# 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 and mentoring for those new to inquiry based learning and a supportive network for exchange of ideas for both novice and experienced users. For example, we offered both novice and more experienced users a workshop on Friday October 10, 2014, just before the Fall MAA Seaway Section Meeting, in Alfred, NY. We will continue building our network of IBL practitioners through our e-mail distribution list, the postings on this website, and dinner series events.

## What is going on in the consortium?

### Dinner Series: Rochester

Eight 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 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. The

of this page have not been reviewed or approved by Saint John Fisher College.