Monday, November 17, 2014

How I am teaching culinary math the second time around.

After teaching culinary math for the first time I've learned a few things, the most important being the primary student learning objective; Complete a recipe costing form. The course does discuss a few topics that are outside of this form, but this one objective contains about 90% of the course material. It might sound a bit funny, it takes teaching a course once to find out the real student learning objective, but as with many things in life "You truly learn something the first time you teach it."

For those of you in education you might be asking "What is a recipe costing form?" With a current average of 5.1% profits, maintaining high efficiency and cost control for restaurants is a necessity. To do that detailed records of how much everything costs must be kept, and the menu prices of dishes need to be firmly based on their costs. Simply put, a recipe cost form is used to determine how much it costs to make a recipe. With the base cost of the recipe, how many servings it will produce, and the target food cost for a restaurant (25-35%) a restaurant manager can get an idea of how much to price a dish. There are other things to consider (target clientele, location, marketing, etc.) but a recipe cost is a good starting point to base prices on.

This might sound simple, but there are a few ideas that need to be addressed. As an example, let's look at yield. If you order a pound of potatoes for $2.00, are you going to serve exactly that pound of potatoes? No, you have to skin, trim, and wash them first. You loose a certain amount of the weight (that you paid for), so you now have 87% of that pound (the yield). That pound of potatoes now costs $2.00/87%, or about $2.30. The terminology used is: as-purchased (AP) cost is $2.00/lb but the edible-portion (EP) is $2.30/lb. If a recipe calls for 3 pounds of prepared potatoes (skinned, trimmed, and cleaned) we simply multiply this amount by the EP cost of $2.30/lb to get $6.90. Do that for each of the ingredients, add them up and you have the final recipe cost. These forms setup these calculations in a consistent manner so they are easily done, can be read by other people, and different recipes can be compared. (There is an exception to using yield when a recipe calls for a number of something, like one whole apple. If you paid for each apple, not by the pound, yield isn't necessary since you didn't 'lose' a part that you paid for.)

All this is to say that these recipe costing forms are the true final assessments of the course, and using a backwards design model, the course should be focused on getting students to complete them. Thus all the assessments are going to target different aspects of these forms. To scaffold these skills I changed the learning activities (handouts) to include two parts:

1. An Exercises portion of various questions that we discuss in-class, with the answers provided at the end. I generally start the day with an example or a discussion of the idea, then do one of the first few questions, and slowly step back my instruction as students attempt more of the questions on their own.
2. A Graded portion that they are to turn in over the next few days. Answers are not provided, but they can work with each other.

To ensure students complete the Exercises portion I have a notebook check during test days where I review their notebook. These notebooks are not my idea, I have to thank Rhonda Hull at Clackamas Community College for the inspiration. She designed the MTH111 College Algebra course that I teach occasionally, and in addition to using a flipped classroom model, uses notebooks to ensure students are completing their work.

I also included a quiz each Wednesday, and a test every second Friday. I like the regularity of these assessments, in the hope that they reduce cognitive load on students, but also allows them to plan on these activities.

I'll make a few future posts about how this class goes, the one idea that is outside of the recipe costing form (kitchen ratios) and potentially about a new culinary math project. If you have any questions for me, about the course, my approach, the activities, or anything else, just post a comment below.

Thank you for reading!

Monday, November 10, 2014

Reflection: Teaching culinary math for the first time.

Last week marked the end of the math class I taught at a culinary school, and I wanted to reflect on how the term went. I'll have another post about what I intend to do for the next term, which started today

Before the course started I did a bit of my own research and found Culinary Math by Blocker and Hill to be immensely helpful. It provided much needed guidance on how to approach teaching certain topics, terminology used in the industry, and various forms and conversions. The school uses a college math textbook that is targeted to general undergraduate students. I have been told this is to save money, but was (and am) frustrated that there is a perfectly good text out there that addresses exactly the kind of knowledge students should know. In fact they used Culinary Math before this textbook. I recommended students buy Culinary Math for their own use, and a number of them did so. Powell's Books seems to have copies for around $17 (where I bought mine) so it didn't seem to be a big hardship for students to buy this in addition to the textbook.

At the start I was also worried about student's perception of me being a 'math person' and not being a 'culinary person'. Would they resist me talking about conversions, yields, and fractions because I had never worked in the kitchen? I tried to address it head-on by sharing my independent research, how I read books by chefs regularly, I consider myself a home cook and have made Thanksgiving dinner in addition to regular meals, and tried to be honest about where I was coming from. It seemed to make an impact as students were comfortable talking to me about recipes and other topics.

Before this class students had taken 3 6-week terms of culinary classes, and thus had quite a bit of culinary knowledge that I didn't. Because of this imbalance in understanding, I gave them much more leeway in explaining a concept or idea than in other undergraduate classes. Usually I have students attempt an explanation, but if they're getting off track I'll gently correct them by asking a question or pointing something out. Here I didn't feel comfortable doing that, and had students correct each other's arguments in-class. I wasn't explicit that this is what I was doing, but let it happened naturally.

The students themselves came from a wide range of backgrounds, experiences with math, and (most importantly) attitudes toward math. One student had pre-calculus classes in high school, others got through with the minimum, and one was home schooled. I tried to target most of the material on authentic examples, but also included 'naked' math questions to delineate if students were having issues with computations or with understanding a contextual question. This seemed to work for everyone, the high-anxiety students had their own understanding of the situations we were talking about (they had worked with measuring cups and volume measures before this class) and the low-anxiety students were able to rely on their previous math experiences.

Later this week I'll detail how I'm setting up the next section of this class. If you have any thoughts or questions, feel free to share below!

Thursday, October 9, 2014

Student Expectations Presentation

Out of my previous post I created the following presentation. While nothing revolutionary, it allows me to talk about the college atmosphere, introduce new college students to the idea of acting in good faith in an academic setting, and what I expect from them. I will be using this during the first day of classes from now on, and most likely put them in my syllabus.

If you have any suggestions and comments, feel free to share!

Wednesday, October 8, 2014

Student Expectations

This term I've encountered some behavioral issues with a student in a class that is focused on group-work. It isn't a flipped classroom, but one where we struggle through questions in class and students are expected to work on them outside of class. I wasn't expecting to deal with behavioral issues this early in the term, but they have given me the opportunity to formalize some of my student expectations. This is the list I've come up with so far:

- Everyone should treat everyone in the classroom with respect.
- Everyone should come to class prepared to learn and teach.
- Everyone should come to class with a positive attitude about the material.
- Everyone should help the students in their group during group work.
- All questions should be asked in the spirit of learning and exploration of the topics.
- All answers should be provided to explain and educate.

- Everyone is capable of understanding, and answering each question.

That first one is something I've mulled over for a few years, and I think I have a good approach on now. If a student is not acting in good faith then they are acting, or saying things that aren't true. If that happens, how can I get accurate information from formal and informal assessments? I need to use those assessments to determine if students understand an idea or concept, and if not how to adjust and change my explanation, resources, tools, and materials.

My hope is that by talking about these expectations openly and honestly, I will address the behavior issues with this particular student, and also create a positive environment with everyone.

Tuesday, September 30, 2014

Fall 2014 Schedule

This fall term I have contracted for the following classes at a local community college:

- A developmental algebra course. I haven't taught a course at this level in a year and am looking forward to getting back to the math teaching/life coaching dichotomy these classes require. The course uses PowerPoint files the utilize 'clickers', an online homework system, group activities, and group exams. I'm looking forward to trying to make the PowerPoints a bit more engaging. There's such an awful head space with them, I'm just unsure how best to use them.
- A college algebra course. Fairly straight-forward flipped-classroom model that I've taught a few times before. We've met once and they seem fairly young, and a bit disinterested, but I'm optimistic.
- A pre-statistics course that focuses on combinatorics, and some financial math. The assessments are fairly unique, nine quizzes and one final, and there is no textbook. Not sure if I'm looking forward to or loathing not having a resource to rely on. Might be a good time to prep my own book on the topic.

I have also been contracted to teach a culinary math class at a local (although corporate) culinary school. The course mainly covers in-the-kitchen topics, like conversions, yields, and plate costing. The course is fairly small (10 students) and they all seem to be fairly motivated. All of them have taken 3 kitchen basics classes, so I feel there won't be much 'weeding out' as in other math classes at this level. Some students did mention that they've covered some of the more advanced topics in the course in other classes, so I'm a bit unsure of the role of the course. If there is quite a bit of overlap, I am looking forward to getting the syllabi of the other courses and seeing where I can support their course objectives.

I will also be doing some after school tutoring for a few high school students, taking a class or two through Coursera (more on that later), and enjoying the married life.

Friday, September 26, 2014

Culinary Math and Visual Mnemonics

For the upcoming fall term I've been contracted to teach a culinary math class at a local culinary school. The course deals primarily with units of measure, yields, and recipe costing. Doing my own research into the course content I found an excellent resource in Culinary Math, by Linda Blocker and Julia Hill. Overall it is an excellent introduction into the mathematical topics that are important to cooks and chefs, and the terminology they've developed around them.

One aspect of the book that I really enjoyed is its use of visual mnemonics. The first one they use is this one to show the relationship between cups, pints, quarts, and gallons:

Within each 'P' there are two 'C's, indicating that there are two cups in every pint, and so on; two pints to a quart, four quarts to a gallon, etc. This has a really nice recursive relationship as well, within each 'Q' there are four 'C's, meaning there are four cups in a quart. The design of it is pretty simple, nesting letters inside of each other. Compare this with the 'normal' way of looking at unit conversions, a table, and the benefits are pretty clear.

While the table is only good for one conversion at a time, the above image shows the relationship of four different units. The succinctness of the image is powerful.

The other visual mnemonics are based on the below image:

To find one of the parts cover it up and follow the below 'rubric'.

- If 'P' was covered up, mutliply the 'W' (whole amount) and the % (the percent given).
- If 'W' was covered up, divide 'P' (part) by the '%' (percent).
- If '%' was covered up, divide 'P' (part) by the 'W' (whole amount).

While not the most ingenious thing, it is a fairly simple mnemonic to follow, and the text uses it in a number of different contexts (edible portions, as purchased portions, etc.)

Have you encountered an interesting visual mnemonic? I'd like to hear what you've encountered out in the 'wild'.

Wednesday, August 20, 2014

Worksheet Wednesday - Summer Statistics Surprise!

I hope your summer has been enlightening, relaxing, and/or lazy, whatever your preference may be. I've been focusing on two big events, planning and preparing for my wedding at the end of August, and teaching a summer Statistics night class. The former has been stressful, challenging, and rewarding... as has the later actually. I don't think students enjoyed the class much (summer, night, 8-week class), but I'm hoping they'll keep a few of the lessons in mind as they continue their academic careers.

To help you in your future Statistics classes (either as an instructor or a student) below are my In-Class Activities. Most of them are what I call 'call and response activities', where I usually gave these out during lecture, and in-between direct instruction, scaffolded examples, and discussions, I would have students complete a few of these questions. I would 'call' with doing a simple example, and they would 'respond' by doing a similar example. At the end of lecture they would then be responsible for completing them before the next test. I tended not to give makeups for these activities, as I would drop the lowest two.

MTH243 Statistics I - Activity 01 - 2.7 - Standard Deviation
MTH243 Statistics I - Activity 03 - 6.1-6.4 - Experiments
MTH243 Statistics I - Activity 04 - 7.1-7.3 - Empirical Probability
MTH243 Statistics I - Activity 05 - 7.4-7.5 - Theoretical Probability
MTH243 Statistics I - Activity 06 - 8.1-8.3 - Discrete and Continuous Variables
MTH243 Statistics I - Activity 07 - 8.4-8.6 - Normal Random Variables Activity
MTH243 Statistics I - Activity 08 - 9.1, 9.3 - Sampling Distributions
MTH243 Statistics I - Activity 09 - 9.10, 9.2 - Central Limit Theorem
MTH243 Statistics I - Activity 10 - 9.4, 9.6 - Applications of the Central Limit Theorem

If you do use them, feel free to share with me either through email or commenting below how the activity went.

Tuesday, July 22, 2014

Creating an activity about Bayes' Theorem from a blog post

When I teach a topic I haven't taught for a while, I usually refer to some old texts, my course notes, and the internet for new ways of presenting the topic. In my statistics class we were to cover Bayes' Theorem, a topic I have always enjoyed presenting, but never felt that I got quite 'right'. Students seemed disconnected from the idea, and weren't able to answer basic questions about the idea during the first lecture.

To address this I wanted to create an activity where students were to apply Bayes' Theorem in a relatively simple way. Searching the internet I found the article (an essay really) An Intuitive Explanation of Bayes' Theorem by Eliezer S. Yudkowsky, and thought it did a good job explaining the basic idea, and even includes different presentations of the same example. These different presentations are used to discuss innumeracy in health professionals, but provided me a variety of ways of presenting this example.

After some self-editing and debate, I settled on using the simplest presentation of this example; Statistics I Activity - Bayes' Theorem. While the questions aren't directly about Bayes' Theorem, it gets students more familiar with conditional probabilities and how to compute them.

Creating an activity from a blog post or article has some advantages I didn't realize until I presented the activity to students:

  • Students are able to confirm their answers by reading the article, a noble goal by itself. 
  • I don't mention where I pulled the example from, so they have to search through the article to find the 'answers'. If they read through parts of the article by accident, even better.
  • The content becomes richer by pulling from outside resources. I dislike the idea that a course is just about what I, as the instructor, want from students. The ideas and concepts we are talking about are greater than just me, the textbook, and the student. Using someone else's perspective on the topic makes the course 'bigger'.
If you have any questions, comments, or suggestions, feel free to share them below.

Monday, July 21, 2014

What would you like to see on Applied Abstractions?

As with most data-driven people, I've been keeping an eye on the (limited) statistics for the site, and I've noticed some trends I would like to follow-up on. Please fill out the following form to help drive where this blog goes.

Friday, July 11, 2014

Part III - Forming an interesting in-class Statistics activity

I've discussed what I wanted for this experiment activity, what my plan was, and now I'll talk about how it went and what to change in future activities. Overall I thought it went pretty well, but there were a few major changes that had to be made on the fly. The biggest one being the math tests themselves; I completely underestimated my student's basic math ability and we came up with useless data. Someone mentioned that they thought it was part of the activity, and was a great way to show how 'messy' statistics really is. I'm glad they thought that, because I really didn't anticipate it.

The initial discussion of how to construct this experiment was useful and demonstrated a number of ideas we discussed in class. Controlling for certain variables turned into a big part of the discussion, namely how to control for people with natural math ability. We decided to do a paired sample, pairing those people of the same math ability by their score on the first test. I asked if this was really the best measure, and we had a good conversation of how to measure someone's math ability, and how for some people, that's their job.

To control for some of these variables, and to construct a basic demographic survey, I had students develop a few survey questions that may help explain some variation in math ability. This discussion included what to ask, how to ask it, and what kinds of variables (categorical, numerical, etc.) we were measuring. I suggested a question about how long it has been since you took a math class, and some students wanted to do a categorical variable of 0-6 months, 7-12 months, etc. I responded with the question "Is it easier to turn numerical data into categorical data or categorical data into numerical data?" and we talked about converting from one data type to another, and how we were going to use the data.

We also talked about what would happen if a person took two similar math tests back to back. One student mentioned that people would become fatigued,  and rightly so. To limit this I asked what we could do to limit the fatigue, and we discussed the pros and cons of long and short tests. I also mentioned the idea of activating previous knowledge and that after seeing the first test, students would remember how to complete the questions for the second test. We 'settled' on giving both tests to both control and experimental group, and 18 basic math questions... since thats what was in the packet. I know this isn't in the true spirit of exploratory activities, and some people might deride me for exerting this amount of control over the process. I want students to explore this material and engage with it, but doing everything on the fly doesn't seem conductive to these aims. Without some kind of structure students get bored, annoyed, disengaged with the learning process. I can deal with the first two things (barely) but the third I can't.

Students then took the survey we constructed together (number of months since last math class, sex, age, handedness, work status) and the first test. I took them all, handed them back out randomly, and we graded them. I then had students come up to the computer to enter in the information in Excel. This was a good step since it showed that data entry is an important step, one people take for granted. It is time consuming work, and must be done accurately. This was at the 1-hour mark and once they entered the data we had a 5-minute break.

Once the data was entered there were some survey responses that didn't make sense. Instead of age, one person put 'old'. For the number of months since last math class, someone put the categorical variable response 0-6 months even though we settled on a numeric one. I then discussed data cleansing and that our simple decisions on how to handle these discrepancies has real impact on our data. For the 0-6 month responses, we inputted 3 and included an asterix. For the 'old' response we took the oldest age in the data set (26) and replaced 'old' with that number, including an asterix.

After grading and inputting the data, all but two people received perfect scores on the first test. We discussed how we couldn't use this data since we are looking for improvement in math ability after attempting this puzzle, and we can't show improvement if everyone scored perfectly the first time. I quickly made another test that was more difficult (basic algebra, roots, percentages), had students complete it, graded it, and the scores were much more varied.

This turned out great, even though my veins went to ice when I looked at the initial scores. Students saw that our question couldn't be answered with the data set we so carefully constructed and we had to start again. This demonstrates the 'messiness' of statistics I try to get across to them and how you really have to rely on sound statistical principles, and your understanding of the context to get good data.

Creating the sample was now fairly simple, we paired people based on their initial scores and randomly assigned one to the control group and one to the experimental group. In the pairing we noticed that we had an odd number of people. I asked if there was an observational unit (person) that their initial test and survey information seemed to be outside everyone else's. We decided to remove the 'old' entry from above, since it did not seem comparable with the others. Once we did that we created each of the groups.

The experimental group then had 10 minutes to work on the puzzle. I did not say they had to complete it, just that they had to attempt it. The control group worked on the part of the activity that was to be turned in, descriptive statistics and a box-and-whisker plot of the four data sets (pre-test/post-test, control/experiment). Once the time was up I made another quick test, administered it, we graded it, and I collected the scores.

Getting all the data together there was a distinct difference in the control and experimental group. Averaging the before and after puzzle scores for both groups, it was clear that the experimental group's averages were about ten percent higher than the control group's. I then found the differences in scores, averaged those, and found the percent increase to be about six percent. These two averages came out to two different numbers, but I asked which one would I pick to use to sell my puzzle? We then had a conversation about these sorts of averages, how to compute other similar numbers, and how marketers do similar things in their promotional materials.

Overall I thought it was great, and would probably keep most of it, including the too-easy of tests. I would be a little more prepared and have some back-up tests to use, but it really demonstrated that your initial plan sometimes doesn't work. I would like to include scatterplots and linear regression models next time, but it is not included in our Statistics I course.

I could have done a better job of demonstrating how to control for a variable, and used some basic descriptive techniques to do so. For example, breaking the control and experimental groups into sex, handedness, or work status could show if there were any significant differences in these groups.

Thank you for reading these posts about me struggling through the planning, development, and execution of this activity. If you have any thoughts or questions feel free to post them below.

Thursday, July 10, 2014

Forming an interesting in-class Statistics activity - Part II

After the last post I spent some time thinking about my options for an experiment to do in-class that fulfilled all of my requirements. After some thought I decided on the following plan.

  • Claim to the class that I have a logic puzzle that I believe will help people with their math skills. I want to be able to put something on my website saying that this puzzle helped people with their math by some incredible percentage.
  • Walk students through how I was to do this, including samples, factors to control for, and how to create the tests. I guided the conversation so that we would also collect information on how long ago they took their previous math class, to ensure that the control and experimental groups had a variety of math ability levels (measured by an initial test), to anonymize the results, and discuss how we would use the class setting in the most appropriate manner.
  • I created a packet with all the necessary tests, the puzzle, and data recording forms. When printed I assigned random numbers to each packet. I would hand out these packets at this time, asking students to remember their number.
  • Students took the first test, I collect it, hand it back out randomly, and we graded the results.
  • Collecting the data in Excel on the projector, we would then make our sample based on the survey questions we agreed on and the scores. At this time we would compare different sampling methods and how to make them work.
  • Have the students in the experimental group work the logic puzzle, and the control group start on computing descriptive statistics of the pre-puzzle scores. I would later ask all students to compute descriptive statistics for both tests, both samples, as what they were to turn in.
  • After 10 minutes, have all students take a similar test, collect them, hand them back out randomly, grade them, and collect their scores.
  • Having collected this information we would then do some basic statistical analysis on each group, comparing means, medians, standard deviations, and possibly five-number summaries. Comparing the means and medians of each group, and comparing the difference in the two scores and then their means, I would create two different reasonable measures for what I could include on my website. I would like to do some linear regressions, but that material isn't covered in this class but in Statistics II. 
  • Wrap-up with a discussion on how to make this experiment better. Guide the conversation to the placebo effect (I did mention to everyone that I thought these puzzles would help.), blinding, sources of bias, and anything else students mentioned. 
Here is the packet I put together, Statistics I In-Class Activity: Experiment. Tomorrow's post will be about how the activity worked, what didn't, and how I'd like to change it in the future.

If you have any suggestions, or you use this or a similar activity in your Statistics class, feel free to share by commenting below. Thanks!

Tuesday, July 8, 2014

Forming an interesting in-class Statistics activity.

This Wednesday I've scheduled an in-class activity that relates some of the ideas we've discussed in my Statistics I class. So far they include surveys, descriptive statistics (mean, median, quartiles, and standard deviation), sampling, experiment design, and observational studies. Writing this on Tuesday morning, I have nothing written down but I have a couple ideas of what I want this activity to include:

  • Perform an experiment and/or an observational study. I covered what these are in a lecture, but I really want them to attempt one (or both) on their own so they get a concrete idea of what they are. Doing both would be best since they would then be able to compare the methods of both.
  • Take appropriate samples based on the research question. Ideally this would be done with students in the class so they can see how to take appropriate samples.
  • Compute and use descriptive statistics to compare and contrast different samples. Quantitative reasoning and analysis are a core focus in statistics. 
  • Talk about statistics. Whether it be in groups or in a presentation, forming ideas and communicating them to others is another core skill in statistics.
I also know what I don't want:
  • A rote activity that requires no input from students. I want them to struggle with questions about sampling, which statistic to compute, what to do next. Through this struggle I want them to appreciate principles like variability, controlling for certain variables, and how to construct arguments for one action or another.
For an experiment I have a few ideas:
  • Performing an intervention dealing with basic math skills. The idea would be to assess if a certain intervention (a logic puzzle, or a game) has any effect on student performance of a basic math test. We would discuss how to create a control, how to create the samples, how to administer the tests, etc. While the direct applicability of this example may be a stretch, it would be a constructed activity that students could perform.
  • Have the students develop their own question and proceed from there. This has some issues, primarily because of the unending and uncertain nature of such a question. Without some guidance the possibilities are a bit too large, which generally leaves students not choosing anything at all.
  • Provide a context (marketing manager, nurse's aide, etc.), and have students develop an interesting question that can be answered in-class. While being more specific we may not be able to answer such questions in-class. For example, if we wanted to do A/B testing of a website, we would have to construct this example fairly quickly, and perform the experiment on people who weren't part of the development of the website.
For an observational study:
  • Given a data set have students develop an appropriate research question, and try to answer it using the data. This could be generalized further by having multiple data sets and have students pick one, or assign different groups different data sets.
  • Taking the survey data collected at the beginning of the course, ask an appropriate research question that can be answered either by the previously collected data, or by another survey in class. The survey data is anonymous so it would be difficult to answer some questions.
You can probably guess which way I'm leaning, but I'll post the completed activities tomorrow. Feel free to post in the comments if you have any ideas or suggestions. 

Wednesday, May 21, 2014

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!

Friday, May 16, 2014

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.

Wednesday, May 7, 2014

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.

Wednesday, April 23, 2014

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.

Wednesday, April 16, 2014

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.

Friday, April 11, 2014

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.

Wednesday, March 26, 2014

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.