## Posts Tagged ‘Calculus II’

### Calculus II Planning Postmortem

September 4, 2020

I am finally finished planning my Calculus II course for the year. This is good, because it is 3/4 of my teaching load. I want to evaluate how I spent my time so that I can be better when course planning in the future (which means Monday: I start teaching a pre-statistics course that starts around Halloween. I haven’t started planning it at all yet, and I have never taught it before).

I basically worked on this course for 9 weeks. Very roughly, here is how I spent my time by week. My plan is to look at this through a Pareto lense: I want to identify the 20% of efforts that are going to produce 80% of the results. I haven’t done this yet as I write this sentence, but the rules are that I get to pick only two weeks (out of 9, which is close to 20% of my efforts) that I think are the most valuable (If you are guessing that I am reading Essentialism right now, you are right). I will conclude that I should have have tried to compress the other stuff into waaaaay less than seven weeks. Try to guess what I will decide.

1. Dee Fink’s Significant Learning
2. Thinking about the course format with respect to the block/hyflex constraints.
3. Identifying Learning Outcomes for the course.
4. Writing quizzes, projects, and other assessments.
5. Making Yoshinobu-ish tutorials (2 weeks)
6. Making in-class worksheets with solutions for every day in class. (2 weeks)
7. Writing the syllabus, specifications, setting up the Canvas site, and the like.

I am not including the work I did when I was trying to figure out how to make make my course more accessible, since that is perhaps a general professional development jag that should help me for all future courses (Sadly, I am not implementing it this semester since (1) Canvas doesn’t play well with it for some reason—I think that it doesn’t use MathJax, and Math ML is giving me problems— and (2) I might not need it if I don’t have students who require it. If I do have students, I will figure that out on the fly, which now won’t be hard given what I learned this summer. I just don’t have the time for it right now).

The Fink work is out. It was valuable, and it is useful to do every couple of years, but it didn’t help me get a course ready. The syllabus stuff needs to get done, so I suppose I have to put it in. So I am going to completely cop out on this: I would do most of this, but only spend 20% of my time on it. Here is how I might design it if I had to do it in 14 days (which I don’t—I have 1.5 months for my next course, even if it will be filled with a bunch of other stuff). So here is how I would do a macro timeblocking if I had to do it in two weeks.

1. Spend one day on the learning outcomes. These are vital, but I think that I over-thought it. Just get it done.
2. Spend four days writing assessments.
3. As much as I hate to do it, I would skip Stan’s tutorials. They are great, but I think that the in-class stuff will be more valuable, and I need to choose between the two.
4. Spend three days on in-class worksheets; I wouldn’t provide written solutions, which would make this possible.
5. Spend two days on the syllabus and Canvas.

Obviously, I don’t have to limit this to two weeks, so this is not what I would actually do—this is just an exercise in prioritizing. In fact, if I had to do it in two weeks, I think that I would blend the tutorials and in-class worksheets into one Tutorialsheet chimera. I think that the tutorials are immensely valuable, and I am glad I did them (and the idea of the Pareto principle is not simply “only do 20% of the work”).

### Checklists

August 28, 2020

Classes start on Monday. We are on the block schedule right now, and I don’t teach in the first block (except for a weekly class on Wednesdays). I am grateful for a bit of extra time, although I am almost done planning—I need about four more good days before my class is completely done.

Here are two of my favorite things I have done in the past ten years with respect to course planning.

1. I keep a text file in my course’s folder named NextTime.txt. Here is where I keep notes on what I would change for next time—perhaps I have a mistake in a set of solutions, or my grading system is too lenient, or I find a textbook that I really want to look at. The next time I teach the course, I just copy the folder, and I look first at NextTime.txt to see what I should be thinking about.
2. I always make a huge checklist of things to do for the class. When I start planning for a class, I copy the old one and modify it. Only once I have a global view of what needs to be done do I start actually working on the class.

My to-do list for Calculus II is below. It is not edited for your convenience, so I think that not everything will make sense. I put an “X ” at the beginning of the line when I have completed it, and then I move it to the bottom of the page (I think do a find-and-replace to delete these when I start planning a new version of the course). Also, “tickle” comes from the idea of a tickler file—these are the things that I know I will need to remind myself of when the course actually happens.

Enjoy!

————————————————-
IN-CLASS OUTCOME PRACTICE PROBLEMS/ESP PROBLEMS
D1: I1 Separable I2 IBP
D2: I3 Slicing
D3: A1 Approximate Integration/A2 Euler
D4: I4 Improper
D5: S1 DCT/S2 Integral Test
D6: S3 power series
D7: A3 Taylor poly
D8: E1 Error integration/E2 Taylor error
Work through trapezoidal rule error bound
D9: S4 epsilon-N
D10: I5 Double

D11: O1 Optimize 3D function
D12:
Math 120: Fourier, 1-variable wave equation, series solutions
D13:
\sigma(n) is sum of positive integers that divide n; Let H_n be 1+1/2+1/3+…+1/n. Is the following true for n \geq 1? sigma(n) \leq H_n+ln(H_n)e^{H_n}? Jeffrey Lagarias proved this is equivalent to the Riemann Hypothesis.
D14:
D15;
————————————————-
SOLUTIONS FOR QUIZZES
————————————————-
TICKLE
Daily engagement question
Close breakout rooms automatically (and lower countdown from 60 seconds to 20–30 seconds)
Day 1: use collaborations
Run through Piazza set-up on Piazza
Create Teams on Saturday before class; email class about who gets to go to class on Monday
set up Collaborations once we have the teams
Uncover new quiz
Move Modules to top
Check Perusall
Change Missing Pacework This Week on Mondays in gradebook
Put Pacework in spreadsheet and Canvas
Do Daily video in response to Muddiest Point
Office hours from 9–10 every day
Add CAs and CA OH to “Teaching Staff” section in syllabus
Monday for Pacework tokens (and last day of class)
Daily 3-2-1-Go engagement question
Tickle 3-2-1 go for all problems
X Detailed class plan? ( 20 minutes Tutorial Q&A (to 20 min), 10 minutes new Learning Outcome problems Individual (to 30 min), 15 minutes new Learning Outcomes team (to 45 min), 10 minutes solutions (to 55 minutes), 5 minute break (to 60 minutes) 10 minutes Individual ESP (to 70 min), 25 minutes ESP Small teams (to 95 min), 20 minutes large group ESP (to 115 min), 10 minute break (to 125 min), 35 minute project (to 160 min), 10 minute outro Q&A (to 170 min), 10 min OH (to 180 min));
Tickle challenge problems
python random call
Create teams after CCI, tickle when to do new teams, or
Daily: Grade muddiest point, schedule assignment, each LO Assignment
Put conversation opportunities in front of them (at each week, offer them a chance to meet with you via, say, a 10 minute phone call)
Create Guided Practice
Team based learning?
Create Mazur-type real-world problems—you know the outcome you want, but you don’t know how to achieve it; these should be Significant, Same problem, Specific choice, Simultaneous reporting (NOT THIS SEMESTER)
in class projects
Emily’s discussion roles: have the students analyze roles (interrupter, facilitator, challenging, etc). Do this in TBL in particular.
Have students do 2 examples: once correctly, then once incorrectly. Then have students identify wrong ones

Due dates for all homework (MyOpenMath, Projects/Drafts, Homework, Journals)
Solutions for quizzes (TA just uses videos—better that way, since TA understands problem better)

Print Team Rosters for folders
Make Team Folders
Make sure that A,B,C,etc options are in Folders

Check Piazza a lot
Tickle: create muddiest point assignment in Piazza each day
Turn camera off to support Zoom burnout, ask students to start with camera off (more private, allows for better connections) and turn on cameras/microphones only if comfortable

Python: Make daily task reminder sheet (Update Canvas)
MWF: Bring laptop for PollEverywhere, Change Canvas
T: Post Quiz solutions after 2:25 pm
W:
R:

Tickle post quiz solutions
Put solutions in the right place
Bring laptop for PollEverywhere
Tickle Bring area function worksheets
Tickle bring Gateway practice worksheets
Tickle update Gradebook each week before email goes out

Tickle Start all python programs
Tickle get quizzes to Wilmot (either once or weekly)
Tickle make tRandom
Tickle mutt .alias file
Tickle Put teams in Peer Evaluations on Canvas
Tickle Print rosters (331, too)
Tickle start grade update email on cron
Tickle CA (Gateways and Quizzes)
Tickle Make Teams on First Day
Tickle Precalc MOMHW due on 9/19; check morning 9/20 for 100%
Tickle Team Tests are 25 points each
Tickle bring Team Tests
Tickle “do peer assessments” (one practice by 10/12, one that matters by 12/13)
Tickle Precalc MOMHW due on 10/17; check morning 10/18 for 50%
Tickle “do midterm evaluations on Forms Manager” https://www.csbsju.edu/forms/IWHN2KIIM9
Tickle “It is harder to teach this way (closer to evals)”
————————————————-
OTHER
Intro video about me and course (essential questions and my passion)
Due dates for projects
3 drafts of Covid 19 Project
2 drafts of Sagatagan project
4 drafts of the integration individual project
Assign each team member to a different individual project
Have students work on their integral for 10 minutes on the first day; if they solve it, convince their team
Fix closed captioning
Convert PDFs to htmls via XML
Daily social justice idea
Mathographies of current mathematicians
————————————————-
X LEARNING GOALS
————————————————-
ASSESSMENTS
X Journal
X Math 120: Weekly portfolio: review work, claim standards
X Muddiest Point/Schedule
X Have them write journals on how they view themselves as a mathematician/metacognitive stuff
X https://www.francissu.com/post/7-exam-questions-for-a-pandemic-or-any-other-time
X Journal on learning goals (as opposed to learning outcomes)

X MyOpenmMath
X myopenmath.com (organize by day?)
X My OpenMath Assignments

X Specs/Rubrics (general for Take-Home Quiz, Journal, MyOpenMath, Projects)

X Goal-less problems
X Students submit videos, Video creation: https://www.tandfonline.com/doi/full/10.1080/10511970.2017.1396568, FlipGrid?
X Homework/Quizzes/Exams
X Homework solutions for Canvas
X Video solutions (Accessibility)
X daily graded homework (do n, I give feedback on n-k)
X Final exam?
X Create sample learning goals/quiz/tagging
X Make sample quiz with tagging
X Do labels, no labels, or combination on quizzes (Default is “no labels;” but they can be labelled, in which case there is no other possible credit)
X Come up with codes for the goals

X Proof Problems
X Write Challenge/Proof Problems (include oral exam at the end) for A

General
X Explicitly tie task to learning outcomes
X Give students choices
X Grade shorter, more frequently with rubrics (three levels for struggling student/average student/excellent student, then give 3 sentences of details)
X Redo assignment list when done

X Projects
X Give them intermediate due dates (drafts)
X Come up with a Team Capstone project for last couple of weeks/end of unit (wine glass? Then Gabriel’s horn (smallest surface area to volume ratio) Use the digits 1–9 at most once to maximize \int_a^b x^n dx; Use digits 1–9 to get the derivative of f(x)=ax^d+bx^e+ce^x to be close to 1205 as possible, )
X Students submit videos
X Write up 118: Find messy, real-life projects for them (use calculus and real data to predict how many people will live in Minnesota in the year 2300; use calculus and real data predict US GDP in 2300, Use calculus and Google Earth to figure out how big of an area CSB and SJU are (separately), Use calculus and real world data to minimize the amount of money you need to spend on heating, cooling, and insulation for a new home (how much insulation should you put in?), use calculus and real-world data to predict number of walleye in Mille Lacs in 2050. Use Calculus and real world data to determine how to save the most money over 10 years/20 years/30 years/50 years with a mortgage
X TEAM: Covid 19: adapt Euler’s method to predict how many cases on December 31, 2021; predict total number of cases (numerical int), need model parameters, estimate error on both #cases and cumulative #cases.
X TEAM: Pump out koi pond and lake sagatagan (work—how much money?)
X DO NOT DO: INDIVIDUAL: Series solution to ODE: Fail, numerical solution with estimation, Taylor with estimation
X INDIVIDUAL: Movement. Integrate \int_0^1 e^{x^2}. Fail, numerical solution with estimation, Taylor with estimation (note large movement with different methods, and local movement with better approximations/more terms)
X Put in Portfolium assignments into courses
————————————————-
SYLLABUS
X Prepared and engaged/Grade the IFAF
X Quizzes only test CORE (grade accordingly)
X Tokens for extra video attempts (make expensive)
X Student Hours, not Office Hours
X Don’t give feedback on all of it, but tell students why you aren’t giving feedback on everything)
X Make due dates Tuesday at 1 pm so that they don’t feel the pressure to cheat (vs Sunday at midnight)
X OpenStax volumes 2 and 3 (not much of 3)
X remind.com (you can text to them)
X Tell them how you want to communicate with me
X TEMP: Change syllabi from youcanbook.me to Starfish (when ready)
X “if you are here, you belong here.”
X Tokens (5?)
X Put General Education learning outcomes on syllabus
X CCI/Calc-Readiness (put on DoM sheet, too)
X Final from 10:45–12:45 on Thursday, 12/14
X Precalc myopenmath
X 119 myopenmath
X Quizzes (DoMs—include project/Walk’s videos)
X Grades are based on # of DoMs
X Peer evaluation multiplier
X State what is on gateways in syllabus (implicit for Derivatives, trig for 119, not trig for 118)
X Write sections for each assessment
X Make generic class schedule (2G/1B, discuss all problems/solutions, presentations (Bret talks about all results), “thanks,” quiz)
X Put “don’t” study into syllabus, first day slides (http://www.ipsative.com/blog/10)
X Explain grading philosophy in syllabus
X Incorporate WolframAlpha so that students can practice and check their answers
X In syllabus, explain what office hours are for
X Put make-up quiz policy in syllabus (no make-ups)
X Figure out how many quizzes are sufficient
X Decide on final learning goals
X Syllabus: grading is quizzes (including team-based stuff), project (unstructured, real-life, messy one?), proofs (later: Rats?, Peer Assessment, Proof Problems, Project, some sort of team-based HW thing?)
X mutt .alias file
X python email
X Put learning outcomes/CC/IC outcomes, S-U grading, legalese on syllabus
X “This is the plan, up until it is no longer the plan.”
————————————————-
X Use pandoc for slides
X PreTeXt? (no—pandoc)
X Testing effect (every day)
X Worked examples (6.2,6.4, 6.5, 7.8, 8.2, 11.4)
X Sage/Python
X Talk about MOVEMENT (estimation to a better approximation)
X Read with Perusall; a few videos to help
X 3 most important: access, assessment, inclusion
X Assume they are using a phone (91% of people near St Cloud have a phone; poverty to 200% poverty is 96%)
X Assume asynchronous (then f2f/synchronous is optional)
X Time-shifted:
X Flipped classroom (new information on their own, practice with us)
X Get them away from the device—have them communicate with a bank, for instance, and then have them come back to Canvas
X -Universal design—give students multiple ways to learn and multiple ways to demonstrate what they know
X -GET RID of “respond once and respond with two of your colleagues.” Instead, ask students to “advance the conversation.” Give them an open Zoom room.
X Use questions like Minerva: here are the steps of an optimization problem; which steps are incorrect or unclear?
X Do daily RATs?
————————————————-
————————————————-
SYLLABUS UPDATE
X Python Pacework
X Gradebook (including Lifelong Learning eligibility—done with Pacework, at least 35 DoMs)
X Change Specs (pace, project presentations, Lifelong Learning Assignments videos, Quiz)
X Project Specifications
X Whiteboard/markers required?
X Jamboard/docs?
X Detailed class plan? ( 20 minutes Tutorial Q&A (to 20 min), 10 minutes new Learning Outcome problems Individual (to 30 min), 15 minutes new Learning Outcomes team (to 45 min), 10 minutes solutions (to 55 minutes), 5 minute break (to 60 minutes) 10 minutes Individual ESP (to 70 min), 25 minutes ESP Small teams (to 95 min), 20 minutes large group ESP (to 115 min), 10 minute break (to 125 min), 35 minute project (to 160 min), 10 minute outro Q&A (to 170 min), 10 min OH (to 180 min));
X QR Rubric
X Intellectual Property disclaimer
X Perusall Syllabus
X Individual Project
X Monday is MOMWork catchup
X Fix: Grading and descriptions (challenge problems and entry criteria, tutorials)
X Re-think grading–not RATs (VideoProjects for AB/A after X MOMWork points and X total DoMS, peer review? Team Quiz?)
XX “Keeping Pace” homework instead of MOMWork
X Daily Quiz
X Resubmit previous day’s quiz
X Peer review?
X Change to Homework Assignments
————————————————-
————————————————-
CANVAS
XX Day 1 Assignments
X Read Syllabus, study stuff, set up Piazza
X Video on how to navigate Modules
X Zoom: Require picture
X Erica’s Form for making teams
X Do learner autobiography

X D1
X -FAQ area
Zoom: large group: camera and microphone off; breakouts, audio and video are both on (unless you have a bad internet connection)
X -“Here is how you can talk to me if you are stressed about the midterm.”
X -INCLUSION: put in specific, intentional conversations where you talk about community in the course
X -minimum expectations for online conduct (ask for student input, change syllabus)
X IT services for Tech Support
X Perusall
X Piazza
X Perusall video

X Piazza set up (folders for LOs muddiestpoint projects Pacework syllabus/course policies, latex how to)
X midterm evals
X Erica’s Quiz
X https://www.geogebra.org/m/nbjfjtpv
X Insert projects into modules where appropriate (continue working on projects)
X Canvas set up (post syllabus, my OH sign up page, learning outcomes, videos, project, etc, read syllabus, SRL stuff) (later semesters: mindmap link, latex help, latex template, Sage help, sagemath link,mind map reminders, buy markers)
X Syllabus
X Do conditional release on assignments
X Tutorial/Tutorial solution the next day
X Collaborations
X Do Days
X Requirements
X Do tutoriiial solutttions
X Prereqs
X Contact Bret (to to Piazza)
X Piazza
X Fix Perusall
X Assignment: look at what is due for the next week
X Everything due at 11:30
X Peer Review all quizzes
X Quiz/Peer review the next day
X Lifelong Learning Assignments
X Pacework
X Perusall
Convert LGs, Syllabus, Specs, etc to html
X Lower time pressure (remove all time limits; use analytics to see how long they take; double check super-fast and super-slow students)reate daily canvas plan
X PollEverywhere (not Nearpod) Canvas Technologies, Canvas txt to bring device every day)
X DoM sheet
X Team Test Sheets
X Pffaf’s files on Canvas
X Poll Everywhere (not Nearpod) link
X Bring computers for RATs
X Bring computers for evaluations
X Make Peer Evaluation forms on Canvas
————————————————-
OTHER
X Zoom policies: change breakout room times/countdown times
X Fix closed captioning
X Convert PDFs to htmls via XML
————————————————-
X Create Sage stuff for Eulers/Trap/Midpoint/Simpsons
X Compile video playlist
X Project Plan (in F20Actual)

X Use pandoc for slides
X PreTeXt? (no—pandoc)
X Testing effect (every day)
X Worked examples (6.2,6.4, 6.5, 7.8, 8.2, 11.4)
X Sage/Python
X Talk about MOVEMENT (estimation to a better approximation)
X Read with Perusall; a few videos to help
X 3 most important: access, assessment, inclusion
X Assume they are using a phone (91% of people near St Cloud have a phone; poverty to 200% poverty is 96%)
X Assume asynchronous (then f2f/synchronous is optional)
X Time-shifted:
X Flipped classroom (new information on their own, practice with us)
X Get them away from the device—have them communicate with a bank, for instance, and then have them come back to Canvas
X -Universal design—give students multiple ways to learn and multiple ways to demonstrate what they know
X -GET RID of “respond once and respond with two of your colleagues.” Instead, ask students to “advance the conversation.” Give them an open Zoom room.
X Use questions like Minerva: here are the steps of an optimization problem; which steps are incorrect or unclear?
X Do daily RATs?
X Due dates for projects
————————————————————–
X “Set of Me” assignment (https://busynessgirl.com/spicing-up-those-introduction-posts/)
X Weinberg’s SIR Method video (for project)
X Close caption videos

X RATS
X study guides for rats
X Create RATs
X Syllabus RAT (with wrong answer)
X Put RATs on Canvas
X Print out RAT questions as back-up
X Create RATs
X Require Whiteboard and markers (add to syllabus?)
X Clean up 120 folder
————————————————-

### Thank you Stan!

August 14, 2020

I just hit frantic mode: I am going to start getting up at 5 am to get another two hours of prep time in. However, I am feeling good about things, thanks to Stan Yoshinobu. His last post was brilliant, and just what I need.

I was planning on having the students do some reading prior to class. This was fine, and I was going to make it semi-sorta-interactive by using Perusall (which I am still going to use, since it will allow me to interact with students right in the textbook). However, I knew this was pretty meh. They probably wouldn’t learn a ton from it, even with some supplementary videos.

Enter Stan. He recommends having them complete worksheets, which he calls “tutorials,” prior to class. These seem like extremely highly structured IBL notes, and this just feels right to me. He links to an example of a tutorial in that post, but it is pretty buried so I am providing a link here. He provides them with solutions after class; I think that I am going to provide them with solutions once they submit their completed tutorial, since I believe Canvas can do such things (also, we are on the block system this year, so one day of class is like one week of a usual semester).

I need to create 15 of these, one for each of my learning outcomes. I have completed six of them already. In a stroke of luck, Stan’s tutorials are for Calculus II, which is exactly the class I am preparing; I am going to hit him up for his and offer mine up.

This tutorial idea makes me much more excited about the semester!

### 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.

### 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?

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

-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

“…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

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

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

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

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

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

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

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?

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

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

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

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

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

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

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

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

How to be good students: “…have a growth mindset.”
Ways of assessing: Journaling
Helpful resources: Mindset articles, What Works in Learning

Ways of assessing: Authentic Projects
Actual teaching-learning activities: In-class projects

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

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

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

### 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.”