This group is from 2002.
Problem 2
Difficulty: Easy and fun.
Problem 40
Difficulty: Fairly difficult for your students.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 02 and answer 40.
Thursday, March 31, 2011
Wednesday, March 30, 2011
The daily Two, from 2002: 1 and 41
Labels:
UVM-Fractions,
UVM-Geometry,
UVM-Trigonometry
Starting a new set! This group is from 2002. As with the previous ones, I'll post two at a time so you won't be tempted to work through all 41 at once. You have to eat, you know. Just looking out for your basic health.
Problem 1
Difficulty: Easy and fun. I really don't get why students freak out over these simple fraction problems. Okay, I do understand ... not enough practice. So here's another practice problem.
Problem 41
Difficulty: Until you see it, "What?" When you see it, "D'oh!"
Simple geometry and two nifty trigonometric doodads.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 01 and answer 41.
Problem 1
Difficulty: Easy and fun. I really don't get why students freak out over these simple fraction problems. Okay, I do understand ... not enough practice. So here's another practice problem.
Problem 41
Difficulty: Until you see it, "What?" When you see it, "D'oh!"
Simple geometry and two nifty trigonometric doodads.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 01 and answer 41.
Tuesday, March 29, 2011
Tuesday Child is full of grace ... 20, 21, and 22.
Labels:
UVM-Algebra,
UVM-Statistics
Problem 20
Difficulty: Easy, but fun. A new way to look at averages and the effect of an addition on the average, depending on n.
Problem 21
Difficulty: Linear programming.Any bets this will somehow work out to an integer?
Problem 22
Difficulty: Easy. Once you've got the details right.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 20, answer 21 and answer 21.
Difficulty: Easy, but fun. A new way to look at averages and the effect of an addition on the average, depending on n.
Problem 21
Difficulty: Linear programming.Any bets this will somehow work out to an integer?
Problem 22
Difficulty: Easy. Once you've got the details right.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 20, answer 21 and answer 21.
Monday, March 28, 2011
Monday's Child has Two: 19 and 23
Labels:
UVM-Geometry,
UVM-Probability
Problem 19
Difficulty: easy. Notice we didn't specify which color.
Problem 23
Difficulty: Very clever geometry question.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 19 and answer 23.
Difficulty: easy. Notice we didn't specify which color.
Problem 23
Difficulty: Very clever geometry question.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 19 and answer 23.
Sunday, March 27, 2011
Delicious pair o'Problems: 18 and 24
Labels:
UVM-Algebra,
UVM-Trigonometry
Problem 2*3²
Difficulty: easy-ish. A little trigonometric - algebraic manipulation and "Surprise!"
Problem 2³*3
Difficulty: Easy. At least once in every test, in some form or another, the creators work the year into a problem. This test was for 2007.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 18 and answer 24.
Difficulty: easy-ish. A little trigonometric - algebraic manipulation and "Surprise!"
Problem 2³*3
Difficulty: Easy. At least once in every test, in some form or another, the creators work the year into a problem. This test was for 2007.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 18 and answer 24.
Saturday, March 26, 2011
Are you teaching Calculus next year?
Labels:
Calculus
I've been doing it for how many years now? 27 years (I think) ... so much time, so many really cool kids. I guess one thing I really like about teaching calculus is that I can't recall a bad student.
Anyway, for those who are setting up a course for next year:
Text (by author):
If you want to stretch your boundaries and go 21st Century on your kids, there are many online texts. I'd love to try this and I'm planning on putting selected sections on the Moodle. WolframAlpha will be required for some assignments.
AP insists you fulfill their audit process - mostly they need a syllabus, but you have to complete it if your school wants to put the "AP" label on it. Someone at your school may have already fulfilled that requirement -- make sure to check. Soon. Here's my syllabus if you want to copy it.
The Summer Before
If you can, and can afford it or if your school with cover costs, hit up a summer AP seminar. The Summer AP Institute at St. Johnsbury VT is one of the best.
http://www.stjacademy.org/page.cfm?p=278
http://www.stjacademy.org/uploaded/documents/AP_Institute/AP_Institute_2011.pdf
The environment is as close as you can get to smart-people nirvana. One week surrounded by a bunch of AP teachers in an informal setting in the Vermont summer. Learn, work, relax, eat REALLY good food, play bocce on the lawn and drink free beer with a slew of brilliant people till dinner. Like you can get better than this? It's $1100 but worth it ... especially if your school will pony up. Skip the dorm and use the savings and a little extra of yours and take your wife -- a hotel isn't much more and it's a wonderful town.
Yeah, what the Hell, TI?
(from Randall at XKCD) And the marginally colored TI-Inspire doesn't get you off the hook, either.
Technology
Anyway, for those who are setting up a course for next year:
Text (by author):
- It will probably be Larson or Stewart. Stewart is the more common college text, but Larson is the more HS-friendly. I personally use Larson 7th. I've taught from this book since the third edition and I feel very comfortable with it.
- Hughes-Hallet-Gleason did things in an odd organization, IMNSHO. In a tutoring situation, I had this thing and it was oddly laid out, with integration happening before the end of differentials. You might like it, but I'm too used to the Larson / Stewart / Thomas Finney organization.
- Ostebee-Zora is dense for highschool students.
- Thomas and Finney was cool ten years ago but seems to have fallen out of favor. Don't know why.
If you want to stretch your boundaries and go 21st Century on your kids, there are many online texts. I'd love to try this and I'm planning on putting selected sections on the Moodle. WolframAlpha will be required for some assignments.
- Neat place to start is the California site: http://www.clrn.org/home/
- http://www.whitman.edu/mathematics/calculus/
- MIT OC: http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm
- http://www.math.temple.edu/~cow/
- http://archives.math.utk.edu/visual.calculus/
- and of course, Salman Khan on YouTube.
AP insists you fulfill their audit process - mostly they need a syllabus, but you have to complete it if your school wants to put the "AP" label on it. Someone at your school may have already fulfilled that requirement -- make sure to check. Soon. Here's my syllabus if you want to copy it.
The Summer Before
If you can, and can afford it or if your school with cover costs, hit up a summer AP seminar. The Summer AP Institute at St. Johnsbury VT is one of the best.
http://www.stjacademy.org/page.cfm?p=278
http://www.stjacademy.org/uploaded/documents/AP_Institute/AP_Institute_2011.pdf
The environment is as close as you can get to smart-people nirvana. One week surrounded by a bunch of AP teachers in an informal setting in the Vermont summer. Learn, work, relax, eat REALLY good food, play bocce on the lawn and drink free beer with a slew of brilliant people till dinner. Like you can get better than this? It's $1100 but worth it ... especially if your school will pony up. Skip the dorm and use the savings and a little extra of yours and take your wife -- a hotel isn't much more and it's a wonderful town.
Yeah, what the Hell, TI?
(from Randall at XKCD) And the marginally colored TI-Inspire doesn't get you off the hook, either.
Technology
- Every kid should have a TI-84 or the equivalent. I don't require them to buy one but I'll warn them that the ones available in the room for borrowing are often changed and reset by the algebra I kids, making it difficult for the occasional user to get started. "Radians or degrees", language set to Deutsch, etc. There is a new wrinkle, though: The graphing calculator app for iPhone and Android devices. It's got a better screen resolution and it only costs $3 for the phone they already own.
- Excel is useful - Google apps works, too. Just be ready to reserve time occasionally in the computer room.
- Pencil and paper
Calculus Syllabus for the AP Audit.
This was enough to satisfy the review process wonks. Feel free to use it verbatim as I can't claim to have made much up on my own. It is mostly a regurgitation of the table of contents.
I certainly don't feel that anyone should spend an iota of psychic energy on the syllabus - spend it making plans and working toward the best you can do for your students.
Case in point: "Definition by limit: epsilon-delta." was de-emphasized in AP years ago, is usually ignored by most college professors for MAT121 but emphasized by the Audit review process. I couldn't get the audit accomplished without lip service to it.
A change from this syllabus for me: I am changing from a school-hosted ePortfolio to a Moodle, blog and Wiki based on my personal server. There are several places to find free hosting for those. Additionally, I will be requiring certain homework to be done on WolframAlpha since no one can afford Mathematica. I'd love to require an iPad but I'll have to win the lottery first!
Good luck in your setup.
Calculus Syllabus
Instructional Materials
Introduction: What is Calculus About?
Functions Review
Derivative Applications
I certainly don't feel that anyone should spend an iota of psychic energy on the syllabus - spend it making plans and working toward the best you can do for your students.
Case in point: "Definition by limit: epsilon-delta." was de-emphasized in AP years ago, is usually ignored by most college professors for MAT121 but emphasized by the Audit review process. I couldn't get the audit accomplished without lip service to it.
A change from this syllabus for me: I am changing from a school-hosted ePortfolio to a Moodle, blog and Wiki based on my personal server. There are several places to find free hosting for those. Additionally, I will be requiring certain homework to be done on WolframAlpha since no one can afford Mathematica. I'd love to require an iPad but I'll have to win the lottery first!
Good luck in your setup.
Calculus Syllabus
Instructional Materials
- Textbook: Calculus, 7th edition by Larson, Hostetler, Edwards; Houghton – Mifflin Publishing Company.
- Technology: TI-83 / TI 84 graphing Calculator
- When appropriate, the class will make use of Geometer's Sketch Pad, excel, Google apps.
- a gmail account would be most helpful.
- E-Portfolios will be a part of the Course. See ____ for account and access information. Work will be done in groups, handed in separately (and included here). Typical Contents:
- Your two sets of school-wide showcase materials
- Chapter projects/labs assigned monthly.
- Past years FRQ questions worked out and scored by each other.
- Inter-curricular questions.
Introduction: What is Calculus About?
Functions Review
- I. Sign Graph solutions
- II. Coordinates, Slope
- III. Linear Equations: [point slope, slope intercept, general]
- A. Formulae [ distance, angle, perpendicular, bisectors]
- IV. Polynomial functions – library of Functions
- A. Domain, range, discontinuities, roots, synthetic division
- B. Odd, even, Symmetry
- C. composite functions g(f(x)), (g*f)(x), (gof)(x)
- D. Slope = derivatives, differentiability,
- E. "How to say it in Math." Introduction of proof techniques and format.
- I. x =>a, one sided limits at discontinuity, peak, break in curve, inf. disc, etc.
- II. [ graphically, algebraically, numerically]
- III. definition of derivative as lim h =>0, delta, epsilon (refer back to "More or Less")
- IV. Limits : add sub / mult / div
- V. Infinite Limits
- VI. Continuity, max-min theorem, Intermediate Value Theorem, Computer/calculator-aided exploration of situations in which lim f (x) x a D.N.E.
- I. Definition by limit: epsilon-delta.
- II. Computer-aided exploration:
- A. Using the definition of the derivative as a limit of slope
- B. secants to plot f'(x)vs x. The relationship of the graph of f'(x)to f(x).
- III. Power Rule, Constant Rule, Sum Rule, Product Rule, PowerRule2, Quotient Rule
- IV. Implicit Differentiation
- V. Chain Rule: composite functions
- VI. "Explain" "Show that" "Why or Why Not" – how to justify an answer. Includes review of past free-response questions, and scoring methods, practice developing an appropriate answer with explanations. presentations by students
- VII. Trigonometry
- A. one-day review of basic functions, then Derivatives of trig functions
- VIII. Linear
- A. Tangents and Normals, Linear Approximations and Differentials – ZOOM and compare – analytic results vs. calc – relate back to epsilon/delta
- B. Newton’s Method – writing a recursive program
- C. Calculator computation of derivatives and graphs of derivatives.
Derivative Applications
- I. Sign Graph analysis recap
- II. Graphing
- A. First derivative: increase, decrease,
- B. Second derivative: concavity
- III. Symmetry
- IV. Asymptotes, limits, dominant terms, derivative of hyperbola vs parabola: behavior at extremes
- V. Extrema Theory: Relative and Absolute Maxima and Minima;
- A. 1st derivative test and the Extreme Value Theorem; Intervals,
- B. Continuity;
- 1. Why are the notions of continuity and limit crucial to the Calculus?
- 2. Informal discussion of "function niceness."
- 3. Definition of continuity theoretically compared to on the TI.
- C. 2nd derivative test for maxima and minima
- VI. Recap of "Explain" "Show that" "Why or Why Not" – justify an answer. "How does one know f(c) is minimum?" 1999 FRQ BC:4 Student Sample A and others.
- VII. Maxima and minima: Problems
- VIII. Related rates of change, physics, chemistry, Real Problems, dist-vel-acc-jerk, best solutions. Include here the instantaneous numerical calculations.
- IX. Rolle's Theorem, Mean Value Theorem, Intermediate Value Theorem
- X. Indeterminate forms and L'Hopital's Rule
- XI. Fall School-wide Showcase: Presentations and Explanations (similar to typical portfolio except this is a chance for students to present some of their work to parents, faculty and members of the community.)
- I. Indefinite Integrals - Primitives (antiderivatives) differential equations, Separation of variables, basic integration formulae, constant of integration.
- II. Finding the constant of integration (C)
- III. Substitution Method - U and dU
- IV. Integrals of Trigonometric Functions
- A. Basic Functions
- B. Using Trig identities to solve integrals
- V. The Area Under a Curve - Definite Integrals
- A. Rectangles & Summation (Sigma notation)
- B. Riemann Integral = Lim as number of rectangles incr. to infinity
- VI. Calculating Areas by Summation
- A. Rectangles
- B. Trapezoids
- VII. Fundamental Theorems of Calculus -
- A. First F.T. of C. -- definition of Primitive F(x): derivative F(x) is f(x)
- B. Second F.T. of C: definite integral is equal to F(b) - F(a)
- VIII. Substitution
- IX. Approximations of Definite Integrals
- A. Trapezoidal Rule A=h/2 (1 2 2 2 2 ...... 2 1)
- B. Simpson's Rule A= h/3 ( 1 4 2 4 .... 2 4 1 )
- I. Distance - velocity - acceleration - jerk
- II. Areas: horizontal rectangles - dy, f(y), g(y); vertical rectangles - dx, f(x), g(x)
- III. Volumes, by revolution
- A. Creation: use potter’s wheel as example; zucchini-carving to show slicing; cardboard discs, wood tiles. Group–think: Given a lathe template for vase, find the volume
- B. Volumes of revolution around x-axis and y-axis using Discs, Washers, Shells
- IV. Known Cross Section
- V. Average Value, average rate of change
- VI. ** Optional extensions of integral theory
- A. Length of Plane curves, Area of Surface of Revolution
- B. Physics: Moment of Inertia, Center of mass, Centroids, Nonuniform mass distribution, Work done by variable forces (concurrent physics preferred)
- I. Inverse Functions and their derivatives
- II. Inverse Trig functions
- III. Derivatives of the Inverse trig functions and associated integrals
- IV. Natural Log and Derivative
- A. INT (1/cabin) d(cabin) = log (cabin) + C = houseboat
- V. Exponential and logarithmic functions
- A. derivatives and integrals
- B. Applications [ rates of growth, decay, compound interest, Richter scale]
- VI. Spring School-wide Showcase
- I. Basic Forms
- II. Integration by parts [Berger method]
- III. Trig Functions, odd powers and even powers
- IV. Trig Substitutions
- V. Integrals involving .....
- VI. Partial Fractions [Alfonso’s Method, Matrix solutions, Millitello cover]
- VII. Numerical integration
- I. Conic Sections – Definitions and uses of calculus – areas, etc.
- II. Hyperbolic Functions –
- A. Definitions, Derivatives and integrals
- B. Cables, Catenaries (Gateway Arch and Power lines), and the suspension bridge.
- C. Inverse Hyperbolics
- III. Polar Coordinates
- A. Graphing and common figures,
- B. Derivatives and integrals in Polar coordinates
- II. Infinite Sequences and series
- A. e, sin, cos, pi expansions
- B. Taylor, MacLaurin etc.
Just don't call it tracking
Labels:
School Policy
Mike Petrilli on Education Gadfly:
It doesn’t take a rocket scientist—or even a cognitive scientist—to know that kids (and adults) learn best when presented with material that is challenging—neither too easy so as to be boring nor too hard as to be overwhelming. Like Goldilocks, we want it just right. Grouping kids so that instruction can be more closely targeted to their current ability levels helps make teaching and learning more efficient.Apparently, it takes someone a lot more intelligent than a rocket scientist because it's news to all the guidance counselors and schedulers that I've talked with.
Happy Saturday. Here's your daily double: 17 and 25.
Labels:
UVM-Algebra,
UVM-Logarithms,
UVM-Logic
Day Seventeen
Difficulty: easy-schmeasy, if you subtract. More complicated if you try to add.
Problem 25 = 5².
(I wonder how often you can switch the digits and still write an equivalent expression.)
Difficulty: Medium. More damned logarithms, but there's a neat little prime factorization going on, too.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 17 and answer 25.
Difficulty: easy-schmeasy, if you subtract. More complicated if you try to add.
Problem 25 = 5².
(I wonder how often you can switch the digits and still write an equivalent expression.)
Difficulty: Medium. More damned logarithms, but there's a neat little prime factorization going on, too.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 17 and answer 25.
Friday, March 25, 2011
Gruesome Twosome: 16 and 26
Labels:
UVM-Algebra,
UVM-Logic
Sweet Sixteen
Difficulty: easy-ish. Another SAT-type reasoning question. Fun to watch the students work out the ramifications.
Problem 26
Difficulty: Medium. Is it wrong of me to get really annoyed at this question? It's not terribly difficult, but it is so ... artificial.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 16 and answer 26.
Difficulty: easy-ish. Another SAT-type reasoning question. Fun to watch the students work out the ramifications.
Problem 26
Difficulty: Medium. Is it wrong of me to get really annoyed at this question? It's not terribly difficult, but it is so ... artificial.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 16 and answer 26.
Thursday, March 24, 2011
Daily Problematic Pair: 15 and 27
Labels:
UVM-Geometry,
UVM-Probability,
UVM-Series
Day Fifteen ... We're almost there.
Difficulty: pretty easy. Kids will get wrapped up in the P(A) and if-then, but it's an example of a problem that is much easier if you imagine the grid of all possibilities. Definitely a candidate for the SAT.
Problem 27
Difficulty: Medium. It's funny how easily the kids get thrown by an infinite series.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 15 and answer 27.
Difficulty: pretty easy. Kids will get wrapped up in the P(A) and if-then, but it's an example of a problem that is much easier if you imagine the grid of all possibilities. Definitely a candidate for the SAT.
Problem 27
Difficulty: Medium. It's funny how easily the kids get thrown by an infinite series.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 15 and answer 27.
Wednesday, March 23, 2011
Daily Think. Problems 14 and 28
Labels:
UVM-Geometry,
UVM-Logarithms,
UVM-Logic
Day Fourteen
Difficulty: easy-ish. It's similar to a lot of SAT questions in that you don't actually solve for a, b or c but use them all in concert to find some other value.
Problem 28
Difficulty: Medium. Advanced Logarithmic manipulation.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 14 and answer 28.
Difficulty: easy-ish. It's similar to a lot of SAT questions in that you don't actually solve for a, b or c but use them all in concert to find some other value.
Problem 28
Difficulty: Medium. Advanced Logarithmic manipulation.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 14 and answer 28.
Tuesday, March 22, 2011
Why I support Unions.
Labels:
Just a rant,
NEA
The Union will block spurious, petty and mean administrators from firing the competent as well as the incompetent. This is good because the administrator usually has no real idea which is which.
The Union will ensure that teachers get a fair shake when they are dealing with someone who has no real need to be fair. This is not the owner of a company who is watching every dollar out of his own pocket -- this is a transient employee who has too much power and not enough knowledge.
They float through once, twice a year in a choreographed display of feigned interest in what I am doing. Three weeks before, I get a note saying when they'll arrive and which class they'll be observing - get a lesson plan ready and do the pre-observation meeting. Then they'll watch the class, make a few notes. In the case of the more recent attendees at admin training workshops, they'll attempt to record my speech verbatim in the vain hope that recording every word spoken will somehow tell them more than just listening attentively. This is real?
We meet for the post-op and I'll be given a letter that specifies what they observed. Some of the more insightful comments were "Good lesson" and "knows the material." One of the less insightful was "Separates the kids into two groups by gender." I taught algebra in the chorus room -- apparently Mr. HIP didn't notice that the aisle down the middle separated the kids into two groups and that they took the same places as they normally did during chorus -- I don't do seating charts and usually pay no attention to where students sit. No, he thought I was being discriminatory.
I went 6 years before I was observed again. How was that principal supposed to know anything about me or anyone else in the building? How were they (five in six years) supposed to determine that X should go?
When an admin played games, got in the face of someone improperly, tried to ruin a teacher, there was always the Union stepping in to make sure that things were proper. That is its best role, to act as a buffer, to make sure that each i is dotted and t crossed. I was lucky (knock on wood). I had developed a CYA model and kept tons of paperwork and evidence. When parents complained or school boards took a closer interest, I always had a defense. What if I weren't paranoid?
The Union negotiates a contract. The contract is held up as a object of derision by many on the right - "Look at this egregious waste of taxpayer money. Look at this contract. We shouldn't allow teachers to quote the contract when they might get into trouble!" What an incredible thought, that a contract shouldn't be followed by both sides. "Gullible Boards sign outrageous contracts!" Actually, they sign a contract that both sides agreed to.
Show me any industry that breaks contracts at a whim. I'll wait.
Everybody complains about the LIFO, salary schedule, no merit pay clauses in the contract. When the dust settles, these clauses are seen as the most manageable. Since the admins are rarely around long enough to figure out the names of the teachers in the building, how are they supposed to know which one is worth keeping? The one who has been there for ten years or the kid just out of college who has no idea of what she's getting into? If you eliminate the salary schedule, then you'll have people like me getting $15,000 signing bonuses and thousands more than the English teachers. Really? Same job. Same experience. Think there won't be any bad feelings? Think the school will run just fine anyway? If you don't have a contract, then I'll demand more money and different working conditions because I know the school is desperate. Maybe I'll train for six weeks and be a dilettante TFA who does the school a favor by my presence and leaves when a real job is available.
The Union works for that contract and makes sure that both sides abide by it.
As for merit pay, this is a fantasy dreamed up by a billionaire. If I get a bonus every year because I suck up to the principal, how long do you think there will cooperation in the department? If I don't trust him to know his ass from a hole in the ground when it comes to hiring and firing, I sure don't want a large fraction of my income held over my head - "maybe you will and maybe you won't."
Far from being the leech on the blood veins of education, unions are the force that makes education work as smoothly as it does.
The Union will ensure that teachers get a fair shake when they are dealing with someone who has no real need to be fair. This is not the owner of a company who is watching every dollar out of his own pocket -- this is a transient employee who has too much power and not enough knowledge.
They float through once, twice a year in a choreographed display of feigned interest in what I am doing. Three weeks before, I get a note saying when they'll arrive and which class they'll be observing - get a lesson plan ready and do the pre-observation meeting. Then they'll watch the class, make a few notes. In the case of the more recent attendees at admin training workshops, they'll attempt to record my speech verbatim in the vain hope that recording every word spoken will somehow tell them more than just listening attentively. This is real?
We meet for the post-op and I'll be given a letter that specifies what they observed. Some of the more insightful comments were "Good lesson" and "knows the material." One of the less insightful was "Separates the kids into two groups by gender." I taught algebra in the chorus room -- apparently Mr. HIP didn't notice that the aisle down the middle separated the kids into two groups and that they took the same places as they normally did during chorus -- I don't do seating charts and usually pay no attention to where students sit. No, he thought I was being discriminatory.
I went 6 years before I was observed again. How was that principal supposed to know anything about me or anyone else in the building? How were they (five in six years) supposed to determine that X should go?
When an admin played games, got in the face of someone improperly, tried to ruin a teacher, there was always the Union stepping in to make sure that things were proper. That is its best role, to act as a buffer, to make sure that each i is dotted and t crossed. I was lucky (knock on wood). I had developed a CYA model and kept tons of paperwork and evidence. When parents complained or school boards took a closer interest, I always had a defense. What if I weren't paranoid?
The Union negotiates a contract. The contract is held up as a object of derision by many on the right - "Look at this egregious waste of taxpayer money. Look at this contract. We shouldn't allow teachers to quote the contract when they might get into trouble!" What an incredible thought, that a contract shouldn't be followed by both sides. "Gullible Boards sign outrageous contracts!" Actually, they sign a contract that both sides agreed to.
Show me any industry that breaks contracts at a whim. I'll wait.
Everybody complains about the LIFO, salary schedule, no merit pay clauses in the contract. When the dust settles, these clauses are seen as the most manageable. Since the admins are rarely around long enough to figure out the names of the teachers in the building, how are they supposed to know which one is worth keeping? The one who has been there for ten years or the kid just out of college who has no idea of what she's getting into? If you eliminate the salary schedule, then you'll have people like me getting $15,000 signing bonuses and thousands more than the English teachers. Really? Same job. Same experience. Think there won't be any bad feelings? Think the school will run just fine anyway? If you don't have a contract, then I'll demand more money and different working conditions because I know the school is desperate. Maybe I'll train for six weeks and be a dilettante TFA who does the school a favor by my presence and leaves when a real job is available.
The Union works for that contract and makes sure that both sides abide by it.
As for merit pay, this is a fantasy dreamed up by a billionaire. If I get a bonus every year because I suck up to the principal, how long do you think there will cooperation in the department? If I don't trust him to know his ass from a hole in the ground when it comes to hiring and firing, I sure don't want a large fraction of my income held over my head - "maybe you will and maybe you won't."
Far from being the leech on the blood veins of education, unions are the force that makes education work as smoothly as it does.
Daily Think. Problems 13 and 29
Labels:
UVM-Algebra,
UVM-Geometry
Day Thirteen
Difficulty: easy-ish. Mostly, it's an interpretation question.
I love this next problem. So very cool.
Problem 29
i.e., find the shaded area.
Difficulty: Medium.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 13 and answer 29.
Difficulty: easy-ish. Mostly, it's an interpretation question.
I love this next problem. So very cool.
Problem 29
i.e., find the shaded area.
Difficulty: Medium.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 13 and answer 29.
Monday, March 21, 2011
Daily TwoProblems, 12 and 30
Labels:
UVM-Combinations,
UVM-Logic,
UVM-Trigonometry
Day Twelve
Difficulty: easy-ish. Does your student remember his trig identities?
Problem 30
Difficulty: Medium.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 12 and answer 30.
Difficulty: easy-ish. Does your student remember his trig identities?
Problem 30
Difficulty: Medium.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 12 and answer 30.
Sunday, March 20, 2011
Daily Two 11 and 31
Labels:
UVM-Algebra,
UVM-Pre-Calculus,
UVM-Probability
First, an easy one.
And then something more complicated, though personally, I'm not a fan of probability questions.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 11 and answer 31.
And then something more complicated, though personally, I'm not a fan of probability questions.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 11 and answer 31.
Saturday, March 19, 2011
Daily two puzzles for contemplation. 10 and 32
Labels:
UVM-Algebra,
UVM-Geometry,
UVM-Probability
Day Ten
Difficulty: easy-ish.
Problem 32:
Difficulty: Tricky. It seems easy, but then tries to kneecap you.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 10 and answer 32.
Difficulty: easy-ish.
Problem 32:
Difficulty: Tricky. It seems easy, but then tries to kneecap you.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 10 and answer 32.
Friday, March 18, 2011
Daily Two. 9 and 33
Labels:
UVM-Algebra,
UVM-Sequences
Day Nine.
Difficulty: easy-ish.
Number 33:
Difficulty: Hard.
(or as the kids said, OMFG)
It's actually more complicated than hard.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 9 and answer 33.
Difficulty: easy-ish.
Number 33:
Difficulty: Hard.
(or as the kids said, OMFG)
It's actually more complicated than hard.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 9 and answer 33.
Thursday, March 17, 2011
Daily Two. 8 and 34
Labels:
Logic,
No Calculator,
Puzzles
Day Eight will make you think a second ... or ten.
Difficulty: easy.
Difficulty: Hard-ish
(if they don't know the 3D Pythagorean theorem and have to work it out.)
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 8 and answer 34.
Difficulty: easy.
Difficulty: Hard-ish
(if they don't know the 3D Pythagorean theorem and have to work it out.)
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 8 and answer 34.
Wednesday, March 16, 2011
Daily Two. 7 and 35
Labels:
UVM-Algebra,
UVM-Geometry,
UVM-Logic
Problem 7
Difficulty: so easy the kids kept second-guessing themselves. ;-)
Problem 35
Difficulty: Hard (last page)
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 7 and answer 35.
Difficulty: so easy the kids kept second-guessing themselves. ;-)
Problem 35
Difficulty: Hard (last page)
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 7 and answer 35.
Tuesday, March 15, 2011
Daily Pair of Problem Puzzles. 6 and 36
Labels:
UVM-Algebra,
UVM-Geometry
Day Six will make you think a bit.
Difficulty: easy - ish.
Difficulty: Hard (last page)
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 6 and answer 36.
Difficulty: easy - ish.
Difficulty: Hard (last page)
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 6 and answer 36.
Monday, March 14, 2011
Daily Problem Pairing. 5 and 37
Labels:
No Calculator,
Puzzles
Day Five, Number 5
Difficulty: easy.
and Problem 37 because 38 was already posted and I didn't want to lose any of the comments.
Difficulty: Hard. (Last page)
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 5 and answer 37.
Difficulty: easy.
and Problem 37 because 38 was already posted and I didn't want to lose any of the comments.
Difficulty: Hard. (Last page)
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 5 and answer 37.
Sunday, March 13, 2011
Daily Puzzle Pairing. 4 and 39
Labels:
No Calculator,
Puzzles
Problem (4)
Difficulty: first page.
Problem 39
Note: Remainder.
Difficulty: Hard. (last page)
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Yeah, I know, it should read "larger" and "smaller" but I didn't have the energy to fix it.
answer 4 and answer 39.
Difficulty: first page.
Problem 39
Note: Remainder.
Difficulty: Hard. (last page)
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Yeah, I know, it should read "larger" and "smaller" but I didn't have the energy to fix it.
answer 4 and answer 39.
Saturday, March 12, 2011
Daily, they'll get harder. 3 and 40
Labels:
No Calculator,
Puzzles
Day Three
Difficulty: easy.
I'm going to save my self some time and just include the difficult one with the easy one every day.
Please enjoy this mathematical tidbit.
Difficulty: Hard.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 3 and answer 40.
Difficulty: easy.
I'm going to save my self some time and just include the difficult one with the easy one every day.
Please enjoy this mathematical tidbit.
Difficulty: Hard.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 3 and answer 40.
Friday, March 11, 2011
Daily Puzzle Pairing. 41
Labels:
UVM-Algebra,
UVM-Geometry,
UVM-Trigonometry
Since there are so many truly able mathematicians among my readers, I've decided to give them something to keep busy with! This set will start at the hardest and work backwards.
Difficulty: hard.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Answer is here.
Difficulty: hard.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Answer is here.
Daily, they'll get harder. 2
Labels:
No Calculator,
Puzzles
Day two.
Difficulty: easy.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Answer is here.
Difficulty: easy.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Answer is here.
Thursday, March 10, 2011
Daily, they'll get harder. 38
Labels:
No Calculator,
Puzzles
Daily, they'll get harder. How hard? Try this one:
Difficulty: hard. Especially when you aren't using a calculator.
However, this does mean that the problem is solvable that way and stuff will cancel when you realize the method to use. Of course, when you don't see the method, it's frustrating as hell.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Answer is here.
Difficulty: hard. Especially when you aren't using a calculator.
However, this does mean that the problem is solvable that way and stuff will cancel when you realize the method to use. Of course, when you don't see the method, it's frustrating as hell.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Answer is here.
Daily, they'll get harder. 1
Labels:
No Calculator,
Puzzles
Day one. Question 1
Difficulty: easy.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Answer is here.
Difficulty: easy.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Answer is here.
Tuesday, March 1, 2011
Bill Gates and Teacher Spaghetti Sauce
Labels:
Critical Thinking,
Professionalism,
School Reform,
Standards,
TED
Bill Gates is at it again. For such a smart guy, it is amazing how dense he can be when it comes to education reform. To wit:
Hey ! "Find out what makes them so effective"???
If you don't know WHY the great teachers are great, how in Bloomberg's Bloomers can you say definitively that
There might not be a best, only a best for you. That teacher might not be the BEST because you can't define best for more than one type of student. There are more types of teachers than there are types of spaghetti sauce. Go watch the Malcolm Gladwell talk at TED.
We can “flip the curve,” raising performance “without spending a lot more,” if we “measure, develop and reward excellent teaching." ... of all the variables under a school’s control, the single most decisive factor in student achievement is excellent teaching. To flip the curve, we have to identify great teachers, find out what makes them so effective and transfer those skills to others so more students can enjoy top teachers and high achievement.SO, Billy, we have to identify great teachers and find out what makes them so effective. Then we have to transfer that to other teachers. That will flip the curve.
Hey ! "Find out what makes them so effective"???
If you don't know WHY the great teachers are great, how in Bloomberg's Bloomers can you say definitively that
- You can identify these great teachers and find out what makes them so effective.
- These unknowns are transferable.
- This transference will raise performance “without spending a lot more."
There might not be a best, only a best for you. That teacher might not be the BEST because you can't define best for more than one type of student. There are more types of teachers than there are types of spaghetti sauce. Go watch the Malcolm Gladwell talk at TED.
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