MTH 124 has run for three semesters at Grand Valley, and I taught sections of it in both fall 2017 and winter 2018. The audience is students who have passed or placed out of Intermediate Algebra, but who otherwise would take 3-credit courses in both college algebra and trigonometry. Because college algebra (MTH 122 at GVSU) and trigonometry (MTH 123 at GVSU) are stand-alone courses that serve large numbers of students as terminal courses, and we found that many aspiring math, statistics, computer science, engineering, and physics majors — whose ultimate goal was to complete part or all of our calculus sequence — were taking MTH 122 and 123, we decided to create MTH 124 to focus on ideas that are most important for calculus to strive to prepare them as much as possible.

This aspiration begs an important question: what prerequisite ideas are most important for calculus? In the 2015-16 academic year, a group of us at GVSU thought about this carefully, and developed a syllabus of record for the course. As colleagues and I have taught the course, we’ve gotten a better sense of what should be included. Indeed, as I’ve worked with my students, I’ve written a fairly extensive set of activities; if you read the table of contents, you’ll get a good idea of how the course is organized.

**So, my ultimate question is to potential users out there, before I start writing in earnest:** what topics and ideas would you most like to see? From my existing table of contents and activities, what is missing? Are there things you see in the existing materials that don’t belong?

Another question I have is: what would you like to see process-wise? I expect to write in a style very similar to Active Calculus, with a preview activity followed by 3-4 activities per section, along with a handful of challenging writing exercises. I also plan to include WeBWorK exercises in each section. There are emerging possibilities with interactive graphics and more, so if you have thoughts, please share them. The goal will be a very student-driven, active-learning text.

Finally, a relatively minor question – but still one that is important to me – is: what should the title of the book be? The working title is “Active Precalculus”, as the text will very much be written in the style of Active Calculus. But the word “precalculus” is often misused in our community, so I’m inclined to try not to use it. I’ve thought of “Prelude to Active Calculus” or “Getting Ready for Active Calculus” … neither seems quite right. If you have a good idea, I’d love to hear it.

I would welcome hearing from you in the comments, on Twitter, or directly via email at boelkinm at gvsu dot edu. Your feedback will be most helpful if I receive it by June 15.

]]>At least one faculty member is already using Edfinity’s product with *Active Calculus*. In the months ahead, I will be learning more about these opportunities, and I wanted to share this news with others as I think this approach has the potential to provide a strong supporting resource to free and open-source textbooks. Here’s a blurb from Shivram at Edfinity if you are interested in piloting in their NSF-funded project:

Subject: New NSF-funded Homework System | Invitation to Pilot

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EDFINITY (NSF-funded and NSF Small Business Innovation Research award winner) is a hosted, modern and “textbook agnostic” homework system.

**HIGHLIGHTS**: Hosted. Mix and match with OER. Seamless use of WeBWorK problems without the hassle of installation. Leverage over 250 mature courses readily available. Import your own. Create new courses from over 50,000 problems. Share and collaborate. Device friendly.

**INVITATION**: Edfinity is inviting educators to pilot EDFINITY at no cost during spring/summer/fall 2018. Our eventual price point is estimated to be $1-$2 per student/month

Please visit edfinity.com/webwork and/or feel free to contact shivram@edfinity.com | 650-380-3627

++++++++++++

If you are using this, I would love to hear from you to know more about your experience.

]]>- The statement of the quotient rule in Section 2.5 mistakenly stipulated that the derivative of the denominator be nonzero, when of course it’s the denominator function itself must be nonzero.
- In Exercise #6 in Section 3.4, the cost of the top was accidentally omitted from the problem statement; it should be the same as the cost of the bottom of the box.
- In Activity 4.4.4, the accompanying graph in Figure 4.4.8 was from a previous version of the text/activity and thus the graph didn’t match the problem statement. The graph has now been updated.
- In the WeBWorK exercises for Section 4.4, I realized that the exercises there were identical to those in Section 4.3, so those exercises in 4.4 have been updated.

These errors will persist in the print and PDF versions until I release the 2018 version this summer, but the issues have now been fixed in the HTML posted at https://activecalculus.org/single/. If you have visited the affected sections in the past, you will likely need to refresh your browser and/or clear your cache in order to get the corrections to show.

I’ve also added short titles to each of the WeBWorK exercises; this gives the reader a bit of a clue to the nature of the exercise without having to click on the link to expand the knowl.

At the bottom of the contents that appear in the lefthand panel, there’s a “feedback” link that connects to a Google form. Thank you to each of the people who have used this to alert me to errors or recommended changes. You can use that link or send me email directly at boelkinm at gvsu dot edu.

]]>In particular, you can find sources of real world data for your classes – especially stats, calc, or any QL course. You can also find updates on sustainability issues such as climate change, inequality, the environment, social justice, and more that you can use both to be a more informed citizen yourself and to potentially share with your students.

You can follow Sustainability Math at

http://sustainabilitymath.org

https://twitter.com/SustMath

https://www.facebook.com/SustainabilityMath

In the short term, I will keep the HTML version also at its original home on my faculty web page until people are aware of the new URL. Please point your students and any bookmarks to https://activecalculus.org/single/, as that will be the main site going forward.

At the Joint Meetings in San Diego, the American Institute of Mathematics will be hosting a launch party at 1 pm on Thursday, January 11, to celebrate the release of the new site. If you are going to be present at JMM, I’d enjoy meeting you at that time at the AIM booth (booth 215) in the exhibit area; I expect to be present from about 12:45 to 1:45.

I’m deeply grateful to the American Institute of Mathematics (AIM) for their support of this project in many different ways, and for their support of open textbooks generally. David Farmer of AIM has been instrumental in helping me convert the original text from LaTeX to PreTeXt so that the HTML version was possible; I’m grateful for both his technical support and his strong advocacy for the project. As always, thanks also to Rob Beezer for creating and maintaining PreTeXT and for the opportunities this language provides to authors, as well as to Alex Jordan for his substantial assistance with graphics in the HTML and PDF versions of AC and for his work in making live WeBWorK exercises possible in HTML.

If you have questions about any aspect of the book, I welcome hearing from you at boelkinm at gvsu dot edu.

]]>My phenomenally talented friend and GVSU colleague David Austin is working to address this situation by making linear algebra more accessible to students. He has just released the first public draft of his new free, open-source textbook, Understanding Linear Algebra, which is available in HTML format thanks to PreTeXt. The HTML version of the text has interactive Sage cells and stunning interactive graphics (scroll down, for instance, to the moveable figure in Activity 2.6.2).

I urge you to not only check out the text, but also David’s new blog, More Linear Algebra. He has a high quality product, keen insights, and more on the way.

]]>“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.

]]>$199. Sigh.

A Proven Calculus Reform Course Package Get Your Copy |

View as Webpage |

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. |

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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