Here is a series of post I made on the Batman theme. I also presented on this topic at the Fall 2014 ArizMATYC meeting.

Here are posts about presentations I have made at conferences over the past few years.

I have also made several presentations based on my “zombie learner” postings.




Topics Covered

Model PE Ratio (2 Group Projects) Calculus

Limits, modeling with polynomials, rational functions, rates of change, quotient rule, tangent line approximations

College Costs 2 College Algebra Modeling with linear and nonlinear functions
Medical Insurance College Algebra, Precalculus, Finite Math Piecewise linear functions
Medical Insurance 2 College Algebra, Precalculus, Finite Math Piecewise linear functions
Medical Insurance 3 Calculus Piecewise linear functions, continuity
Blending Scotch Whisky Finite Math Systems of linear equations
Doctors and Nurses Calculus Rational functions, polynomial modeling, limits
Solar Toasters Calculus Business functions, marginal profit, derivatives
Solar Toasters(Group Project) Calculus Business functions, marginal profit, derivatives
Home Mortgage Finite Math Amortization, future value of an annuity
Home Mortgage (Group Project) Finite Math Amortization, future value of an annuity
Tax Examination Finite Math Conditional probability, Baye’s Rule
Total Cost to Produce Turbo Blenders Calculus Area, left and right sums, fundamental theorem of calculus
Lake Pollution Calculus Area, left and right sums, fundamental theorem of calculus
College Costs College Algebra Equations of lines, solving linear equations
Students and Teachers College Algebra Equations of lines, linear modeling, solving linear equations
Students and Teachers 2 Calculus Rational functions, polynomial modeling, limits
Gas Prices College Algebra, Finite Math Systems of linear equations
Death College Algebra, Precalculus, Calculus Piecewise functions
Do Homework? College Algebra, Finite Math Linear modeling
Biscuits College Algebra, Finite Math Matrix multiplication
Cell Phones College Algebra, Precalculus, Calculus Rational functions, polynomial modeling, limits
Arsenic Removal From Drinking Water College Algebra, Finite Math Systems of linear equations
Arsenic Removal from Drinking Water (Group Project) College Algebra, Finite Math Systems of linear equations
Arsenic and Selenium Removal from Drinking Water at Minimum Cost Finite Math Linear programming
Arsenic and Selenium Removal from Drinking Water at Minimum Cost (Group Project) Finite Math Linear programming
What Should Have Happened on Gilligan’s Island? College Algebra, Precalculus Exponential functions
Arches College Algebra, Precalculus Quadratic functions, solving quadratic equations
Potassium-Argon Dating College Algebra, Precalculus Exponential functions, solving exponential equations
Boogie Boards Finite Math Simplex method
Maximizing Movie Revenue College Algebra Calculus Optimization, quadratic models
Brewery Finite Math Simplex method


Student and Teachers 2 Calendar

Week 1 – Cover quadratic functions Distribute Project Letter
MML Homework Due from Week 1
Week 2 – Cover polynomial and rational functions
Tech Assignment: Scatter Plots Due
MML Quiz Due from Week 1
MML Homework Due from Week 2
Week 3 – Cover exponential and logarithm functions
Tech Assignment: Regression Model Due
MML Quiz Due from Week 2
MML Homework Due from Week 3
Week 4 – Cover limits and discuss technical memos
Tech Assignment: Rational Model Due
MML Quiz Due from Week 3
MML Homework Due from Week 4
Week 5 – Cover Continuous functions and rates of change
Tech Assignment: Limits at Infinity Due
MML Quiz Due from Week 4
MML Homework Due from Week 5
MML Quiz Due from Week 5
Project Due

Expectations in Face to Face and Online Classes

My colleagues often say that” if only the students would read the section in the text before they came to class….I could make better use of the limited time the students have in class.” Each of us has surely told students to read the material before they come to class. How many students actually do it? We are left with the impression that in order for the students to learn the content in the class, it needs come out of our mouths. Personally, I am not able to deliver the entire contents of an Applied Calculus or Finite Math text in 3 hours per week over 15 weeks. They MUST work outside of class to learn the materials!

A few years ago I embraced the use of MyMathLab to deliver a large portion of the class content and to involve the students actively in their learning. I find that students are inherently motivated to do homework and quiz problems because their grade depends on it. Instead of lecturing on a particular section in class and then having them complete a homework assignent or quiz afterward, I have the students do the homework first. For instance, during Week 1 in the week above, the calendar indicates that the students will cover quadratic functions. The homework for that material is due at the end of that week on Saturday and is administered through MyMathLab. I use the class meeting (if there are any) to go over the syllabus, how to use MyMathLab and class policies. During the second class meeting, I give a mini-lecture or do an in class activity over quadratic functions. This is enough to get them started on the homework and to allow them some success on the first few questions. Students typically work on the homework during this week utilizing online videos, the textbook and the ever populat “Help Me Solve This” button. Students must achieve 75% on the homework to be eligible to take the quiz on that material.

After the homework due date, typically on Sunday, I go over the assessment analysis in MyMathLab to see what they had trouble with. If a student is in a class with face to face meetings, the first class of week 2 is dedicated to helping the students overcome those troubles. Typically I need to go over 3 or 4 problems in depth. Any other time is used for in class activities or going over technology issues. I post handouts to the class discussion board on these same problems so that the online students benefit from the assessment analysis. Over the past few semesters, I have developed an extensive list of handouts and I find that I rarely need to create very many new handouts. Students are prepared to take the quiz on the Week 1 content after going over the problems in class or online and I make the quiz due the following Thursday.

During the second class meeting of week 2, I introduce the content for week 2 and the cycle repeats.

  • Homework is due every Saturday (or Sunday).
  • I go over the homework in class or online every Monday (or Tuesday).
  • I give a mini-lecture or student activity on new material Wednesday (or Thursday).
  • Quzzes are due on Thursday (or Friday).
  • Technology assignments are always due on Wednesday.

It is not easy divorcing yourself from being the only content deliverer in class. Initially I was skeptical that I could pull it off. However, if you set the expectations for the students and are able to deal with the volumes of email you might get, you might find that your students get more out of the classes and the discussion boards in your class. With this type of calendar, students are not able to be sporadic in the efforts. Coming to class and/or reading discussion posts is very important to them…they need to be there to have their questions answered.

Student Grades

gradesI am a firm believer that it is not possible to assign a grade completely on machine graded problems. I want to see the work my students are producing and to grade their ability to solve and explain their work.

Because of this belief, no more than 50% of the grade in my class is machine graded (in my case MyMathLab). The other 50% are assessments that I grade (in my case projects). Here is the break down I use in all of my classes:

  • Homework and Technology Assignments – 20%
  • Quizzes – 30%
  • Project Technical Memos – 50%

I do not give exams in my classes. I consider the project technical memos to take the place of traditional exams. I gave exams for over 20 years and I was never completely comfortable with their ability to assess student learning. In addition, over half of the students I teach are online. The logistics of administering exams at many different locations securely is overwhelming. The other possibility of requiring students to come to campus is not feasible since many of my students are from out of state or even out of country. I am not completely against exams, but I don’t think they are as secure as many faculty believe.

Student integrity in classes is a very important issue. Students have cheated in the pass and will probably cheat in the future. Technology has only made it easier for students to cheat. Camera phones, easily duplicated fake IDs, instant messaging and many other technical achievement make it very easy for students to cheat in class and online. If you are in doubt, try a search on YouTube with the phrase “how to cheat”. The search results are funny, but a bit disheartening.

The best I think I can do is to teach students about integrity and professionalism…and to make it hard for them to cheat. Requiring several intermediate assignments, like technology assignments, encourages students to start early on their project. In the Student and Teachers project, there are four technology assignments that students complete. In addition, there are 50 different sets of data that you can assign to students. After a year or two, students will often find copies of project memos from previous semesters. Luckily, the NCES updates the data in this project annually and I get new datasets each year. If you need more than 50 sets of data, you could organize the data by school district. There are hundreds of school districts across the country so the number of unique projects is essentially unlimited.

Another strategy I use is to have each student create their own project based on some personal identifier. In the Arsenic project, students mix together water from three different wells to come up with a blend that is 8 parts per billion. The level of arsenic in each well and the daily demand for water is established using the number of letters in their first, middle and last name. Although this leads to some overlap in projects, all; of the blends do not meet the requirements in the problem. Students then attempt to change the problem in a reasonable way to meet the criteria.

In the Gas Prices project, students attempt to mix together three different grades of gas. The blend must have a specific octane and fill the tank of their own car. By using their own tank, they start to customize the problem. In addition, I ask them to do this as cheaply as possible where the prices for regular, mid, and premium gass come from their local gas station. Since prices change almost daily, octanes are different in different states, and tanks have different sizes, I never get projects with exactly the same data.

The Student Experience

rat_func_AKProject-based learning requires a sustained effort from instructors and students. Students cannot expect to start the project the week it is due and to turn in a professional looking document or to complete some other assessment on the project. However, many students attempt to do that even if you nag them incessantly. Because of this, I develop a set of technology assignments for the first project in each course I teach. The goal of these assignments is to get them using the technology they will need for the project and to let me look over their shoulders, electronically. I try to give them a sample of what to expect in the project, but generally they will get different results. I ask them to contact me or post on the class discussion board if their results seem off. They are then able to get help with their problems a few weeks before the project is due instead of the day before it is due. On this particular project, students struggle with how their model should behave asymptotically. They often try to find a rational model that has a nonzero horizontal asymptote even though the number of students is decreasing and the number of teachers is increasing. By requiring them to submit a technology assignment on that topic two weeks before the due date, I can give them feedback on their choice of models for the numerator and denominator.

Technology assignments also have another added benefit. I have found that students who cheat, do it out of desperation. Most of the students who have cheated in my classes do it because they have not completed the technology assignments and start the project memo at the last second. If I can get them to complete the technology assignments, a sustained effort over several weeks that is easy to grade, they very rarely cheat. Once they have invested time doing the project that was created specifically for them, they want to follow it through. Certainly students will cheat. But in every instance I have caught (and that is many), it was easy to detect the cheating because they turned in a project memo that was not the one they were assigned or is not consistent with the technology assignments they submitted.

After the first month, students have learned most of the technology tools they will need and I have fewer technology assignments. Typically later projects have only one or two technology assignments. My goal with these assignments is to see how they are doing on the project and to give them feedback along the way.