AMS Blog on Teaching and Learning Mathematics

Math instructors, check out a great blog on teaching and learning by Ben Braun, Priscilla Bremser, Art Duval, Elise Lockhart, and Diana White that is run out of the AMS.  Their latest series is on active learning and worth your time.

AMS Blog On Teaching and Learning Mathematics

Day 1 Activity: "What is one of your hobbies, and how did you get good at it?"

Day 1 is here at Cal Poly (Quarter System).  I know we are a month behind nearly everyone else, but day 1 is still day 1.  This quarter I am working with Professor Choboter on Calculus 1, and we implemented one of the strategies to build student buy-in our classes.

We asked students via email before the first day to think about one of their hobbies and how they became better at it.  In class, we have students talk to a neighbor to introduce themselves and share with one another their hobby and what they did to get better at that hobby.  We then asked each pair to talk to another pair and introduce their neighbors.  So each person interacts with 3 other people right away.

Next, students were asked to write on the board their hobby on the left side, and on the right side I asked them to write how they go better at the hobby.  Here are images of the boards.

   

Hobbies

How they go better at their hobby

No one wrote, "I sat back and watched someone, and that's how I got better at it."  I use their statements about how they get better by discussing with them that it's the same with math.  I mention that we get better when we practice regularly, both individually and collaboratively.  Therefore, we are running this class via IBL and we are going to work as a team on the math.  Students seemed ready to get on with it, so that was it.  With that done, it was time to dive into the first math activity of the term!

Ongoing work to continue building student buy-in is also important.  More on that in future posts...

Quick Post on Nuts and Bolts: Index Cards

I am teaching calculus 1 this fall quarter to mostly freshmen, and truly excited about being in the classroom again after a summer off!  Day 1 is tomorrow.

This short post is about the basics. I'm bringing index cards, my binder full of activities, and colored pens.     The index cards are useful for making name "tents" on day one.  I can start day one by learning names and calling on students to share their ideas and strategies.  One of my classrooms has stadium seating, which makes it difficult or impossible for me to get t the middle of the class. Using index cards (and maybe some creative seating strategies), I’ll still be able to engage with all students and learn their names.

Index cards can also be used to write student names to select students (or groups) randomly, for keeping track of student presentation, for mixing people into groups (by writing numbers or letters), and for writing question prompts to pass out to groups.  I am sure there are more uses.  I keep a couple of stacks handy at all times.

Edit:  I use some cards to help me learn names.  I use other cards to mix groups.  I used to mark presentations on a card, but now write notes and use a spreadsheet.  The point here is that cards can be used for lots of things, and having them around is really useful.

Quick Post: Positive Coaching

This is a quick post on a basic idea, called informally positive coaching.

One of the larger issues that comes up in discussions with new IBL instructors is student buy-in.  Students enter a class with default expectations about what a math class should be like.  Since teaching is a cultural activity, significant changes from the default requires the instructors to do some work to reset the norms.

Some of the usual expectations students come in the door with on day one are:

• The instructor does all the work, and students are supposed to imitate the instructor to the letter.
• Faster is better.  (Hence, slower is dumber.)
• The teacher or the textbook is the external source that validates when an answer is correct.
• Getting stuck is a sign of struggle and not getting it.

When students are in an IBL class setting, they are required to engage in mathematics differently, and they are assessed differently.  Some students may feel as if they don't know how well they are doing.  They are not getting graded the usual way, they are spending more time per problem, and they are appealing to logic and reason, instead of the instructor (or the back of the book) for knowing if they are correct.  It's understandable if students feel unsettled, especially in a first experience with IBL.  

One of the important roles for an IBL instructor is to continuously be a source of positive, constructive feedback (i.e. positive coaching) in ways that students know what they understand and what they need to work on to get better.

Positive coaching can come in many forms.  Here are some examples:

• Letting students know that they are on track and succeeding and meeting your expectations.
• Restating something that a student did (strategy, use a concept, etc.) that was useful or important for a solution.  Affirmation!
• Solution recaps.  These are quick takes on a just presented solution or idea.  ("Let's look at what so-and-so just shared again... Here's what we discovered was needed in this problem...")
• Emphasizing and praising productive failure.  ("Look what so-and-so discovered... This is great, because now we know what directions we can try next!")
• Giving students feedback on how they doing a problem, when visiting groups.  ("Show me what you tried... That could work.  Keep up the good effort.")
• Mini-talks or mini-lectures that set the stage.  ("This next set of problems is challenging, but we are going to work together to work through it...")
• Once a solution has been presented by a student, to be willing to go over it with students again and again in office hours.
• Giving students progress reports on their current grade.

All of the above should come with praise for students' efforts and creativity. In this way the instructor is giving affirmation and guidance on what students are doing that will help them succeed.

Last word.  Coaching and cheerleading are not the same thing.  See the Coaching vs. Cheerleading post.