When “Good Enough” is Good Enough (and pandoc)

August 5, 2020

It is now August, and classes start in less than a month. I have given myself permission to declare that “good enough” is good enough. I give you permission, too.

I had high hopes for my classes this summer. I have been working diligently, and I have incorporated many of my ideas. But now is the time when I just need to get a course together—I need to be happy with “90% of its potential and done” is better than “100% of its potential and not done.”

Here is one example of the corners that I am starting to cut: I wrote last time about using PreTeXt to make accessible documents instead of \LaTeX, which produces inaccessible PDFs. In the name of universal design (which helps all students), I am prioritizing writing accessible documents. The idea is that you write in PreTeXt, which is a math-friendly flavor of XML, and then you can easily convert that file to a PDF (good for printing, but not accessible) or HTML (bad for print, but accessible—and particularly useful for when students are remote).

The problem is that I am fast at \LaTeX and slow at XML. The August “Good Enough” solution: write in \LaTeX, and then use pandoc to convert to html. Pandoc converts files from one type to another—most importantly, it converts .tex files to .html files. So this is the new plan.

Here is one more thing that I am not doing this time. About five years ago, several smart people—I don’t remember exactly who, but it was some combination of Dana Ernst, Theron Hitchman, and Robert Talbert—tried to convince me to start writing everything in Markdown. I had no idea why they would consider such a thing then, but I get it now. At some point, I will try to mostly write in Markdown and use pandoc to convert to whatever file I want. But not this August.

I am pretty new to the Markdown/PreTeXt/XML/mathjax world, so I would appreciate any information that you have about them in the comments.

So feel free to go for “excellent” instead of “perfect” now that it is August.

Goal-free Questions, and LaTeX and Accessibility

July 28, 2020

Today is about two different topics, although they will be tied together in a single example at the end of this post.

First, I am going to employ goal-free questions this semester. I first learned about this about a decade ago from Kelly O’Shea A goal-free problem is one where you give a context, but not a question. In the most extreme example, I might just give my students a function f(x)=x\sin(x) for a quiz problem, but no prompt of “Find the integral from 0 to 1 of this function” or “Find the Taylor’s series of this function.” There are three reasons why I am trying this out.

  1. There is evidence that these questions are in some ways easier for students. In particular, novice students often suffer when given a specific prompt because they engage in a “means-end” search to find the problem—they focus so much on the end that they don’t have any room to explore. One of the examples from the literature is a problem of a polygon with only some of the angle measures fill it. Students did better at finding the angle measure of vertex A if they were instructed to “Find as many angle measures as you can” versus “Find the measure of angle A.” Students in the latter case tended to get tunnel vision on A, ignoring other information.
  2. I have hopes that this will improve my students’ metacognitive abilities. Given the goal-less problem f(x)=x\sin(x), my students will need to figure out how to apply as many of the learning outcomes as they can. Some students will integrate by parts, some will find a Taylor polynomial, some will use numerical integration to integrate it, and other students will surprise me. In each case, the student will need to explicitly state which learning outcome they are demonstrating. To do that, they will need to be very mindful of what they are doing.
  3. We will be at least partially remote this year due to Covid 19. I am guessing that these problems are tougher to cheat on, since there are a lot ways of approaching the problem.

The second thing is that it has come to my attention that \LaTeX might not be very accessible. In particular, it seems that screen readers have a very tough time interpreting math formulas in PDF documents. They apparently do a lot better when using HTML and MathJax. Additionally, I need to assume that students will be doing the course on a phone when remote, and PDF files generally are subpar for this.

Since I am working on universal design (since it is better for everyone), I decided not to punt on this issue, even though it is a crazy year already.

The best solution, thanks to Mitchel Keller, seems to be PreTeXt, which is a \LaTeX-y version of XML. You produce a document in XML, and then you can use that to produce several types of documents, including PDF and HTML. This is what I am planning on using for most of my content for my course.

I found PreTeXt pretty easy to use, if only in a hack-y sort of way, where I just change example files. But this is all I need for right now. I found the notes from Keller’s and Crisman’s MAA course on PreTeXt (produced with PreTeXt, of course) particularly useful.

To tie this together, I have written up all of my goal-less quizzes in PreTeXt. It is easy to include Sage cells, so I did for good measure. Here is an example of such a quiz. [This link is broken right now. I am working on getting it fixed—sorry.]

Learning Outcomes for Calculus II

July 15, 2020

I have one rule in life: when Robert Talbert issues me a personal challenge, I respond. I have created learning outcomes for my Calculus II course, which are below.

There are a couple of things to note. First, this might seem to imply that I have thrown out the work I did on Dee Fink’s Significant Learning planning. This is not the case, though. Doing Fink’s exercise helped prep me for these learning outcomes. More importantly, Fink’s exercise was focused on “What do you want your students to remember several years from now?” I clearly could not assess such long-term goals in Fall 2020, so I needed to approximate the goals from the Fink exercise to something that I can assess this semester. This is the result.

Second, I intend to focus much more on applications than I normally do. I will couch differential equations in terms of Covid 19 modeling, and I will do much of integration in terms of probability (improper integrals and double integrals) and applied work/density problems. Series are then motivated by trying to solve differential equations and integrals that have no “nice” solution. I additionally will focus on successive approximations and estimating error—starting with a rough solution, and working toward a better one.

Third, we are on the block system this year, so I am intensively teaching this course over the course of four weeks. The advice I have gotten is that you must cut content in such situations, which is why I am missing your favorite convergence test for series (although there are some that are hidden in other outcomes).

I haven’t thought much about my assessments yet, so the implied modules below (Integration, Optimization, Series, Approximation, and Error) might change. In particular, I suspect that I might have several projects, and the modules might change to match the needs of the project rather than the more conceptual categorization below. I don’t know for sure, though.

Below are my learning outcomes for Calculus II. I welcome all comments, compliments, and criticisms.

  • Group I: I can use integrals to solve authentic real-life application problems.
    • I1: I can solve separable differential equations.
    • I2: I can compute integrals using integration by parts.
    • I3: I can solve real-world problems by slicing and integrating.
    • I4: I can compute improper integrals.
    • I5: I evaluate a double integral over a general region.
  • Group O: I can find optimal solutions to multivariable functions.
    • O1: I can optimize a 3D function.
  • Group S: I can determine whether series, including power series, converge.
    • S1: I can define what it means for a series to converge.
    • S2: I can show con(di)vergence of a series using the Direct Comparison Test.
    • S3: I can show con(di)vergence of a series using the Integral Test
    • S4: I can find the interval and radius of convergence of a power series.
    • S5: I can prove a sequence converges using an \epsilon-$N$ argument.
  • Group A: I can find good approximations to functions, values of integrals and solutions to differential equations.
    • A1: I can approximate the value of an integral using the Trapezoidal Rule, Midpoint Rule, or Simpson’s Rule.
    • A2: I can approximate the value of a solution to a differential equation using Euler’s Method.
    • A3: I can approximate a function with a Taylor polynomial
  • Group E: I can bound the error associated with the above approximations.
    • E1: I can bound the error when using the Trapezoidal Rule, Midpoint Rule, or Simpson’s Rule.
    • E2: I can bound the error when using Euler’s Method.
    • E3: I can bound the error of a Taylor polynomial using Taylor’s Theorem.

Creating teams in Hyflex while social distancing

July 13, 2020

My school is doing a block plan with hyflex this year, and we will almost certainly have social distancing guidelines for our classrooms. Likely, this will mean that only 1/4 to 1/3 of our students can attend class on any given day (which gives hyflex a bit less flex).

Several of us have been talking about how to create teams in a way that accommodates these constraints. Roughly, there are two ways of forming teams. The first way is to have “mixed” teams, with some proportion in class and some proportion remote. The second way is to have, as much as possible, teams all in class or all remote (a team may be all online one class, but then be all in class the next. So they can rotate).

The main advantage of mixed teams seems to be that it gives the remote students a larger voice in the classroom. If they have a question, they have have their in-class representative ask it. Also, each team would have representation in class every day. This means that the instructor would never have to be on Zoom during class.

However, I am thinking that this is not the way to go right now. Thinking from the student perspective, being remote is basically going to be the same experience regardless of whether one of your teammates is physically in class—that teammate is still a small picture in a Zoom window, no different from any of the other students in any of the other Zoom windows.

And is it really going to be easier for a remote student to tell their question to their representative student, and then have the representative student relay it to the instructor? That seems like a game of Telephone, which seems like a bad idea.

My colleague Robert Campbell keeps asking: “What is the advantage of being in class?” in this context. This is a good question, and I don’t have a good answer for it for mixed groups.

Right now, I am planning on having the in-class students be one team. Then they get the psychological benefits of interacting with people as much as possible (there may be a couple students in the team who opt to be remote—this is hyflex, after all. But nothing is perfect). The remote students have the same experience as they would otherwise, only now the instructor will be checking in with them via Zoom (rather than relaying their thoughts through a representative). This just seems better—no student has a worse experience, some students have been experiences (and, theoretically, all students have a better experience 25% of the time), and the remote students get more time with the instructor (the one cost is that I have to check Zoom during class, but that seems like a tiny cost).

So what is wrong with this plan?

Hyflex and Block Course Format

July 9, 2020

I am going to be looking for criticism, so please read this with a skeptical eye. I am starting to think about what my class will look like. As a reminder, we are doing the block plan with hyflex. That is,

  • Students take one course at a time for four weeks. We meet for three hours each day on every day but Wednesday.
  • Students have the option of being face-to-face (with Covid 19’s permission) or remote each day.
  • We are almost certainly going to need to socially distance, so we probably can’t have more than one-quarter of the students can face-to-face at any one time; because we have two campuses six miles apart, this means that really we can only have one-quarter of the students in class per day.

It should come as a surprise to exactly no one that Robert Talbert has already written about this. Roughly: he is planning on splitting the class into two groups, and the groups alternate days when they can come to class. Each lesson is repeated twice, so every group is face-to-face for every lesson. The rest of class is done online, likely asynchronously.

Keep in mind that I have different constraints than Talbert has, since it could appear like I am about to criticize his model. And I suppose I am, but only in the context of my school—I am not saying that he (or you) shouldn’t use it.

My issue with his model is that my students specifically come to my school because it is not online. They value—and are willing to pay—for personal contact with the professor. Talbert’s model cuts that contact time in half at the beginning (note that I am including remote, synchronous interactions as “contact with the professor” because Covid).

This might just be an optics problem, but I could imagine a lot of students objecting to paying $X thousands dollars per year but only getting time with the professor half of the time they are paying for (there may be accreditation issues at schools that don’t usually do online courses, too, but I don’t know about that).

My current thinking is this: Build the best asynchronous class I can. This is the course skeleton, and students should be able to complete the course just with this, if they choose. Then spend class time in some combination of two ways. The first way is through something akin to the Emerging Scholars model: work in small groups on challenging problems. The second way is some variation of a tutorial model, where I meet with, say, 7 students at a time to give them more individual help.

To make this work, I need to balance a couple of things. First, I need to make sure that students are getting rough the amount of time they are paying for. Second, I need to make sure that I don’t assigning too much teaching time to myself—the tutorial system is certainly going to cause me to teach more than three hours each day.

Here are my initial thoughts for a daily routine from a student’s point of view:

  1. Have a 15 minute Q&A as an entire class on last night’s assignment. I might have them submit questions prior to class so I can more efficiently pick them.
  2. Have 75 minutes of Emerging Scholars-type work as an entire class. Students can see different solutions.
  3. Have a 45 minute RAT on the new material.
  4. Meet for 15 minutes in a small group to prep for their meeting with me.
  5. Meet with me for 30 minutes.

That sums to 180 minutes, which is what they are supposed to have.

From my point of view, I only need to be there fore the Q&A, Emerging Scholars-type work, and 30 minute meetings. If there are four teams, this gives a total of 3.5 hours, which is very reasonable.

I could imagine a variation like so:

  1. Have a 15 minute Q&A as an entire class on last night’s assignment. I might have them submit questions prior to class so I can more efficiently pick them.
  2. Have 60 minutes of Emerging Scholars-type work as an entire class. Students can see different solutions.
  3. Have a 45 minute RAT on the new material.
  4. Meet for 15 minutes in a small group to prep for their meeting with me.
  5. Meet with me for 45 minutes.

This would keep the students at 180 minutes, and I would have 4.5 hours. This might be a bit much for me, but I like them having 45 minutes with me.

So: why is this a bad idea?

Dee Fink’s Significant Learning for Calculus II (Part IV, Final)

June 29, 2020

This is Part IV—and the final part—of my documenting using Dee Fink’s significant learning course design tool for Calculus II. Here are the first three parts.

This post is about STEPS 9–12: Final Design Phase, Important Remaining Tasks. My notes are below.

Reflection: This whole process, STEPS 1 through 12, probably took four hours. I don’t think that I could have completed it in one day since it was useful to give thoughts time to bounce around in my head, but perhaps three days. I found it to be time well-spent. My outline of the course changed a lot from beginning to end. I am happy with where I am, and I am looking forward to filling in the details (which is a lot of work).

Do it if you are interested.

STEP 9: HOW ARE YOU GOING TO GRADE?
Action: What are the key components to your grading system?

This will be a specs/SBG hybrid course. Students will often have to identify which standard they are applying in order to get credit for it, with the goal that this will boost their metacognitive skills.

There are four main components:

Online Homework: I want them to have online homework so that they can get immediate feedback on some problems. This will be a relatively small part of the semester grade, and students will be able to reattempt problems as many times as they like without penalty. I am deciding between Alta (adaptive, $40) and myopenmath.com (non-adaptive, free). This will mostly be for more rote skills. This will be daily.

Homework sets: Students will do a small number of problems for each class that will be given extensive feedback. These will be for non-rote problems. This will be daily. Students can resubmit and get credit via SBG from these. It will be a medium part of the grade. Some of these problems might be goal-less (Here is a situation, but there is no question. Tell me everything you can/want about the situation).

Individual Quizzes: I am going to choose a small number of topics for students to demonstrate on quizzes (e.g. setting up integrals for slicing problems).

Team Quizzes: This follows the Readiness Assurance Test format of TBL (take a multiple choice test individually, then take the same one as a team with immediate feedback). This will be graded in some sense, but it is more a teaching tool. It will not count a lot toward the final grade. I will have to omit this if we are asynchronous.

Projects: I will give students several projects to do as teams and individuals. These will mirror homework sets, but count more for the grade. They are weighted heavily.

Self-Regulated Learning Activities: Students will be graded on reflections and readings to help them become better students. These will be graded Complete/Not Yet, and will not be weighted heavily.

Action: What are the relative weight of the grade components? Are you going to determine that yourself, or will you involve the class in this problem?

See above for relative weighting, which will be done as specs/SBG grade bundles. I may create a couple of bundles that I am happy with and have students choose which they like best on the first day.

STEP 10: WHAT COULD GO WRONG?
Action: What problems might arise int eh course design as you envision it at this time? What might you do to solve these problems?
-We are transitioning to the block plan AND hyflex during the biggest pandemic in 100 years. So, I can’t really think of anything that could be a problem.
-Well, the biggest thing is technology. I am going to build the best asynchronous course I can to avoid the tech issues, and then I will figure out how synchronous/f2f classtime can superpower the asynchronous class.
-I need to be careful not to give my students too much work each night. This is a 4-credit class, which amounts to about 4*3*15=180 hours worth of work. We will have 15*3=45 of the hours done in class, so there are about 135 hours to be done outside of class. This amounts to about 5 hours per day, every day (including Wednesdays and weekends). Students—particularly returning students, might not expect that. (Put this into the syllabus, talk about this in class).
-Technology issues could make students unable to access the course. (Make an asynchronous option; give students information on how to get help from Canvas/IT/not me).
-There may not be enough time for students to do reassessments. (I can always switch to points-based).
-I may not have enough time to both grade and help students. (Use TAs/CAs/Teaching buddies for this).
-We still don’t know how to use TAs/CAs.

STEP 11: LET STUDENTS KNOW WHAT YOU ARE PLANNING
Action: What information do you want in the course syllabus?
I this dialled in already, although I want to add sections about hyflex, block, time expectations, and where to get tech help.

Action: How do you want to communicate the syllabus to students—on paper, online?

Online. Perhaps will do a syllabus quiz on the second day.

STEP 12: HOW WILL YOU KNOW HOW THE COURSE IS GOING? HOW IT WENT?
Action: What sources will you use to evaluate the course and your teaching?
-Biweekly “muddiest point” assignments
-Daily online homework
-Weekly evals
-End of semester official surveys

Action: What questinos are your trying to answer wiht this evaluation?
-What student needs did I not think of?

Dee Fink’s Significant Learning for Calculus II (Part III): Intermediate Design Phase

June 24, 2020

This is Part III of my course design for Calculus II. Here are Part I and Part II. As usual, you were not the audience for this, so please pardon cryptic parts and typos.

This is Steps 6 through 8, known as the Intermediate Design Phase. Basically, the idea is to create a schedule for the course. I feel like I have a much better handle on the course after doing this. I finally figured out the organizational structure for the course, which I needed to do in order to do Steps 6 through 8. I tried to organize it more by application than mathematical topic, for better or worse. I am also not sure if I should have combined the probability and physics applications for integration, but I wanted fewer topics. :

TOPICS:
1. ODEs: SIR with Covid 19
a. Differential Equations (Modeling, exponential and SIR)
b. Differential Equations (separable) (initial exponential estimation of covid 19 cases)
c. Differential Equations (Euler’s Method/CAS)
d. Series and Sequences (Taylor series, series solutions)
e. Fourier Series solutions to PDE

2. Applications of Integrals: Work in Physics and Probability/Normal distribution/joint probabilities/conditional probability of continuous random variables (virus load given antibody counts)
*a. Integration (slicing/applications)
*b. Integration (parts)
*c. Integration (improper)
d. Integration (numerical)
*e. Series and Sequences (Taylor series)
f. Multivariable Calculus (iterated integrals over general regions)

3. Optimization: No context (but applied)
*a. Multivariable Calculus (optimization)

4. Series No context, just to help with SIR
a. Partial sum definition, problematic series (\sum (-1)^n, -1/12)
*b. Series and Sequences (ratio, alternating series test, comparison test, harmonic series/p-test, integral test–estimation!)
*c. Series and Sequences (N-epsilon)
d. Fourier Series

5. Error Analysis
a. Series (alternating series error estimation)
b. Series and Sequences (Taylor Series Error)
c. Euler’s Method (geometric series for Euler’s Method)
d. Integration (improper)

Here are Steps 6 through 8, noting that I left Days 13–15 blank because I want a buffer/time for presentations:

STEP 6: COURSE STRUCTURE
Action:
-Identify 4 to 7 major concepts, issues, or topics in your course.
1. ODEs: SIR with Covid 19
a. Differential Equations (Modeling, exponential and SIR)
b. Differential Equations (separable) (initial exponential estimation of covid 19 cases)
c. Differential Equations (Euler’s Method/CAS)
d. **Repeat**Series and Sequences (Taylor series, series solutions)
e. Fourier Series solutions to PDE

2. Applications of Integrals: Work in Physics and Probability/Normal distribution/conditional and joint probabilities of continuous random variables (virus load given antibody counts)
*a. Integration (slicing/applications)
*b. Integration (parts)
*c. Integration (improper)
d. Integration (numerical)
*e. **Repeat**Series and Sequences (Taylor series)
f. Multivariable Calculus (iterated integrals over general regions)

3. Optimization: No context (but applied)
*a. Multivariable Calculus (optimization)

4. Series No context, just to help with SIR
a. Partial sum definition, problematic series (\sum (-1)^n, -1/12)
*b. Series and Sequences (ratio, alternating series test, comparison test***estimation***, harmonic series/p-test, integral test–estimation!)
*c. Series and Sequences (N-epsilon)
d. Fourier Series

5. Error Analysis
a. Series (alternating series error estimation)
b. Series and Sequences (Taylor Series Error)
c. Euler’s Method (geometric series for Euler’s Method)
d. Integration (improper)

-What is the appropriate sequence for instroducing these to the students?
Due to the block plan, I am going to interleave these. However, I want to do selected ODEs and integration prior to series in order to motivate series, and I want to do integral slicing problems before iterated integrals in multi, I want to do geometric series before Euler’s Method error.

-What initial ideas do you have for assignments or problems that would reflect the increasing complexity of the subject as students move from topic to topic?
Generally: start with a standard problem, then move to a messy real-world project
This might be it. Calculus II is just a pile of somewhat unrelated topics, so they don’t build much. I think the building will come from the projects.

STEP 7: INSTRUCTIONAL STRATEGY
Topics:
Differential Equations (separable and numerical solutions)
Integration (parts, applications, numerical, improper)
Series and Sequences (N-epsilon, various tests for convergence, Taylor series)
Multivariable Calculus (optimization, iterated integrals over general regions)
Error Approximation

Differential Equations (separable and numerical solutions)
Day 1 In-Class: Set up models for coronavirus; basic exponential (with separable solution) and SIR
Between 1 and 2: Practice separable solutions
Between 2 and 3: Do prep work for Euler’s Method (think about best guess, read, watch), Review tangent line approximations
Day 3 In-Class: Euler’s Method Practice, Solve with Taylor series
Between 3 and 4: Euler’s Method practice, Practice with Taylor Series
Day 4 In-Class: Practice with Taylor series
Between 4 and 5: Practice Taylor series
Between 7 and 8: Review Taylor series by practicing
Day 8 In-Class: Review practice with Taylor series
Between 9 and 10: Review Euler’s Method
Day 10 In-Class: Practice Euler’s Method
Day 13 In-Class: Show Fourier solutions to PDEs
Between 13 and 14: Practice Fourier solutions to PDEs
Day 14 In-Class:
Between 14 and 15:
Day 15 In-Class:

Integration (parts, applications, numerical, improper), Work and Probability
Day 1 In-Class: Integration (slicing/applications), Integration (parts)
Between 1 and 2: Practice with Integration (slicing/parts), watch intro to probability stuff (no multivariable), watch intro to improper and numerical
Day 2 In-Class: Intro to probability (improper, exponential model, problematize with normal model), numerical to deal with normal
Between 2 and 3: Practice improper and numerical, watch Taylor series motivator video
Day 3 In-Class: Practice with Taylor Series intregration of normal model
Between 3 and 4: Practice integration with Taylor Series (do for both sin x both ways, etc), conditional probability introduction
Day 4 In-Class: Practice double integrals with probability
Between 4 and 5: Multiple integral practice (setting up double integrals in two ways)
Day 5 In-Class: Double integral practice
Between 7 and 8: Review slicing, parts, improper
Day 8 In-Class: Practice slicing, parts, improper
Between 10 and 11: Review Numerical Integration
Day 11 In-Class: Numerical integration practice
Between 11 and 12: Practice work/parts
Day 12 In-Class: Practice work/parts
Between 12 and 13:
Day 13 In-Class:
Between 13 and 14:
Day 14 In-Class:
Between 14 and 15:
Day 15 In-Class:

Series and Sequences (N-epsilon, various tests for convergence, Taylor series)
Between 4 and 5: Taylor series practice
Day 5 In-Class: Transition to series (plug in numbers into Taylor series), talk about partial sums, convergence
Between 5 and 6: Videos on convergence tests
Day 6 In-Class: Practice convergence tests (geometric, ratio, alternating, comparison, p-series, integral test)
Between 6 and 7: Practice convergence tests (geometric, ratio, alternating, comparison, p-series, integral test), video on N-epsilon
Day 7 In-Class: Practice convergence tests (geometric, ratio, alternating, comparison, p-series, integral test), practice N-epsilon
Between 7 and 8: Practice N-epsilon
Day 8 In-Class: Practice N-epsilon
Between 8 and 9: Practice N-epsilon, Review alternating series, Taylor Series
Day 9 In-Class: Practice Alternating series, Taylor Series
Between 11 and 12: Review N-epsilon
Day 12 In-Class: Practice N-epsilon
Between 12 and 13:
Day 13 In-Class:
Between 13 and 14:
Day 14 In-Class:
Between 14 and 15:
Day 15 In-Class:

Multivariable Calculus (optimization, iterated integrals over general regions)
Between 1 and 2: Optimization Intro video
Day 2 In-Class: Optimization practice
Between 2 and 3: Optimization practice
Between 5 and 6: Optimization practice
Day 6 In-Class: Optimization practice
Between 6 and 7: Optimization practice
Between 12 and 13:
Day 13 In-Class:
Between 13 and 14:
Day 14 In-Class:
Between 14 and 15:
Day 15 In-Class:

Error Estimation
Between 9 and 10: Series error estimation video
Day 9 In-Class: Series error estimation practice
Between 9 and 10: Series error estimation practice, Euler’s Method Error Estimation video
Day 10 In-Class: Euler’s Method error estimation practice
Between 10 and 11: Euler’s Method error estimation practice, Numerical Integration error estimation video
Day 11 In-Class: Numerical Integration Error Estimation practice
Between 11 and 12: Numerical Integration Error Estimation Practice
Between 12 and 13:
Day 13 In-Class:
Between 13 and 14:
Day 14 In-Class:

STEP 8: CREATING THE OVERAL SCHEME OF LEARNING ACTIVITIES

Day Xa means the first part of the day (roughly 1 hour), and Xb is the second

Day 1a In-Class: Set up models for coronavirus; basic exponential (with separable solution) and SIR
Day 1b In-Class: Integration (slicing/applications), Integration (parts)
Between 1 and 2: Practice with Integration (slicing/parts), watch intro to probability stuff (no multivariable), watch intro to improper and numerical Practice separable solutions, Optimization Intro video,
Day 2a In-Class: Intro to probability (improper, exponential model, problematize with normal model), numerical to deal with normal
Day 2b In-Class: Optimization practice
Between 2 and 3: Practice improper and numerical, watch Taylor series motivator video, Do prep work for Euler’s Method (think about best guess, read, watch), Review tangent line approximations, Optimization practice
Day 3a In-Class: Euler’s Method Practice
Day 3b In-Class: Practice with Taylor Series intregration of normal model, Solve ODE with Taylor series
Between 3 and 4: Practice integration with Taylor Series (do for both sin x both ways, etc), conditional probability introduction, Euler’s Method practice, Practice with Taylor Series
Day 4a In-Class: Practice with Taylor series
Day 4b In-Class: Practice double integrals with probability
Between 4 and 5: Multiple integral practice (setting up double integrals in two ways), Taylor series practice
Day 5a In-Class: Double integral practice
Day 5b In-Class: Transition to series (plug in numbers into Taylor series), talk about partial sums, convergence
Between 5 and 6: Double integral practice, Videos on convergence tests, Optimization practice
Day 6a In-Class: Practice convergence tests (geometric, ratio, alternating, comparison, p-series, integral test)
Day 6b In-Class: Optimization practice
Between 6 and 7: Practice convergence tests (geometric, ratio, alternating, comparison, p-series, integral test), video on N-epsilon, Optimization practice
Day 7a In-Class: Practice convergence tests (geometric, ratio, alternating, comparison, p-series, integral test)
Day 7b In-Class: practice N-epsilon
Between 7 and 8: Practice N-epsilon, Review slicing, parts, improper,Practice N-epsilon, Review Taylor series by practicing
Day 8a In-Class: Practice N-epsilon
Day 8b In-Class: Practice slicing, parts, improper
Between 8 and 9: Practice N-epsilon, Review alternating series, Taylor Series, Series error estimation video
Day 9a In-Class: Practice Alternating series, Taylor Series
Day 9b In-Class: Series error estimation practice
Between 9 and 10: Practice Series Error Estimation, Review Euler’s Method, Euler’s Method Error Estimation video
Day 10a In-Class: Practice Euler’s Method
Day 10b In-Class: Euler’s Method error estimation practice
Between 10 and 11: Euler’s Method error estimation practice, Review Numerical Integration, Numerical Integration error estimation video
Day 11a In-Class: Numerical integration practice
Day 11b In-Class: Numerical Integration Error Estimation practice
Between 11 and 12: Practice work/parts, Review N-epsilon, Numerical Integration Error Estimation Practice
Day 12a In-Class: Practice work/parts
Day 12b In-Class: Practice N-epsilon
Between 12 and 13: ??
Day 13 In-Class: Show Fourier solutions to PDEs
Between 13 and 14: Practice Fourier solutions to PDEs
Day 14 In-Class: ??
Between 14 and 15: ??
Day 15 In-Class: ??

Dee Fink’s Significant Learning for Calculus II: Initial Design Phase (Part II)

June 23, 2020

I am using Dee Fink’s Self-Directed Guide to Designing Courses for Significant Learning on my Calculus II classes for next year. I might post more frequently than weekly for a bit, since I am going to document how I am designing a Calculus II course for a block plan (three hours each day, four days per week, 4 weeks) and hyflex (students can participate either face-to-face or remotely; ideally, the remote students will have the option to participate synchronously or asynchronously). For the record, I am confident that I can figure out how to do the block plan; I am less confident about hyflex right now, but I know that I will eventually figure something out.

I have completed the initial design phase, which probably took me 3 hours in total (plus weeks of it bouncing around my subconscious mind). The first hour, Steps 1 and 2, can be found here. Steps 3–5, which took about two hours, is below.

As always, this is what I wrote, warts and all. I was just writing for myself (in particular, you weren’t the intended audience), and I didn’t proofread. Also, this is a pretty high-altitude view of the course, so I am hoping that Fink instructs me to get into the weeds later. Enjoy.

STEP 3: FEEDBACK AND ASSESSMENT PROCEDURES
1. Forward-Looking Assessment:
-When will the number of new infictions (in the world) of Covid 19 be less than 100/day?
-How much fuel does it take to fly a jumbojet from MSP to Oslo, Norway?

2. Criteria and Standards for “…habitually make progress on solving a problem by first developing an imperfect solution.”
Two criteria (each with 2–standards) that would distinguish exception achievement from poor performance:
a. Students identify and make assumptions needed to make progress.
Standard: Students explicitly state what they need to know in order to make progress on a solution.
Standard: Students explicitly state what they will assume, but do not know, in their solution.

b. Students can identify how to improve their solution.
Standard: Students explicitly state the limitations of their solutions.
Standard: Students explicitly state how they might improve upon their solutions if they had more time.

3. Self-Assessment: What opprtunities can you create for students to engage in self-assessment of their performance.
When submitting an assignment, students will self-assess according to explicit criteria I give them. This will ideally be a checklist and and short answer questions about what they did well, where they need help, and where they are confused. The assignment will not be accepted without the self-assessment.

4. FIDeLity Feedback: What are the procedures for:
Frequent Feedback: Online homework will be due every day. I will also likely have some amount of homework/projects due most every day.
Immediate Feedback: I will use an online, adaptive homework platform. I will also likely use some sort of iRAT/tRAT-type individual/team quizzes in class for immediate feedback.
Discriminating Feedback: I will use some combination of Specifications Grading and Standards-Based Grading. There will likely be some procedural-type Specs, but students will have to explicitly “claim” standards to get credit.
Loving Feedback: I will explicitly write, “I am writing this because I want to help you learn.” I will also try to write more positive comments than I usually do. I will also separate the feedback from the grade.

STEP 4: TEACHING/LEARNING ACTIVITIES
Action: Identify some learning activities to add to your course that will give students a “Doing” or “Observing” Experience. What “Rich Learning Experiences” are appropriate for your course?

-Debates via Peer Instruction
-Authentic projects (how many Covid 19 deaths by end of 2021?)
-TRIUMPHs primary source projects?
-ClearCalculus projects?

Action: What kinds of Reflective Dialogue can you incorporate into your course?
-Minute “papers” regularly (at least hourly) via a “backchannel” (Zoom chat?)
-Journal for class
-Portfolio of solved problems with reflections

Action: Other than lectures, what ways can you identify to cause students to get their initial exposure to subject matter and ideas (preferably outside of class)?
-Use Canvas with prerequisites to lead students through a variety of readings, videos, quizzes, and graphing activities to prepare them for class.

STEP 5: INTEGRATION
Foundational Knowledge:
“…habitually make progress on solving a problem by first developing an imperfect solution.”
Ways of assessing: Authentic Projects
Actual teaching-learning activities: In-Class projects, readings/videos on numerical integration/Taylor Series/Euler’s Method
Helpful resources: Text, CIC, ClearCalculus, YouTube

“…habitually measure how far away they are from a real solution.”
Ways of assessing: Homework
Actual teaching-learning activities: In-class projects, readings/videos on numerical integration/Taylor Series/Euler’s Method
Helpful resources: Text, CIC, ClearCalculus, YouTube

Application Goals:
Critical Thinking: “…examine the results of a mathematical model to determine how useful it is.”
Ways of assessing: Authentic Projects
Actual teaching-learning activities: In-class projects, real data
Helpful resources: CIC?

Creative Thinking: “…be able to make simple mathematical models to examine some real-world situations.”
Ways of assessing: Authentic Projects
Actual teaching-learning activities: In-class projects
Helpful resources: Birgen, CIC

Practical Thinking: “…make decisions based on a mathematical model.”
Ways of assessing: Authentic projects
Actual teaching-learning activities: In class projects, Peer Instruction
Helpful resources: Birgen, CIC, goodquestions

Skills: “…know that they can re-learn about slicing problems with integrals, differential equations, Taylor series, and multivariable calculus if they need.”
Ways of assessing: Quizzes
Actual teaching-learning activities: In-class problems
Helpful resources: Textbook, YouTube

Skills: “…know that they can re-learn Wolfram Alpha and Sage to help them compute.”
Ways of assessing: Authentic projects
Actual teaching-learning activities: In-class projects, in-class demos
Helpful resources: Wolfram Alpha, Sage

Complex Projects: I do not think that this is the course where students learn to manage complex projects.

Integration Goals:
Connections:
Ideas within the course: “…know that we often approach the ideas of integration, series, and differential equations with a notion of successive approximation.”
Ways of assessing: Authentic projects
Actual teaching-learning activities: In-class projects, text, videos
Helpful resources: CIC, Wolfram Alpha, Sage/Python, text

Other courses: “…know how calculus can be used in fields such as biology, economics, and physics.
Ways of assessing: Authentic Projects
Actual teaching-learning activities: In-class projects
Helpful resources: Text

Personal, social, and/or work life: “…use the ideas of successive approximation and error estimation to solve problems in their personal lives. That is, they do not need to start with a full solution—just something that is close, where they have an idea of how close the solution is.”
Ways of assessing: Journaling
Actual teaching-learning activities: Examples viaa lecture?
Helpful resources: NA

Human Dimension Goals:
What should students learn about themselves? “…know that they can think carefully about problems without need a formula to plug into.”
Ways of assessing: Authentic Projects
Actual teaching-learning activities: In-class projects
Helpful resources:

What should students learn about interacting with others? “…consider the audience in any presentation, being careful to understand that the audience does not know everything that the presenter does.”
Ways of assessing: In-class presentations (or videos), writing for peers
Actual teaching-learning activities: In-class presentations (or videos), writing for peers
Helpful resources: NA

Caring Goals:
What changes/values do you hope students will adopt?
Feelings: “…feel that they can powerfully and individually use mathematics to help them acheive their goals.”
Ways of assessing: Journaling
Actual teaching-learning activities: Authentic Projects
Helpful resources: NA

Feelings: “…feel responsibility for helping their teammates succeed.”
Ways of assessing: Journaling
Actual teaching-learning activities: Peer Instruction and TBL
Helpful resources: NA

Interest: “…be interested in the ideas behind formulas, not just applying formulas.”
Ways of assessing: Journaling
Actual teaching-learning activities: Text, Lecture, Videos
Helpful resources: Text, YouTube

Ideas: “…adopt the notation of incremental improvement.”
Ways of assessing: Journaling
Actual teaching-learning activities: Projects, text, lecture, videos
Helpful resources:

Ideas: “…appreciate that mathematics can be used as a tool in many fields.”
Ways of assessing: Journaling
Actual teaching-learning activities: Authentic projects
Helpful resources: NA

Learning-How-To-Learn Goals
How to be good students: “…use research-based, effective ways to study.”
Ways of assessing: Journaling
Actual teaching-learning activities: Assigned Readings
Helpful resources: Mindset articles, What Works in Learning

How to be good students: “…have a growth mindset.”
Ways of assessing: Journaling
Actual teaching-learning activities: Assigned Readings
Helpful resources: Mindset articles, What Works in Learning

How to learn about this particular subject: “…be brave in attempting to solve problems that they may not know the answer to.”
Ways of assessing: Authentic Projects
Actual teaching-learning activities: In-class projects
Helpful resources: NA

How to learn about this particular subject: “…be in the habit of actively learning by creating toy examples when reading and watching videos of mathematics.”
Ways of assessing: Authentic Projects
Actual teaching-learning activities: In-class Projects
Helpful resources: NA

How to to become a self-directed learner of this subject (having a learning agenda AND a plan for learning it): “…create schedules prior to doing the work so that they can create accountability for themselves in getting the project done.”
Ways of assessing: Journaling
Actual teaching-learning activities: Assigned journals
Helpful resources: NA

How to to become a self-directed learner of this subject (having a learning agenda AND a plan for learning it): “…habitually monitor and evaluate their own work (use metacognitive skills).”
Ways of assessing: SBG (they claim standards)
Actual teaching-learning activities: Projects
Helpful resources: NA

Dee Fink’s Significant Learning for Calculus II (Part I)

June 15, 2020

I am teaching Calculus II for the first time in five years (and the second time in 18). It is almost certainly going to be most of my teaching assignment for next year. Because of this, I have decided to honestly do Dee Fink’s guide for designing courses for “significant learning”. He has a Self-Directed Guided, which I am using.

I went through Steps 1 and 2 (out of 12) today, which took me about an hour. I am posting the results below in their unpolished form, since I am mainly doing this for myself. However, you may (or may not) be interested, so I am posting it here. I would also love to get feedback on how I could improve my “Caring” Goals and my “Human Dimension” goals. These are responding directly to the worksheets for Steps 1 and 2 found on Page 7 and Pages 11–12.

SITUATIONAL FACTORS:

1. Specific Context of the Teaching/Learning Situation
-Roughly 25 students in the class
-Mostly First Years
-Lower division course
-Classes are 180 minutes, four days per week, for 3.5 weeks
-Hyflex course, so we need to be able to have a similar experience online and face-to-face

2. General Context of the Learning Situation
-Abstract Structures designation in Integrations Curriculum (and Mathematics designation in Common Curriculum)
-Movement theme
-Service course for Chemistry/Biochemistry, CSCI, and Physics
-Part of Mathematics major
-There is a “standard” Calculus II course nationwide.

3. Nature of the Subject
-This is a combination of theoretical and applied knowledge.
-I used to think that the material is divergent, but I think it can made convergent by thinking of the course as a study of “successive approximation and error estimation,” which supports the Movement theme.
-There are no changes to the field, although the way calculus is being taught is gradually changing.

4. Characteristics of the Learners
-Most learners will be 18–19 year old, traditional students. Most will want to major in Math/Chem/CSCI/Physics, although most won’t know waht they want to do for a career.
-All students will have had Calculus I; some will have had Calculus II.
-Students will generally have a positive attitude about mathematics, since this course is not required by the college. However, most may think of mathematics as being more computational.
-Students may expect more computation and less thinking. This may create friction if I ask them to do a lot modeling and estimation.

5. Characteristics of the Teacher
-I believe that all students can improve their mathematical ability, and I can improve my teaching ability.
-I haven’t been excited about teaching calculus in the past. This is in part because I did it a lot earlier in my career, and partially because I do not enjoy teaching rote skills. However, I also now think that I was teaching it wrong, so I am excited to teach this again.
-I love my students, and I am excited to work with them. I also do not usually teach 100-level students who expect to have positive interactions with their professor, so I am particularly excited about that.
-I know calculus well, although I am not as strong on the error estimation as I should be. I am looking forward to learning this.
-My strengths in teaching are that I recognize that I can improve, I am fearless about trying new things, I genuinely care about my students, and I have experience teaching in a variety of manners.

LEARNING GOALS:

“A year (or more) after this course is over, I want and hope that students will…”

Foundational Knowledge:
“…habitually make progress on solving a problem by first developing an imperfect solution.”
“…habitually measure how far away they are from a real solution.”

Application Goals:
Critical Thinking: “…examine the results of a mathematical model to determine how useful it is.”
Creative Thinking: “…be able to make simple mathematical models to examine some real-world situations.”
Practical Thinking: “…make decisions based on a mathematical model.”
Skills: “…know that they can re-learn about slicing problems with integrals, differential equations, Taylor series, and multivariable calculus if they need.”
Skills: “…know that they can re-learn Wolfram Alpha and Sage to help them compute.”
Complex Projects: I do not think that this is the course where students learn to manage complex projects.

Integration Goals:
Connections:
Ideas within the course: “…know that we often approach the ideas of integration, series, and differential equations with a notion of successive approximation.”
Other courses: “…know how calculus can be used in fields such as biology, economics, and physics.
Personal, social, and/or work life: “…use the ideas of successive approximation and error estimation to solve problems in their personal lives. That is, they do not need to start with a full solution—just something that is close, where they have an idea of how close the solution is.”

Human Dimension Goals:
What should students learn about themselves? “…know that they can think carefully about problems without need a formula to plug into.”
What should students learn about interacting with others? “…consider the audience in any presentation, being careful to understand that the audience does not know everything that the presenter does.”

Caring Goals:
What changes/values do you hope students will adopt?
Feelings: “…feel that they can powerfully and individually use mathematics to help them acheive their goals.”
Feelings: “…feel responsibility for helping their teammates succeed.”
Interest: “…be interested in the ideas behind formulas, not just applying formulas.”
Ideas: “…adopt the notation of incremental improvement.”
Ideas: “…appreciate that mathematics can be used as a tool in many fields.”

Learning-How-To-Learn Goals
How to be good students: “…use research-based, effective ways to study.”
How to be good students: “…have a growth mindset.”
How to learn about this particular subject: “…be brave in attempting to solve problems that they may not know the answer to.”
How to learn about this particular subject: “…be in the habit of actively learning by creating toy examples when reading and watching videos of mathematics.”
How to to become a self-directed learner of this subject (having a learning agenda AND a plan for learning it): “…create schedules prior to doing the work so that they can create accountability for themselves in getting the project done.”
How to to become a self-directed learner of this subject (having a learning agenda AND a plan for learning it): “…habitually monitor and evaluate their own work (use metacognitive skills).”

Virtual Conferences

June 9, 2020

I had virtual conferences these past two weekends. I “attended” the Zassenhaus Group Theory Conference and the Mastery Grading Conference these past two weekends.

I have previously expressed interest in largely replacing face-to-face conferences with virtual conferences. Now that I have actual experience, I can say something a bit smarter about it.

My opinion is that, for both of these conferences, I got at least 80% of the benefit at about 0% of the cost (each would have cost about $1000 in travel, and maybe 500 to 700 pounds of CO2 for each). I think that this is a fiscally and environmentally responsible way to proceed, even in non-Covid 19 times.

Note: I am not saying that the conferences were equally good as face-to-face conferences. Certainly, there are losses. I mainly miss the social time with my friends, but I am also missing out on side conversations with other people there during breaks and meals. This is a genuine loss. In particular, there is a sense of community that is lost.

But it is not true that face-to-face is absolutely better for building community. In the Mastery Grading Conference, there was a chat that was unbelievably active during the conference. I feel like I know some people there even though I don’t know what they look like. This has real benefits—I am more likely to reach out by email to some people due to the chat. I believe that this chat would not have been possible in a face-to-face conference, since there are social conventions that make it seem rude to be typing on your phone while you are ten feet away from a person who is trying to give a lecture.

Also, I would not have gone to the Mastery Grading Conference if it hadn’t been virtual—I just didn’t have enough funding (I was committed to Zassenhaus prior to the announcement of the Mastery Grading Conference). Virtual conferences allow me to go to more conferences. Moreover, there are people who cannot attend a conference due to health-related reasons, so there is are equity advantages in terms of access (health, financial, and likely others).

Here are some things that one or both conferences did well:

  • They were all ridiculously helpful and patient with technology.
  • They planned ahead for technology issues (even though there weren’t many).
  • They gave a lot of breaks between sessions. Mastery Grading roughly did “one hour of talks, 30 minutes of break” throughout the days. Zassenhaus did roughly “25 minutes of talks and questions, and 20 minutes of break.”
  • They took questions by filtering them through Zoom. One of the awkward things about Zoom is when two people start talking at once; having the moderator direct traffic made things go much smoother (I need to remember that for teaching in the fall).
  • Mastery Grading had small break-out sessions to discuss the ideas from the conference. This made me feel much more involved (I should remember this for teaching in the fall).
  • Mastery Grading had an active chat. This made me feel much more involved (I should remember this for teaching in the fall).

Here are suggestions to (slightly) improve the conferences:

  • Have some sort of structure for informal conversations. One idea would be to have a Zoom session designated “break room” for people just to go and socialize. Ideally, there would be a moderator who could put people into break-out rooms if they want to have a private conversation.
  • I think that Zassenhaus was smart to put 20 minutes between talks. However, I think that this could be reduced to 15 minutes in the future. I also think that they could have had a couple more slots per day—perhaps 10 per day rather than 8. This would have put the conference over one weekend instead of two.

When (if?) Covid 19 wraps up, I think that there is great potential in distributing these conferences over the course of the year. Perhaps we could have talks weekly/bi-weekly, which would allow us to build a bit more community. It is also easier to sit through one talk per week every week for a year 8–10 talks per day for a weekend (I am guessing attendance would be lower, though).

The organizers of these conferences did a seriously great job. This is a workable model for the indefinite future.