Dr. Dawn's blog

These are the slides to accompany a research talk I gave at the Cuntz Semigroup Workshop in Kiel, Germany.

For the  review for test 1 in my Business Calculus course, I used the “Find Someone Who” activity featured in a previous post.  When it was time to review for the second test, the students asked if we would be doing that again.  Unfortunately, it didnt’ feel like a good fit with the content at that point in the class.  So instead I concocted a low budget escape room.  The pdf of my escape room is available here.  If you want the .tex code you can acces it here, but I took out the QR code and link to my form, since you’ll need your own.  If you want to try it our before you adapt it to your class, feel free to submit your answers to my Google Form (use the QR code in the pdf).

I got the idea for a digital escape room from a video I watched early in the pandemic.  I learned the details of how to set one up using Google Forms from Bespoke ELA ‘s blog post.  She explains the mechanics very well, so I won’t go into the details here.  However, I will mention that the key step is to use “response validation” in the Google Form so that the students can’t go on unless they have entered the correct code.

For me the hardest part was thinking of a suitable story to frame the escape room and finding the right “voice”/writing style.  In the end I chose to have the students need to find the manual over ride for the self-destruct sequence on our interstellar spaceship.  I wrote in a campy style reminiscent ot the Choose Your Own Adventure books of my youth.

Here’s the introduction to my escape room:

We are the crew of the intergalactic spacecraft the USS Titan*. Captain Archey tripped and fell. On her way down, she hit her head on the self destruct button**. Now, she is unconscious and the 50 minute self-destruct count down has begun. Without the captain’s voice print, the only way to deactivate the self-destruct sequence is using the manual override switch.

The communications officer says, “I remember Captain Archey mentioning the instructions to deactivate it being on her e-reader.”

The exobiologist says, “I bet her e-reader is in her quarters. Does anyone know the passcode to enter her quarters?”

The head of security says, “She told me she left a hint to the code on a paper in her shoe whenever she had to change the code. Let’s hope she changed it recently.”  The head of security removes Captain Archey’s shoe and finds the next page of this packet.

* Our university mascot is the Titans.

**I had three students at the front of the room to be the officers and read their parts.  At this point in the story I flopped down on the floor and stayed down throughout the introduction.

All the “locks” in the escape room were codes to enter in the Google Form until the very end.  After the students enter

ed the third code, which was the combination to my gym locker, they could head over to the front corner of the room where I had a laptop case/small carry on suitcase labled, “Captain Archey’s gym locker.”

Inside the “gym locker” they found a “key” (a picture of a key on cardstock) and a note indicating that the door to the manual shut off was in the back corner of the room.

In the back corner of the room there happened to be a little funny space between the wall and the window.  Inside that space I put a switch controlling a red light (made of my kids’ Snap Circuits) and some cheap prizes like Lifesavers and pencils.  To cover the space I had taped up a piece of paper with a door knob on it.

It was all kind of silly, but the students were good sports.  One even asked me, “Are we really going to die if we don’t finish all these problems?”

I was actually walking around the room, but because in the story I was unconcious, the students made more of an effort to figure things out on their own (for example, digging through their notes rather than asking me for a formula).

Two of the three groups of students finished the activity and the third group was close.  I was afraid that the students who didn’t finish might feel discouraged or disaapointed, but they actually came up to me after class and said what a great activity it was.

I use a flipped  classroom for Calc 2.  I am mostly using GVSU’s Active Calculus as the textbook (section numbers in my file names line up with that book too).
Its available for free on line at: https://activecalculus.org/single/frontmatter.html

Before class students are asked to:
1)  Read a (half page) document containing learning objectives (these are very heavily based on the learning objectives documents that people at GVSU gave me).  This is my folder of the learning objectives documents: https://udmercy0-my.sharepoint.com/:f:/g/personal/archeyde_udmercy_edu/EmkYd1ZEs0VMtVEEmM1sIQMBNXuB0PEbpqM0cF0lss7S8Q?e=txdNGp

2) Skim the section in the active calculus book.  If the active calculus book doesn’t have a section on a certain topic that my department covers, I assign readings from the OpenStax Calculus book instead

3) Watch a few videos  (I try to keep it to less than 30 minutes per week per credit hour.  So for my 4 credit class they are watching less than 2 hours of video, sometimes significantly less than that).  This is my video play list for the course:
https://youtube.com/playlist?list=PLwYL3PO-9SUF-Y8ZXE8aYyn6rtzIAR2YX
Its a little bit out of order at the moment, but I can try to straighten it back out, if that would help.  Grand Valley State has a play list too, but I cover some topics they don’t.

4) Do a preclass activity to check that they are ready for class (its a carrot to get them to do the readings and videos, generally graded on effort/completion rather than accuracy.
Most frequently the preclass activity is a two or three question quiz (that is very heavily based on the video lectures) or a Desmos activity.  I’m not sure I can easily share my whole list of Desmos preclass activities, but if there’s a specific topic you want to see, just let me know.  Also, the Active Calculus book has preview activities which people have already implemented in Webwork (https://github.com/djhunter/webwork-open-problem-library/tree/master/Contrib/Westmont) and in Desmos (https://sites.google.com/view/taylorshort/preview-activities) available for anyone to use.

During class I usually
1) Give a brief (10-15 minute lecture) focusing on the big picture, connections to other topics, or tricky points.  These are the slides for my brief in class lectures: https://udmercy0-my.sharepoint.com/:f:/g/personal/archeyde_udmercy_edu/EmOHoiobAfFPuUO1ZWtsNV4BfK8zBLPPRxSZ8i9sBZ-cTQ?e=iZ3XgQ

2) Ask the students to do a group activity such as a worksheet.  These are the ones I use.  https://udmercy0-my.sharepoint.com/:f:/g/personal/archeyde_udmercy_edu/EtGLNQv8cV9ArlGmc2-7proBEb-eiASksB6ayS6a7OJNWA?e=dfKQFt

Please feel free to use anything that helps you and to  email me with any questions.

It’s a perennial problem in math classes: Its review day for the test and the professor asks “are there any questions?” only to be met with silence.

Of course there are many reasons students might not ask questions.  Probably the main ones are:

They haven’t started reviewing yet, so they don’t know what questions they have.

They have mostly mastered the material and don’t need to ask questions (this is probably a very small minority).

They aren’t comfortable to ask a question.

Of course there are many reasons why a student might not be comfortable enough to ask a question: thinking that asking is a sign of weakness, worry their their question is dumb, fear that they are dumb or others will think they are, because the professor is an authority figure, stereotype threat,  a past traumatic experience asking a question in a class, or difficulty formulating a coherent question to name a few.

Whatever the reason for the lack of questions, students need to ask questions in order to succeed mathematically.  Therefore, in an attempt to avoid the awkward staring at each other while the students don’t ask any questions, I decided to try a completely different review activity in my Business Calculus class this week.  The activity was called “Find someone who.”  I got the idea from the book Choosing to See: A Framework for Equity in the Math Classroom by Pamela Seda and Kyndall Brown.  They learned about it from the book Kagan Cooperative Learning.

In the “Find someone who” activity, the professor prepares a worksheet formatted like a bingo card/ tic-tac-toe board.  The students are asked to move around the room asking their classmates to explain a problem to them.  Once the student has understood how to solve the problem, the explainer signs that square on their worksheet.

This activity can be adapted for any topic.  Mine was the review for the test on the basics of derivatives (including limit intuition and secant lines).  You can access the PDF  here: FindSomeoneWhoTest1Review .  To tantalize you, I’ve also included a picture of the worksheet.

Handout for Find Someone Who

The energy in the room during this activity was fantastic!  At first most students only wanted to talk to the people next to them, but with some gentle prodding and some affirmations, the students got into it.  I got to hear fun snippets of conversation like one student explaining the chain rule to another, “and then you stuff it back in…”.

As a review for the test, this activity allowed students to solve problems (as most reviews do), but also allowed them to explain concepts and procedures which helps the explainer to learn and remember the material.

Besides serving as a review for the test, the activity served a few other functions.  Students got/had to ask questions in a non-threatening environment–everyone had to ask questions, so there was no stigma attached to asking.  Hopefully, this will also have a longer lasting effect of normalizing asking for help and increasing student willingness to ask questions of me and each other.  On a related note, the activity helps to “include others as experts” which is one of the pillar’s of Seda and Brown’s titular framework for equity. As the name suggests, this pillar is all about establishing that the teacher is not the one and only source of knowledge–other students and the student’s own self also bring valuable knowledge.

At the end of the class period, I asked students to write me a couple of sentences about how they thought the activity went.  I tried to encourage honest responses by being completely honest with them. I said, “I’ve never done an activity like this before; I read it in a book, so I want to know how it worked from your perspective.”  Most students were enthusiastic in their positive review of the activity.  The students also identified many benefits of the activity, such as:

Getting to know classmates

Teaching classmates helped me remember the steps

Greater confidence for the upcoming test

Hearing the steps out loud and in different ways

Experiencing the value of learning from peers

Awareness of weak spots in knowledge of the material, which will help with studying

I was delighted that the students were extremely engaged and that they were able to articulate some of the many benefits of the activity for themselves. This activity powerfully demonstrated that our classroom is a safe space for asking questions.

Sources:

Pamela Seda and Kyndall Brown, Choosing to See: A Framework for Equity in the Math Classroom (San Diego, CA: Dave Burgess Consulting Inc., 2021) https://www.daveburgessconsulting.com/books/choosing-to-see/

Spencer Kagan and Miguel Kagan, Kagan Cooperative Learning (San Clemente, CA: Kagan Publishing, 2009)  https://www.kaganonline.com/catalog/cooperative_learning.php#BKCLW

From Equity Talk to Equity Walk: Expanding Practitioner Knowledge for Racial Justice in Higher Education by
Tia Brown McNair, Estela Mara Bensimon, and Lindsey Malcom-Piqueux is a great book for anyone working in higher education.  It provides a theoretical framework, action steps, and examples.

A few key take a ways from this book:

1) Disaggregate your data in lots of ways (race, gender, course, learning outcomes).  (This made me uncomfortable due to small sizes of subgroups until I realized we aren’t trying to make claims of “statistically significant differences,” but rather looking for actionable patterns.

3) Don’t put the responsibility to fix the problem (of difference in outcomes by racial groups) on the very groups who are suffering from it.  They have enough to do.  And also, its our (white people’s) fault due to slavery, land grabs, racist housing policies, etc.

I wrote some story problems about Pokemon cards for my son’s first grade class.  I gave them to the teacher during the last month of school.  The students really enjoyed that their classmates’ and teacher’s names were in the problems.  The problem set is a mixed review of many different problem types the students had done that year.

Here are the problems:

Name_________________________________

Pokémon Story Problems worksheet (mixed types)

1. Mustafa has three basic Pokémon cards in play. Each one has two energy cards on it.  How many energy cards in all?
2. Half of Maria’s Pokémon cards are Water Type Pokémon. Maria has 16 Pokémon cards.  How many Water Type Pokémon cards does Hazel have?
3. John had 137 Pokémon cards, but his sister spilled milk on 6 of them. How many Pokémon cards does John have left?
4. Jaelle had 101 Pokémon cards. She got 4 more for her birthday.  How many Pokémon cards does Jaelle have now?
5. Ms. Daniel said, “No Pokémon cards in class.” But every day someone brings in Pokémon cards and Mrs. Daniel has to take them away.  She will give them back at the end of the day on Friday.  On Monday, Mrs. Daniel took away 7 cards.  On Tuesday she took away 3.  On Wednesday she took away 4.  On Thursday she took away 6.  On Friday she took away 1.

a. Make a graph that shows how many Pokémon cards Mrs. Daniel took away each day.

b. On which day did Mrs. Daniel take away the most cards?

c. How many cards did Mrs. Daniel take away in all this week?

d. On which day did Mrs. Daniel take away the fewest cards?

e. What fraction of the cards did Mrs. Daniel take away on Monday?

One of the challenges in creating realistic problems for my students is finding good/interesting sources of data.  I will list here some useful site for finding data along with a brief description of the sorts of data one can find there.  I have to confess that this post is largely self-serving, providing me with a record of data sources I have heard of or used before.

Data.gov is “the home of the US Government’s open data.”  There are over 300,000 data sets, for example Chicago crimes from 2001 to the present and national hourly precipitation data. 

Data.detroitmi.gov is a data base of information on the city of Detroit.  Information includes government data, public health data, and education data.

data.nasa.gov is NASA’s data base which includes climate change data.

http://mlb.mlb.com/stats/sortable.jsp has the statistics of every major league  baseball player which can be sorted and filtered by things like team and position.

http://www.ncaa.org/about/resources/research/data-sharing is a source of data about NCAA teams/players.

https://www.cia.gov/library/publications/resources/the-world-factbook/ is the CIA’s “World Fact book” containg a wide variety of information on all the world’s countries from land area to GDP to major exports.

https://www.bls.gov/data/ the US Bureau of Labor Statistics.

https://pollingreport.com/ has results of American Opinion Polls.

World Values Survey https://www.worldvaluessurvey.org/wvs.jsp .

https://www.datafiles.samhsa.gov/data-sources (The Substance Abuse and Mental Health Data Archive).

https://data.cdc.gov/ Center for Disease Control.

The skills of estimating and performing unit conversions are useful in mathematics at many levels as well as in many scientific situations. The estimation challenge works on both of those important skills. In this challenge students are asked to answer odd questions such as “How many slices of Kraft American cheese would it take to wallpaper this room?” The goal is not to get the “exact right answer” but rather to determine the magnitude of the answer (the power of 10 part when expressed in scientific notation). This gives a sense for how big the quantity is.
After all groups had estimated their answers, we compared answers and discussed any questions the students had.

Here is the text of the Order of Magnitude Estimation challenge:

******************************************************************************************

ORDER OF MAGNITUDE

Work out your estimations on scrap paper, and record the ten-to-a-power part.

1. How many slices of Kraft American cheese would it take to wallpaper this room?
2. How many cherries would fit inside the four tires on a school bus?
3. How many gallons of water would it take to fill this building?
4. How many pounds does the ancient statue The Sphinx weigh?
5. How many dollar bills laid end-to-end would it take the reach the Sun?
6. How many kernels of corn are in full square mile cornfield?
7. How many poker chips would it take to fill the High Bay at UDM?

****************************************************************************

The Order of Magnitude Estimation Challenge was developed by a colleague of mine (Dr. Jeffery Boats) here at the University of Detroit Mercy. He designed the activity as part of the mathematics content of a summer experience for incoming freshmen. This activity along with some jelly bean estimation, were the first of four days of mathematics content. The student participants in the summer experience are planning a variety of majors in biomedical fields. Funding for the summer experience is provided by the National Institutes of Health (NIH) as part of a $21.2 million dollar grant over a five year period. For more information about the grant and the summer experience, visit rebuildetroit.org.

One of the challenges of teaching mathematics to this group is the wide variety of mathematical backgrounds and placement scores the students come in with (anywhere from developmental math to calculus 2). It is important to provide activities which engage all students without overwhelming or boring anyone. The solution devised by the mathematics department is to present topics that are off the beaten track or that recur in many courses.  This estimation challenge isn’t a part of any standard course and also uses the skills of number sense/estimation and unit conversions which show up in many courses.  As another example, on the fourth day of the mathematics portion of the summer program students used K’nex construction toys to investigate function composition as described in a previous post on this blog

Working together with my best friend since the 5th grade who is now a nurse practitioner, I developed this problem in which students have to use exponential decay (half life) to protect their patient from dangerous drug interactions.

Your patient has a fungal infection and is taking ketoconazole 400mg daily for 10 days. During this time they have been advised to stop taking their atorvastatin because of the potential for severe interaction. They may begin taking the atorvastatin again when the concentration of ketoconazole is at 12.5% of the original amount. The half life of ketoconazole is 8 hours.

How many hours after the last dose of ketoconazole can you patient resume taking the atorvastatin?

Here are the slides from the Project NExT panel presentation I did on contextualizing mathematics at the 2017 Joint Mathematics Meetings.

jmmtalk2017-contextualizingmathematicspanel