Worksheet Wednesday - Calculus Quizzes Part I

This week I'll be sharing a few quizzes from my 5-credit Calculus I course that meets three days a week. I have students complete a daily quiz that contains fairly simple questions about the material covered in the previous lecture. My intent is to make sure students put in time daily to practice the material and struggle with concepts in the course. So far it has worked fairly well, students seem more capable this term, they understand the expectations I have of them, and their performance on tests is exceptional. I will be doing some rudimentary comparisons of this class with my previous Calc I, so stay tuned for that.

Below are quizzes for a few of the first sections from Stewart's Calculus: Concepts and Contexts 4th edition. We don't cover epsilon delta arguments so a few of the limit questions may seem a bit rudimentary, and in reality they are. I feel uncomfortable asking students to do a lot with limits since we don't cover what is 'really' going on. Then again can we teach it at this level?

Quiz 1 - Review - In this quiz I have them do a few things they should know how to do that are pre-skills for the course; finding the slope of a line, finding the equation of a line that goes through two points, and finding a parallel line.

Quiz 5 - Continuity -

Quiz 6 - Miscellaneous -

Quiz 8 - Definition of a Derivative -

If you have any feedback, or you use them in your class modified or not, please post a comment below! You can also email me at robert dot weston dot 82 at gmail dot com. Thank you for reading!

Course Observation - Definitions

Life has been pretty hectic lately, I moved apartments (in the same building), interviewed for a full-time position at the college I am currently teaching at, and have generally been a mess teaching 20 credits, two new classes (to me), developing interesting lectures and activities, and grading (oh the grading). I enjoy it and love the challenge all of this offers me, but makes it hard to post regular updates. Hopefully you've enjoyed (or been amused by) the worksheets, activities, and quizzes I am posting every Wednesday. Feel free to drop me a note or post a comment below if you find anything on this blog particularly engaging or interesting.

This week a seasoned math instructor asked if he could observe my class and I gladly said yes. Sure, it can be stressful having someone in your class that isn't one of your students, but I am always looking to improve my teaching, and if that means a bit of discomfort, so be it. My desire to become a better teacher is greater than my desire to avoid criticism, constructive or otherwise. Lucky for me the feedback was very constructive, and I plan on discussing it in a few posts. Here I will only talk about one part of that feedback, the balance between core skills and more abstract ideas.

They observed a day when we went over graphing functions based on their derivatives. I have had previous conversations with this instructor about this lesson, and it was by chance the they observed this class. The previous conversations were about an esoteric point about the definition of a phrase that impacts how we answer certain questions. I mentioned this in class and how the book and I differ on this one definition, and how it could change our answer.

The observer commented that this fine distinction might not be the best use of time and energy. They were worried that few students would understand what the impact of this difference is, and most students would get nothing from it. Students have a difficult enough time understanding the book's definition, mentioning my definition may confuse them.

I understand this concern, and appreciate the fact that this instructor has spent much more time with this student population. I will likely not mention this difference in definitions in future classes, but I do want to spend time explaining why I included this difference. This lesson is at the end of a section that is very computation focused where they apply different rules. With this small diversion into how the book and I differ, I was hoping to demonstrate that mathematics isn't just a matter of following rules and computing things. This aspect of having and using precise definitions is also important and one they are going to be exposed to in future classes. I still like this idea and would like to incorporate it into another lesson. If you have any ideas about how to do this, feel free to share below.

I'll be discussing the other feedback they provided in future posts. I'm doing so partially to help myself think through the feedback and to reflect on how I can use it to become a better teacher. I also want to be able to talk about these ideas without sounding defensive. I think about my teaching pretty carefully, so sometimes I get wedded to an idea without talking to others about it. When this happens and I get feedback to the contrary I can feel myself respond defensively, and I don't find that response very useful, or frankly, professional. Part of it is this math culture of being right that I've internalized, but it also comes from my own self-doubt, both things I need to shed.

On that happy note, feel free to share your comments or email me directly.

Worksheet Wednesdays - Complex Numbers, Power Series, and Taylor Series, oh my!

For this week I have another twofer, two in-class activities dealing with complex numbers, power series, and Taylor series.

Complex Numbers and Power Series - Students were introduced to some of the properties of complex numbers, and the first page of this activity has them explore operations and graphs on the complex plane. The second page has students identify the radius of convergence of given power series, with a little analysis of the coefficients on the third page. The last two pages have students graph partial sums of power series, with a hint as to what they approximate.

Taylor Series - In this activity students are given two different functions and are asked to analyze their power series about different points, and look at a very special relationship. The first function is a simple rational function, the second being the exponential function. Students are asked to numerically compare Taylor Polynomial Approximations of the rational function centered at different points, and are asked to provide a basic comparison of the approximations of the exponential function as well. The last page walks students through a derivation of Euler's Identity. For the most part students were pretty impressed with the identity, with the exception of the student asking "Is this going to be on the test?" right after the derivation.

Worksheet Wednesdays - Trigonometric Trickiness

For this week I have a fairly basic in-class trigonometry activity, having students develop a deep understanding of these ratios, and to use them in application questions. During lecture I completed a number of 'naked' examples, without an authentic context. Here I have them start solving application questions using trigonometry with some fairly basic questions. I do include one question that increases the difficulty, but with a few hints dropped students seemed to get the basic idea.

As students work on in-class activities I usually go around the room and answer any questions they have. I do so using the Socratic Method, answering their questions with questions. They usually find this annoying, me answering their questions with questions, but over time I have noticed that students become more thoughtful with their questions. They anticipate how I will answer their questions, and so modify their phrasing so they are not just asking for numbers of values, but for methods. Near the end of an activity I will hear many more "How do I..." type questions than "What is the value for...". This demonstrates a greater appreciation of method, something I think is the goal of all mathematics educators.

Right Triangle Trigonometry - Students first confirm a few trigonometric ratios for a randomly drawn right triangle, and then answer a few application questions. Granted, it is only two pages, but if this is done the first day the sine, cosine, and tangent functions are defined, it will take 30 minutes to 1 hour.

If you have any feedback, or if you use these worksheets, let me know! Feel free to post a comment below, or email me directly.

Worksheet Wednesdays - Sequences and Series In-Class Activities

This is the inaugural post of Worksheet Wednesdays where I will post some of the worksheets, in-class activities, quizzes, and other assessment items I have develop in teaching college mathematics courses. Today will be a twofer, two in-class activities for my Calculus III course.

I have students start in-class activities during class, but they are free to complete them afterwards. In order to receive credit for completing them I have them show it to me before the next test. When they do I usually go over it with them, providing for some 1-on-1 feedback and developing a repertoire with them. So far this has worked out well for three of my classes, but as I write this it is only Week 2 so that may change. Anyway, on to the worksheets!

Monotonic and Bounded - This activity walks students through a variety of sequences and introduces the idea of monotonic and bounded sequences. They then classify each of those sequences as monotonic and bounded and then see if these sequences are convergent. Students should identify the pattern that all sequences that are monotonic and bounded are convergent, but it is not necessary for a convergent sequence to be monotonic or bounded.

Integral Test - From lecture it was clear that students' integration skills were a bit rusty, if not a bit poor. Thus I created this in-class activity to get students to practice their indefinite, definite, and improper integration skills, and to use the integral test of convergence of a series. There are a few curve balls, and we had a good discussion of how to deal with them.

If you have any feedback, or if you use these worksheets, let me know! Feel free to post a comment below, or email me directly.

2014 Spring Term

For this term I'm teaching four classes as a part-time adjunct for a total of 20 credits. A bit of a load, but I'm pretty confident about it.

College Algebra - I taught two sections of this course last term, and I found it pretty unique. It uses a flipped classroom model with Handouts to be completed in-class and at home, quizzes in Moodle (our LMS), group tests, and traditional individual tests.

Pre-Calculus/Trigonometry - First time teaching this course at this school, a long time since I've taught it. I'm using completion based in-class activities, daily quizzes, and tests for assessments.

Calculus I - I've taught this course before and already have homework assignments in Moodle. I have daily quizzes to make sure students keep up with the course, and am introducing thee in-class activities from POGIL, a resource recommended by a colleague.

Calculus III - This is the first time teaching this course, and the highest level mathematics course I have taught. The curriculum is changing to align to a course at our state school intended for engineering students. Half the course is the traditional series and sequences material, and the other half is an introduction to Linear Algebra, as opposed to advanced integration techniques. The class meets three times a week, the first two class meetings being lecture, and the third day being a review of the material, a quiz, and an in-class activity. I am very excited about this course and will share a few of my in-class activities here for feedback.

My schedule this term is a bit rough, consisting of either 8 am or 11 am morning classes, or 6 pm night classes. After this term I will only take one night class, as two are kind of rough on the home life.