Friday, August 18, 2017

Charlottesville, Courage, Starter Steps

I've been meaning to post again on regular IBL topics, but current events have left me in a state that I have never felt before.  I needed time to process all the thoughts and emotions swirling through my mind and my heart in the aftermath of Charlottesville, and the responses by various people and groups since last weekend.

To be clear, as Director of AIBL and on behalf of the IBL community, I state emphatically that we are against hate, racism, sexism, discrimination, and white supremacy in all its forms, either overt or implicit.

It's time that all teachers, math teachers included, rise up from our old practices and engage in new ways to deal with the current threats to our institutions and society. Although we are teachers of Math classes, fundamentally we teach students. And ignoring issues that are tearing the fabric of our democracy apart is immoral. It's equivalent to ignoring climate change, because it's not our subject. While it may seem difficult to have to address these issues, I think the stakes are too high for us to hide behind the misconceived idea that "Math is apolitical."  Sitting on the sidelines is no longer an option.
Courage is the most important virtue, because without courage you cannot practice any other virtue consistently -- Maya Angelou

As I mentioned in my talk at MathFest, we need math instructors to be courageous. Managing discussions about social or moral issues are not things we regularly do or have done historically in Math.  It's hard for us.  But it's time to rethink. Silence in the face of vile inhumanity is quiet acceptance and tacit support. Remaining silent is simply not an option. We need to exercise a little courage to make some small, yet meaningful changes in our teaching.

One practical hurdle we need to get over as Math instructors is that we are not geared up for discussions of social issues in a math class context.  We enjoy the challenge of learning Math, and that has been and will always be the focus of our classes.  While I agree it's a tough challenge, let's put those feeling to the side for now.  I think there exist practical ways to implement small, yet valuable strategies.  Professor Brian Katz has just posted on the AMS Blog on Discussing Justice On the First Day of Class. That post has some some bold ideas that are truly worth the read!

This post is about adding on to Discussing Justice On the First Day of Class with some simple, starter steps we can take as instructors. These baby steps are not sufficient, but gets us off the sidelines and into the game.

Syllabus Statement
Add something to your ethics section!  An ethics statement is usually required in syllabi, regarding cheating and other issues of that type. In your syllabus you can expand on this.  "As your instructor, it is my belief that hate, racism, sexism, and other forms of discrimination are immoral and have no place on our campus or in our society.  Our class is one community. We learn together. We work together.  And we will respect one another.  I teach all students, regardless of background or beliefs. All students are equally welcome and valued.  Growth mindset includes our ability to grow together, learn to be more tolerant, and become more compassionate. No one is being asked to leave the table. Everyone is being asked to make room at the table, so that everyone has a seat and a fair chance."

Inclusivity or Diversity Messaging
Another strategy is to show symbols on your slides, handouts, coffee mugs, etc. your support for common decency. This needs to be done tactfully, but there are options.  At Cal Poly, faculty and staff started an inclusivity movement with the words, "Love, Empathy, Respect, #mustangsUNITED". (The mustang is the Cal Poly mascot.) The image can be used to express via a visual symbol the campus ethos.

Additionally, AIBL has "IBL for All" images, which you are free to use on your class slides and handouts. I suggest including  statements like "All students can learn math. You belong!"  To further emphasize the message of inclusion.
A Note on Class Teaching Methods
Teaching methods matter a LOT.  IBL teaching methods are helpful in this context, since we use democratizing methods, spreading opportunities fairly. When we ask students to present and chime in, there exists ways to spread the chances so that all students are involved in the discussions and chances to share.  I won't go into the long list of strategies here, but there are ways to get everyone talking and contributing, and feeling like they belong. This is where the inclusivity beliefs hit the practical ground in math classes.

A point that should be emphasized is that good IBL teaching AND positive inclusive messaging goes a long way. We know from research studies (highlighted here) that gender gaps are reduced or eliminated IBL courses, while still benefitting all students.  The impact can be even greater with positive messaging about inclusivity.

Teachers, especially college math instructors, are respected and have social leverage. By empowering through good teaching and positive messaging, many of your students can see that you are there for them.  That is one of the manifestations of "love conquers hate."  When you show compassion and caring for the wellbeing of all your students, it helps to disarm hate and build a sense of community, so that those who are marginalized are included.

Final Thoughts on the Future
I'll end with a note about the IBL Community Challenges. Challenge 4 Inclusion is the challenge to level the playing field, and in the next 20 years eliminate the gender and minority gaps.  The IBL community is actively working on diversity and inclusion. It's not just something we say to make ourselves feel better, we are working on it for real.  Come join us!

Links
I have so far only glanced at the materials on Teaching Tolerance, which look promising. While focused on the Humanities, my sense is they can be adapted.

More resources on the AMS Blog re-posted HERE

Saturday, July 29, 2017

The Next 20 Years: Moonshot Challenges in Post-Secondary Math Education and IBL

This talk was presented at MathFest 2017 at the IBL Conference, July 28, 2017. The text is provided here for those interested in the IBL Community Challenges. Please sign up and join the effort by going to www.inquirybasedlearning.org/challenges


Title: The Next 20 Years: Moonshot Challenges in Post-Secondary Math Education and IBL


Good evening!
Hello IBL SIGMAA!
Hello IBL Community!
It’s so great to see you here!


First thank you Alison, Patrick, Susan, Brian, Victor for inviting me to speak tonight to the IBL SIGMAA and the IBL community. It is truly an honor to be here tonight, and thank you for putting together such a wonderful event!


This is a picture called Moonrise Carrizo Plain
Moonrise Carrizo Plain, Stan Yoshinobu
“Glory lies in the attempt to reach one’s goal and not in reaching it.” - Mahatma Gandhi


Tonight I share with you moonshot goals.  We are going to aim high to see where that gets us.  I’m going to share a subset of some big challenges that lie in front of us that I think we can make progress on in the next 20 years


Before I share some moonshot challenges for the next 20 years, it’s time to think about how we got here and the past 20 years.


I personally have many people to thank...  Ed Parker, Carol Schumacher, Bob Eslinger, Sandra Laursen, Bill Jacob, Ralf Spatzier, John Neuberger, Tom Ingram, Ted Mahavier, Bill Mahavier, David Clark, Lee May, Mike Starbird, Albert Lewis, Norma Flores, Harry Lucas, Jr. and so many more…]  All of them mentored, supported or encouraged me, and most importantly made me feel like I was part of this community. I felt welcomed. Never in my professional life have I felt so welcomed. So thank you! Thank you for all you have done for me.


This highlights the importance of community.  Feeling welcomed and receiving support is in my opinion the greatest strength of this movement, and what I am most grateful for.


On that note, let’s extend this thank you to all those in the first generation. All those here tonight, who were at these conferences during the early years. You know who you are. Please stand up…  Stand up!  It’s time we said a proper thank you. Let’s all thank these pioneers for what they have done for us.  


Thank you!  Thank you for your leadership. Thank you for your courageous efforts. We would not be here today without you.  


Carol Schumacher gave a keynote talk at an IBL conference a few years ago about how students find innovative ways to deal with math challenges that we did not envision... It was an inspiring talk about ways of thinking about IBL teaching!  We create problem sets (AKA the bridges), thinking that’s what students might need to reach the learning goals.  And then they go and find their own way to the solutions.


In parallel some of what we have achieved in this community is unplanned and unexpected.  We have done things that few thought would land us here tonight under these circumstances.


I personally have had zero IBL courses in my education, K through PhD.  This movement started in the south.  The only thing southern about me is that I’m from Southern California.  Apparently that’s not the same thing. Yet, here I am, as someone who has been a part of the IBL movement for more than a decade, speaking in front of you tonight.


This actually makes a lot of sense, once you think about it.  Once you go beyond mere surface features, you see that we are all in the same family.  We have shared goals and shared interests.  We have common understanding that authentic learning experiences is what is best for our students. One of the great, transcendental powers of community is to be able to see past the surface and rally around fundamental values.


I’m going to share a few examples of successes you may not have been fully aware of, to further highlight the point of unexpected successes.


In 2006 I was told we would be lucky to have a 3 participants of the first IBL workshop actually use IBL afterwards.  That’s 3 out of 22 participants.  That was nice in a way, because it set the bar low.  I remember talking to Ed Parker thinking “Okay, we can probably get three.”  Well we did much better than that.  Fast forward a decade.  In total when combining all the workshops run by the IBL Centers and AIBL, over 11 years, we have reached more than 500 participants. Our uptake rates are over 70% in the cohorts for the AIBL workshops, which is a tremendous result for faculty professional development.


In just the highlighted in red workshops (2013-15), we had 138 participants, who taught 180+ sections of IBL courses to 4600+ students. This is in just the first year after participants attended a workshop. The impact will continue to grow for this group! That’s just a slice of the success story when it comes to our workshops.


I am going to highlight Sandra Laursen’s work...
“Overall, IBL approaches leveled the playing field by offering learning experiences of equal benefit to men and women, while traditional courses were more discouraging and less effective for women.”


One of the unexpected successes is that IBL can reduce or potentially eliminate the gender gap in Math. You can level the playing field, without lowering the standards.  I’d argue that we’re raising the standards, and are finally creating math courses worthy of women’s intelligence!


The CBMS has urged our profession "to invest time and resources to ensure that effective active learning is incorporated into post-secondary mathematics classrooms."  


I did not expect that CBMS would take this unified stand.  That is a sign of major progress!


Many other unexpected successes were achieved that I don’t have time tonight to discuss.  We value and celebrate all those successes, and we can continue the discussion afterwards.


Thus, it is so critical to suspend disbelief and have a growth mindset about our future in education.  Growth mindset applies broadly.  I often run into the word “can’t” when talking to others about education.  We can’t do this. We can’t do that. Or they won’t approve that…  Let us dream a little, because we can succeed in ways that we may not have imagined. Let’s add the word “yet” to those sentences. We can’t do it yet, and let’s keep working on it.


Let’s talk about the challenges.


Challenge 1 Establish IBL Professional Development Centers Across the Nation
This idea is based on MSRI, but smaller and more agile centers. The focus is on teaching.  Specifically, faculty professional development in active learning and IBL. Professional development is one of the main ways for math instructors to gain the skills and practices needed to be effective IBL instructors. We need dedicated centers, embedded at institutions of higher education, strategically spread across the nation.


Professional development centers can be places faculty go to throughout the year, get help, mentoring, visit classes, study videos, examine course materials, and all that.  Right now we are limited to summers and with soft money. What we have now will not cut it.


Permanent professional development centers can reach thousands of math instructors, and that is the scale we need to be working on. They should be open in that they welcome instructors from elsewhere and have specific programs for any math instructor interested in IBL.


These PD centers should have full-time people, who can continue to improve and expand professional development opportunities, strategies, and assets, that are relevant to their regions. All of us faculty here work on the IBL movement part-time. While that may be a necessity for most of us, there should be some people who can focus on professional development full time. It allows them to solve problems that part-timers can’t.


Currently we are relying on a part-time, volunteer force, with relatively small financial and professional incentives to carry out this work, dispersed throughout the country, in some cases with little support. Professional development centers would take us to the next level.


The PD Centers are a cornerstone to attacking other big goals, as you will see.


Challenge 2a
Increasing use of IBL methods to more than 50% of postsecondary mathematics courses


The IBL community is well-positioned to help make this happen. We have a community that can support faculty in their efforts to use active learning, and a long, successful track record.


Challenge 2b   
"IBL versions" of Calculus will be the most common form of Calculus
By "IBL versions" I mean that IBL teaching methods are used in the course regularly. We are not necessarily suggesting changes to textbooks. There exist strategies for using IBL that can be adapted to a wide variety of situations, including those with relatively little instructor freedom, where instructors work with the materials given to them.


Textbooks reflect the dominant culture. You don’t change culture by changing the textbooks, and it in fact you might run into more obstacles when you focus on textbooks. My position is that we need to work with people, respectfully and carefully over long periods of time. Then the changes we want will evolve naturally.


Most students don’t even read the book. Let’s think about this… Textbook battles are like arguing over what vegetables to put in your kid’s lunch, when you know they chuck the veggies and eat only the sandwich. Let’s make a healthy sandwich. Focus on the instructors!


A focus on higher levels of instructor skills is a stronger way forward, because those IBL skillsets are generalizable and long lasting. Once instructors go IBL they usually stick with it and expand it.


Challenge 3a
Expand the IBL community by two or more orders of magnitude
This can be done via multiple methods including but not limited to developing IBL consortia, expanding enrollment in IBL Workshops, widespread availability of AIBL Small Grants (or similar), and steady outreach efforts to work with our colleagues in the AMS, MAA, AMATYC, SIAM, ASA, NCTM, NAM, AWM, AIM, the flipped-classroom community, POGIL, Inquiry-Oriented Learning, and others.


I love MAA, and MAA is my home organization, but MAA is not the home organization for everyone, and we need to do the outreach work to bring people into the IBL community.


Fittingly, this is a numbers game.


Challenge 3b
Become a partner in efforts to reform and improve K-12 Math Education
I’ll touch only briefly on this one.  While we are focused on college and graduate math teaching, our work is connected to K-12 math education, and every student’s experience incorporates all levels. It is therefore an obligation to continue to build relationships with our colleagues in K-12 math teaching.


The IBL community has a direct connection to K-12 math teaching via courses for future teachers, our involvement in K-12 professional development, and our shared goal of student success. These connections can open doors for stronger ties, partnerships, and collaborative endeavors.


My belief is that we must engage with humility and respect. Just because we might know more math doesn’t mean we know how to solve their problems and challenges. Going in as a collaborator and a supporter, with open minds, will build more bridges. The main way we can help is by our work in our own classes. HS teachers tell me that one of the blocks or obstacles is that they point to colleges and lecture methods. Some HS teachers believe they are just getting students prepared for college by using the lecture method.


Challenge 4
Inclusivity: Women and minorities are represented in Mathematics proportional to their representation in society.


This is a big one and close to my heart. Women and minorities are much more likely to leave the STEM pipeline, and women and underrepresented minorities are not participating in STEM fields and careers at levels proportional their representation in society.  
Female recipients of PhDs in Math hovers around 25-30%.  Referring to the image above, this is not the steady state solution we want. I’m quite frankly tired of looking at this graph.


Where does IBL come into the picture? Research evidence suggests that the IBL framework can help minimize these gaps. Although changing classroom instruction is not enough to solve all of our problems, it is for many students the only opportunity to have a transformative experience that changes the trajectory of their life. It is a place we can start to make a difference, and we can build off of that.  


We have a advantageous position on inclusivity in the IBL community, because our teaching methods have been shown to make a real difference. That’s a good sign. That’s what we needed to hear, and should make you feel optimistic about the future.  There exists a solution and that solution is doable!  We can do something about social justice via effective teaching.


Policy and opportunity matters. So teaching reform isn’t enough. We will need to expand our focus beyond teaching on these issues and become advocates, push for change, and find other strategies we can’t see right now that helps us achieve equity.


Challenge 5 Address Math Anxiety, Promote Growth Mindsets
Math anxiety is rooted in fixed mindsets, poor teaching, and other cultural factors. I hope one day we never have to hear things like "I hate math..." and "I am not a math person..."  


This is a big problem.  It likely affects millions of people. There are 6 million K-12 students in public education in CA.  If 50% have math anxiety, then 3 million students have math anxiety.  That is approximately 24 million K-12 students in the United States.


Teaching growth mindsets, and de-stigmatizing mistakes are two components that can be included in IBL classes. We can once again do something about this via teaching, and we can share our ideas and spread them.


Challenge 6 Informing the general public about IBL
A few years ago when I approached my dean to help with fundraising for AIBL, he said something that really hit the nail on the head. He said that people don’t know about IBL or who you are. It’s hard to raise money for something that no ones knows about.  


Without support from the public, any movement will eventually fade or run into hard limits.  It is therefore our responsibility to inform not just our colleagues, but also the general public about what IBL is, how it helps students, and why it's important for everyone to care IBL. Social media and other avenues exist for us to inform our communities.


7. Other Challenges
This list is a starting point for the IBL Community and how our work connects to larger issues in society. Other challenges exist and are important, and just because something was not mentioned tonight, does not mean that it is not a worthy challenge. And I’ll share how you can put in your two cents in just a moment.  


Courage
Now it’s time to talk about courage. We’re going to need a lot of courage.  


“Courage is the most important of all the virtues because without courage, you can’t practice any other virtue consistently.”
― Maya Angelou


History is full of calls for change in math teaching. The active learning statement by the CBMS is the latest example. The Common Core movement is another. NCTM released the Principles and Standards more than 2 decades ago. John Dewey made calls for engaging students actively about a century ago.  Warren Colburn in 1830, nearly two centuries ago, published an article advocating for engaging students to discover math and think for themselves.  


Math Education has improved over the years, and we have made significant progress. Putting these successes aside for the moment, the calls for change persist. Pure lecture, where teachers do all of the work, still dominates. Fixed mindsets are far too common.


Something powerful binds us, and we are not yet free from these bindings. To change is going to take more than data, or evidence, or a new calculus textbook. Teaching is fundamentally a cultural activity.  We will need to work with people, one-on-one, and do the long work of building and expanding the community. That’s what has been going on here already in the IBL community.  Now the challenge is for us to continue to modernize, evolve, include, and expand our community.


Your courage is needed. Courage to do things that you may not be used to doing. The courage to collaborate when you prefer to work alone. The courage to talk to a colleague, who makes you feel uncomfortable about active learning. The courage to teach using a new method or strategy that you have not used before.  The courage and stamina to stay up late on a weeknight to make changes to your lesson plans, because you know it will be better for your students.


John F. Kennedy said in his Moon Speech in 1962... “We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win, ...”


My goal tonight is not only to share my ideas. My main goal is to share the next thing...


I invite you to join us in this work!  


Please go to the AIBL website and sign up to work on these challenges. Click on the community challenges link.  Read the challenges I shared tonight or think of your own.


When you get to the bottom of the page, you can sign up to join the effort. We need you! We need a big community working together. Tell us who are and what challenges you want to work on, and we’ll get going.


You don’t have to wait for the cavalry to show up. You are the cavalry!


You don’t have to wait for the big donors to show up tomorrow. You can take action now with what we have today!


You don’t have to wait for a superhero or a great leader, because there is much more power in a diverse community that is working together.


You don’t have to be a famous person or be a highly experienced expert on IBL. You just have to care, and be passionate about student success.


Just as we invite our students to share their ideas in our math classes, I am inviting you to join us.  Whether you are joining the community for the first time or for the 20th year we welcome you with open arms.


Two years ago, Dave Kung quoted Martin Luther King, Jr. in his keynote sharing with us that the “arc of the moral universe is long, but bends towards justice… and we can bend it.”  That was a powerful message about what we can do as individuals to enact change.


In a similar way I share with you this...
That the arc of the education is long,
But bends towards the bold and hard working.  
We can bend the arc of education!












While we stand here tonight looking out at the distant moon,
We know we got to the moon before,
And watched the earth rise over the horizon.
We can do it again together.  
And we shall do it again together!
Photo Credit, NASA, retrieved from www.nasa.gov


















Thank you so much everyone!

Sunday, June 25, 2017

Summer 2017: 1 Down, Three IBL Workshops to GO

The DePaul Team just completed workshop #1 of 3.  This summer the strategy is to spread IBL workshops across the nation, with the first one at DePaul University, Chicago, the second at Cal Poly San Luis Obispo, CA, and the third in Upstate NY at Nazareth College.

Team DePaul included
Kyle Petersen, DePaul University
Danielle Champney, Cal Poly
Gulden Karakok, University of Northern Colorado
Brian Katz, Augustana College
Madison Parker, AIBL
Chuck Hayward, Evaluation Team, CU Boulder

The main theme of these workshops is "Big Tent" IBL.  Just as active learning is student centered, IBL Workshops are faculty centered.  That is, we focus on a broad IBL framework, and assist participants in finding a comfortable starting place that works for them, their students, and their institutional environments.  There isn't a single "correct" way of doing IBL. It's a system or framework based on (a) opportunities for students to regularly experience deep engagement in rich mathematics, and (b) opportunities for regular collaboration with classmates and the instructor.

To learn more about IBL Workshops, visit http://www.inquirybasedlearning.org/workshops/ 

Some Images from DePaul 2017







Monday, May 1, 2017

Assigning Seats in College Math Class? Yes, It Makes Sense Sometimes

Most college courses do not have assigned seating. It's not part of the culture to assign seats in math classes at the college level.  There exist courses (say labs), when students are assigned a station.  So why did I assign seats last term and go against the grain?  Equity.  There are several reasons why you'd want to assign seats, but last term equity was the issue.

Last term I had a student with a disability. This disability required sitting in the front row, and the disability was not evident if you met the student.  I use groups regularly, and change the groups every week or two.  The changes in groups requires students to have to find each other and then find a place to sit.  I didn't want to place the student with the disability in a potentially difficult situation, having to explain each time the situation or perhaps the student would not say anything and then sit farther back. The course was also freshman calculus, so it's early in their college careers, and at the beginning of the term (when you need to decide on such things like assigned seating), you don't know your students yet and how they respond to situations.

Normally I assign groups, and let students sit where they want. Part of the fun is figuring out how to negotiate where to sit.  If I did this last term, then the student with the disability would have to talk about the disability every single time, and the student having to ask others to swap seats or move to a specific place.  It can get old to have to meet new people for the first time, and the first thing you have to do is to talk about a disability.

Hence, I assigned seats.  Instead of figuring out where to sit and find each other, more time was spent by students on getting to know one another.  They got in their new groups, and it was on to the learning.

Some have asked if I'm coddling the student the disability.  People say things like shouldn't the student just figure it out and deal with it?  They need to learn how to handle life.    First, I understand why people might think this way.  Second, I disagree with that perspective.  Third, the conclusion I came to is that my goal as a teacher is to provide a level playing field, not a tilted one.  Assigning seats causes no harm to anyone, and it ensures that the student with the disability is accommodated. This student is not getting extra help or a special hand. The student is merely sitting where the learning environment is equivalent to what all the non-disabled students have. It was all seamless to the students, people could be themselves, and the focus of every class was the math. Seems fair to me.

Other reasons to assign seating exist.  One can make sure that certain personalities are together/apart. The physical space in the rooms sometimes have their own quirks, where groups have to be carefully carved out of fixed seating or other factors like limited seating. In some of my classes I have exactly the number of seats as students.  So inefficient group arrangements actually is a practical problem.   Taking attendance, if you do this, becomes a breeze (look at the empty slots), and it saves some time when you regroup. People know where to go, and you get on with the learning.

The usefulness of teaching strategies depends on classroom specifics.  Employing what seems like an arcane idea, assigning seats, actually helped make a more inclusive and equitable classroom.  I am reminded again that sometimes, if we think a little, we can find good uses for our strategies to address specific needs.  A painter (artist) doesn't look at colors and brushes with an ideology of this color is always good and this brush is the best.  The colors and brushes are tools, and should be deployed according to the vision and goals of the art.  Likewise, classroom strategies, tools, techniques, can be viewed the same way.  They serve a purpose of helping students learn, and the teacher's role is to assemble them in ways that provide a fair, equitable, and engaging learning environment.



Friday, March 17, 2017

Teaching with (Selective) Silence

"It's not the notes you play, but in the silence between them."  --  Miles Davis

By silence I mean selective silence at key moments. The technique described in this post is a variation on Think-Pair-Share or alternatively "Teaching with Your Mouth Shut" by Donald Finkel, and I think of it as an entry-level IBL technique. It can, however, be used in a broad range of IBL classes, and it's also a useful IBL starting point.

Suppose you are teaching a Calculus class, and you are at a point where an example would be useful. Instead of the instructor showing all the steps, the instructor can write the task on the board, and ask students to work on it and then discuss with a neighbor. Once students are talking to each other, the instructor can write the solution on the board.

The basic framework is presented here. You'll need to adjust the framework to fit your goals, the content, and the environment.

  1. Give Task  "Find the derivative of..." or "Here's the graph of the derivative, figure out if the function is concave up or concave down or neither of those."
  2. Ask students to try it and discuss with a partner.
  3. Silence Instructor waits in silence, and observes students working on the problem.  It helps to walk to the back corner, and then walk back up to the front. 
  4. Write When students start discussing, the instructor writes the steps on the board. Student can then compare.
Using this method at the beginning of the term, requires setup to encourage student buy-in. You should have some instructor guidance ready.  Examples of these are:

  • "I'd like you to try some problems sometimes before we look at solutions, so here's how it'll work when we do class activities..."
  • "It's important for you to practice and ask questions, so we can help each other..."
  • "This is like practice in sports or music lessons. It's time for you to try it, and for me to listen..."
This is Think-Pair-Share light. Students are not voting, suggesting, or sharing their solutions. But those options are on the table, and the instructor can opt-in to those. Instructors can elect to have students share their ideas when appropriate.

One advantage of this technique is that it does not require the same level of intensive preparation and class management as a more heavily student-centered IBL experience, where the sequence of problems and class discussions have to be organized carefully.  That is, you can throw this into your teaching toolbox and use it frequently.

One of the common instructor concerns is when students sit quietly and are not active.  I have talked to instructors who say that their students don't work in groups or don't want to work in groups. Getting students to try the problem and discuss is the instructor's responsibility. The main advice is to have students move their desks (if possible) or at the very least know who their partner is ("Point to your partner!").  The instructor should give clear instructions.  "Try this problem. Talk to your partner.  I want to hear you all talking." Then go visit quiet areas and gently ask them to talk to their neighbor.  Opting out should not be an option.  Moving to the side or to the back of the class momentarily helps visually cue that it's time for students to get to work. The act of walking off the stage sends a message that the instructor will be silent.

It's not a zero-sum game:  Frequent use pays off. What I mean by this is that as you get students more and more engaged, then it opens new possibilities to do even more inquiry. Students are more engaged.  They start asking more questions.  You get to know what their strengths and weaknesses are better, so you can make better informed teaching choices. And then this cycles in a positive feedback loop.

Interestingly, if you look at students' notebooks, you'll see nearly the same things as if you had done all the work on the board without asking students to take a turn. The difference is not usually evident on the pages of the notebooks. The difference is in the experiences getting those words and symbols onto those pages.

Lastly, one of the ways we learn about student thinking is to listen. It's much easier to listen when you are silent ;)

Miles Davis -- So What




Monday, March 6, 2017

IBL Mini-Conference at MathFest 2017

Here's a note from Alison Marr, Southwestern University and Patrick Rault, University of Arizona. Alison and Patrick are conference co-chairs of the IBL Conference at MathFest 2017, and are putting together the program for this year.

Interested in learning more about inquiry-based learning (IBL) and active 
learning? Have insights on how IBL works in your classroom? Then please consider attending the mini-conference, Constructing the Future of IBL: The Past 20 Years and the Next 20 Years, that will take place in Chicago as part of MathFest on Friday, July 28, 2017 from 5:30PM-9:30PM. The conference will include a panel discussion exploring various aspects of the diversity of IBL, a contributed poster session, roundtable discussions, and a plenary talk on the future of IBL by Stan Yoshinobu. More information about the conference and poster abstract submission can be found at 

http://www.inquirybasedlearning.org/ibl-conference/

There is a $25 registration fee which includes heavy hors d'oeuvres, and you must register for the mini-conference when you complete your MathFest registration. We hope to see many of you there!

Alison and Patrick

Thursday, February 16, 2017

Part 2: Dr. Esselstein's Students

The following interviews are five of Dr. Esselstein's students mentioned in Part 1 of the interview. Five CSUMB students, five wonderful stories!

Transformative experiences are highlighted by the IBL community. Those of us who have used IBL methods in our classes have seen students flourish in ways that changes the trajectories of their lives. It sounds like we are exaggerating, as if we are making promises of rainbows and unicorns.  But there are many instances, when things go right, the students buy-in, and the entire class (including the instructor) comes together like a championship team.  It doesn't always happen, it's not easy to pull off, but it's why we work so hard to try and get to that special place.

In this particular instance, Dr. Esselstein taught a proof-based course for math majors, where the opportunities to build Math from first principles, parallel to how research mathematicians do Math.  Authentic success, the greatest confidence booster there is, did it's work.  This experience left a lasting impression on these students, who proceeded to earn their undergraduate degrees and then go to on to graduate programs.

Yes, you can make a real difference!

1. Diana and Alfred


2. Sandra



3. Helen



4. Daniel


Monday, February 13, 2017

Part 1: IBL Instructor Interview: Dr. Rachel Esselstein

This blog post is an interview in a Q&A style. In this edition, I interview Dr. Rachel Esselstein, University High School in San Francisco.  Her experiences teaching at both the university level and high school level, gives her interesting perspectives and insights into IBL teaching. Thank you, Rachel!  (See also Part 2: Dr. Esselstein's Students)


Hi Rachel! Thank you for agreeing to be interviewed. You’ve had an interesting and inspirational trajectory in your IBL teaching. Please tell us about it.  

My first attempts at IBL were as a professor at California State University, Monterey Bay where I worked for 7 years.  I decided to attend an IBL conference at University of Michigan after a discussion with a friend and collaborator, Fran├žois Dorais.  This led me to apply for a mini-grant which I used to create an IBL Intro to Proof course with Carol Schumacher as my grant mentor.  The course ran several times over two years and I found it to be a very challenging but rewarding experience.

In 2014, I accepted a position at the Bay School in San Francisco where I taught math for two years, learning the ins and outs of the independent school world and how to work with younger students.  Bay’s pedagogical philosophy is student-centered and so I had many opportunities to implement IBL in my classes.

This year, I started work at another independent school, University High School in San Francisco.  I am very happy in my work at UHS.  I am surrounded by other faculty who are incredibly talented both as teachers and as practitioners of their discipline.  UHS has a reputation for being an environment for students who appreciate a good challenge and it has been fun to work with amazing students who enjoy being pushed out of their comfort zone.


Please share with us how you use IBL methods in your classes.

It was a revelation for me to realize that I could use IBL when I found it applicable and use other pedagogies in other instances.  In other words, there is no need to commit to a full IBL course.  Now days, I pick and choose how and when to use IBL methods in my courses.  For example, in an introduction to linear programming for Precalculus, I gave my students an open ended problem with no prior instruction about optimizing the packing of supplies for a space mission.  Of course, they were not expected to discover linear programming for themselves in that one lesson but many of them created systems of linear inequalities, graphed them and then started hypothesizing about the optimal solution.  We then had a week-long discussion on why the optimal solutions would happen at the corners of the fundamental region and the students came up with two different ways to explain this phenomenon.  The unit wrapped up with a problem set in which the students worked collaboratively on very challenging problems that asked them to assimilate their understanding of the unit followed by a unit test that was fairly standard compared to what you might see at any other high school covering this topic.

On the other end of the spectrum, there are some topics that I have found are challenging enough and simply frustrate the students if they are asked to learn them via inquiry.  This is especially true for algebraic processes with younger students such as completing the square in an Algebra 1 course. In these cases, I still rely on group work and the unit will always end with a problem set of problems that ask the students to apply and assimilate their understanding but the material is introduced using other pedagogies.


How is teaching HS similar/different compared to teaching at the college level?

One of the biggest obstacles of using IBL at the high school level is working with the parents who may or may not understand and support their child learning in a style that does not reflect their own high school experience.  At independent schools, the parents are generally very supportive of the faculty but they also are very concerned with the success of their student.  I have found that it is always crucial to communicate the purpose and intention of IBL with my students but, at the HS level, it is also important to get the parents on board.  I try to make my grading scheme clear to both the parents and students and I make detailed notes and rubrics that help my students and their families track their progress.

At independent schools, our class sizes are much smaller than I had at CSUMB.  This means that working in groups is much easier to facilitate and I can take much more detailed notes about the work each student does when they are problem solving or presenting.

The resources for finding interesting problems to give my students are quite different.  While it is usually easier for me to construct challenging problems for high school level math than for college level math, my students are not as developmentally ready for things such as proofs or problems that require significant work.  They also seem less adept at working with open ended problems although I do believe that this is something they can overcome (as opposed to not being developmentally ready to handle).  I have found NRICH to be a wonderful resource for challenging problems as well as old Math League exams and occasionally old Math Olympiad tests.  The textbooks I am asked to use are good for practice problems for my students but they don’t provide the right problems for IBL so I mostly make my own materials.

Students are very self-conscious at the high school age.  This seems to be especially true for freshmen who are desperate to fit in and look smart or successful.  I have found it to be even more crucial to create a safe and welcoming environment in the high school classroom in order for students to truly engage in IBL.  Thankfully, my classes are smaller and the students are very well-intentioned and driven by curiosity.

I don’t emphasize presentations of solutions at the board as much at the high school level, especially with younger students.  I will scribe at the board (or get one of my more restless students to scribe at the board) while the presenter describes their work.  I have also found success with asking students to share back what they understood about their peer’s solution.  This helps them make sense of the work for themselves rather than just having them copy the work down on their own paper.


What have been some of your biggest challenges teaching Math?

The most challenging thing is that I spend copious time and effort creating a project or problem set that is successful for one group of students but falls flat with another.  Sometimes this is due to the abilities of the groups being different but it seems to mostly relate to the personalities in the class.  I find that IBL at the high school level (and somewhat at the college level) really relies on finding the right hooks; the problems must be engaging and tractable.  High school mathematics has many more venues for applications and so sometimes I can just tweak a problem to relate to a particular group of students.  Other times, I need to completely scrap an activity that I worked so hard to create the year before.

I also found collaborative teaching to be challenging when using IBL.  IBL is easiest to run if you have complete autonomy over the course and can adapt to the students’ interests and abilities.  I have found that my calibrations for my students are very different than other teachers’ for their own students and it means the courses might go at different paces and focus on different activities.

IBL at the high school level gets LOUD!  I have had to find ways to monitor the noise level when they are working in groups or debating a solution to a problem because their enthusiasm and energy cause the volume levels to get extremely loud.  High schoolers often have less social maturity than college students and so I have found it necessary to instruct them on how to give constructive feedback to their peers.


What have been some of the successes?

I don’t know that I have been teaching at the high school level long enough to see measurable successes in terms of students going on to find success in college level math.  I have had multiple students from my IBL courses at CSUMB go on to graduate school in math with great success and I have also had some students become high school teachers themselves who are using IBL in their courses.  I anticipate that we will see much more IBL in high school math as the Common Core State Standards and training around them continue to roll out.  Common Core has been a great touchstone for teachers to re-think their pedagogy and how it reinforces the mathematical practices and habits of mind.

I have absolutely seen an improvement in my students’ abilities to solve problems that are unfamiliar to them.  I also noticed the time my students spend working on a problem before asking for assistance has increased although I haven’t recorded or measured this formally.

Many of my students describe the IBL units as the “most fun” they have had in a math class.  Students like discovering the material and solving puzzles.  They love being challenged when they know that the stakes are non-threatening.  They find that IBL makes them feel successful in math because they aren’t just memorizing but understanding the material.


Here’s a video clip of two of your former students from CSUMB, Alfred and Diana. Something special happened in this class, where your students went were transformed learners. What happened in that class?

I don’t know how to describe what happened in that class but it really was magical for both the students and me.  I had Carol Schumacher as well as you, Stan, as resources and you both were very helpful in providing me with encouragement and advice when both were needed.  The stipend from the mini-grant allowed me to put much more time into preparing the course than I would have been able to spend otherwise.  Still, the money wasn’t commensurate with the workload.  It was a lot of work!  I had a great group of students who were open-minded enough to go through this experiment with me and I had very clear outcomes that I wanted to reach.  I think the success of this class was mostly due to the fact that IBL works when it is done well.


Any thoughts or advice for instructors thinking about using IBL but have not tried it yet?

IBL is a lot of work but it forces you to make your teaching student-centered. You will be surprised by the things your students discover and understand.  The best feeling is when a student or a group of students has a break-through and they want to celebrate it with you.  As mathematicians, we are used to the elation of a breakthrough on a tough problem but, for many of our students, this is the first time they have ever experienced this.  They cheer, give high-fives, post things on their refrigerators at home, and develop a more favorable opinion of math class.  It is a lot of work to run an IBL course but it is so much more fun for everyone.

Because it is a lot of work, find a teacher mentor who can help you troubleshoot any issues that come up.  It is best if they are at your school so that they know the school culture but even long-distance mentors are better than going at it alone.

Make the expectations clear to your students (and their parents) as well as your department chair and anyone supervising your work.  Students sometimes panic that you are “not teaching” and their complaints to supervisors can be detrimental to your career if the supervisors are not aware of your pedagogy.  Give the students ample positive feedback and opportunities to reflect on how far they have progressed.  Happy and well-supported students will put in significantly more effort than unhappy and frustrated students.

Observe a class that is using IBL and attend conferences such as the AIBL conference.  They are inspirational and motivational.

Continue reading Part 2: Dr. Esselstein's Students