Greater Upstate New York Inquiry-Based Learning Consortium
For several years a small group of professors in upstate New York have been meeting informally to share their enthusiasms, frustrations and triumphs related to the use of inquiry based learning in their mathematics classes. We are excited to announce that with generous funding from the Educational Advancement Foundation we are building this community in new and profound ways. Keep reading to find out what's going on and see how you can get involved!
Where are we? What can we offer you?
We are all over the place! There are currently IBL practitioners or instructors interested in IBL at the following institutions in the greater upstate New York region:
Specifically, the consortium offers
- Support for your IBL experience. We have dinner meetings and e-mail conversations to discuss all aspects of teaching IBL: planning, initial implementation, daily workings of the classroom, grading, and the writing of course notes.
- Mentoring for those who would like a personal connection to another IBL practitioner. This allows for a supportive network for exchange of ideas for both novice and experienced users.
- Workshops Our next workshop will be on Friday, November 6, 2015, just before the MAA Seaway Section fall meeting at Saint Lawrence University.
- Open classrooms of IBL practitioners in the area so that you can visit an IBL class of one or more professors in the area. Visiting classrooms is one of the most enriching experiences that can be done, regardless of your experience or comfort level with IBL.
- Funding to do many of the activities listed above. Mentors and mentees can get funding to visit each other's classes if distance is prohibitive. There is also support to attend the workshop at the Seaway Section meeting. Other types of funding is available; please ask!
What is going on in the consortium?
The project continues!
The Educational Advancement Foundation has generously agreed to match some funds that were raised to continue our project into the 2015 - 2016 year. We are beginning to plan a workshop at the MAA Seaway Section fall meeting at Saint Lawrence University on Friday, November 6, 2015. We are also in the planning stages of a K-12 Teacher Workshop to be held at SUNY Plattsburgh. We will continue to have mentoring, possibilities for class visits, and dinner meetings. Stay tuned as we announce our programs. If you have suggestions, contact us at email@example.com.
In order to achieve funding for this year, we'd like to thank the following institutions for their generous contributions which promote our cause:
- Nazareth College
- North Country Teacher Resource Center
- Saint John Fisher College Department of Mathematical and Computing Sciences
- State University of New York at Geneseo
- University of Toronto Mississauga
- National Science Foundation, award 1525058
Workshop on Inquiry-Based Learning in Calculus
At the MAA Seaway Section fall meeting at Saint Lawrence University on Friday, November 6, 2015, we will host a workshop on IBL Calculus hosted by W. Ted Mahavier of Lamar University. The workshop will run 12:00noon until 5:00pm. Details on the content are listed below. Those interested in attending should send e-mail to firstname.lastname@example.org indicating their interest. We also have a limited amount of funding available for those who would like to attend but have already exhausted their institutional travel money or planned it away on other things. Send us an e-mail if you would like to apply for funding.
IBL Calculus -- An Interactive Workshop
Whether you want to dip your toes gently into IBL Calculus or dive in head first, we have something for you! From references addressing the efficacy of IBL, to sources for materials, to grading, to developing your own materials, to failed techniques, we will do our best to address it all. We will demonstrate via video what an IBL course might look like in real time. We will try to show the excitement that can come from a successful IBL course and share student comments on IBL courses. We will address the trades in learning outcomes that are made when using IBL over more content-oriented pedagogy. Mostly, we'll just have some fun and think about new way to teach.
Flipped Classrooms and Inquiry-Based Learning
On September 21st, 2015, I visited James Madison University in Virginia. I had the chance to visit two of Dr. Cassie Williams' classes, the first an IBL class on Number Theory and the second a partially flipped class on Calculus II. The juxtaposition between the two learning styles was striking, which motivated me to write this BLOG entry. Both courses had a required assignment to learn about a new topic before class, either to read a page of an IBL textbook or to watch a flipped class video. Dr. Williams held students in both classes responsible for having finished the assignment, by calling for speakers in the IBL class and by giving a 2-minute quiz in the flipped class. In parts of both classes students were split into groups for discussion or problem solving. Small-group and whole-class discussions took place in both classes, leading students to actively learn the material.
One interesting difference was the level of complexity of the assigned tasks: in IBL number theory, students were asked to prove substantial and fundamental theorems after reading but before class. W. Ted Mahavier described the step-by-step process of a student solving a problem using a metaphor of crossing a stream over stepping stones: if you place one stepping stone in the center of a river, the student making a leap will instead take a plunge and have few good memories of the experience; if you place too many stones in the stream then the student will cross without noticing nor learning; but if the stepping stones (or subproblem steps) are placed a perfect distance apart, a student will move (or think) carefully while learning about foot-eye coordination (or Number Theory). This key difference between IBL classes and flipped classes thus makes it essential that IBL instructors provide some additional feedback mechanisms to provide extra stepping stones when needed. This may be done via office hours, through some between-class scratchwork assignments, or by purposefully running into students in the hallways. A student is then asked to prove the theorem in class, and in rare educational situations (such as what happened once in this day of IBL Number Theory) another student may present a very different proof of the same topic.
Selecting a teaching style is a difficult decision, as it needs to balance the department goals, the students' goals, and your personal goals for each class. Flipping a class requires a substantial amount of time and equipment to record and re-record videos, but is more efficient than lecture for conveying material. Creating an IBL class requires a substantial amount of time to tailor a class script or textbook to your students and to provide continual feedback, but is more efficient than lecture for creating independent problem solvers. In today's world we encourage everyone to transition to active learning classrooms, in light of the NSF's press release "Enough with Lecturing." I hope that this BLOG post will help you to understand some of the differences between these two teaching styles, which I myself hope to explore more of.
Patrick X. Rault, Associate Professor of Mathematics at SUNY Geneseo
The lighter side of IBL
On September 10th, 2015, I visited the Kutztown University of Pennsylvania. With several people in the department using IBL, they are an ideal place to visit and observe different techniques. Indeed, Dr. Padraig McLoughlin's calculus 1 class was different than anything I had seen before. To prepare students for later more traditional IBL courses, he spent most of the class guiding the students through a Q&A session about horizontal, vertical, and oblique asymptotes. The Freshmen were not used to speaking in a mathematics class, but his dauntless onslaught of humor throughout the discussion broke the ice and made students feel comfortable. Through a combination of self-deprecating humor and indirect praise of the students, most were comfortable enough to answer his questions and derive mathematical conclusions (both true and false, but working toward true). The reader may think that in such an informal environment, students would be less likely to take the mathematics seriously, but Dr. McLoughlin brings formality into the equation by referring to students as Mr. Jones or Ms. T. Even the quiet students sitting next to me told me after class that they enjoyed his style; this is one step away from accepting an invitation to present on the blackboard. In my mind, the McLoughlin Method (itself derived from some descendants of Moore) involves a heavy dose of comforting informality, combined with a healthy dose of serious formality to keep students on task. While every instructor must find what works best for them, I look forward to bringing some of these elements into my own classes.
Patrick Rault, Associate Professor of Mathematics at SUNY Geneseo
The post-class e-mail
Last semester I began sending an email to my class after every class session. I've actually been doing this for a while, but in the past it was a quick two or three lines, setting an agenda for the next class period or reminding them of upcoming deadlines. Early last semester I also included a bulleted list of who did what that day. From there it grew into a sprawling and subjective narrative of the days events as well as my hopes and dreams for the next class period. An example:
Great work today! I really like the way Greg fielded the barrage of questions when he was presenting Exercise 62. I personally feel overwhelmed when several people are yelling out answers while I'm up at the board. I prefer to call on people individually. As I mentioned in class, when you are up on the board there is an assumption that you have tried your best. You do not need to be able to answer every question asked of you. Saying "I'm not sure" or "I don't know" is perfectly acceptable.
Jan's progress on 59 was exceptional. Breaking down a big problem into smaller ones in a real skill that takes practice. I think we can take care of the last two pieces next class.
I mentioned in class that there was an alternative solution to problem 60. I've posted it on the website. Please look it over carefully. The notation on the board in class was a little sloppy today. The notation on the website should be correct.
I know exercise 61 was pretty straightforward and everyone was at least close in the scratch work, but please keep chatter to a minimum when your classmates are at the board presenting.
By tomorrow afternoon, please turn in scratch work for the missing parts of 59, 63 and 64. Be careful about 64! There is a new definition with a little nuance to it. I believe we can get through all of these and start with fresh material for next week.
I have a terrible impulse to lecture and make side comments. The post-class email is very therapeutic for me. It's like lecture methadone. If I want to say something in class, I say it instead in the email. I can make sure my side-comments stay on the side. I can re-read my email before sending it out to make sure I'm not giving too much away, another problem I have.
Knowing that I will write an email like this has made me a better listener and note taker. My students knowing that I pay attention to them has also made them more conscientious.
Phong Le, Assistant Professor of Mathematics, Goucher College
Dinner Series: RochesterEight professors representing seven institutions gathered for a dinner discussion of IBL on Wednesday, April 29. In the conversation that ensued, we learned many things:
- One new practitioner confessed that her IBL course this semester was the best teaching experience she has had.
- There are many users of the priority sorting program used by Patrick Rault (and developed by one of his former TAs) to determine the next presenter in an IBL class.
- Nazareth College is now teaching all of their Calculus courses using IBL. All six full-time instructors in the math department taught via IBL in the 2014-2015 academic year.
- Interesting uses of giant post-it notes can showcase a student's work
- One serving of baklava is really too much for one person!
Reflections on a trip to Westfield State
On April 2 and 3, just before the Easter, I had the opportunity to visit some classes developed by the Discovering Arts of Mathematics (DAoM) group at Westfield State University. I was not surprised that the attendance of the classes was slightly lower than usual but I was surprised by the amount of energy that the students had working on serious and hard mathematical problems before a big holiday. The Mathematical Explorations class is designed for the general liberal arts major students to fulfill the math requirements for their degrees at Westfield State University. The four collaborators of the DAoM group will teach a various number of sections each semester and they all choose different topics for different classes so no section will have exactly the same material as another section.
In Dr. Ecke's class on Thursday, students were divided into groups of three to four exploring a puzzle developed by DAoM called Radon-Kaczmarz puzzle. The puzzle involves filling in a square grid with numbers 1-9 (repetition allowed) so that the sums of each row, column, diagonal and off-diagonal is equal to some prescribed numbers, which are called aggregates. In the beginning, students were given some 3 by 3 and 4 by 4 solvable puzzles, and later some unsolvable puzzles to work on. Students then realized that in order to have a solution to a puzzle, certain conditions of the aggregates must be satisfied. Dr. Ecke walked between tables/groups to check on how students were doing, encouraging them, and answering their questions by asking more questions. This class only meets twice a week so each class is 75-minute. After working for about an hour, some students started to run out of steam especially with some of the not-so-straightforward questions. One girl confessed that her brain was fried and could not think anymore. Dr. Ecke encouraged her to take a few minutes, close her eyes and take some deep breaths, or even temporary left the classroom and took a short walk. This actually turned out to be a good thing for the student, as she was able to make some more progress during the last few minutes of the class.
In one of Dr. Fleron's class on Friday, students just finished a big sliceform project so the class started with a small sliceform exhibition. There were some really well made sliceforms that students had spent hours and hours making them. The fact that students were willing to work this many hours after class simply tells me that this math class is no longer a hurdle for them, it is something they enjoy doing as part of the education. In the other class of Dr. Fleron, students were exploring a geometric drawing game called Spirograph. The ultimate goal of this learning unit was to find out the symmetry group of the geometric shape given the numbers of teeth of the gears without actually drawing it. Students were asked to draw some simple shapes in the beginning using different holes in the rotating gear and record the numbers of teeth at the same time. Then after drawing several of them, students would start to explore the relationship between the symmetry and the numbers. I played the Spirograph as a kid a long time ago but never thought about the mathematics involved in the game. As I was observing the students working on some examples, I figured out the mathematics behind the game and the process was not instantaneous. After realizing that, I was a little concerned how long it would take for the students to figure this out but Dr. Fleron promised me that it would take one more class before the students arrive the conclusions. This was certainly beyond my expectations for what non-STEM students are capable of in a 100-level class. The class ended a few minutes after the period because Dr. Fleron mentioned it as no students realized that. Another thing that I learned during the trip was that having a structural way of informing students about their participation grade could have a big impact on their performance of the rest of the semester. In all of my IBL classes, I evaluated students' participation performance and record them in a spreadsheet but no students have ever asked me about their grades. I took it as a positive sign because I thought the students were enjoying doing the mathematics and not worry about their grades. My students do not seem to be bothered by their grades and they can freely express their thoughts during the class discussion without worry about saying something wrong. But the slackers will also convince themselves that if they just say one thing every other class, then they are doing fine because the professor did not say otherwise. One thing that I will probably start doing in the future is to send each student an email about their participation performance at least once during the semester to communicate my evaluations of their participation performance, whether they need to keep on doing the good work or making more efforts for a better quality work.
At the end, I would like to thank the DAoM group for their hospitality and their time for share their teaching experience with me, and the Greater Upstate New York Inquiry-Based Learning Consortium for supporting this trip.
Xiao Xiao, Assistant Professor of Mathematics, Utica College
Morrow wins Clarence F. Stephens Distinguished Teaching Award
Margaret Morrow, Associate Professor at SUNY Plattsburgh has received the 2015 Clarence F. Stephens Distinguished Teaching Award from the Seaway Section of the Mathematical Association of America. This award goes to recognize teachers of Mathematics at the post-secondary level who have been widely recognized as extraordinarily successful. Their teaching effectiveness must be documented and must have had influence beyond their own institutions. Margaret clearly fits this profile, and the UNY IBL consortium is evidence to this. As the Seaway Section comprises Upstate New York, most of Ontario, and all of Quebec, there are a substantial number of mathematics professors in the section, so this is a great honor. Margaret will be the Section's nominee for the MAA's Haimo Award for Distinguished Teaching this year. She was presented with the Clarence F. Stephens Award at the MAA Seaway Section meeting at Colgate University on April 17. (By the way, Margaret is also one of the leaders of the Upstate New York IBL Consortium!) Congratulations, Margaret!
Rault wins Alder Award
Patrick Rault, Associate Professor at SUNY Geneseo, has received the prestigious Henry L. Alder Award for Distinguished Teaching from the MAA. The award is meant to honor beginning college or university faculty whose teaching has been extra ordinarily successful and whose effectiveness in teaching undergraduate mathematics is shown to have influence beyond their own classrooms. Each year, at most three professors win this award nationwide, so this is truly a noteworthy accomplishment. Patrick has also been the principal leader in the Upstate New York IBL Consortium. His vision and persistence lead to the acquiring of the grant which formed the consortium, as well as the dinner series and the connections which predate the consortium. For more information about the award, see the press release. Congratulations, Patrick!
Do Grades Matter?
In February, I visited the IBL classroom of Phong Le at Niagara University. In April, Phong returned the favor and visited my class at Saint John Fisher College. Because of the back-and-forth visits, we were able to have similar conversations at separate points in the semester. One of the aspects of teaching that I am particularly bad at is giving the students constant, transparent feedback about their performance directly as it pertains to their grades. Phong introduced me to the system he is using in his IBL geometry class this year. He admitted that he has struggled with this in the past, so to fix the problem he would make this a focal point of student feedback. Students in his class are updated with their presentation grades on a weekly basis. Students who do not participate regularly can watch their grades slip via this process. Students who participate in class discussion but don't present work on the board can watch their grades hold steady or slowly erode. Students who do neither can watch their grades fall quickly. When the students do present, they can watch their presentation grades improve. Perhaps this method provides the necessary amount of carrots and sticks to provoke students to do the presentations before they hit panic mode at the end of the semester.
Ryan Gantner, Associate Professor and Chair, Department of Mathematical and Computing Sciences, Saint John Fisher College
IBL as independent study
One of the students in my spring 2014 IBL Introduction to Abstract Algebra class was keen to continue learning math using an IBL approach - so he undertook an independent study with me in Fall 2014. I will call the student Jim (not his real name). Given his interest in number theory and Abstract algebra, we chose as the basis for the study portions of the notes A Do-It-Yourself Introduction to Number Theory, by William Priestly, derived from notes by James Cross. (See JIBLM, No. 20, Dec. 2010.) These notes provide an introduction to number theory while simultaneously developing relevant ideas from Abstract Algebra. (Jim had worked with some, but not all of the Abstract Algebra ideas in his previous course- notably the independent study provided him the opportunity to explore rings.)
Doing an independent study based so firmly on IBL was a completely new experience for me. At first I had some concern about how slowly we seemed to be progressing through the material. However in retrospect, there is a huge difference between a student undertaking an IBL study on his own, and a class of students working on the material; Jim had to develop every idea on his own, without the benefit of other students to sometimes pick up the slack and guide the work forward. So, again in retrospect, I think the amount of material Jim ultimately mastered was amazing - and of course, this being IBL, by mastery I mean a deep and flexible understanding of the ideas.
We met for a minimum of one and a half hours each week. Jim came well-prepared with problems he had solved, and with questions on material that puzzled him. He maintained a careful notebook recording completed problems and key ideas.
The notes did a beautiful job of examining fundamental concepts of units, associates and primes, and how the existence of a Euclidean algorithm in a ring leads to unique factorization. The ideas were developed first in the very familiar context of the ring of integers, then generalized to the ring of Gaussian integers, and finally considered in polynomial rings. The notes also explored an extension ring of Z in which unique factorization does not hold. We ended the study by skipping to the last chapter in the notes to explore in more depth the characterization of primes in the Gaussian integers. At this point Jim independently and with no prodding from me developed an effective strategy for factoring a Gaussian integer into primes in the Gaussian integers; he derived a great deal of satisfaction from this - he got a real sense of being a mathematician.
As a final project Jim developed a 50 minute talk titled "Prime factorization in the integers and beyond" which he presented to his peers in the core mathematics class. He did an excellent job of selecting material accessible to his audience, and in crafting and delivering the talk. Jim obtained high praise for his obvious mastery and comfort level with the material.
In conclusion, a well-structured set of IBL notes and a willing and enthusiastic student are a winning mix for a highly successful independent study. Well done Jim!
Margaret Morrow, Associate Professor, Mathematics Department, SUNY Plattsburgh
Visit causes contradiction?
Patrick Rault visited my Introduction of Proof class on Sep. 19, 2014. Students presented three tasks on proof by contradiction in a 50-minute class. One of my students was confused about which statement to negate in the beginning of a proof and had trouble deciding at the end what was actually proved. Patrick gave me the following useful advice on this. When one needs to show a theorem of the form P => Q by contradiction, instead of start the proof by saying
"For the sake of proof by contradiction, we assume that P is true and Q is not true",
one should start the proof by saying
"Suppose P is true. For the sake of proof by contradiction, let us assume that Q is not true."
The second version has the advantage that once a contradiction is reached at the end, students can immediately go to the sentence that has the word "contradiction" and be able to say that Q must be true (instead of trying to decide what to do with P).
After discussing my syllabus with Patrick, I also realized that I probably have over-worked my students by assigning too many homework. My students have daily homework, weekly homework, class presentations, portfolio, weekly journal and three exams. This makes me think about my objectives for each assignment and how I can re-design them to reach the same goal.
Xiao Xiao, Assistant Professor of Mathematics at Utica College
Dinner Series: Buffalo
On Saturday, September 13th, three IBL practitioners gathered in Buffalo for a 3-hour lunch discussion. We discussed strengths in our courses and students, challenges which we've faced and ways to overcome them, and plans for the future.
One highlight was the idea that a lecture-based class usually has a "learning outcome for the class period," whereas in an IBL class we often think in terms of a "learning outcome for the time between class periods." Indeed, in an IBL class we might think of one unit as beginning halfway through a class period and ending halfway through the next class period. This is illustrated as follows.
|Class period 1||Class period 2|
|Lecture:||Begin topic A, end topic A.||Begin topic B, end topic B.|
|IBL:||End topic A, begin topic B.||End topic B, begin topic C.|
For this reason, it often makes more sense for a class observer to visit two classes in a row in order to see the entire progression of the topic. Though this is difficult for out of town visitors, local visitors should be encouraged to observe either two full classes in a row or two half classes in a row (i.e. the end of one class and the start of the next).
Please bring your own thoughts on this, or other IBL topics, to the upcoming MAA Seaway meeting. Or e-mail your own post for this BLOG to Ryan Gantner (for example, we would love to hear from someone about the Kenyon workshop or a mentoring trip). Or tweet using #UNYIBL.
Patrick Rault, Associate Professor of Mathematics at SUNY Geneseo
Calendar of Events
For questions or more information, please send e-mail to UNY.IBL@gmail.com .
The views and opinions expressed in this page are strictly those of the page author. Theof this page have not been reviewed or approved by Saint John Fisher College.