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!

Hello Russian friends!

I have gotten an influx of traffic from Russia recently and just wanted to welcome you all to this blog. If you have any questions or would like to see specific types of content or material, just let me know.

Reflections: What I do once a class ends.

This is the second in my line of posts about reflections, why they're useful, what I do to reflect, and what I do to help my students reflect on their own performance. Today we're looking at what I do at the end of the term, and how I prepare for the next time I teach a class. As an adjunct I regularly teach the same classes from term-to-term and anything I can do to help my future self quickly prepare for a class is beneficial.

At the start of each term we all have ideas about learning activities, assessments, grading structures, rubrics, and other aspects of how we are going to run (or at least manage) a course. At the end of a term we have seen how they have worked, how they didn't, and ideas for how to make them better. During finals week, for each class I take a half-hour to an hour and write a page or two on all the components of a course. This is a short example of what I started with for my Calculus III course:

Calculus III Reflections notes. 

These are very rough notes. Some of these notes I would have probably edited for wider distribution ("... if you don't force them to!"). But this is what I wrote when I was trying to get these ideas on paper. And this is the point of this exercise, get your ideas on paper quickly before the term is over and you forget. I usually create these notes during my final exams, so I can see all my students and remember what worked and didn't work for them. It also helps me think of policies to include in the syllabus if there was a particular situation that arose with a student. I include these notes in the front of my course folder.

At the start of the next term, I open my course folder and the first thing I see is this list of do's and don'ts, and don't even think about it's. These notes have helped me start preparing for a course much more quickly. I can focus on what needs to be revised, updated, or created, instead of wondering what I did last time. 

What do you do to at the end of each term to help yourself prepare for the next? Please share your experiences with me here on the blog, on LinkedIn, or Twitter. 

Reflections: Just like checking solutions, something else we don't do, but should.

Living time linearly it is sometimes hard to think back and remember how classes started. I always start with good intentions, like "I am going to return every piece of graded material back by the next class session." or "I will create a dynamic learner-centered classroom." or "Active Learning is my watchword." or some other well-intended but doomed to failure dictum. To help make these things a reality for myself, but also for my students, I'm starting to institute end-of-term reflections. My next few posts will explore two types of reflections I am using this term, how they started, and how they are working out this term.

• Student Reflections - These have taken the form of a 1 point extra credit assignment after a student has completed their final. This short, 5 question assignment asks them to think about what they should have done this term, and what they will do next term. 
• Course Reflections - After finishing a class I will write a page about what worked, what didn't work, and what to do next time. 

Stay tuned this week for my reflections... about reflections? (R-squared? R(R(x))?) And feel free to add your own!

Finally! A Win! How I expressed my concerns and students actually listened.

I had a Win yesterday! A capital 'W' Win! It kind of made my day and thought I'd share it with you all.

This term I am teaching an alternative pathway mathematics course. Traditionally students are expected to take anywhere between 1-4 remedial mathematics courses, for which they don't get college credit. These courses are not college-level (below 100-level), so they get credits for taking them but they don't apply to degree programs or requirements. For each remedial math course a student takes their chances of failing (and subsequently) dropping out increase. So to help non-STEM students get around these courses  (which are frequently focused on STEM students) many colleges and universities are trying these alternative pathway courses. Many other organizations and publications have talked about this trend.

One of the instructional methods in the course is group work. There are a number of times in a class where I or my co-teacher might say "Let's have you all work on the next question as a group." I find this to be a great way for students to learn from each other, develop their communication skills about mathematics, and help build a learner-centered classroom. The drawback has always been their propensity for getting off-topic. Giving them space for talking through these questions has turned into a space where they can talk about everything else.

Yesterday I started a topic and I could already feel the wheels coming off. Students started chatting (albeit quietly) and it was clear they were not on-topic. I could also feel myself start building up with anger and frustration. From previous experiences I knew I could not just say how I was feeling, but I needed to put into context of what students were doing, and what I expect them to. So I laid it out to them in something like this:

I really enjoy how we can talk about many different topics in this course, and it is really rewarding for me. But this class (as a whole) has a habit of getting off-topic. I know this course is structured a bit differently and it allows you all to talk through questions. This is very different than my other classes where the focus is on lectures and I know exactly what will happen next. So what I would like today is for all of use to be a little more focused, and stay on-task. Again, I love talking to you guys, but we have material to talk about today.

After that, they paid attention, focused on the material, asked some great questions, and I even received some praise from my co-teacher someone I look up to. A capital 'W' Win!