, a tool in introducing algebra.
My worry is that taking mathematics away from a strictly classroom instruction, I may end up alienating some students from mathematics. Also, I fear that the unspoken threat of pop quizzes as a classroom management tool may discourage some students from continuing on in mathematics.
I would like to thank you for making mathematics fun for me. Although I decided not to continue on in math, I did find that your course was my favorite because of the laboratory "experiments" you included in the course. It really helped me to understand the concepts being taught, particularly algebra and trigonometry. I wasn't a fan of the word problems, but at least I could see how I could actually apply all the materials that I learned in class.
You really helped to make the subject "exciting" by being excited about teaching. I had a tendency to fall asleep in some of my other classes, but I was always able to stay awake in your class.
Mr. Bayer,
I wanted to let you know that I really did not enjoy your class. First, I thought that your "pop quizzes" were an extremely unfair form of punishment against the class for acting up and not focusing on work. Second, since when does Math need labs? If I wanted labs, I would take a science class. If I wanted a "sanity check", I would see a psychiatrist. You teach math... you shouldn't be doing anything other than punching numbers into a calculator. You suck.
Oh, and "Think-Pair-Share"? Why couldn't we do this on tests?
SUMMARY: My hopes and worries.
From my written work, I hope that I can convince most students that mathematics does not have to be dry, and I hope to accomplish this by incorporating simple physics concepts as a tool to teach mathematics, such as throwing a ball against a wall to measure velocity, a tool in introducing algebra.
My worry is that taking mathematics away from a strictly classroom instruction, I may end up alienating some students from mathematics. Also, I fear that the unspoken threat of pop quizzes as a classroom management tool may discourage some students from continuing on in mathematics.
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