The Excitement of September

It’s September, and my wife, my daughters, and I have all started our school years. I am excited, as I am nearly every year at this time. September is the time for hope. I have new students that will be engaged and, I hope, experience the joy of learning. I am teaching a course that I have never taught to a group of students, most of whom I have already had. I am excited about working with new content and seeing the ideas that students will bring to it.

In just two class meetings, there have already been some highlights. In one class, the students were deeply engaged with the concept questions that I used with them. The debate was lively, and this set the tone for good discussions of student presentations. In my other class, we left a question unresolved, but two students turned in two different, but both viable, solutions to the problem, which will lead to a good discussion this coming week. 

I hope your year is off to a good start. 

Keep Tinkering

I am always making adjustments, tinkering with my courses, both during but especially between iterations of the courses. My teaching is never a finished product. It is in the nature of teaching that what worked in one year for one course may not work for another course or in a subsequent year of the same course. I want to share one change that I have made over the past year, the effect it had, and what I am doing as a result.

In my Transition to Proof course last fall, I began building concept questions to supplement the regular proofs, and using them to target specific misconceptions or difficulties that students are having (or that I expect based on past experience). By concept questions, I mean short questions, usually multiple choice or true/false, that are designed to draw out students’ thinking and generate productive disagreement. Every time we had one of those discussions, I was exhilarated by the amount of discourse in the room. This practice evolved because I promised myself that I would focus on getting more discussion out of students in that class, since, in the past, I felt that there were too few students able to comment or question the proofs presented by their peers at the board. With the concept questions, I felt like I was seeing what the students were getting or missing from those proof presentations. In particular, the questions really helped to draw out the main points of proofs, points that I thought they would have gotten from a direct discussion of the proof, but which may have been less apparent than I had assumed. I almost feel like students in previous iterations of the course were shortchanged because they did not get this added layer of discussion to push their thinking forward. That’s when tinkering pays off.

As a result, I have planned some form of concept questions into both of my courses for this fall. Accompanying this change, I have also included the concept questions into the course grade. In addition to using the concept questions as a teaching tool, I am curious as to: (a) whether simply participating in the concept questions correlates with performance in the course, and (b) whether answering questions correctly on the first try correlates with performance in the course. Most of all, I would like to know whether using the concept questions as a tool in class improves the class’ understanding of the key concepts, but this will be hard to measure. I am thinking that I may have some items on some exams in one of the classes that I will reuse from prior years, so that I can compare performance. That’s not as good as an experiment, but at least I will have a basis for comparison.

The larger message is that it is healthy to revisit one’s goals for a course, to think about personal goals for improving one’s teaching, and to be willing to try new ideas that show promise of bringing students closer to the learning goals, and to measure the impact of the changes so that what works remains in place, and tactics that don't work are revised or edited out of the course. 

Most popular posts from one year of blogging

The Math Switch began one year ago, in July, 2013. In that time, I have enjoyed sharing ideas on inquiry-based learning and on educational technology. In the last few months, I have been able to post regularly, at 3 Tuesdays per month. Over that time, the most popular posts have been:

1. 9 Ways to Engage Reluctant Students, aka Tackling the Startup Problem 
2. Harnessing Your Personality 
3. Dealing with misconceptions, Part 1: Seven ways to handle misconceptions in the moment 
4. Engage! 
5. A Critical Examination of my Transition to Higher Mathematics course, inspired by Grant Wiggins 

Thank you to all who have stopped by to read the posts. A special thanks goes to those that have re-shared, or commented on the blog. 

9 Books to Read and Reread

In this post, I offer some suggested readings that I find help inform my approach to teaching. The books are listed in no particular order. 

For any teacher, I recommend:

• What Works in Schools? Robert J. Marzano, Debra J. Pickering, and Jane E. Pollock. (Note that there is now a second edition available with a substantially different organization. Either edition is valuable.) This book (first edition) discusses nine strategies shown by research to be effective in improving student learning outcomes. Sometimes the strategies are “obvious,” but it can still be helpful to be reminded that they are important teaching tools. For instance, summarizing and note-taking are effective. However, for me, many of my students have never been taught how to take notes, or have never discussed strategies for taking notes. So I make an effort to tell students when someone states an idea that I think everyone should write down, and I set aside some time for students to discuss what they should write down during class. Other strategies take a more concerted and planned effort to implement. For instance, generating and testing hypotheses is another strategy. While this is a natural part of doing mathematics, this reminds me to include tasks in which students do more investigative work. More than a list of nine ideas, the book has specific recommendations that are helpful. For instance, what are some important features to make cooperative learning successful? These are the kinds of specifics that are discussed in the book.
• Why Don’t Students Like School? Daniel Willingham. Willingham is a cognitive psychologist who poses some key questions and answers them from the perspective of his discipline. There are a few things that I like about this book, and that make me go back to it. One of the things I like is that each chapter closes with implications for the classroom. For example, one chapter discusses our human tendency to prefer and make sense of things as stories. In a course like precalculus, this might be used to frame “telling the story of a function,” where a function has properties like limits as x goes to infinity, asymptotes, periodic behavior (or not), symmetry, and so on. In calculus or analysis, the story idea might be put in terms of the central “conflict,” will a sequence converge or not, or another, is a function continuous or not. Rereading (or skimming) this book and thinking about the implications often inspires me to find ways to improve my day-to-day plans.
• What’s the Point of School? Guy Claxton. Claxton describes what he believes are the core goals of an education. These are big-picture concepts like developing people who are curious and are lifelong learners. While this is not a book that I return to for help in thinking through the details of teaching, I find that it helps to remind me of what is really important in my role as an educator.
• Switch. Chip and Dan Heath. This book inspired the name of my blog. The Heaths describe how to make a switch—a change—either in yourself or others. The single most important idea is that a lot of what we do is driven by emotion, and so we need to think in those terms when looking to effect change. The authors go through several ways of activating the emotions that will enable a switch to happen. I have returned to the book many times, for example, to remind me of how to approach students who are struggling, to help them find the emotion that will drive them to turn around their performance in my classes.
• Understanding By Design. Grant Wiggins and Jay McTighe. This is a book that puts forth a framework for thinking about curriculum design by starting with the end results, then thinking about how those results will be measured, and only then moving into designing the learning activities that will produce the desired end results. I return to this book from time to time to remind myself of how to frame my goals, and how to find ways to measure progress towards those goals.
• Mindset. Carol Dweck. Dweck has done significant research into the power of having a growth mindset, a mindset in which one believes that through hard work, one can get smarter or better. In the book, she describes some of this research and how it can make a difference across different domains of school and life. The book helps to remind me of why a growth mindset matters, and serves up examples that I use in explaining the power of the growth mindset to students.

For math teachers at any level, I recommend:

What’s Math Got To Do With It? Jo Boaler. Boaler has studied high school students experiencing problem-based curricula and compared them with those in traditional curricula in two different countries, the US and the UK. This book describes some of what was learned in those settings, and distills for a general audience—including parents of schoolchildren—some of the key ideas of what mathematics learning is, or should be, about. From the perspective of a math teacher, this book is less likely to offer ideas for day-to-day decisions, but like Claxton’s book, helps to remind me of the goals of teaching mathematics.

For college teachers, I recommend:

What the Best College Teachers Do. Ken Bain. Bain’s book centers how the select group of highly-respected teachers he studied approach teaching, from preparing for class, to setting expectations for students, to conducting class, and so forth. Each chapter holds a wealth of good advice, like seeking the commitment of the students: asking them to consider whether they are willing to do what it takes to succeed in the class, and therefore have them commit to the effort required. I find I sometimes return to the questions he poses in the chapters as a way of gaining a fresh perspective on my courses.

Finally, for college math teachers, I recommend:

The Moore Method: A Pathway To Learner-Centered Instruction. Charles A. Coppin, W. Ted Mahavier, E. Lee May, and G. Edgar Parker. The four authors of this text each describe how to implement the Moore method, as they see it. The book offers the reader a chance to consider various aspects of teaching in a learner-centered environment, and benefits from the approach of the authors, which is essentially to offer their individual responses to the key questions in setting up and operating a Moore Method course. This variations-on-a-theme approach has the effect of providing the reader with a canvas and a palette, rather than promoting a specific paint-by-number prescription. The authors take on a wide variety of issues associated with implementing the Moore method, including such topics as, What if no one has anything to present? How do I grade? and many others. I have returned to the book many times to seek out new ideas of how to handle syllabus construction, or to remind myself of ways to approach managing an IBL classroom. (In full disclosure, I should mention that I am personally acquainted with the authors, and have worked closely with Ed Parker.)

What are some of your favorite or most inspiring reads from the educational realm?