You CAN Ace Calculus

### Calculus Topics Listed Alphabetically

Single Variable Calculus

 Absolute Convergence Alternating Series Arc Length Area Under Curves Chain Rule Concavity Conics Conics in Polar Form Conditional Convergence Continuity & Discontinuities Convolution, Laplace Transforms Cosine/Sine Integration Critical Points Cylinder-Shell Method - Volume Integrals Definite Integrals Derivatives Differentials Direct Comparison Test Divergence (nth-Term) Test
 Ellipses (Rectangular Conics) Epsilon-Delta Limit Definition Exponential Derivatives Exponential Growth/Decay Finite Limits First Derivative First Derivative Test Formal Limit Definition Fourier Series Geometric Series Graphing Higher Order Derivatives Hyperbolas (Rectangular Conics) Hyperbolic Derivatives
 Implicit Differentiation Improper Integrals Indeterminate Forms Infinite Limits Infinite Series Infinite Series Table Infinite Series Study Techniques Infinite Series, Choosing a Test Infinite Series Exam Preparation Infinite Series Exam A Inflection Points Initial Value Problems, Laplace Transforms Integral Test Integrals Integration by Partial Fractions Integration By Parts Integration By Substitution Intermediate Value Theorem Interval of Convergence Inverse Function Derivatives Inverse Hyperbolic Derivatives Inverse Trig Derivatives
 Laplace Transforms L'Hôpital's Rule Limit Comparison Test Limits Linear Motion Logarithm Derivatives Logarithmic Differentiation Moments, Center of Mass Mean Value Theorem Normal Lines One-Sided Limits Optimization
 p-Series Parabolas (Rectangular Conics) Parabolas (Polar Conics) Parametric Equations Parametric Curves Parametric Surfaces Pinching Theorem Polar Coordinates Plane Regions, Describing Power Rule Power Series Product Rule
 Quotient Rule Radius of Convergence Ratio Test Related Rates Related Rates Areas Related Rates Distances Related Rates Volumes Remainder & Error Bounds Root Test Secant/Tangent Integration Second Derivative Second Derivative Test Shifting Theorems Sine/Cosine Integration Slope and Tangent Lines Square Wave Surface Area
 Tangent/Secant Integration Taylor/Maclaurin Series Telescoping Series Trig Derivatives Trig Integration Trig Limits Trig Substitution Unit Step Function Unit Impulse Function Volume Integrals Washer-Disc Method - Volume Integrals Work

Multi-Variable Calculus

 Acceleration Vector Arc Length (Vector Functions) Arc Length Function Arc Length Parameter Conservative Vector Fields Cross Product Curl Curvature Cylindrical Coordinates
 Directional Derivatives Divergence (Vector Fields) Divergence Theorem Dot Product Double Integrals - Area & Volume Double Integrals - Polar Coordinates Double Integrals - Rectangular Gradients Green's Theorem
 Lagrange Multipliers Line Integrals Partial Derivatives Partial Integrals Path Integrals Potential Functions Principal Unit Normal Vector
 Spherical Coordinates Stokes' Theorem Surface Integrals Tangent Planes Triple Integrals - Cylindrical Triple Integrals - Rectangular Triple Integrals - Spherical
 Unit Tangent Vector Unit Vectors Vector Fields Vectors Vector Functions Vector Functions Equations

Differential Equations

 Boundary Value Problems Bernoulli Equation Cauchy-Euler Equation Chebyshev's Equation Chemical Concentration Classify Differential Equations Differential Equations Euler's Method Exact Equations Existence and Uniqueness Exponential Growth/Decay
 First Order, Linear Fluids, Mixing Fourier Series Inhomogeneous ODE's Integrating Factors, Exact Integrating Factors, Linear Laplace Transforms, Solve Initial Value Problems Linear, First Order Linear, Second Order Linear Systems
 Partial Differential Equations Polynomial Coefficients Population Dynamics Projectile Motion Reduction of Order Resonance
 Second Order, Linear Separation of Variables Slope Fields Stability Substitution Undetermined Coefficients Variation of Parameters Vibration Wronskian

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17calculus > for teachers

As a follow up to a blog article I wrote several years ago, which was directed to students about having a terrible teacher (reproduced here.), I thought I would write down my thoughts about how to be or not to be a terrible teacher.

STUDENTS: If you have an instructor who is not as helpful as you think they should be, see the suggestions we have on how to learn from any teacher.

 Students are very perceptive. They can tell when we don't know what we are talking about.

We need to teach students to learn on their own and love learning, so that they no longer need us.

Teachers - Please understand that this page is meant to get your attention and to help you, not condemn you. All of us have rough semesters where we do not teach as well as we would like. I, personally, lost a close friend one summer and consequently had difficulty teaching, not being as effective as I would like to have been. But the point is, I learned from it and have since improved. I am sure I have helped many students without knowing it but I am still learning too. I hope this page gives you some ideas on how you, also, can be a better teacher.

 Students are wonderful people and your life will be greatly rewarded by becoming a better teacher and pouring yourself into them. One way to do that is to think of yourself as a coach instead of a teacher.

How to be a terrible teacher

If you want to be a terrible teacher, do as many of these things as you can. But usually just one or two will work really well.
1. Do not listen to your students.
2. Be inflexible in your demands when it doesn't really matter. When it does matter, be as inexact and vague as possible and vascillate often.
3. Dislike your students.
4. Do not be available to help your students unless you absolutely have to (for example, set office hours when the least number of students are available).
5. When your students ask for help, be as condescending as possible. After all, YOU are the teacher and THEY are only students. This will also discourage them from 'bothering' you again.
6. Be as vague as possible when teaching and giving directions.
7. If English is not your first language, don't bother trying to improve.
8. Stop learning anything.
9. Coast to retirement. After all, you either have tenure or the school probably won't fire you anyway, so why work?
10. Be inconsistent when grading. After all, don't we all hate to grade homework and exams and just want to get it over with as quickly as possible?

 . . . deep down we don't really want to be bad teachers. Things happen, our lives don't turn out the way want . . .

Now here are some suggestions specifically for terrible math teachers.
11. Teach only the equations and do not explain where they come from and when to use them properly.
12. In lecture, work examples that are extremely easy and that will not help the students work their homework problems.
13. Lecture in a monotone voice and do not allow questions during class time.
14. If you don't completely understand the math that you are teaching, fake it and don't try to learn what you need to know about the material.
15. For exams, make them as easy as possible without the students having to learn anything, which means they can just regurgitate the equations and pass. Then, when they get to the next class where they have to use the material that you are teaching, they will fail.
16. Do everything for the students so they don't have to work at anything and learn. That way they can be totally dependent on you and you can feel needed.
17. Hate the math that you are teaching.

I'm sure there are lots of other things you could do to be a bad teacher, but actually, deep down, we don't really want to be bad teachers. Things happen, our lives don't turn out the way want and things just start to slip until we find ourselves doing something that we don't want to do. It happens to everyone. The problem is that we are responsible for a lot more than most people. We have an incredible opportunity to impact young lives for either good or bad. And we will have an impact, whether we want to or not. So we can either bury our heads in the sand and continue the way we are going or we can decide to change a few things.

Students are very perceptive. They can tell when we don't know what we are talking about. And when they do, they will make our lives more difficult, usually unintentionally.

 Do you really want to continue to teach? If not, start things in motion to change careers right now. You will be glad you did.

How do you know if you are a bad teacher?

Honestly, some teachers don't know they are bad. They think the student evaluations are inaccurate or skewed. Or maybe they don't even read student evaluations! GASP!!! Let me say right now that YOU NEED TO BE READING THEM and taking them to heart, even if they hurt.

One or two bad reviews each semester is not indicative of your teaching skill. You are never going to be able to reach every student. And students come into your class with a lot of preconceived ideas that may or may not be correct. If your reviews (which you should be reading and taking to heart) are mostly neutral or positive, keep working on improvement and know that you are probably an okay teacher. Also, an occasional semester with a majority of bad reviews does not mean you are a bad teacher. Life happens.

However, if most of your reviews are bad most of the time, then you need to rethink your life. Do you want to continue teaching? If so, then it is time to improve. Looking at the list above, there are many things you can choose to improve on. Choose one that you think will have the most impact and work on it. Then, once that new change is thoroughly embedded in you (usually after one or two semesters), choose another. Be brutely honest with yourself and work on being a better teacher.

Students need to struggle. They need to be uncomfortable to learn. That is just part of learning. But they don't need to feel completely abandoned. Get to know them. Different students need different types of help. Some need to have a concept explained in a different way. Some need to be listened to. Some need to pushed and challenged. Students are wonderful people and your life will be greatly rewarded by becoming a better teacher and pouring yourself into them. They will thank you for it, maybe not now but eventually.

We need to teach them to learn on their own and love learning, so that they no longer need us. Important! - I am saving the most important point for the end. Here it is. We, as teachers, are mostly older than our students. We need to take the lead as far as making things better. Don't think that you just need better students to be a better teacher. That is not the case. We have to take the initiative to change and improve or it just won't happen. We are the more mature adults. We must make changes to improve our teaching skills, which will then enrich our students lives.