M.A.T.H. Tips: Vol. 19
What are your plans for implementing a co-req model at your school? Get advice, hear tips & successful implementation stories from other Math Faculty during our recent Co-Req Summit. We hosted four speakers, and you can watch these pre-recorded sessions in any order. Click on the links below to review these sessions.
Every once in a while it’s fun to let your students see math in the real world, but math that is wrong, very wrong is a reminder that they too can help improve the world when they catch these math FAILS!
Great for final exam day to have sitting on your desk! Or recognize your most improved students with one of these gems!
When students realize that time is getting short and they need to get their grade up, they often look to get tutoring. The problem is many students need tips on how to make the most of a tutoring sessions! Here are some suggestions to share with your students to help them have a better tutoring experience so they can see the benefits of preparing for a session and asking the right questions while they are in session!
- They are in control of the tutoring session.
- They pick the topic.
- They indicate whether a calculator is permitted.
- They need to decide what method they would like to use when there is a choice.
- The more clearly students can articulate WHAT is confusing to them, the easier it will be for the tutor to provide useful help.
- They should prepare for the tutoring before they arrive so they can maximize what is accomplished in limited time.
- Have questions marked with post it notes or other markers.
- Don’t have 100 loose papers to shuffle through!
- Know what chapter, section, and page numbers questions relate to.
- Going to tutoring sooner rather than later is always best, but even a cram session can help, if it is effectively done.
- It helps if they can estimate the amount of time needed to meet their goals.
Many students arrive at tutoring and by the time they shuffle through papers, vent about their teacher, and tell their life story there is not much time for the actual tutoring session. To make the experience as helpful as possible, here are some do’s and don’ts.
5 ineffective tutoring starters…The DON’T’s!
- I am totally lost…
- I don’t know what section we are on…
- I don’t know how my teacher does it…
- My teacher is awful because…
- Let me look for my _____….
5 GREAT question starters… YES, DO these things!
- I am OK with steps one and two but I don’t understand where this number came from in step three…
- I don’t fully understand what the word_______ means…
- Could you review the steps for _____________ with me…
- In this formula I don’t understand what the symbol ____ represents…
- Here is the way my teacher does it (show the tutor your notes), I would like you to show me how to do it using that method…
Share this post with your students so they can be time efficient and walk out of a tutoring session with the skills they need to move forward!
Unlike lower level math courses where creating real world problems can sometimes seem a bit artificial, Calculus lends itself to including mathematical models used in fields from economics to infectious disease. With the wide variety of models available calculus instructors can create meaningful and memorable problems for students. Extending the idea further instructors can projects for students using project-based learning.
Thomas Markham describes project-based learning (PBL) as: “PBL integrates knowing and doing. Students learn knowledge and elements of the core curriculum, but also apply what they know to solve authentic problems and produce results that matter. PBL students take advantage of digital tools to produce high quality, collaborative products.” (2011 Project Based Learning. Teacher Librarian, 39(2), 38-42) Project based learning takes on different forms depending on how an instructor chooses to implement. Calculus, with its reach into in a variety of disciplines, lends itself to PBL. There are several ways to integrate PBL into the classroom. Some ideas for PBL are
- A single project that students work on over the duration of the course.
- Smaller mini projects that take 2-3 weeks to complete.
- An interdisciplinary project that has students work on projects that combine information from different courses.
And for some inspiration regarding the types of projects possible:
- High Point University has a short project involving limits and an oil spill https://bit.ly/2GiODRI
- A group of math professors at the US Naval Academy have a great site to get you started with a variety of projects https://bit.ly/2uyAlXZ .
And Murray Bourne wrote an easy to digest piece on the logistic model and H1N1 which can be used as the basis for a project on disease modeling and inflection points https://bit.ly/2Ijfp9f
Last month Robert Langlands won one of math’s post prestigious prizes, The Abel Award, for his life’s work on what is known as the Langlands Program. The Program’s inception occurred in 1967 when Langlands wrote to Andre¢ Weil regarding a new approach to mathematics that linked together the fields of number theory and harmonic analysis. What began in that letter spawned decades of seeking, by mathematicians of all stripes, for a unified theory of maths. In his book Love and Math Edward Frenkel writes of his own introduction to and subsequent fascination with and immersion into the Langlands Program. Frenkel’s book not only gives the reader a glimpse into the world of the Langlands Program but also lays bare that the pursuit mathematics is a labor of love.
- What is your current job/career?
I am a freelance math and science writer. The vast majority of my articles are about math, but I do occasionally get to write about physics, engineering, and other sciences. I have regular monthly blogging that I do in addition to articles for websites and magazines. I blog for Scientific American at Roots of Unity and for the American Mathematical Society at the Blog on Math Blogs. My work has appeared in Slate, Nature News, Smithsonian, Undark, Nautilus, Science News for Students, and Muse Magazine. I recently started a math podcast called My Favorite Theorem with Kevin Knudson. It’s been fun to stretch myself by working in a really different medium. My writing process is slow. I let things roll around in my head for a while before I put them on paper, and after I’ve written them, I rewrite and tinker a lot before I feel like something is ready. The podcast is a spontaneous conversation, and I have to think on my feet a lot and not get too upset if things don’t come out as polished as my writing is. I’ve grown a lot by doing it, and I must say I’m very proud of what we’re creating.
- How do you use math or mathematical problem solving in your work? How does your math background help you in your job?
Many math and science writers don’t have a math background, but for the way I think and write, my math background helps me every single day. One important way is that I understand how mathematicians think and what questions they tend to find interesting. I think that understanding helps me when I interview mathematicians for articles I write. Mathematics is a very broad discipline, so there are many areas of math I know almost nothing about, but even in those areas, having that baseline common point of view helps me ask the right questions.
- What motivated you to study math?
I went to the Texas Academy of Math and Science, a public high school where students enroll in college classes for their last two years of high school, so I graduated high school with a lot of math and science credits. I wasn’t interested in math as a major or career, but I was very close to having a math minor in college just with my TAMS credits, so I took a few more classes to get that major. In one of them, an introduction to proofs class, I fell in love with math. I hadn’t seen it as a creative subject, and I think of myself as a person who needs to be doing creative things to feel satisfied. Once I saw math as creative, I wanted to go further and further in it. I had a lot of interests in college, including biochemistry, classics, music theory, and music performance. It took a lot of soul-searching to decide to do math as a career, but that class is what set the ball in motion.
- What would you say to a student who is thinking about studying math but doesn’t want a typical teaching career.
In college and graduate school, our role models in math are all teachers and professors, so we sometimes think that is the only or best math career option. We also have some offensive ways of talking about that: “leaky pipeline” comes to mind, describing people (usually women) who leave the academic track. I “leaked” out of that pipeline into a career that makes me happier than I was in academia. Should I feel like a disappointment for that, or should my mentors feel like they failed? Perhaps it is a useful metaphor at a community level, but I think it also hurts people who are considering other careers. All of that is to say I think a big barrier for students interested in math is the idea that there is one preferred career path — academia — and everything else is a consolation prize.
If you aren’t interested in an academic career, you’ll want to look outside the math department for information about those careers and advice about how to prepare for them. The BIG math network is one resource students might look at to start. I wrote about that and some other resources in a post for the AMS called “What are you going to do with that?” [Link if you want it: https://blogs.ams.org/blogonmathblogs/2017/05/15/what-are-you-going-to-do-with-that/ ] If you know alumni of your program who have gone into other careers you’re interested in, talk with them too.
- Other advice or comments?
Ask for help when you need it. I was sort of cocky as a student, and when I started having trouble in grad school, both with math and with my mental health, I felt like I had to cover it up. There’s no shame in getting help when you need it.