Student Guide Corner

By  Jessica Deshler ,  West Virginia University There is something beautiful about the structure of mathematics that we can all appreciate, but it�s equally beautiful because it can be creative and messy. So is the teaching of mathematics. As mathematicians, we know and understand the complexities involved in our discipline, but sometimes overlook the underlying complexities of our classroom environment when preparing to teach. You�ve likely heard about the leaky pipeline � the phenomenon that describes the loss of women from STEM fields at various points in the academic pipeline. Because many undergraduate women leave the STEM pipeline after taking a mathematics course , our discipline can especially benefit from classroom practices known to help retain and support these students. You might wonder whether the gender breakdown in our classes or variation in our students� cultural and social backgrounds matter. We posit that these do matter, and that they can impact whether stu...

By Rick Cleary (guest blogger), Babson College A note from the Editors: This semester Teaching Tidbits will have several posts highlighting the new Instructional Practices Guide ( IP Guide ) from the Mathematical Association of America ( MAA ). The MAA has a long tradition of reporting what content should be taught in the mathematics classroom through its Curriculum Guide ; now the new IP Guide addresses how things could be taught in the mathematics classroom, how one could to design that experience, and how one could assess that experience. The suggested practices are well grounded in research on student learning. In our first post about the IP Guide, we dive deeper into the Assessment Practices section of the guide. Thanks to Rick Cleary, a lead writer for this section, for providing this post. The opening statement of the Assessment chapter of the MAA Instructional Practices guide makes the following claim: Effective assessment occurs when we clearly state high-quality goals for...

Over the years, I have argued often on this blog that one of the really weak spots in education was the failure of students to close the holes on what I call �Swiss Cheese Knowledge.�   Thus, on the first day of class last week, I drew a block on the board and put holes in it.  I then explained the drawing to my students. When you leave class every day, your knowledge looks like a block of Swiss cheese.   It appears entirely solid.  However, it is full of holes�things you missed, things you misunderstood, things you did not quite catch.  I know the knowledge feels solid, but it really is not.   If you do not take action, those holes just get bigger as time passes and your memory begins to fade.   Having taught for nearly 50 years, I know where the holes are likely to be.   I can and will write test questions to expose those holes.  In many ways, testing is just an attempt to measure the quantity and size of the holes ...

By  Lew Ludwig  (Editor-in-Chief),  Denison University As the semester begins and we prep for classes, the practice of backward course design is a powerful way to get the most of the learning experience for our students. With this in mind, I thought I would share one of my favorite exam questions for a first semester calculus course, which appears below. I call it �the one question calculus final.� Now of course this is tongue-in-cheek, as the one question has over 15 questions. Nonetheless, this one question tour de force covers the full range of a first semester calc course. To substantiate this bold claim, I found a comprehensive list of typical topics in such a course at Wolfram Mathworld Classroom . The chart below cross-references each alphabetically listed topic with its specific question. While some questions touch on a range of topics, the cross-referencing refers to the primary reference. Why I like this question: I really like this question because it requires...

By guest bloggers Martha Abell, Georgia Southern University , and Linda Braddy, Tarrant County College If you enjoy Teaching Tidbits , be sure to get an electronic copy of the Mathematical Association of America Instructional Practices Guide, which is chock full of great ideas to help you and your students. The guide is available as a free download on the MAA website . The MAA IP Guide is intended for all instructors of mathematics: New graduate teaching assistants  Experienced senior instructors  Contingent faculty member at a two-year institution  New faculty member at a doctoral-granting institution  Instructors who want to transform their own teaching  Mathematicians delivering professional development to colleagues The guide boldly responds to challenges articulated in the 2014 INGenIOuS report and the 2016 Common Vision report, which both call for transformation within the mathematical sciences community toward deeper, more meaningful learning experience...

By Julie M. Phelps , Contributing Editor, Valencia College As the end of the semester nears, educators brace for the inevitable student questions about their final grades. If you are anything like me, this can be distracting from my goal of the class: to teach mathematics and make a difference in student lives. Sometimes I find myself dreading the last couple weeks because many students are stressed and solely focused on the final grade, not on learning ways to utilize mathematics in their major. This year I decided to try something new and pre-empt student questions about their grades by having them reflect on their class work and engagement. To do so, I showed a YouTube video called � I am worried about my grade � to my College Algebra students at the beginning of the semester (just before the first test). While very basic, the video goes over the many ways we educators evaluate student performance, and how we make time for students to approach us outside of class. After showing the...

By Dana Ernst , Contributing Editor, Northern Arizona University The purpose of this post is to generate discussion and to get us thinking deeply about our teaching practices. This post introduces teaching concepts that researchers and educators developed to promote student success. In an attempt to understand who is successful and why, psychologist Angela Duckworth has spent years studying groups of people in a variety of challenging situations. Over and over again, one characteristic surfaced as a significant predictor of success: grit. According to Duckworth , grit is passion and perseverance for long-term goals. One of the big open questions in cognitive psychology is how to develop grit. Growth Mindset Research suggests that one of the key ingredients to fostering grit is adopting a growth mindset . Psychologist Carol Dweck defines growth mindset as the view that intelligence and abilities can be developed with effort. In contrast, a fixed mindset is the belief that one's ...

By Darryl Yong , guest blogger,  Harvey Mudd College When we clearly communicate to students the rationale behind our instructional choices, they are more likely to do what we intend, be more motivated to learn, and be more successful. It is an idea that is so simple and obvious and yet often overlooked. Recent research suggests that being more transparent with our students can improve their learning. In one study , conducted at the University of Nevada, Las Vegas (UNLV), first-year students who took introductory-level courses from instructors trained to be more transparent were more likely to enroll the subsequent year (a 90 percent retention rate compared with the prevailing 74 percent rate for first-time, full-time, first-year students). Mary-Ann Winkelmes and her colleagues at UNLV have developed a useful framework for making our teaching more transparent. Be more transparent about the purpose of your course content and activities. What knowledge and skills will stude...

(If you would like for me to send you an email whenever I post a new blog entry, just drop me a note at Jhoyle@richmond.edu and I'll add you to my list.) On October 1, 2017, I posted the first of a two-part blog entry on the importance of the 2-4 days after the first test of the semester.  This initial essay included an email that I sent to my current students immediately after their first test.   My assumption has long been that students are most interested in how to do well in a course as they leave the first test.   The email encouraged them to consider two specific aspects of their post-test assessment.  First, if they felt they had not done well, I made three suggestions about what might have gone wrong.   It is hard to improve without some identification of the problem.  Students who do not do as well as they had hoped should come up with an honest ending to this sentence prompt, �I did not do well on the first test because . . .� ...

By Rejoice Mudzimiri , Contributing Editor,  University of Washington Bothell Do you have a hard time keeping up with your grading? Do you have to cut back on your homework assignments to make grading manageable? Have you ever considered making your students grade their own homework? Well, if you answered yes to any of these questions, this post is for you! Having students grade their own homework is valuable, saves teachers time, and enhances student learning. I had always hesitated to have my students grade their work, however, when I could not keep up with my grading, I decided to give it a shot. I wish I had considered doing this sooner! How to let students grade their own work? Please note that I do not let my students grade all their homework. Personally, I grade every other homework assignment, starting with the first one, so that they get used to my grading style. There is more than one way you can have students grade their work. Some instructors, like Nelta M. Edwards , h...

I have long asserted that the most important days of any semester are the 2-4 days immediately after the first test.  So many good things and so many bad things can happen in this short period of time. They can make the semester more wonderful or they can ruin the semester.  It is the point where the group is of no importance but the individuals are of maximum importance. Because of the importance of this period, I have started (as of this semester) doing two things.   I sent my students the following email immediately after their first test with the subject line �Please Read.�   I want to get their attention.   Then, a couple of days later when I get ready to return the graded exams, I take the first 5-10 minutes of class time to talk with them about my view of the learning process.   I will describe that talk in my next blog posting in a few days. Email to my students: I have not looked at the test yet but I will try to get an answer s...

By E. Fuller , WVU Mathematics (guest blogger) Students at almost every institution of higher education will encounter a recitation as part of their mathematics class at some point, part of the class time set aside to repeat foundational mathematical equations. Graduate teaching assistants (GTAs) are frequently called on to lead these smaller groups of students through the basics of finding the roots of a quadratic equation or computing derivatives using the chain rule. Recitation time is often left for practice of the techniques students learn in lecture. But what if we could do more during this class time? What would that look like? Here are a few approaches you can take to change your students� experiences during recitation. 1) Focus on getting students to do the work instead of doing it for them. Homework problems are great and it�s sometimes easiest for us to go to recitation prepared to work out many variations of problems we�ve done ahead of time. The problem is that we alrea...

A few days ago, I posted some advice that I had given to my students about the amount of true study time they needed to invest to succeed in my class.  In that essay, I made the point that students need someone to give them some direction now and then.   That is one of the reasons many of them come to college.   I doubt that anyone disagrees with the idea that a college teacher can provide guidance to students about their study habits.  You might not do it but I do not suspect that anyone thinks it is a problem. Today, I want to talk more about sharing advice with students.  This might be a bit more controversial.   I never take class time to give advice outside of subject matter.  Never.  However, I do use email to do so.   If I see or read something that I think students should consider, I put it in an email and send it to them.  Most of the time it is about a book or a movie that I think is worthwhile.  Is tha...