hi Jessica,

I'll add to Stan's response:  evaluation data indicates that the workshops' "big tent" approach to inquiry-based learning is important in helping participants recognize that they'll need to adapt the general IBL principles to their own course and student audience.  The facilitator team members' experiences, and the collection of materials gathered to support a variety of courses, together provide lots of examples of specific ways instructors can accomplish those principles.

We ❤️ your skills and passion, Volker!

Agreed! Thank you, Volker for the great comments and contributions to the IBL community!

hi Lou,

Great questions!  We don't have enough studies of IBL at the college level to have review articles yet, but we do have some prior research evidence that points to differences in student outcomes of participating in IBL classes at different stages of the  math curriculum.  I'd characterize it as intriguing rather than definitive. 

On surveys, students in first-year IBL courses report higher gains than do students in courses later in the curriculum.  Students find the first-year courses an exciting intellectual experience that differs from what they have experienced in high school; it seems to raise their sights on what college is all about. They also report that thinking clearly and logically through a problem or proof and having to explain themselves is very relevant to their other college courses where they are writing papers. 

We also have some data showing that students who have a first-year IBL experience take more math courses than do their peers in lecture-based courses.  We don't see a persistence effect for students taking IBL later, but it's also harder to fish it out for this group-- they have fewer courses left to take and are more likely already committed to finishing the math major, vs. the first-year students who have more room to choose in or out.  

Students taking IBL courses later in their major report being reinvigorated - they remember why they like math; it's fun again.  Also within these later courses, we have some evidence that initially lower-performing students - those with lower GPAs coming into the IBL course - see greater improvement to their subsequent math grades than do their higher-GPA peers or their low-GPA peers in the comparative, lecture-based course.  The courses get harder and most students' grades tend to drop a bit, but not for this group. They are taking something with them that is of lasting value - a change in their study habits or ways of learning math (we don't know the details of what they are doing differently, just that their grades go up - would love to follow up on this).   I will also note that building student good will is an important teacher role at any age and stage.

Laursen (2013) has a good summary of findings including the first-year vs more advanced student data; Kogan & Laursen (2014) has the grade and persistence data - full references at the link below.

https://www.colorado.edu/eer/research-areas/student-centered-stem-education/inquiry-based-learning-college-mathematics

It would be fun to do a study with a good, validated concept inventory.  Unfortunately Epstein died before he could publish a validation of the CCI.  If the workshops succeed in supporting enough faculty to use and thrive in teaching with IBL, someday maybe we'll have the large comparative sample sizes from a single course that are needed to do that kind of study.  Our studies so far have used more general measures that can be applied across multiple courses.

Thanks Elizabeth! Looking forward to summer 2018 workshops!

Hey Amy! I agree completely! I have seen students' trajectories change for the better.  

DC next month at the MAA Carriage House will be an awesome event!

Thank you, Courtney! Common factors span a wide range of topics. There's the instructor and getting ready to teach via IBL -- this is why we have workshops, and there are IBL teaching skills, course materials, class management, and assessment issues to learn and make decisions about. Student buy-in and colleague buy-in are other common factors. And then there are environmental factors like class size, specific course, classroom layout. 

As for challenges we see with students entering the college pathway... For the early courses I feel the challenges are there no matter the teaching method, with the possible exception of student buy-in. This is a critical period of time for many STEM majors, and I see great opportunity here in increasing the number of students getting through the pipeline with IBL and perhaps other student support (e.g. tutoring or supplemental workshops). 

Cheers!

This is a great question, Courtney, which was front of mind for me when watching the impressive work demonstrated here--and I appreciate your response, Stan, about the omnipresent challenges students face at this mathematics "gateway," which they will have to traverse regardless of classroom approach.  The big "Ask" for instructors of these courses is to get students over the hump of college math (and the shock that initially comes with for many) and keep them on their pathways to math/STEM careers.  While IBL seems to hold promise for meaningfully engaging all students in mathematics, it seems an especially crucial conduit for students who have been let down by traditional trajectories of math mastery.  My mind does wander back to the inordinate challenges underrepresented students (who seem to respond particularly well to IBL) face in accessing and persisting in STEM college pathways, and I wonder how instructors are encouraged to respond to their unique needs, circumstances and prior experiences in this student-centered approach.  The emphasis on the TEACHING in this initiative is a pleasure to see, and positioning these instructors as agents of change in students' math success can only lead to more good things. 

Hi Jessica! Thank you for the thoughtful and insightful comment.  My mind also wanders back to the challenges faced by underrepresented students. What I feel is also an area of work is in instructors learning about what else they can do, when they have opportunities presented to them to do something. What I mean by this is that when we teach via IBL, we have so many more interactions with students. We visit groups, have presentations, and this leads to more office hours visits. The number of times we engage with students is high. These interactions leads to learning about our students, and then there are opportunities for faculty to mentor and guide in ways. I feel there are opportunities here that are not be taken advantage of, and this is an area where instructors can make significant impact especially for underrepresented students. Preparing instructors to see this as an opportunity, perhaps get beyond their own implicit biases, and have the skills to take action is a challenge for the IBL community.  

Hi Dave -- Thank you for the thoughtful reply! I agree that students' mathematical identity can have a major impact on their learning. One way we have tried to highlight the benefits of IBL on this is via our YouTube Channel's "Student Voices" series.  Here's a link: 

Student Voices AIBL YouTube Playlist

I'll add that we've previously studied affective outcomes such as confidence to do mathematics and beliefs about how to learn mathematics.  IBL experiences do contribute more positively to these outcomes than do the comparative classes.  However, like other researchers, we find student attitudes the hardest thing to budge...  one IBL course experience does not typically overcome years of 'training' that mathematics is about watching and copying expert examples, about reproducing procedures fast and accurately.

We also have evidence that students developing more expert-like conceptions of mathematics as a discipline:  that it is creative, that students themselves can be the authority in discovering and evaluating mathematical truths, that there are multiple ways to solve problems, that struggle can be fruitful, that talking with others about something you've already struggled with is a useful path to deeper understanding. I would say these things are elements of a mathematical identity, but I would not go so far as to say we are routinely seeing students develop robust mathematical identities from coursework in the way that, say, an undergraduate research experience can develop a science or math identity.  It would be great to see if a curriculum including multiple IBL experiences would have that effect - we're not at the point yet where we can test that idea.

We know more about this for women in IBL classes, where we see particularly strong growth in confidence.  Interestingly, the women perform just as well as men in the non-IBL classes, but they don't feel they've mastered the material or are good at doing math. That is, the issue doesn't seem to be a real "achievement" gap but differences in how women and men interpret their experiences of the course.

We believe that the experience of explaining and discussing mathematics is powerful for women: they have the floor; they realize that their ideas are as good or better than others'; they find out that they can make sense of things and discover solutions. They also see their peers making mistakes or solving problems less elegantly than they did themselves.  Everyone's successes and goofs become more public, so students seem to have a better sense of where they stand among their peers and a better understanding that failure is a common and natural part of learning mathematics, and indeed an opportunity to improve and learn.  So it becomes more clear to women that they are just as good as their male peers even though the guys talk a better game  ?

Our results show that, on average, IBL is beneficial for everyone--but our data show that it makes a bigger difference for some groups who are particularly DISadvantaged in more traditionally taught classes.  We describe this as leveling the playing field - IBL instruction is not fixing women, but fixing a problematic environment for some students, including women.  I think there are interesting cultural reasons why mathematics can be uncomfortable for women and for men and women of color; a good current read on this topic is Sara Hottinger's Inventing the Mathematician.

It's important for instructors to understand that IBL, like any other active learning approach, is not a magic bullet for classroom equity. IBL approaches offer chances for all students to reap these benefits from deep thinking and fruitful discussion, but they also offer chances to exclude or marginalize people.  In the workshops we are talking more about facilitation tactics that help instructors include everyone and be sensitive to differences in their own and students' positioning.

I'll add on RE the last comment about opportunities to help/not help equity. I believe IBL has to be implemented with intent in order to address equity. It's not something that happens automatically.  I believe though unlike conventional lectures, IBL at least provides a framework for addressing equity. For instance, the instructor can ensure that all students are participating, every student gets a chance to share or discuss in their group roughly equally, grouping strategies can be made to ensure marginalized students are not marginalized, and avoiding the situation where only the "usual suspects" are answering questions or commenting in class.  

Thank you, Agnes! I appreciate the comment!

Hi Rebecca -- thanks for the comment and good question! 

There can be pushback or concerns from colleagues in courses where the material is needed in future courses. There are a few layers here. One is that with flipped learning, reading assignments, and/or targeted lectures, faculty can in fact cover the material needed. This issue can be mitigated or eliminated adding in this type strategy. For entry-level courses, often the IBL methods used lean more on group work and less on student presentations of ideas/solutions. This allows instructors a bit more consistency with planning and moving through the material. For upper-level courses like Number Theory, where there isn't a second course, often reading assignments and the occasional lecture is used to fill-in gaps that won't be covered by students via IBL. Not everything has to be covered the same way.  Hope this helps!

Thank you! 

From data from people coming to workshops, we know that instructors do worry about coverage.  This concern generally damps down after workshops but does not disappear. From data from instructors who already use IBL, we know that they worry less about coverage after some experience  - they know that the first few weeks may be painfully slow but that students' movement through the sequence of problems will accelerate; they know where the sticky spots are and often invent new problems to scaffold across those spots. They also hone their problem sequence to get to the things they care most about, and learn to trust that if students have deep understanding of the big ideas they can work out specific applications or variations or extensions when these are needed.

Hi Allison,

We have not expanded officially to HS, although the IBL Workshop model could one day be adapted. I have also been personally involved in K-12 PD in math, so I can say this with some experience. Our focus on college is intentional given the need, funding limitations, strategic importance of colleges, and people time. I do know though that IBL can be used K through college. It's been done already by teachers. PD in K-12 is different due to factors like state testing and district mandates, that complicates matters. For the time being, we're not going in this direction, but may one day  offer some support aside from IBL Workshops for teachers who want to use IBL methods in their K-12. Cheers and thanks for posting!