The Pedagogy Puzzle

We were 75 minutes into class and her engagement and grasp of the content was wonderful! 😊 She had, with minimal guidance, derived the formula for the length of an arc of a circle by applying proportional reasoning. When a student makes a cross-topic connection like this, it is rewarding!  😇  Now, we were solving questions to cement her understanding of the concept. We reached the last question in the set: The second hand of a clock is 10 cm long. How far does the tip of the second hand travel in 20 seconds? She racked her brains for close to 10 minutes before concluding that she was stumped! 😵 I asked her to share where she was getting stuck. She replied that she didn't know the speed at which the hand was moving - so, she couldn't find the distance that the tip had travelled. I realised that she was thinking of the {speed = distance ÷ time} formula. So, I gave her a hint that knowing the speed at which the hand was moving wasn't required in this case. In addition, I...

These 7 seemingly innocuous words come together 12 times as starred footnotes in a popular class 10 mathematics textbook. A textbook that is likely to have been consulted by around 21,50,000 students (perhaps more) during the 2020-21 academic year. When do these notes appear? Is there a pattern to the excluded content? What is the subliminal message that it might send to children? Is the note subtly symptomatic of bigger issues that plague the Indian education system?

Here is where the series stands... The first post (Nov. 18th, 2018) dove into my students' perception of understanding ⇓ The second post (Jan. 24th, 2019) explored my own evolving views on understanding ⇓ The third post  (Mar. 24th, 2019) introduced the TfU framework ⇓ The  fourth post  (Jul. 28th, 2019) discussed the second and third elements of the TfU framework ⇓ The  fifth post  (Jan. 11th, 2020) went into the fourth element of the TfU framework ⇓ The  sixth post  (Feb. 29th, 2020) explained the fifth and final element of the TfU framework In this piece, I unpack how I used the TfU framework to plan a course on developing logical thinking skills in a manner that would drive deeper understanding.  I have already written about  my teaching experiences in that course  here .

In earlier posts in this series, I introduced the teaching for understanding framework and some elements of the framework ( here and here ) . I encourage you to go through these posts before reading on as each element of the framework builds on the preceding ones. Here, I will discuss the fifth and final element of the framework viz.  ongoing assessment .

In earlier posts in this series on understanding, I analysed my students' perception of understanding , dove into my own evolving views on understanding , introduced the teaching for understanding framework and discussed some of the features of the framework . I encourage you to go through these posts before reading on...

Since it has been some time since I have written a post in this series, a recap would be helpful... In the first post , I described my students' perceptions of understanding and came to the following conclusions: For many students, understanding means  being able to answer the question types that appear on exams . Exploring the deeper 'why' behind concepts is often sacrificed due to limitations of time, amount of syllabus, exam patterns and, in some cases, limited pedagogical expertise of the teacher. Perhaps, in some cases, students are not even aware of the superficiality of their understanding . Recalling formulae without understanding their origins is accepted as  understanding . Carrying out procedures without understanding the reasoning behind them is also accepted as understanding .

I recently began a book called An Imaginary Tale - The Story of √−1  by Paul J. Nahin. The book traces how mathematicians regarded negative numbers and their square roots over the past ~2000 years, the birth of complex numbers , the development of complex number theories and their applications in diverse fields. My reading of the first few chapters which paints a fascinating history of the origin of complex numbers planted the seed in my mind from which this post germinates...

In the next four posts in this series on  understanding  (here are the links to the first  and second ), I shall discuss a framework that teachers could adopt to take a step towards teaching for the  deeper understanding  that I wrote about in the previous post .

I recently had the opportunity to represent Educational Initiatives at an academic consultation workshop hosted jointly by Bodh Shiksha Samiti, Sattva Consulting and the Michael and Susan Dell Foundation (MSDF) in Delhi. The goal of the workshop was to review content for a project that the three companies are piloting in government schools of Rajasthan and Haryana. In this post, I would like to share my experiences and takeaways from the six-hour long workshop.

In this essay, the first in a series, I shall share examples of what my students think understanding means in the context of their school subjects. As a majority of my teaching experiences over the past 5+ years have been in mathematics, the cases discussed are from that domain. However, I have attempted to present my points in a way that is accessible to a reader from any discipline by foc using more on underlying mindsets rather than going into the specifics of the subject matter. Case 1 The image below lists three fundamental identities in trigonometry that students across the globe cover in grades 9 and 10. I have taught this concept to a wide spectrum of children across Indian and international contexts. What follows is a typical conversation regarding these identities: Me: Have you seen these identities before? Student: Yes, these are in the section on important formulae  at the end of the chapter. Me: What would it mean for you to  under...

Random uncle: So, now that you have completed your degree, where are you going to work? Me: I'm joining the Teach For India fellowship in Pune. I'll be teaching a set of children studying in low-income schools for two years. Random aunt (joining in the conversation with an expression that simultaneously showed consternation and condescension): Teach? Why? Did your campus placements not go well? Me: No, aunty. It's not like that. I want to teach and work with children. Random uncle (struggling to digest this):  Why did you work so hard all these years just to become a teacher? Your parents didn't spend on your education for you to do this! Back in 2013, conversations that resembled this one were quite the norm. Once I decided to explore teaching and the education sector as a serious career option, I was met with looks of sympathy tinged with the implicit assumption that I had settled for something 'less' due to my inability to secure a 'better...

(An abridged version of the following essay appears as a chapter  titled 'Delivering Excellence'  written by the author in the book "Chalk and Challenges" published by Central Square Foundation and the Centre for Teacher Accreditation in India. The book is written by teachers for teachers and aims to speak directly to their needs by sharing practices that can be replicated in classrooms across the country.) ~ ~ ~ A misty January morning found me with my 5th grade kids out on the school grounds. The children had their pens and notebooks out so it was clearly no games period! We were on an exploratory walk to apply the concept of tally marks to count the numerous trees that lined the boundary of our school. My students had a basic understanding of what a tally mark was and each of them prepared a simple table in their notebooks before heading out. They were expected to make a tally mark in the table each time they observed a tree and enter the total number of t...