This blog has been re-posted with permission and originally appeared on the blog Math-World Liaison.

For 14 years I have been reinventing my instructional wheel each summer to build student achievement.  I’ve used creative images and rhymes (anchors), interactive games (engagement), 3-Acts, Notice & Wonder, Front Loading, and constant review. However, I am not happy with just high scores on state exams. What I teach, too often, doesn’t stick in the long-term…regardless of how much time I spend reviewing the material.  It’s not just me. While I teach in an award-winning district, the truth is that only 56% of our students who go off to college finish within 6 years; and probably half of those degrees are not aligned with the job market.  The debt and underemployment that results has an effect on the entire economy.  The fact that 56% is well above average for other districts in my state brings me little comfort; so I’m driven to find solutions.  I have had a good degree of success with the few inquiry-based learning (IBL) activities I wrote; so when I had an opportunity to pilot an inquiry-based ebook this fall, I set aside all of my creations in hopes of seeing stronger retention. The results have been phenomenal, but herein lie the concerns and caveats.

IBL can be “fuzzy.”  I credit University of Winnipeg math professor Robert Craigen co-founder of Western Initiative for Strengthening Education in Math WISE Math for taking the time to explain the problems he and others see with IBL.  The first part of our discussion was to clarify what we meant by direct instruction (DI) vs. IBL.  He is not suggesting teachers lecture students seated in desks nailed to the floor; and to earn his attention, I had to assure him I was not referring to giving students a “project” they fooled around with for days without achieving comparable objectives.  During our discussions, he helped me understand how IBL can be disastrous for students.  I am indebted to him for helping me avoid serious errors that are not always made clear to teachers taking the plunge.

1.  IBL may not be time efficient.  Observers of an IBL environment often question whether learning time is spent wisely when students are trying to figure things out that can be explained directly very quickly.  I could show students where the on button is on their calculator in 2 seconds.  On the other hand, if they have to look for it, they are likely to remember because hunting isn’t fun.  I may or may not tell, depending on the circumstances.  My students are clearly remembering content better since I starting IBL. From my observations, the time spent analyzing and explaining to each other in groups has not only been more effective for their retention, but the students are also enjoying themselves far more and growing in confidence.  I’m not boring.  I am willing to sing, rap, dance, whatever it takes to hold a class’s attention, but IBL has me beat.  My students are now high-fiving on a regular basis.  Instead of spending time with games & various other drills, each activity connects and reviews as we continue to move forward.

2.  Students just wait for teachers to provide the answers. I would argue that the worst teaching comes from teachers who don’t buy into what they are doing.  If teachers do not believe in IBL, they probably will not have the patience to wait for students to think, to coach them into thinking deeper, or to provide them with enabling questions. Students have to be trained to read carefully, read multiple times, and interpret with the aid of their seatmates.  If IBL is used in other classes like science, the practices transfer easily; but like any classroom management issue, students must be held accountable for their progress and behavior in their roles.  Difficulties with reading can and should be addressed as an interdisciplinary support.

3.  IBL activities are too difficult.  It is important to use IBL activities with a low floor and high ceiling to build confidence in less accomplished students and challenge highly accomplished students. Activities should work like a road map that takes students deeper into concepts.  I find it is important to not seat the very least accomplished with the very highest because faster students want to learn more and can become impatient.  The slower students may not be able to get through the more complicated inquiry pieces by the end of the class. It is unfair to regularly and drastically hold back a student who is excited about moving on, and the student who needs more time to think should not be made to feel guilty for doing so.  On the other hand, less accomplished students need energy from more accomplished students and more accomplished students need to be challenged to learn how to explain well and to understand how other people think (empathy & perspective).  Inevitably, my less accomplished students have their times to shine when progress is made by thinking outside the box.

4.  Students can come to wrong conclusions.  They can do that with DI also, thinking they understand when they don’t.  In DI, students can also look like they are engaged when they are not.  During IBL, disengagement is fairly easy to spot because the rest of the group is communicating and writing.  If the instructor suspects a student is not engaged, the student should be given an opportunity to explain the group’s progress and conclusions.  A disengaged student is treated as a group’s problem.  It is much easier to control the learning process for 10 groups than for 40 individual students.  Another important practice is lesson closure where concepts are summarized and students check their conclusions in their notebooks.

5.  A student might look engaged but not understand.  It is important to develop empathy within each group such that the teammates care about each other’s progress.  Whole class role-playing is fun and empowering.  A well-functioning team questions each they until they are convinced they all understand. However, I take accountability a step farther and grade homework once every week or two.  At that time, I note whether students are practicing procedural skills accurately.  If not, I make note in the grade book, speak to the student, and assign additional work for them in Khan Academy to hold them accountable for accuracy.  Khan supplies instant feedback and additional learning opportunities through text hints and video.  There are serious unintended consequences with “completion grading, so I avoid that practice.

Choosing a good IBL textbook takes care of most of these concerns.  Activities should not only have low floors and high ceilings, but they should connect and continuously review content.  They should have memorable activities that serve as anchors for recalling relationships and definitions.  I’m piloting CPM because it was rated highly by Edreports, but after looking at Illustrative Mathematics Open Up Resources, I’m thinking that would probably do just as well.  I believe IBL is the key to beating the 56% college success rates, not only because of the dramatically increased retention I am seeing, but also because of the soft skills the students develop (communication, collaboration, persistence, and critical thinking).  My students are happier and more confident.  So next summer, for the first time in more than a decade, I will not have to reinvent the wheel…again.