Metacognition in a calculus prep course

As usual, fall semester flew by. On Monday, August 28, I met with my two classes for the first time, and on that day we did an activity that I recounted in a Facebook post, where I wrote:

“I followed Stan Yoshinobu‘s wonderful first day lead and asked my students as they met one another (a) what is a hobby or interest that you are good at, and (b) how did you get good at it? Their responses were great, as you can see in the attached photos (1, 2, 3, 4). Besides “practice” being the big winner regarding how they got good, I loved the students who said “have a growth mindset”, “be bad at it for a long time but keep trying”, “worked on my weaknesses”, and “my dad has taught me a lot of things”. We also had a discussion about the most important things to take from a college education (hat tip: Dana Ernst), and students generated great lists there, too, one of which I remembered to take a picture of. Big thanks to all the AIBL folks and other math friends who share their good work to help us get classes off to a great start.”

The course I was teaching was GVSU’s new Math 124: Functions and Models, which is a 5-credit class designed specifically for students who are planning to take calculus but are not yet ready to enter that course.  Nearly all of my students were first-years, and one of my goals was to work specifically with them to help them become not only better students of mathematics, but better students generally.

To that end, beyond the aforementioned first-day activity, I added a new assignment to my courses this semester. I had students broadly tackle “metacognition” by doing a range of reading, listening, and watching experts on the topic of learning. If you are interested, you can read the full details of the assignment, which included some TED Talks and videos on failure (thanks, Stan, and the AIBL folks again), one of my favorite podcasts ever from Sam Harris and Tristan Harris (What is Technology Doing to Us?), reading one of several books (including Dweck’s Mindset, Burger & Starbird’s 5 Elements of Effective Thinking, and Bain’s What the Best College Students Do), and blog posts like Dave Richeson’s “Advice for College Students”.

In the last week of class, students turned in 3-page essays on what they learned about learning. The vast majority of the rest of this post is my students in their own words:

  • I decided to delete all of the social media apps from my phone. … I learned that I was very susceptible to the addiction of getting notifications and having people want to talk to me.
     
  • Failure is part of learning and it’s only really failure if you don’t learn from it.
     
  • It is important to learn by failure and work on your weaknesses. I have learned that it takes an immense amount of courage to admit to imperfections and to continue to work on strengthening them.
     
  • Raising questions personally has been difficult for me to overcome. I know I shouldn’t be afraid to show ignorance and ask if I don’t understand something.
     
  • The biggest thing I learned from this video is that obstacles and failures aren’t meant to destroy you, they are meant to show that you might need to change the way you’re approaching a problem because it will help you in this moment and later in life.
     
  • Before doing this assignment, I never thought about which mindset I was or what different mindsets there were.
     
  • In her book, Dweck states “Remember that having innate talent is not a goal. Expanding skills and knowledge is.”
     
  • After learning about growth mindset, one practical thing I will do to improve my life is to embrace challenges rather than avoid difficulties.
     
  • This course has made me realize how important is to have the right mindset. … I learned that if I approached assignments with a mentality that it would be challenging, and would take many hours and lots of patience, I was better off than when I started out being frustrated and feeling sorry for myself.
     
  • Surface learning versus deep learning was something new that I had never heard of before. After reading Bain’s What the Best College Students Do, he summarized that there are 5 types of college students: 1. The ones who get good grades but do no better than those who get C’s and D’s. 2. The ones who get good grades and become deep learners. 3. The ones who get mediocre grades but learned deeply. 4. The ones who receive bad grades, give up, and depend on the the other. 5. The ones who receive bad grades and tell themselves they’ll get better. I found this interesting because I can see some of these students in my classes. I also realize that surface learning is how I’ve been studying my whole life.
     
  • Recognizing and understanding your thought process on the path to an important part of success is an important part of continuing your success, however, I believe a more important part is recognizing and understanding your thought process on the path to failure, as it can help you learn and mitigate the decisions that lead to failure. Sitting here, late at night, writing a 3-page essay the day before it is due, I realize that the path to success is not the one I have followed.
     
  • One thing I want to do better in my learning is to put more effort into my work. This means getting an early start on assignments and studying, as well as going to all my classes. For me to do this, I need to reduce the usage that my phone plays in my life. Instead of being on my phone for hours on end, I should use that time to study or do homework instead.
     
  • You must go into the unknown to unlock the potential to reach the alternate and more beneficial solutions to a problem … I am seeing that in mathematics especially there is not always one path to the solution, but rather many.
     
  • The other big idea I took away from this project and math this semester in general is that you are never going to get in trouble for asking for help, and by not asking the only person you’re hurting is yourself because you’re the one who doesn’t understand the information.
     
  • Through this assignment as a whole I have learned just how importantly my mentality towards school affects my learning, how to find a solution to a problem I may not have planned on answering, and to view every failure as a possibility to try something new.
     
  • I can confidently say that I’ve learned more than just math in my MTH 124 course. I’ve learned how to be a better student, employee, and even a better person.

I, of course, learned a lot (or was reminded of many things I sometimes forget) through this assignment, too.  Briefly:

  • most college students have a lot to learn about being learners; many of my students reflected on how their high school experience didn’t prepare them very well for college
  • every single human being is afraid of failure, but failure (and learning from it) is essential to living a healthy and productive life
  • things that I tend to take for granted in my students are things I need to talk about with them more:  how to study, how to ask for help, how to grow as a learner, …

A big thank you to all my students from this past semester for the opportunity to work with them, to learn from them, and to hopefully help them take few steps further down the path to success.  I’m also very grateful for their honest and thoughtful essays, which were fun to read at the end of a long and full semester in which I graded a lot of other work.

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“Priced at nearly $100 less than the competition”

(I’m overdue to post something meaningful in this space, but today’s email made this post irresistible).  Following is clipped from my email, and here’s a direct link to the text: https://he.kendallhunt.com/product/calculus.  The tag line is “Priced at nearly $100 less than the competition, …” and when you click through to their web page, you see the price is (wait for it): $199.

$199.  Sigh.

A Proven Calculus Reform Course Package
Get Your Copy
View as Webpage
Calculus
Professor Boelkins,
Priced at nearly $100 less than the competition, Calculus blends the best aspects of calculus reform along with the goals and methodology of traditional calculus. The complete turn-key package is enhanced, but is not dominated by new technology.
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Active Calculus 2017 – print copy now via Amazon

In an earlier post, I noted that the 2017 version of Active Calculus – Single Variable was available for purchase via CreateSpace.  There were some minor technical issues with getting the text available on Amazon, but those have now been reconciled, and you can find it directly at this link.  It’s even available for Amazon Prime shipping, so total cost is $19.50 for Prime members.

The free HTML version of course remains available; I also recommend that all users download and save the corresponding free PDF.

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Active Calculus 2017 – print copy available

The bound, print copy of Active Calculus 2017 is available from CreateSpace for $19.50.  As soon as the Amazon site page for the book is built, I will post the URL for it, too.

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2017 version of Active Calculus: more updates + notes on differences from 2016

Here are several updates to follow my most recent post.

+ The 2017 PDF version has been finalized and posted online; the HTML has been slightly updated as a result of work to get the PDF looking suitable. If you have previously been accessing the HTML via my site, be sure to refresh your browser in any pages you’ve viewed.

+ Steve Schlicker has an updated version of the multivariable text online and that now has a print-on-demand option.

+ Note well that there are now both 2016 and 2017 editions of the single variable text. Please take care in pointing students to the version you want to use.

The 2016 version is essentially unchanged from the one posted August 2016 and will remain static going forward. For the 2017 version, the main differences are:

HTML version that can even be used on smartphones
– live WeBWorK exercises in the HTML version
– the WeBWorK exercises change the numbering of the non-WeBWorK exercises from 2016 & prior
– renumbering* of preview activities and activities from 2016 & prior

* in the 2016 and earlier versions, typical numbering was, for example: in Section 3.2, Preview Activity 3.2 followed by Activity 3.4, 3.5, and 3.6, as the activities were numbered sequentially throughout the chapter. In the 2017 version, both preview and regular activities are numbered in sequence within the section. So, in Section 3.2, you’ll find Preview Activity 3.2.1, followed by Activity 3.2.2, 3.2.3, and 3.2.4. There has been little to no change in the activities themselves.

In a forthcoming post here on the blog, I’ll offer some suggestions about how to use HTML vs PDF vs print.  While I expect that HTML will be the primary interface for most users, having at least a PDF copy will be important and having a print copy may be ideal.

+ Speaking of print, I’m in the final stages of the process to get a print-on-demand version of the 2017 text available from Amazon via CreateSpace. I’m optimistic that will be up and for sale by the end of next week (Friday, August 25), and hopefully sooner. I will post a link on my main home page and add a post here on the blog when it’s available.

+ I’ve created activities workbooks to go with chapters 1-4 and 5-8 for the 2017 edition.

More to follow soon.  As always, thanks for your interest in and use of AC.  I welcome hearing from you with questions or suggestions.

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2017 version of Active Calculus (single variable)

I’m excited to announce several changes to single variable Active Calculus along with some corresponding updates that will occur over the next month or so.

+ There is now a new HTML version of the text.

Thanks to Rob Beezer’s Mathbook XML (now called PreTeXt), this output format is optimized for viewing on a range of devices, including smartphones. Many times over the past several years I’ve had my students come into my office to ask a question, only to pull up the PDF of the text on their phone and pinch and squeeze their way to some problem or statement. The HTML version looks fantastic on a phone and is in many ways far superior to PDF; please check it out. I find it likewise better for viewing on a projector screen in a classroom.

+ The HTML version includes live WeBWorK exercises.

Thanks to the programming and technical support of Alex Jordan at Portland Community College, if you follow the link above and navigate to the end of any section, you’ll see each section starts with several WeBWorK exercises (usually 4-8 of them).  These newly included exercises (all of which come from the OPL) are more routine than the original exercises in the text, which remain but are now numbered differently. The WeBWorK exercises provide live anonymous feedback; do note that even if your department is a WeBWorK platform, students can’t log in to complete these problems. These are intended to be optional supplementary exercises.

+ A corresponding new PDF version is forthcoming.

I’m still working to get the 2017 PDF ready; I expect that will take another couple of weeks, at which point I have to get it set up with Amazon. Regardless, that will be ready by the start of fall term (late August) for print versions. It will be important for users to download the 2017 PDF regardless, since the HTML version requires an internet connection to function. More to follow when the 2017 PDF posts. Also, see next item for why I’m writing “2017 PDF”.

+ The 2016 version will be available but unchanged going forward

The 2016 LaTeX/PDF version will continue to be available, but my plan is not to make any further changes to that source code and instead view that source as “frozen”. If in the past you have requested the original TeX source from me, you’re welcome to ask for the most updated version of that, which I last changed a month or so ago to reflect the errors that various users found and reported during the 16-17 academic year. This 2016 PDF version will continue to be posted online and will also be available for purchase in print/bound form from Amazon, etc.

Looking ahead to the start of fall semester: if you use either the 2016 or 2017 version and intend to encourage your students to buy a print copy, it will be important that you clearly direct students to the correct print version to purchase. There is a new cover image and a slightly different color scheme for 2017 to help distinguish the two versions. More info on this (with direct links) will follow — for sure on my blog and likely via email — sometime in mid August, including an overview of the differences between the two versions, which are modest but will likely affect communication with students when directing them to portions of the text.

+ Active Calculus – now on GitHub

For GitHub users and those interested in using/learning Mathbook XML/PreTeXt, the XML source files are now on GitHub. I am a novice GitHub user, but as I continue to learn, submission of issues and pull requests will be very much appreciated. In the not-distant future I plan to post the 2016 LaTeX source files to GitHub as well.

+ More updates to follow

I’ve recently updated my web page for the text, and I expect that additional updates will follow there along with here on the blog in the coming weeks.  Beyond information regarding this new version and format for the text, I’m planning to post more frequently this fall to share user feedback on the HTML version and some other hoped-for future developments.

Thanks for reading and for your interest in Active Calculus.

 

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Active Calculus: usage statistics

One of the superb librarians at GVSU who manages the site that hosts AC sent me access to a dashboard that reveals a lot of interesting user data.

For example, after GVSU, the 10 locations/institutions that have downloaded AC most are:

Westmont College
Foothill-DeAnza Community College District
University of Redlands
Keene State College
St Ignatius High School
Middlebury College
University of British Columbia
Adelphi University
Nevada System of Higher Education
Washington & Lee University

In addition, there are some really interesting maps of download data, such as these (which summarize the downloads in calendar year 2015):

AC global usage statisticsAC NA usage statistics

I’d like to reiterate a request I have made in the past: if your HS/college/university has adopted AC, could you please send me a direct note to let me know that?  Also, if you email me directly for anything related to AC, I’ll add you to my email list of contacts, which I use a couple of times a year to share text updates directly.  You can reach me at boelkinm at gvsu dot edu.

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Active Calculus: Preview Activities in WeBWorK

David Hunter of Westmont College and Branden Stone of Adelphi University have been working on WeBWorK versions of all of the Preview Activities.  David recently emailed me to share that these are now all available in the national problem library:

 

Also, the Preview Activities have now been added to the WeBWorK Open Problem Library. The easiest way to find them is to use the “OPL Directory” button in the Library Browser. After clicking this button, a drop-down menu will appear listing OPL Directory Problems. Choose the directory “Westmont/ActiveCalculus/Preview_C_S”, where “C” is the chapter you want and “S” is the section. Let me know if you hear any complaints about bugs, etc. I’ve used the Previews for Chapters 1-4 a few times, and I’ll be class-testing the remaining Previews this semester.

 

Huge thanks to David and Branden for their work to make this happen and for making it public for others to use.
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Active Calculus (Single Variable): 2016 Edition now available

It’s August (and Mathfest!), so time for an annual update to AC.

I have fixed every known error in the 2015 version and have implemented nearly all of the requests/suggestions that users sent me over the past year. The new version of the PDF is now available in the usual location at http://scholarworks.gvsu.edu/books/10 (you may need to refresh your browser if you’ve downloaded it from there before).

For the 2016 version, note that the cover color has changed to blue (from green), which will hopefully help identify the current edition more easily for students if they choose to purchase the print version. The 2016 print-on-demand version is also now available, for instance via Amazon via Lightning Source.

(The 2016 version is quite similar to 2015, and there haven’t been any changes to exercises or activities beyond fixing errors, so it shouldn’t be a big deal if students have an earlier version. There are likely some slight changes in page numbers. I have found that if I don’t give my students a direct link to the particular edition at Amazon or B&N and they go searching themselves, they often end up with other versions than the most current.)

There are corresponding updates to the activities workbooks.  You can find the links to those along with information about other complementary resources for AC in this post from 2015; don’t forget there are lots of great videos that accompany the text, too.

I want to express my considerable thanks to everyone who sent me errors and suggestions over the course of the past year. I hope that if you are using the text you will continue to send me ways you see for how the text can be bettered.

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A new free mathematics journal

Interesting read here: http://www.forbes.com/sites/kevinknudson/2016/04/30/the-future-of-mathematics-publishing-an-interview-with-sir-timothy-gowers/#5d41b5a52467

I’m mainly posting this so I have a record of it, but there’s lots of similarity between what Gowers says about his journal and what we say about free textbooks.

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