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.

## Monday, November 23, 2015

## Wednesday, October 21, 2015

### 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.

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.

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.

## Tuesday, September 22, 2015

### 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

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.

## Monday, September 21, 2015

### 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?

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

## Tuesday, September 8, 2015

### 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

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.

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!

## Tuesday, August 4, 2015

### 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.

## Monday, June 15, 2015

### 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.

## Monday, June 8, 2015

### 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!

## Friday, May 8, 2015

### 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!

## Monday, April 20, 2015

### Twitter, Statistics, and Failure: What I can learn from other's successes.

The Chronicle just posted the article "With Twitter, Statistics 101 Takes Flight" by Mark E. Ferris about his use of Twitter to help students understand how statistics is used in different contexts. Overall he does a great job of offering a structured learning activity that exposes his students to uses of statistics. A short summary:

Have you used Twitter in any of your classes? Do you have any tips or suggestions? Feel free to share below!

- Requires all students to create a Twitter account for the course.
- Each week students are to follow 10 new statistics-based organizations, post 7 tweets about statistics (retweets of those organization's posts?), retweet 2 of Ferris' posts to keep up on the topics he is covering on his feed, and post 2-3 tweets of their own by discussing interesting statistics they find.
- Each Tuesday they are to do a short write-up of one of their weekly tweets, which is worth 15 percent of their grade.

This made me think of my own recent failed attempt to use Twitter to teach statistics. This term I am teaching Inferential Statistics and I thought I would offer students an alternative method to communicate about the course. (While I love Moodle, I know Moodle Discussion Forums are not that exciting.) I did not make it part of the grade, but merely suggested it at the start of the term. I think you can get an idea of how it went....

```
Hey everyone! Feel free to use this hashtag for discussions about statistics, inference, and the course in general. #CCCStatsII
```

— Robert Weston (@rw_161803399) March 30, 2015

This is the **only**tweet with the hashtag #CCCStatsII, so I suppose its rare and valuable, I guess? (I wonder how much I could get for it...) After talking to students further it was clear that none of them had a Twitter account, and didn't really see the point in what I was doing. This is the first time I have taught this course and creating a whole new assignment category on the fly during Week 2 did not sound very appealing, so I dropped it. The idea ended in failure, but after Ferris' article I think I'll try it again with additional structure, and make it part of their grade.

Have you used Twitter in any of your classes? Do you have any tips or suggestions? Feel free to share below!

## Saturday, April 11, 2015

### Pre-Calculus, the next topic in need of reform?

Jack Rotman did (or is doing) an interesting presentation at the 2015 Michigan Mathematics Meetings looking at Pre-Calculus reform. He draws an analogy to the current Developmental Mathematics reforms (alternative pathway, career-ready, etc.), shares some data on Michigan's approach to Pre-Calculus, and asks that big question "Are Pre-Calculus classes really preparing students for Calculus?"

I think its pretty safe to say that most states are in a similar situation regarding Pre-Calculus where colleges and universities have different requirements. In academia I know we don't like comparing institutions, but when students are transferring between different institutions (especially with costs going up) a certain level of state-wide consistency is beneficial to everyone. Students learn material that actually prepares them for the next course/future content, dropout rates lower (as a consequence of having to take less classes), completion times lower, etc.

I think its pretty safe to say that most states are in a similar situation regarding Pre-Calculus where colleges and universities have different requirements. In academia I know we don't like comparing institutions, but when students are transferring between different institutions (especially with costs going up) a certain level of state-wide consistency is beneficial to everyone. Students learn material that actually prepares them for the next course/future content, dropout rates lower (as a consequence of having to take less classes), completion times lower, etc.

## Tuesday, March 24, 2015

### Excellent article on why stating Learning Objectives might not be the best thing.

__While__ going through the Quality Matters training it always seemed a bit odd to share the learning objectives with students right away. From the design side they are absolutely necessary, from a student engagement perspective they always seemed dull. This article by Donald Clark verbalizes what I was having issues with. Definitely makes me rethink reviewing outcomes on the first day of class.

### Spring Break! Beer, sun, and crazy parties!... I mean prepping courses, and catching up on friends.

So that whole promise of regular updates was not fulfilled, at all. Not even an epsilon's worth. Sorry about that. I'm good at lists though, so let's write some of those.

Courses for Spring Term 2015

Courses for Spring Term 2015

- Contemporary Mathematics - This is a new course and is part of a state-wide effort to offer an alternate pathway for non-STEM students the demphasizes algebra. It is the first time the course has been run, and we are using co-teaching to ensure there are enough hands available for the first run through. I hope to post more about this course and provide some context on the state and national levels as well.
- College Algebra - Fifth time I have taught this course, fairly straightforward at this point. However I do want to include more demonstrations of what I expect them to do each week.
- Calculus III - Very excited about this course. I taught it last year for the first time and am looking forward to getting back into it. I would like to include daily quizzes, but I am unsure if I can make that happen this term. I need to balance my time with remember most of what is in...
- Statistics II - This will be the first time I have taught this course, and frankly, I'm pretty rusty on hypothesis testing. I used it when I took the course, touched on some of the ideas in Real Analysis, but other than than, not so much. If you have any suggestions feel free to share below!

Things I Tried Last Term

- Post Exam Reflection Prompts - I had students complete reflection prompts after they completed their second test, and for the most part it did not have the desired effect. Most of their writing was about the course structure, me, and how difficult the material was. My intent was for students to reflect on their performance, how they prepared, and what they want to do differently for the next exam. I have used these prompts in the past for final exams, which seemed to have the desired effect.
- Talk about National Adjunct Walkout Day - While I did not actually walkout, I did talk to students about adjuncts, how they are compensated, and how it affects each student's education. It was a difficult discussion for me to have, but I think it educated students on this important topic. The majority of students had no idea what I was talking about, and for the most part we had a good discussion about who is at the front of their classes. I am thinking of having a short discussion about adjuncts half-way through each course to raise awareness and inform students of what happens at their institutions.
- Using Subjective Measures for Grading - There were a few students this term that were borderline passing. This term I decided to look at their previous exams and really assess what mistakes they made. If they did not understand the basic concepts of the course I did not modify their grade. If it was clear that they understood the majority of the course material, I made an informed decision to modify their grade. Grades should reflect understanding, but purely numeric assessment would ignore my role as the instructor of the course.

Recently Completed Projects

- Manuscript edit for a Geometry workbook - This was to align a text to the TEKS/TAKS. Fairly straightforward project, but had to negotiate the initial terms a bit more than I expected.
- Exam development for Pre-Calculus - Excellent project. Wrote a few exam questions, worked in telecommuting teams to review exam questions, and made a final 'difficulty' assessment.

Projects on the Back Burner

- Video series on a specific math applications.
- K-12 Teacher lesson prep materials.
- Developing this blog.

Questions? Comments? Suggestions? Want to tell me how full of it I am? Write below!

## Friday, February 13, 2015

### Why I need everything in an email.

Something happened this week in one of my classes that I wanted to share and get your feedback on. Last week a student asked if I could bring a cord so they could connect their calculator to a computer and update their OS.

Student: Did you bring the cord you talked about last week?

Me: No. Did you email me about it like I asked you to?

Student: No.... But I asked you last week.

Me: If it wasn't in an email, I didn't remember.

Student: [Blank stare.]

In general, whenever I talk to a student verbally and they are asking for something, or I need to follow up on something, I ask them to send me an email reminder. With 1-3 such requests each class, for my four college-level classes that adds up to about 4-12 tasks I need to accomplish. To make sure these things are accomplished I use my email as a to-do list, with student emails as the 'things' on my list.

What about you? How do you make sure all the small requests and follow-ups are completed in each of your classes?

## Monday, January 19, 2015

### Coming back to the blog after a hiatus with some new projects.

My last post was in mid-November and I'm now getting back to the blog in mid-January. Not the longest time between blog posts, but definitely quite a while. For the Winter 2015 term I am teaching as an adjunct at my home institution and working on a few projects. I'll list the classes below, but the hardest thing is the schedule, three of them are back-to-back (-to-back) between 10 am and 4 pm on Mondays and Wednesdays, the fourth at 6 pm. This means I only teach two days a week, but they're pretty rough days. Not being on campus the rest of the week has also given me a disconnected feeling that I can't shake. I may come in on my non-teaching days, but the cost of driving to the campus, as well as the opportunity cost are limiting.

The courses I am teaching this term:

The courses I am teaching this term:

- Algebra I - This below 100-level math course is the second of four such courses offered. There are quite a few resources available (PowerPoint notes, online math homework, etc.) so my prep time is fairly limited. However my time responding to emails and messages is quite a bit more than other classes. These students usually have quite a bit of anxiety, are new to the college experience, and need a bit more guidance than other students. I am happy to help these students, but it does change the focus of my energies.
- Algebra II - The next math course in the series is one I have not taught. There seems to be less support for this course so I am having to prepare quite a bit more. I am focusing on lectures paired with activities, and using the same online math homework as the previous course. Granted not the most innovative structure, but for teaching the course for the first time I'm feeling fairly confident about that choice.
- College Algebra - Two sections of the first 100-level mat course which uses a flipped-classroom model. I have taught this course before so I don't envision many issues.

There isn't much I want to add to these courses, but I do want students more engaged with the discussion forums in our LMS. If you have any thoughts on how to do this, feel free to share.

The rest of the week I will be focusing on the following projects:

- Video series on a specific math application.
- K-12 Teacher lesson prep materials.
- Developing this blog.
- Freelance projects for test develop, content development, and editing/writing for textbooks.

If you have any thoughts or suggestions, feel free to share below. Thanks for reading!

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