Umami and Teaching: "Feeling Closer to the Teacher of My Vision"

Umami is a Japanese term from the culinary world described as meaty, savory deliciousness that deepens flavor (Link).  Umami as an idea has other forms. For example, umami can also be the first sip of coffee in the morning.  Ahhh!  Or it can be taking a refreshing hot shower after a long hike on a warm summer day. Ahhh!

We usually talk about IBL teaching in terms of benefits to students, the key features, or the nuances of how to implement it well.  What faculty gain is talked about less, and is often overlooked.  For many of us  teaching is a calling, and it's not only because we love our subjects. The enjoyment of teaching is in meaningful human interactions, students and instructors working together towards to learn, discover, and grow as humans.  

One of the big reasons why instructors should use IBL methods is because it's enjoyable and fulfilling for instructors. A centerpiece of IBL teaching is building community, and when students and instructors work as a team, then the magic happens. Enabling the dreams of students and transforming their lives is a great thought to wake up to in the morning. That's a form of umami within the grasp of every teacher.

The evaluation team (Sandra Laursen, Devan Daly, Tim Archie, Chuck Hayward) for the NSF PRODUCT asked participants, what did you gain personally from employing IBL methods? Below are a some responses from participants about umami and teaching. Enjoy!

“I personally enjoy going to class more each day.  When lecturing I sometimes found myself dragging myself to the classroom with particularly challenging groups. In IBL classrooms, I am generally excited to see what my students will do each day.” 

“Teaching using IBL methods keeps me excited about teaching, helps me see things from different angles and I learn new things from students all the time.” 

“When I can do it, I feel really proud and energized--feel closer to the teacher of my vision.” 

“I feel that the IBL workshop helped me adapt my pedagogy in small ways to try to create equity and make my students feel that this was their classroom and that I believed in them unconditionally. I held those beliefs prior to the workshop, but the workshop opened my creative thinking to all the ways I could adapt small (and large) behaviors to support my goals.”

“I enjoyed my time in class more, was able to interact more with the students and develop deeper relationships with each.” 

“I've learned more about the material than I thought I had left to know.” 

“I found it much more enjoyable designing a course around IBL methods, and implementing these methods in my classroom. There's only so much you can do with a lecture, and it becomes boring after a while. It was exciting when students surprised me with the answers, both correct and incorrect.” 

“I enjoy teaching more, and find my work has much more value. I'm not just teaching students calculus, I'm changing what they think mathematics is and their views of themselves and their own view of their ability to do mathematics.” 

“It was a lot of fun! It felt like my students and I were working together and that they were like mathematicians in training/apprenticeships.” 

"I Have a Dream": MLK Day, Math, Art, Inquiry

Here we are on the 50th anniversary of the "I have a dream speech."  I thought I'd share something related from the IBL Math world.

In 2012 I was fortunate enough to listen to a talk by Bob Bosch, Oberlin College, at the MAA Pacific Northwest Section Meeting, held at the University of Portland.  The conference was superb, and I learned much from my experience there.  Here's a LINK to Bosch's art.

One of the ideas I came home with was to develop a unit based on Bob Bosch's Domino Art work.  Fast forward to January 2013 around MLK day, I was working with Pacheco Elementary, San Luis Coastal USD, and the 6th grade teachers let me throw a math + art unit into their curriculum for about 4 days.  Thank you Mr. Deutsch and Mrs. Irion, and to Jamie Coxon at the Linker Workshop for preparing the materials and framing it for final display!!

The setup is that the 12 complete sets of double-nine dominos are used to make a mosaic of MLK.   (Bob Bosch has other images besides MLK.)  The mosaic is created from a B&W image, where the image is turned into a gray scale image of squares with 10 grey-scale levels from black to white.  Double nine dominoes have approximately these same 10 steps from black to white.   Thus an image can be made into an array of numbers, where each "cell" has a number from 0 to 9.  That's the mathematization of the image into a mosaic.

The big question is "how do you arrange the dominos to approximate the perfect mosaic?"  This is a challenge, because one of the rules of the game is to use all of the pieces in the 12 sets of dominos.  No replacements are allowed.  Generally, the perfect mosaic is not attainable, so we are left to find the best approximation of it.

This means we have to accept some error.  One way to try and find the best possible approximate mosaic, is to find a way to measure error and then to minimize that error.  That's where modern math comes in, because the number of possible combinations is astronomical.  Bob Bosch sorted that, and I'll send you to his site (and papers) to get the nitty gritty details.

The MLK Domino Mosaic the 6th Graders Built

Sixth Grade isn't the best context for a short course in Linear Analysis ;)   So my challenge was to find smaller problems that are doable by 6th graders.  The math unit is in a beta stage, and needs development.  (More work to do!)  What I have so far is enough to get across the idea that minimizing global error requires increasing local areas in some parts.  Sixth grade students worked on measuring error, and on a task that required groups to cooperate to minimize global error, while accepting greater error in their section of the image.  Even in math, we are better when we cooperate!

Finally there was the phase of cutting, gluing, and putting together the mosaic.  While this activity isn't math or art per se, it's a nice activity that culminates in a tangible finished product.  Sometimes it's important to do something to mark your achievement and appreciate something aesthetically pleasing. (And it only took one or two periods to assemble.)  The tiles were connected and framed up by a local craftsman.  I'll also note that there are extensions from this unit to other subjects (and more math).  This unit could extend to MLK's biography, History, writing, Art (color and gray-scales), etc.  I can see quite a long list of possibilities.

One of the best learning outcomes was something I heard from one of the Moms.  She said that her son was so motivated by the project that he was really excited to go to school and do math that week!  Moreover her son wanted her to take him to the public library so that he could learn more about Martin Luther King, Jr. 

Working Together in Groups

To me, inquiry-based learning or more generally teaching isn't fundamentally about teaching techniques or skills.  These are important and necessary of course, and I'm not trying to minimize them.  I focus and work on them daily!  But teaching techniques, skills, and practices serve a larger vision for education, where students are deeply engaged as explorers and doers.

Real, meaningful education lies at the foundation of modern civilizations, and Martin Luther King, Jr. realized this.  Here's one of his more famous quotes.

"The function of education is to teach one to think intensively and to think critically. Intelligence plus character - that is the goal of true education."