Applied Abstractions

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 m

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

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!

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 act in good faith. ( http://www.merriam-webster.com/dictionary/faith?show=10&t=1412798451 ) - 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 expla

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 forw

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

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.

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 a

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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

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 assign

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 f

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. Th

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 de

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,

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. Nea

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 con

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 wh

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