Engaging More Students Framework

One of the common struggles for instructors is engaging a larger portion of students.  A typical scenario instructors find themselves in is that a small group of students do the bulk of the talking.  The Usual Suspects, The Fab Five, The Fantastic Four... they chime all the time.  There's another, larger group that sits quietly.  What we really want is for the quieter students to talk more and the Fab Five to listen more and pick their spots.  Instead of a polarized class of talkers and non-talkers, we would like to push the poles towards the center, where everyone is engaged.  How can we accomplish this?

Enter the engaing more students framework:

• Pairs or small group discussions to get people talking
• Instructor visits
• Not asking for volunteers
• Calling on groups to "Share what you discussed."

Let's say a student or group just presented or shared an idea or solution to the whole class.  Instead of asking the class for questions right away, the instructor can prompt students to discuss what was just shared in pairs or small groups. They should be instructed to come up with at least one comment, question, or (substantive) compliment.

Groups can be assigned to be the initial commenters.  I sometimes ask two groups to start the class discussion portion of the presentation.  I let them know ahead of time so they are primed and ready (and not cold called), and I rotate these duties around the class to spread opportunities around the class evenly.

Next, while groups are discussing, I make instructor visits to listen in and check in.   If there are 10 groups in a class, I plan on visiting 2-4 per presentations, and remember where I left off.  In the next round I pick up where I left off.  The purpose of visiting is to check in to see how students are thinking so I get a sense for where people are at.  I can also help groups sharpen their questions or comments, and get groups used to talking about the topic so that it is easier for them to chime in.  I also make it a point to talk to the quieter students in my classes in a friendly way, usually 1-1.  "Hey Pat, what did your group talk about?..."

After a short period of time, it's time for a whole class discussion.  One of the main things to avoid is asking, "Are there any questions?"  Instead, I have a plan to call on the pre-selected groups or ask specific groups to comment, where I spread the opportunities evenly over time.  An easy way to do this is to have a seating chart or diagram of the groups and go through the list in order and then repeat. Another simple organizational strategy is to call on the groups who you visited first, and then open the discussion to anyone else.

A key idea here is that you are not asking people to opt-in, by asking for volunteers.  Opt-ins allow students to do nothing to opt-out.  Passive students can stay passive to opt-out, by not responding to "Are there any questions?"  That is, it takes zero effort for students to do the thing you don't want them to do.  Instead by using this framework, all students are prepared to say something. Calling on students in a way that is not stressful and spreads the work evenly ensures equal opportunity for students to participate. Small group discussions also encourages students to engage every round.  (Hence, creating an environment that supports learner agency.)

One of the positive effects of this framework is that the quieter students engage more and the "Fab Five" are not dominating class discussions.  All students can be engaged, and this offers a greater sense of the class working as a team to learn together.   Class discussions are more useful, and more questions can be asked and addressed.

Flexible Framework:  The example above can be adjusted in many ways.  I'll just mention a couple ideas, and let readers take it from there. Instead of a student presentation, the instructor could present a problem or ask students to work on an example or review what has just been presented.  The framework can then be used at that point.  It's also worth pointing out that the framework can also be used by instructors who primarily lecture, and and can be a launching point for instructors to start the journey towards active, student-centered instruction.

Details: some important details include using quality math tasks, avoiding instructor questions like "Are there any questions?", using good, professional technique when doing instructor visits, student buy-in, and setting up a class culture where students feel comfortable discussing and sharing their ideas.

Contrast: Let's look at the opt-in model, where we ask, "Are there any questions?" In this case, students can passively opt-out by doing nothing, and we get the common split where only a small group of students talks and the rest sit back.

The final takeaway is that something useful and doable can be done in essentially any setting to get more students or even all students involved in class daily.  All instructors need is to start with the engaging more students framework and find ways that work for them to implement some form of it.  

\humor

Engage!

More on Productive Failure (#PF)

Another term, another round of productive failure (or #PF) implemented in my classes.  Last term I used #PF in Calculus 1 with freshman.  Previously I included it in a course taken by math majors in the teaching option (i.e. preservice secondary math teachers).   This term (Winter Quarter 2016), productive failure was implemented in a course for future elementary teachers.

This term, students were asked to share two instances where they learned from being stuck or making a mistake.  Sharing would be done via short presentations to the whole class.  Learning is what is emphasized in productive failure presentations, and students were asked to share what they were stuck on and more importantly what they gained from it.

The purpose of highlighting productive failure is to de-stigmatize mistakes.  Most all students in the class commented in their reflective writing assignments that they were taught that mistakes were bad. Mistakes were to be avoided. The goal was to be "perfect." The problems with this type of mindset is clear.  Students who are afraid to make mistakes are not fully engaged in their learning process. They experiment less, are reluctant to try something new, and focus on getting right answers instead of primarily focusing on why things work the way they do.  This is all the more important for future elementary school teachers.  If young children are taught at an early age that memorizing (and only memorizing) is the key to success in math, then they will learn far less than they are capable of. It's a crippled way of doing mathematics really.

Productive failure ties in with Dweck's notion of a growth mindset.  Early in the term, I share a short video of Carol Dweck interviewed by the Khan Academy to help set the stage.

Additionally students are given reading assignments (outside of class) based on Jo Boaler's book, What's Math Got to Do With It?   This book is about major issues in K-12 math education in the U.S., what doesn't work, and some research-based claims of what works.  Boaler's book adds another layer of support for #PF, offering more reasons why productive failure is an important aspect in successful learning.

As the course progressed, more students shared their experiences of being stuck, and after each presentation, they earned a sticker.  Stickers are not necessary, but they add a fun way for students to keep track of how many #PFs they have presented.  Stickers also served as a model for how they could implement #PF in elementary school classes.

Progress...

More progress!

Productive failure is fundamentally about unlocking a robust learning process.  When math classes, especially in K-12, are overly concerned about answer-getting, then students (children) learn to focus almost exclusively on memorizing steps and worrying about not being wrong.  And that's when seeds of math anxiety are planted! Education is about learning to become a powerful learner.  Far beyond memorized algorithms or basic facts lies a much more valuable and useful education.  Society needs independent, critical thinkers, who are filled with curiosity, creativity, and tenacity.  You can't develop these traits, if the predominant concern is not making a mistake.

#PF!