The Pedagogy Puzzle

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 .

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 .

In the first post in the series , I explained, through 4 cases, the ways that my students think about understanding . Not surprisingly, educators themselves have diverse views on the meaning of the word understand (Folk, 2006). In this essay, I shall explore my journey towards making meaning of  understanding . I start with my time in middle school (around the age of 12) because that was when I began to question the how/why of what I was learning in school. Middle school (grades 7 to 10) One day, when I was in 7th standard, I returned from school and asked my mother, " What is the point of all these marks that my teachers give me? " Up until that point, my primary indicator on whether I was doing "well" in school was marks; out of the blue, something (I cannot pinpoint exactly what) was motivating me to question the foundations of that metric.

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...