To err or not to err

The other day a colleague was talking about “making sense of mathematics”. That brought back memories. Years ago, when I and my batch-mates had just started programming on a real computer for the first time (before that we learnt programming only as theory, computers were too expensive to be affordable for my institute, yes stone age….),  one of my batch-mates had the following code in his program,

If (a>b) then

Endif

We incessantly laughed about it (and still do). (OK I admit it, I was about to write something as ingenious, but caught myself in time). When I put this bit of programming wizardry on a social forum another contributor came up with the following gem,

If (a>b)  goto 10

Code ……

10     goto 100

Code …..

100    …………………….

He wrote that the girl who had written the above code was aptly nick-named “go to 10 to go to 100”.  A  professor once told me about people who write the code but forget to output the results, he remarked, even if no one else knows, the computer does know the results (though now, with neural nets,  that statement has taken up a completely new meaning).

On a more serious note, I remember after submitting a particularly tough analysis in an exam,  my Prof. , as was his practice, discussed a bunch of solutions in the class. After discussing my solution (which was wrong), he turned to me and asked,” why didn’t you cross-check?”. I was crest-fallen and thoroughly embarrassed, because cross-checking was very easy and immediately told me that I had goofed.

Through the years I have seen such errors being made by students quite so often.  People get carried away by the processes too much and forget to run simple checks to see how meaningful their outcome has been.  I believe this happens at multiple levels in life, with consequences of corresponding magnitudes.  Teachers get too much involved in grading the students correctly (a colleague, once showed me an old evaluation he had done, ( 2.36 out of 5 marks), and then sheepishly said that he did not really mean that good a resolution) and end up ignoring the  actual goal of learning.

As one of the chef’s in the show “Master-chef Australia” says, taste everything that you cook.

Tech Enabled Education

When some of the online tools and resources are used in the classroom, the student experience becomes quite rich. Following are screenshots from some of my courses

mech-moodle1

I made my lectures available on moodle which is a course management software, and made them available on the internet to everyone, not just my class. There was a discussion forum for students to interact and ask questions and all course related material, including attendance and grading was available from anywhere.

emt-moodle1

It was possible to give quizzes which were flexible in the sense that students got randomly selected questions from a question bank and could answer the quiz on their mobile phones. The quizzes got corrected instantly and could be accessed by students from anywhere.

Interesting open source resources made the courses interesting. I used quite a bit of media from wikipedia. The rewards kept coming in interesting ways. My favorite is that when I was teaching a class in a huge auditorium with about 250 students present, as soon as an animation started, I saw a student nudge his neighbor and asked him to look up because something interesting was taking place.

 

Designs in Action

We had been debating pros and cons of getting students work away from home.

  • It makes them connect and work with new environments and cultures, against it increases the responsibility of faculty members for students wellbeing.
  • It makes them independent versus how do we enforce discipline?

So when the opportunity presented to accompany the Olin colleges ADE (Affordable Design and Entrepreneurship)  team at their “cycle-rickshaw project” site we happily grabbed it. Prafullbhai, the then VC of the Ahmedabad University was very upbeat about learning from the experts and gave us all necessary support.  I am glad we did, because the experience was amazing.

worling-hands-on-1

One cold winter morning, I found myself waiting at the airport for one of the team members, the chirpy and irrepressible Radhika, after I picked her up, chatting about books from Rand to Tolstoy, we draw down to one of the tiny streets of the old city in Ahmedabad, an area I had never visited before to pick-up axels, flanked by several curious urchins and one or two well-dressed goats (in the winter someone had the bright idea of dressing up their goats in discarded cloths).

I could visit the team on-site only for four days due to other engagements but was impressed by the teams discipline and the buzz of activities. We shared all mealtimes, laughter, anecdotes and work-notes.

The world in my classroom

fitting

One of the most satisfying pedagogy experiments I did was in the monsoon semester of 2017-18 at the School of Engineering and Applied Science at the Ahmedabad University.  I am especially surprised by the success of the experiment because it seemed to occur effortlessly and due to spontaneity, demanded by lack of time for planning.  My pedagogy came about as a culmination of multiple factors, following were the major ingredients,

  • I had just come back after spending a semester at the Olin college, where I was involved in a flurry of insightful activities around student centric learning. My major takeaways from that semester were as follows:
    • Design the interaction keeping student background and aspirations in mind, get to know their culture, their fears and their dreams
    • Make students co-creators of your course
    • Give students freedom to express themselves and encourage them in the process
    • Encourage peer to peer interactions
    • Experiment
    • Humanize delivery (can’t stress this enough)
  • Listen to students: This is another point which is very, very important. Students usually are not very free in their interaction with the teachers, due to the power-play involved. So when someone speaks up, it is really useful to make that person feel respected and valued and it is equally useful to show that you are ready to address the point raised by them. I am especially indebted to Prof. Lynn Stein who during her visit at Ahmedabad University and to Prof. Jonathan Stolk during the summer collaboratory at the Olin college in 2015, impressed upon me the importance of listening, encouraging and being non-judgmental.
  • As a result of decades of reading and observing I had come to realize the importance of having a playful and relaxed mind in effective learning. I tried to bring it to practice by starting my classes with music,  TED talks, a short video clip or discussion about a favorite news item by students. Once we played with a ball in the class while discussing very useful mathematics (internally I was quite freaked out, wondering if the youngsters will stay serious about learning while playing but it worked out very well)
  • Encouraging teamwork: This was supported by allowing a lot of discussion time when I discussed a topic that students found conceptually hard. Peer to peer interactions not only as a method of learning but also for social and cultural exchange and psychological well being, was very much stressed on, during the course.
  • Engaging with the class informally, by sharing personal experiencing doing impromptu projects, for example I discussed poetry that I write and one Saturday afternoon a bunch of us went to the workshop and spent several hours designing and laser cutting, card-board earrings
  • Encouraging class to ask “why?” for any curricular component that did not make sense to them, when they did not ask why, I usually asked them as to why did they think they were learning the topic and where were they likely to use it.

Since the course was co-created with students being responsible for their own education and because of having a class which was not traditional, the atmosphere was much more cordial. We laughed a lot, talked about topics from ranging from movies and politics to literature, sports and businesses. It would be great to see if I can better that experience in the coming semester.

Here is a link to my github page with course-notes.

https://github.com/mitaxim/Linear-Algebra