Same course, different terms, completely different classes.

Last term I taught MATH151 Calculus I in the morning daily, and it felt so RIGHT. The pacing of the class, my in-class examples, questions from students, the schedule, the end of week activities that have students explore different topics, everything felt like the best it could ever be. This term for whatever reason things are not going so well. I'm teaching two sections of the class and both feel wildly different.

The morning class seems tired, not really 'there', and swings between general bewilderment and complete boredom at what we're doing. Test scores are low, and there are still (WEEK 7!) students who haven't registered for the online homework system. I've even started moving back to lecturing two days a week since participation through the in-class examples has been low. There are a number of students who think of mathematics in very linear terms which limits their ability to solve application questions, but at the same time their work is unorganized. Other students are unprepared to complete most of the algebra in the course, whom I fear are not going to pass for this reason. In this class I feel like a task master.

The afternoon class is energetic, but has a habit of going off the rails at the slightest provocation. I have to do a lot of sheep-dogging (making sure the group is together) as we go through each question. In-class examples are better received with this class, and they work well in groups, but questions that require a long, sustained method are difficult. Numeric outcomes for this class are generally positive, but I wonder if they are getting the conceptual understanding down. In this class I feel like a positive guide to the discipline.

I hope this doesn't come across as complaining about my students, it just seems that a class reflects both the instructor and students, as it is a culture both groups are building together. I'm coming to recognize that each class has to be different because it contains different people in it. I may have 'empirical' ('imperial'?) methods and assessments, but if they don't somehow reflect the students in the course am I being as effective as I could be?

Experienced Faculty = Font of practical knowledge and hard truths.

I recently had an observation by an experienced faculty member and they gave me some great advice that I thought I would pass along.

• Trying to use random whiteboard markers that don't work looks bad. Every college classroom has an assortment of whiteboard markers in the tray that people have left. Some work, and some don't. When an instructor tries to make a point, but their marker doesn't work it brings up thoughts of the absent-minded professor who isn't prepared for their class. While this is a minor issue it is one that helps set the tone of the class. Solution? Bring your own supply of whiteboard markers, with some kind of tape or rubber band to mark them. 
• Every instructor apparently has some kind of verbal tick. Some phrase or series of words that they use as a crutch to fill the empty space between actual words. Mine? "Right?" I have heard that I use "Right?" before, but after forty times this faculty member stopped counting. I think I get into a 'flow' and don't really think about my word usage sometimes. Since being told this I am trying to be very conscientious about the words that come out of my mouth, but sometimes I just get back into that flow. The observer did ask "If its not harmful to students, is it really something you need to worry about?" to which my answer is no. At the same time, I don't like the idea that my language is not controllable and that sometimes I just say stuff. 
• I pack a lot of material into my courses. Some of it could be done by students ahead of time. In this particular lesson I was having students graph rational functions using their calculator. We were then looking at the patterns in the graphs, factors of the numerator and denominator, etc. looking for the specific patterns we discuss with this subject. The observer mentioned that students can do a lot of this work ahead of time. 

What advice have you received from an observation? Did you incorporate feedback into your teaching?

Changing things up! How to inject discussions into quizzes.

I offer daily quizzes in all my classes. I know that might seem scary to a few (developing, grading, student anxiety) but it is one of the few times I get to see students 'work'. These quizzes are based on three levels of participation (5 points = a quality attempt, 2 points = a minimal attempt, 0 points = no attempt) and have a variety of purposes which I have talked about before. I do review them right after the student's attempt for additional feedback, to model a solution method, and to start the day's lesson.

In Calculus I we are reviewing the limit definition of the integral. Suffice it to say that this is a difficult area because it relies on both conceptual understanding, but also computational understanding of things we have not seen together (limits, summation, etc.) There are three major tasks for each question; setting up a generalized area formula, taking a summation of these areas, and then taking the limit of these areas. The specifics aren't important for this discussion, but if you know them great.

So we have a fairly detailed process to learn and students find difficulty in what to do next. Solution: multiple daily quizzes that are similarly structured, break the question down into constituent parts, and provide a model for how students should approach questions in the homework. This quiz was the last of the four quizzes structured in this way that I gave last week. The only difference between them is the function and the interval we are looking at. (Today's quiz integrated x^2 on [0, x], foreshadowing The FTC.) I had received positive feedback from students that they like how these quizzes broke down the process, and it had helped them in homework.

By Friday I felt that students were getting a little bored of reviewing the same type of quiz, so I wanted to shake students up a bit. Humans love novelty and if I can make my class novel and even silly in pursuit of understanding the material, why not? So at the end of the quiz I made a list in my head of those students who had completed the quiz. At that time I called those students my 'exemplars', took their quizzes and tapped them to different walls. They were to then stand by their quiz and explain to others how they found each part of the process. At the end I collected the quizzes and graded them as normal. In hind sight I should have probably identified their quizzes as 'exemplars' and not the students themselves...

I think this helped all students develop a better understanding of the process, some by talking to these students who provided exemplar solutions, others by having to explain their method. It was also a nice way to break out in a different way, one where the focus was not on me or my methods, but on other students' methods.

Today I asked how last class went, and the response was pretty lukewarm. One student said "I think we got out of it as much as if you went through the quiz." In terms of mathematics, maybe, but in terms of developing connections between students and developing mathematical fluency I think it was better than if I reviewed the quiz.

Have you tried something to break students out of their 'shell'? Would you do something like the above for a participation-based quiz? What about for a graded-quiz? What about for a test? Feel free to comment below.

Is the lecture dead, or just undead?

Molly Worthen wrote an op-ed in The New York Times, titled "Lecture Me. Really", which discusses recent research on the lecture format, the push from STEM disciplines to reduce lecturing in favor for active learning, and a solid argument for why lectures are important and relevant. One passage really struck me.

Listening continuously and taking notes for an hour is an unusual cognitive experience for most young people. Professors should embrace — and even advertise — lecture courses as an exercise in mindfulness and attention building, a mental workout that counteracts the junk food of nonstop social media.

Teaching mathematics quite a bit of my course material is computational and skill based; Find the derivative of this polynomial. A good chunk of the other part is conceptual; When the derivative equals -1 at this value of x what does that mean for the function? Applications makeup the rest: What is the velocity of the ball at this time? All three of these parts of my curriculum speak to each other, and inform how to go about each type of task. Usually I do present or lecture over an example, but I have students try these things out on their own in class.

When short, quick messages and responses are the expectation we lose the ability to think and speak in big ideas. We forget how to piece all these small parts together and reason with them. This synthesis is what we need today more than ever. To use a cliche, the world is only growing more interconnected and we need to pull from myriad disciplines to make sense of it. By modeling this skill of building and connecting ideas we show students a mature and connected way of looking at the world.

I wonder though if I should try lecturing a bit more to model exactly this kind connection building. What do you think? Do you lecture? Did you hate lectures as an undergrad? Did you enjoy them? What about in graduate school? I'd love to hear your thoughts.

Activity Planning: Logic and showing conditions hold.

A big part of Calculus is showing certain conditions hold. The big example is continuity. There is a very natural interpretation of the idea (If you can draw the graph of a function without picking up your pencil, it is continuous.) but then there is the very technical. (Left and right limits agree, function value must exist, and the limits must agree with the function value.) Just the idea of showing conditions hold is sometimes difficult for students, primary because they have never been asked to do this before.

For the first week of my Calculus I course I am doing a lot of review. I know, I know, some of you might yell "But they're in college, you shouldn't have to review." Let's get into that in another post, for now, let's talk what I want them to know before we talk about continuity. I want them to be able to show conditions are satisfied for a definition or theorem. How do we do that? Below are a few ideas, but I would love to hear your thoughts. Share them below!

• Using plane figures and classification of parallelograms to show whether certain conditions hold or not. 
• Giving a variety of pictures where some are classified as a 'thing' and others are not classified as a 'thing' and asking them to create definitions. 
• Something to do with the law and fulfilling certain contractual obligations.

First day jitters!

Question of the day: Why do I always get first day jitters? I have been teaching since 2006 and I still haven't gotten over that first day nervousness of meeting new students. Granted I am at a new institution and I am a little unsure about the population, but I've done this dozens of times by now.

How do you get over the first day jitters? Have you?

New year, new me!... Sorta.

With Labor Day ending my focus is (slowly) shifting from Mai Tai's, road trips, and reading for pleasure to the start of a new term and new position. I am now a tenure-track Mathematics Instructor at Clark College, in Vancouver Washington. Having taught college classes since 2006, my path has not been a straight one: BS in Mathematics, MA in Mathematics, working at a few textbook publishers, teaching at seven different colleges, trying out instructional design at a new online college, starting my own business, closing my own business, and (amazingly) now find myself at the second-largest community college in Washington. I taught a couple summer classes to ease into the position, and everything feels right. All my past mistakes have remade themselves into current success. My courses are well designed, have a clear structure and purpose, and I feel confident in the pedagogical and andragogical decisions I make. At the same time I am looking forward to the tenure process and sharing it here.

My current 4-month plan:

Teaching

• MATH103 College Trigonometry - With a focus on skill-based outcomes, I feel this class would be an excellent candidate for flipping, but I don't know if I have the time to commit to such a project. I have in-class activities for each class that we work through together, but am not sure if I can refit them to this other instructional method. The main thing I would have to add is more instructional text and possibly videos. I know the college has video equipment, but again time really is the issue. I don't like using others' videos for valid reasons (different methods, wording and phrasing, quality) and invalid ones (ego, wanting to provide 'everything' for students). 
• MATH111 College Algebra - While there are a number of skill-based outcomes, there are also a few conceptual-based ones that need to be addressed. This being the case a bit more in-class work could be a good idea. The class meets two times a week for 2 hours 20 min, so one single instructional method would not be appropriate. I may have lecture for the first hour, and a group activity the second hour plus. This would require quite a bit of work, but I am hoping to leverage some OER materials. 
• MATH151 Calculus I - A fairly typical course that meets five days a week for an hour. I am looking forward to developing my course materials (lectures, quizzes, etc.) here a bit further, but also to have group activities for each Friday. I really want students to start developing effective ways of working with others in STEM-focused areas. Because of this goal these activities need to have an incentive, which is why I'm including them in their grading. I haven't decided upon what grading scheme to use (participation, completion, individual based, group based, etc.), so if you have any suggestions feel free to share. 

Common Instructional Methods

• Washington Mathematics Assessment and Placement (WAMAP) - This is a state-wide system for homework questions. I am looking to use this system for online homework for all of my classes. 
• Pre-Quizzes - These are short (1-3 questions) 5-minute timed quizzes at the very start of class. This past summer I graded all of them which made them a bit more intimidating than I want. These will now be participation based with three levels of grading; 0 for no attempt, 2 for a minimal attempt, 5 for full attempt. There are three purposes to these quizzes: 
• Activate prior knowledge that they need for that day's lecture or activity. This could be anything from a previous course, assumed knowledge of pre-skills, and material we covered already in the course. 
• Provide feedback to students as to their standing in the course. Right after students attempt the Pre-Quiz we review it as a class. If it is clear they didn't get things correct they know they should put a bit more time into this material or review those pre-skills. 
• I do put a five minute timer on the overhead so this also acts as a bit of 'exposure therapy' for more math anxious students. The goal here is to get them used to this timed environment and be comfortable answer questions in it. My hope is that when test time comes they don't completely dissociate and use the skills they have developed to cope with these Pre-Quizzes. 
• In-Class Activities - Primarily for skill-based material, these packets take the place of lecture. They usually include a brief description of the property or idea we are applying and a number of questions. I present one or two of these questions, I then ask students to try a few on their own, and we come together as a class to discuss them. In the past students have been fairly isolated in attempting the questions, but I would like to help build more of a learning community around them. If you have any suggestions feel free to share. 
• Group Activities - I would like to do these more often, but they do require quite a bit of time developing. I am looking to use these in my Calculus I course on Fridays as a capstone to the week. These would have more challenging questions and (hopefully) require students to work together. 

Tenure

I have no idea what to expect or prepare for, so my only goal here is to review the policies around tenure and meet with my committee. I will share what information I feel comfortable with, and what the committee feels comfortable with as well.

Professional Development

• Coursera - I went a little nutty last night and registered for a few classes, so I may have to do some curating of what I actually want to spend time on. I signed up for a number of mathematical classes (Fundamentals of Fluid Power, Data Analysis and Statistical Inference, Model Thinking) but also some education and research focused classes (American Education Reform: History, Policy, Practice, Qualitative Research Methods) and you know, a fun one, Soren Kierkegaard - Subjectivity, Irony and the Crisis of Modernity.
• Training at Clark - Being a new faculty member there are a number of trainings I am scheduled for; policy and procedures, the Clark Learning Community, and LMS-specific sessions. Hopefully I'll be able to share what I learn here. 
• I have been thinking about going through a graduate text to keep that feeling of 'I have no idea what I'm doing.' I need to be empathetic to students so I know what to say and do to help them get out of that space. I never got a firm grasp on homology, so if you have any suggestions for a text or a self-paced course on it let me know.

While I am feeling reinvigorated by all these new projects, ideas, and plans, I am feeling fairly confident in myself at this specific moment of time. Not because I know a lot, but because I have made enough mistakes to know what not to do. 

If you have any advice, comments, suggestions, criticisms, or general thoughts feel free to share below. Thank you for reading!