What if my expectation is not reasonable, how do I remedy that problem?
Teaching in the Fall Semester as a Graduate Assistant
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Steven G
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Good job! I went through an extremely hard masters problem (you might be at one as well). The teachers jobs were to kill us. In the end, it made be much tougher than when I finished my undergraduate program.
Yes, you definitely should have improved on proof writing and especially improving your thought process. All is looking good for you. Do you mind telling us which university you are studying at?
Yes, you definitely should have improved on proof writing and especially improving your thought process. All is looking good for you. Do you mind telling us which university you are studying at?
Steven G
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That is hard to answer especially if your expectations are unreasonable and you don't know it.
Here is how I made up exams. I opened the textbook and went to the homework problems from each section that we covered and in each section I picked one problem of each type.
I assure you that if you do that, then students who study will do well and students who don't study probably won't do well.
I'll you a quick story. The 1st time I ever taught was as a graduate student. My students were always well behaved but on this one day they just couldn't stop talking to their classmates. I repeatedly warned them that right after class I was going to be making up their next exam and they don't want me to be upset with them while I was doing so. They still talked and I made the hardest exam that I could come up with. Would you believe that the test grades were not worse than usual! The strong students did well, mediocre students were in the middle and poor students failed.
Your students are not math majors so no proofs on the exams (that's unreasonable).
I am attending Minnesota State University in Mankato.
I have no idea. However, I am leaning three fields: analysis, algebra, or differential geometry.
I will be taking three graduate level course in the fall: Complex Analysis, Abstract Algebra and Differential Geometry. By the end of the semester, I will have good idea of which one course I will do my research on.
I will be taking three graduate level course in the fall: Complex Analysis, Abstract Algebra and Differential Geometry. By the end of the semester, I will have good idea of which one course I will do my research on.
Even though I teach high school (21 years and counting) and not university, here's my two cents on writing exams. One concept, one problem. For example, I don't need to give 7 problems on using the Law of Sines; if you can solve 1, you can probably solve 7. I also like to throw in some conceptual questions like "Given this labeled triangle, which of the following trig ratios are written correctly?" I'll have maybe 6 - 8 ratios written, with 2 or 3 of them correct. Or, "Here are 4 attempts to differentiate various functions. Which one(s) are correct?" My classes are approximately 87 minutes, and my goal is 10 - 15 problems, depending on the material and the class. Remember, you need to grade them, so they should also be fair not just for your students, but for your time as well. Last piece of advice: if you are going to grade with partial credit, work out as much as you can in advance and have it written down; you'll be a more consistent grader that way. You won't anticipate everything the first time, but having an idea of some things will save a lot of potential inconsistencies and "he got -1, but I did the same thing and got -3!!"
Hello again, I had my first year in teaching College algebra. It went fine in general.
In first semester, I had a larger class with 33 students. I had to go very fast about the material. It could have been better in the first semester because I made couple serious mistakes in my practice exams as well as some lack of organization and my ability to answer some questions.
Course-wise, the first semester was brutal with the three 600-level classes such as Complex Analysis, Differential Geometry and Abstract Algebra.
I did well in Complex Analysis. I did good with remaining classes. I couldn't decide on which topic that I was interested in until the next semester.
In the second semester, it went well because I had only a dozen students. But I also had a forgetful moment on how to factor a polynomial during my evaluation. So I wasted at least fifteen minutes on thinking and anxiety that I had. But I moved on to the next point in the lecture. During the second semester, I took my time on the harder materials and give more attention to the technical side of mathematics. My organization was not the best but I had some organization for classes.
Every TA told me that I write very difficult exams for college algebra. For instance, I asked the students to solve the quadratic equation by using the complete the square method. I asked the students justify "why did you do that in the computation?" I introduced some proof writing questions in my exams. I feel like it is a good thing because it forces the students to think critically and understanding the material on the deeper side.
Course-wise- the second semester was not as brutal as the first, but still brutal because I enrolled in two class Topology and Introduction to Functional Analysis. I decided to do my research in functional analysis.
Any tips or recommendations for me?
Thanks,
Cbarker12
In first semester, I had a larger class with 33 students. I had to go very fast about the material. It could have been better in the first semester because I made couple serious mistakes in my practice exams as well as some lack of organization and my ability to answer some questions.
Course-wise, the first semester was brutal with the three 600-level classes such as Complex Analysis, Differential Geometry and Abstract Algebra.
I did well in Complex Analysis. I did good with remaining classes. I couldn't decide on which topic that I was interested in until the next semester.
In the second semester, it went well because I had only a dozen students. But I also had a forgetful moment on how to factor a polynomial during my evaluation. So I wasted at least fifteen minutes on thinking and anxiety that I had. But I moved on to the next point in the lecture. During the second semester, I took my time on the harder materials and give more attention to the technical side of mathematics. My organization was not the best but I had some organization for classes.
Every TA told me that I write very difficult exams for college algebra. For instance, I asked the students to solve the quadratic equation by using the complete the square method. I asked the students justify "why did you do that in the computation?" I introduced some proof writing questions in my exams. I feel like it is a good thing because it forces the students to think critically and understanding the material on the deeper side.
Course-wise- the second semester was not as brutal as the first, but still brutal because I enrolled in two class Topology and Introduction to Functional Analysis. I decided to do my research in functional analysis.
Any tips or recommendations for me?
Thanks,
Cbarker12
Steven G
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A PhD math program should be brutal! It seems that you are doing just fine. For the record, I dropped out of my PhD program after finishing the requirements for the masters program.
I hate when students say that a teacher teaches too quickly. In my opinion, the only ways one can teach quickly is if they finish the material well before the semester ends or they drastically change their speed during the semester. If a teacher teaches at a constant rate and finish within one week of the semester ending (one week is nice to have for review-but it always seems to never happen!) and the students feel that the teacher was too quick, then the real situation is that there was too much material in the course. Here is how I (try to) pace myself. I count the number of meetings minus the number of exam days and I divide that number by the number of meetings. This tells me how many sections I need to cover on average per meeting.
There is nothing wrong with making hard exams. We need to have some standards! When you say that you asked the students to solve the quadratic equation by using the complete the square method, do you mean that you gave them a quadratic equation and asked them to solve it using the completing the square method or did you basically ask them to derive the quadratic equation? If the latter, that would be bordering being too much for a college algebra student to have on an exam. I would have instead told the students that I would ask this question on the exam. Without telling the students, I call that type of question my curve question. If you study that proof, then you get extra points and if you don't, well you don't get extra points. I recall telling my students that I will ask them on the next test to prove that the empty set is a subset of every (non-empty ??) set.
Please have standards in your classroom. Remember that your students come first and you need to teach the class well. Explain everything to them. No rules without proving it or at least motivating it. The problem with math education is that many k-12 teachers just state rules (theorems/facts) and never show why it works. You just can't, in my opinion, tell a student that (ab)n=anbn. I have given some bad reviews to adjuncts when I observed them when they did this. Students need to learn to think and not do things blindly. There is a limit to how much math you can just accept as true before having serious trouble going further in math.
Can you maybe supply us with an exam or two that you gave your students so we can give you better advice?
Functional analysis. I like that too, but I wanted to be an algebraist as most American PhD students. Out of curiosity, may I asked where you studied K-12?
I hate when students say that a teacher teaches too quickly. In my opinion, the only ways one can teach quickly is if they finish the material well before the semester ends or they drastically change their speed during the semester. If a teacher teaches at a constant rate and finish within one week of the semester ending (one week is nice to have for review-but it always seems to never happen!) and the students feel that the teacher was too quick, then the real situation is that there was too much material in the course. Here is how I (try to) pace myself. I count the number of meetings minus the number of exam days and I divide that number by the number of meetings. This tells me how many sections I need to cover on average per meeting.
There is nothing wrong with making hard exams. We need to have some standards! When you say that you asked the students to solve the quadratic equation by using the complete the square method, do you mean that you gave them a quadratic equation and asked them to solve it using the completing the square method or did you basically ask them to derive the quadratic equation? If the latter, that would be bordering being too much for a college algebra student to have on an exam. I would have instead told the students that I would ask this question on the exam. Without telling the students, I call that type of question my curve question. If you study that proof, then you get extra points and if you don't, well you don't get extra points. I recall telling my students that I will ask them on the next test to prove that the empty set is a subset of every (non-empty ??) set.
Please have standards in your classroom. Remember that your students come first and you need to teach the class well. Explain everything to them. No rules without proving it or at least motivating it. The problem with math education is that many k-12 teachers just state rules (theorems/facts) and never show why it works. You just can't, in my opinion, tell a student that (ab)n=anbn. I have given some bad reviews to adjuncts when I observed them when they did this. Students need to learn to think and not do things blindly. There is a limit to how much math you can just accept as true before having serious trouble going further in math.
Can you maybe supply us with an exam or two that you gave your students so we can give you better advice?
Functional analysis. I like that too, but I wanted to be an algebraist as most American PhD students. Out of curiosity, may I asked where you studied K-12?
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In your first question about quadratic equation, the answer is the former. See below for two examples of my exam. In the first exam, it is usually an review of high school algebra and learning about complex numbers, and solving linear and quadratic equations as well as some linear rational equations and applications of linear equations. Exam 3 is about function's operations (arithmetic and composition) and function inverse as well as properties of quadratic functions, analyzing graphs of polynomials functions, division of polynomials, sometimes solving polynomial equations. I try to motivate each concept with an example. I went to a public school system from K to 12 in southwest Minnesota.
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Steven G
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I looked at both exams. I must admit that they require the students to know the material! The students at the community college I retired from would have a hard time with these exams. Having said that, you teach at a university and if your students are able to do these exams by all means keep it up. Having said that, I saw no one question unreasonable. You play hardball with them and as I said if they are surviving then they are really learning.
I had the following reputation as an instructor: If you wanted to learn the material then take Steven, if you didn't want to learn the material then stay far away from Steven. I liked that reputation! It was good that I would not only get students that wanted to learn, but they did learn from me in the end. That was real teaching. You seem to be doing the same at a more rigorous level than I did.
Do you have students getting A's in your class? In a class of 30, having 3-6 students getting A's is just fine.
I had the following reputation as an instructor: If you wanted to learn the material then take Steven, if you didn't want to learn the material then stay far away from Steven. I liked that reputation! It was good that I would not only get students that wanted to learn, but they did learn from me in the end. That was real teaching. You seem to be doing the same at a more rigorous level than I did.
Do you have students getting A's in your class? In a class of 30, having 3-6 students getting A's is just fine.
Steven G
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Does your supervisor write the same exam for all sections of the same course. Your college has high standards. I know you already said in a past post that your supervisor writes the finals--my advice to you then would be to look at the final, judge the difficulty of the final and then gives exams of the same difficulty.
Yes with minor variations (values and order of questions have change) among the sections, but the same format. Throughout the semester, I try to prepare my students by giving them hard exams (like one step below of the final exam in terms of difficulties) mimicking the final exam format.
Steven G
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One step below? Why not one step above? I'm not saying that you don't know your students but I would be as tough on the students that I can get away with! By get away with, I mean that my students can handle. To learn that, give them homework assignments with increasing difficulty and see just how far you can push them. To be honest, I don't think that your exams should be easier than the final.
I went to a college where the math faculty simply tried to kill us! That didn't work out so well for them as they only accepted good students. They didn't try to kill us to be mean, but rather to get us to rise to their expectation. It worked and we all survived. I personally liked that my teachers were hard on us. In addition to being hard on us they were always available to meet with us whenever we came to their office--they actually put down the research work they were working on to help us.
I went to a college where the math faculty simply tried to kill us! That didn't work out so well for them as they only accepted good students. They didn't try to kill us to be mean, but rather to get us to rise to their expectation. It worked and we all survived. I personally liked that my teachers were hard on us. In addition to being hard on us they were always available to meet with us whenever we came to their office--they actually put down the research work they were working on to help us.
I looked at those attachments for that College Algebra exam parts. I was a graduate teaching assistant for three sections of
College Algebra, and I tutored pre-algebra, intermediate algebra, college algebra, and higher level courses as a tutor
elsewhere, and I do so currently.
Here are certain examples/problems/topics that are missing from this College Algebra exam:
Difference quotient: \(\displaystyle \ \ \dfrac{f(x + h) - f(x)}{h}\)
Solving a radical equation \(\displaystyle \ \ \ Example: \ \ \sqrt{x + 5 } \ + \ 1 = x\)
Exponential and Logarithmic Functions
-------------------------------------------
Write an exponential equation as the corresponding logarithmic equation.
Write a logarithmic equation as the corresponding exponential equation.
Expand a logarithmic expression.
Write an expanded logarithmic expression as the logarithm of one expression.
Evaluate the logarithm of a number/expression.
Change of base formula
Solve an exponential equation.
Solve a logarithmic equation.
Sketch the graph of an exponential function.
Sketch the graph of a logarithmic function.
_________________________________________________________________________
Compound Interest: \(\displaystyle \ \ \ Amount \ = \ Principal(1 + r/n)^{n*t}\)
Continuous Interest: \(\displaystyle \ \ \ Amount \ = \ Principal*e^{r*t}\)
_________________________________________________________________________
Also, there are questions here that should be left behind on an intermediate algebra exam.
A quick look reveals those to be numbers 2, 4 a) through c), and 5. The removal of these
would open up space for the missing ones I wrote above.
There are too many helps in the way of formulas given to the students at the end of the
exam parts on each of the attachments. The students should already know fluently
the rules of exponents and the equation for the Quadratic Formula, for example.
Question 3 of exam 1:
3. (5 points) Suppose there was a blizzard in a city. Suppose that there are two snow-plowing companies that the city hired. Since the roads in the city are inaccessible to vehicles, the city request the roads to be plowed in 6 hours. Company A can plow the whole city in 3 hours, and Company B can plow the whole city in 4 hours. Will the job get done in time?
Since either company can "plow the whole city" (perish the thought) - under 6 hours
Why would the city hire two companies ? Does n't the question - "Will the job get done in time" - become irrelevant? Am I missing something?
I could be wrong about my level of difficulty on my exam. My exam could be equally difficult like the final exam. Unfortunately I have no control on the homework questions because my supervisor makes the homework on electronic system. I have control on the exams, quizzes and group work (if I desire to.) I do make quizzes at end of each chapter that does not have an exam assoicated with it.
I provided only two exams (Exam 1 and Exam 3) and different points of the semester. So exam 1, chapter 0 to middle of chapter 1 which is a review of high school algebra and learning about complex numbers, and solving linear and quadratic equations as well as some linear rational equations and applications of linear equations. Then in exam 2, I tested my students on the rest of chapter 1 (which is other types of equations and inequalities and the introduction to functions and graphs of function). Then Exam 3 is stated above in the previous post. Exam 4 is about logarithms and exponential functions.
Depends on my time, I skipped the difference quotient because most students will not be taking precalculus or higher in my class. If they do, they will learn it in precalculus or calculus 1 in my university.
In my class length, I have only 50 minutes to give an exam.
Please don't assume that I missed the topics listed above, it could be that I teach them at a different point of time in semester. I give them a formula sheet because the final exam has a list of all of the formulas that we used in the semester. So I am mimicking that expectation in my exams. But I do not give them all of the formulas because I do expect some memorization of basic formulas after the first exam like the exponent rules in exam 2 and exam 3 as the long division for polynomials in exam 3.
I know that this question is not the best one to ask because it is unrealistic. My supervisor said the same thing. In this exam, calculators was not allowed. So I had it make it an easy computation problem but with idea of a share work problem that was linear. The main point of this question is the set up of the share work problem.