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.

In-Class Activities: A Well I Have Fallen Into

This term I am utilizing in-class activities in all four of my classes in various ways. Previously I've used them only in special cases where the topic is best understood by a hands-on demonstration of the concept. After teaching with a flipped classroom model developed by another faculty member, I am becoming more comfortable with students discovering the material in-class, as opposed to me telling students what the ideas are.

College Mathematics - This is the course I taught last term that utilized a flipped classroom model. Students are to print out handouts before class, take a pre-quiz, come to class, work on the handouts in groups, complete the handouts at home, and take a post-quiz within 24 hours after class. They repeat this for a number of handouts, and also have group tests, tests, and homework. Initially I was worried about, well, everything. Students not showing up, not understanding, waiting for me to tell them what to do, etc. It all happened, but those students who would have done well in a traditional class did well here. Those that would not have done well in a  traditional course... I'm not sure if they did any better using this model. The freedom that students are allowed in this format presents them with a choice, to put the time into understand the material, or not. But this is the choice all students have in any course. At this point I see this method doing no harm, and possibly helping students understand the material a bit better.

Trigonometry/Pre-Calculus - This is a 5 credit hour course that meets twice a week, meaning two and a half hour class meetings. To break up lectures I'm using in-class activities to have students develop concepts, or to gain practice with different skills. The first two had students developing the graphs of trigonometric functions. Students were initially resistant, but during the summation of the activity they were able to answer questions students in previous classes were not.

Calculus I - I'm using the POGIL activities (link to come) another instructor recommended. There are only three in the course, but if the first activity is any indication, I think they'll do well.

Calculus III - Weekly activities meant to simulate a structured recitation. The activities have been successful, but the time it takes to develop them is considerable.

I will be posting these activities in my upcoming Worksheet Wednesdays. Feel free to download them, use them, and send along any feedback.

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.

Harvard's report on MOOCs

Harvard Magazine posted an article yesterday about recent discussions and reports about MOOCs and the university's participation in them. One thing that I noticed:

REPORTING TO the Faculty of Arts and Sciences (FAS) at length for the first time since he was appointed vice provost for advances in learning last September, Peter K. Bol highlighted shifts in the landscape for the much-publicized massive open online courses (MOOCs). At the December 3 faculty meeting, Bol noted that:

• People who register for free MOOCs, like those offered on edX, differ from conventional students, and are not using them like conventional courses.

 Well yeah! I've mentioned before that MOOCs are not comparable to traditional college courses because the people enrolling in them have a variety of goals for the course. Traditionally, college courses are part of a whole curriculum whose aim is to educate students in certain relevant fields, and a specific discipline. These students are usually of the same age, have the same goals for each course (learn enough to move on/get a good grade), and are peers in relation to the discipline. With MOOCs? Sure, a good portion might be these traditional students, but some may be experts in another field who want to get a better grasp of this related subject, a high school teacher who is looking for good applications for their classes, another college instructor/professor who wants to see how the course is taught, etc. You cannot compare completion rates of traditional higher education institutions with MOOCs, its like comparing malus and citrus.

Learning Styles DNE

Learning Styles do not exist (or DNE for you mathematicians). There I said it. I know many of those in the education community and industry have presupposed this conjecture as the basis for many long careers. I understand that many of you at this moment are saying "But I know I'm an auditory learner." I get that it seems like a simple, logical explanation for why some methods work and others don't. But under even a little scrutiny, it doesn't work.

The reason for this post: I recently went to a workshop that I thought was going to be about teaching techniques focused on using applications, but turned into "How to Teach with Learning Styles". For the first 45 minutes I squirmed in my chair as kinaesthetic, visual, and audible were bandied about and how a 5-minute survey would help students determine their preferred method of learning. There was a glimmer of hope when the facilitator said "Now even if a student has one of these learning styles, that doesn't mean the others are neglected." and everyone nodded in agreement, but the discussion quickly turned to the deterministic ways these styles should be used. I kept quiet during the workshop, but thought this would be a good venue to air this out.

I see Learning Styles, and in fact any method of quantizing personality traits, in the same way as the Theory of Forms. These Learning Styles are the deciphering of the proverbial shadows on the cave wall, when what they really want to study is the flickering of the light, the cognition of the brain. The styles are so far removed from the process of how the brain actually works, that they simplify this dynamic process (learning) into three easily understood classifications (or however many finite number of personalities). Cognition, epistemology, psychology, neurology, etc. are the ways we study and learn about how we learn and should be the prime motivators for finding methods of how to teaching.

While reasonable, we haven't mapped the human brain just yet, and therefore most of these disciplines can't help us with the day-to-day "What do I do in the classroom?" questions. There is a large body of work on research based methods for teaching, my favorite of which is How Learning Works: Seven Research-Based Principles for Smart Teaching. The book does an excellent job of summarizing current research, and providing real implementations that produce results.

The comparison of these research based methods and Learning Styles point to a larger issue, the lack of scientific principles used in supporting Learning Styles. Many, many studies show that Learning Styles do not predict anything, are a myth, and have been classified as such for 25 years.

Unfortunately people are going to keep on believing in Learning Styles because they 'believe' they fall into one of the three/finite cases. Their belief will trump any evidence because it is about 'them' and their identity. This is probably the biggest reason why Learning Styles will continue, the narrative of the individual is a powerful force, and a series of scientific papers will not dissuade that narrative. The only way to combat this myth is the slow steady work of changing curriculum, talking to people, and developing materials and products that use research based methods of instruction.

Monday MOOC News - 11/18/2013

For this week a couple of articles, an announcement by Facebook, and an updated graphic of the LMS market.

• Open Source Winter 2014 - Facebook's partnership with a number of universities continues with thier Open Source course continuing into Winter 2014. The program offers a bridge between what software developers do with the academic subject of computer science. Increasing the relevance of academic disciplines is always a good thing, especially for Facebook who can scout out new talent before they're even on the market.
• Common Core State Standards: What do they have to do with Higher Education? - Faculty Focus has an overview of how the CCSS affects higher education, and while helpful if you have never heard of the CCSS, is painfully short and lacks details. How do these standards affect remediation? How can college systems better integrate these standards into their curriculum? What about all these anti-CCSS advocates, are they worth listening to? How do (or could) these standards affect current efforts in OERs, MOOCs, and other innovations/buzz words?
• MOOCs and Statistics Education: Fad or Opportunity? - AMSTAT has a good article on statistics education and MOOCs, with an interview of Brian Caffo, Jeff Leek, and Roger Peng. I completed Peng's Computing for Data Analysis, and 'audited' Leek's Data Analysis. I've discussed both these courses before, and feel this article is a few months too late. However, the article does provide a good overview of the challenges all three have faced, and how they are attempting to meet them.
• Higher Education Market 2013 - Phill Hill has updated his LMS market share graph for 2013. A pretty neat graphic showing the evolution of the market.

---

My MOOCs

I participated a bit more in the Big Data in Education course last week. A number of students have complained that Baker speaks too fast, and the course covers topics too quickly. My response:

First, the guy is from one of the boroughs, he's going to talk a bit fast. I myself have recently moved from New York (7 years) back to my native Oregon, and all my students repeatedly ask me to slow down. In this class you do have the option of slowing down the speed of the videos, by clicking on the '-' button on the bottom left. Unfortunately my students don't have it that easy.

Second, the course is about Big Data in Education, not Big Data, statistics, or how to solve your specific research question. Prof. Baker has to assume knowledge about statistics, tools, and other Big Data odds-and-ends to get to the Education part. I have had to brush up on many of the statistical models, tools, and papers he's discussed. 

Lastly, Prof. Baker's passion and commitment to this subject is inspiring. No other Coursera professor is as active in the forums as he has been, he presents ideas concisely with plenty of avenues for us to research, and provides plenty of links, corrections, and documentation. I feel pretty lucky to be able to take this course.

That second point is something I believe is a consequence of the 'student as a consumer' paradigm some are promoting. Students sign up for some of these MOOCs expecting the instructor to cover the exact area they are interested in, at their ability level. "I'm taking this course, right? Shouldn't I get what I want from it?" Unfortunately the 'consumer' analogy breaks down here, they 'buy' these courses with their time and effort, not their money. Not sure how MOOC instructors and providers get around this paradigm, ignore it? "You are getting what you paid for."? Start charging and then provide greater support?

Another bugbear of mine cropped up in the same forum. There was discussion of MOOCs not favoring passive students, and others saying that this is the reason they have such high attrition rates. My response if you haven't heard it before:

This is a line of reasoning I can't get behind. "MOOCs have high attrition rates relative to traditional courses taught by colleges and universities. Therefore they are inferior to traditional courses." What? That's comparing two totally different things, like citrus and malus. The entry for MOOCs is an internet connection, a computer, and an email address. The entry for a college or university is prior education, placement tests, thousands of dollars, and a host of other things. By not completing a MOOC you've wasted at most a couple of minutes reading about the course and signing up. By not completing a degree, you've wasted years, thousands of dollars, and plenty else. Of course attrition rates are different, the more you invest in something the more you will see it through to completion. 

Also, the aims and motivations of students entering a MOOC can be very different. For a MOOC its not a big deal if you pick and choose the topics you want to learn about, and don't see it through to the end. For other students they want that credential. Even others may be experts in the field and want to hear what Prof. Baker is saying. Since there is no 'gatekeeper' for entry into MOOCs the population entering them will be very different than traditional colleges and universities. Again this leads to higher attrition rates, some student's initial expectations are that they won't 'complete' the course, even though they are getting something from it.

Feel free to join the conversation by commenting below.

Monday MOOC News comes out every Monday (hopefully) and contains my thoughts on current MOOC news, and a brief summary of the MOOCs I am taking. Feel free to join the conversation.