Applying the Teaching for Understanding (TfU) framework

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.

I would suggest reading this post to get some background before continuing with the post below...

The generative topic

"What topics are worth understanding?"

The generative topic for my course was building logical thinking skills through the medium of puzzles. Being able to think logically is a skill that cuts across subjects and disciplines. The choice stemmed from my own involvement with puzzles over the years besides it being accessible and interesting to children.

The throughline

"What are the overarching goals that teachers and children want to achieve?"

I was given 7 hours of instructional time for my course. Thus, I had to be crystal clear in the overarching goals that I wished to achieve from the outset.

The throughline of my course was two-fold:

  1. to have my students appreciate the beauty of using logic to break down problems (here, puzzles)

  2. to ignite a spark within them that I hoped they would fan even after the completion of the course; after all, 7 hours is far too short to explore such a rich topic!

Understanding goals

"What are the enduring concepts in these topics that need to be understood?"

Since the course was a short one, the understanding goals were few but focused. These are the three goals that I wrote down when planning the course...

  • My students will learn the concept of metacognition (thinking about our thinking process) and apply metacognition to understand the how/why behind their approaches to puzzle solving
  • My students will learn/realise that random guesswork on puzzles (or any problem) will not be effective in the long run. They will learn/realise, through multiple examples, that reasoning and logic are far more effective tools for problem solving.
  • My students will do/solve a variety of puzzles to cement the ideas of metacognition, reason and logic.

Notice how each understanding goal is an actionable statement about learning or doing and how each goal is closely linked to the first throughline?

Performances of understanding

"How can teachers help children demonstrate their understanding?"

The basic premise of performances of understanding is that understanding is deepened, as well as made visible, by performing one's understanding. These involve children being able to explain, interpret, analyse, extend, synthesise and apply their knowledge. 
So, what were the performances of understanding that I planned for my course?

For the first understanding goal on metacognition, I designed the 'Thought Book' (read more about this here) so that an activity like metacognition that resides entirely in the mind could be penned down and made visible. You can read interesting samples of actual student work here and here.

Now, carrying out metacognition is challenging for adults, let alone children! So, along with writing, I frequently asked my students to verbalise their thought process - either within the small groups or as part of a whole class discussion. At times, I did a think aloud to model my analysis of my own thought process. In nearly all the course activities, I encouraged some form of partner work or group work so that they would get the chance to actually speak their thoughts - a great example would be the contents and photos in this post!

How about the second understanding goal on reasoning and logic being more effective than random guesswork?

Well, for this goal, children had to experience it for themselves - like the "messing about" phase in performances of understanding that I wrote about here. To support this, I gave them multiple copies of the same puzzle when introducing it, and had them experiment with different approaches with minimal guidance. Most students tended to gravitate towards random guesswork in the beginning as it required less initial effort. However, they began to realise how frustrating and inefficient it was to traverse this route because there was no logical way of correcting their mistakes. In fact, they couldn't even figure out when/where they had made mistakes, because their approaches were haphazard! 😅

Take a look at the Slitherlink and Dissection puzzles from this post for concrete examples of children trying random guesswork before moving to more systematic and logical ways of thinking...

During each puzzle, I reiterated that our focus was on the thought process and not the final answer (read 'Flipping the script' in this post). Furthermore, by the fourth or fifth hour of the course, children realised the futility of guesswork and were prepared to persevere towards a solution in a logical manner.

For the last understanding goal, I exposed them to a variety of puzzles during our 7 hours together that you can read details about in the series! A snapshot here - a cipher introduction (letter + number based), Slitherlink (visual/spatial + basic numbers), Dissection (visual + geometrical), Kakuro (arithmetic i.e. addition and subtraction), Dominoes (visual grid-based) and matchstick puzzles (visual out-of-the-box thinking).

I also curated a booklet of 50 puzzles (intentionally without solutions and different from the ones we did in class) and gave one booklet to each child at the start of the course. We did not discuss these in class but they would run up to me excitedly during break times to verify whether they were on the right path to a particular puzzle or not! 😂 Designing this booklet was a carefully thought-out decision to cater, to some extent, to the second throughline of the course.

Ongoing assessment

"How can teachers gauge what children understand?"

As this was an exploratory course that was a part of a package of seven courses, the time that I got with my students was limited. The sessions would end by around 1 p.m. and we (students and teachers) would have a quick lunch before they left in the hired buses. Thus, I was unable to conduct formal ongoing assessments and use these as inputs back into the course. However, I did informally carry out two ongoing assessments so that I could give periodic feedback to my students (during breaks and lunch) and summative feedback to the parents on the open day.

First, their thought books. These served as de facto course journals as their path to decoding each puzzle was written inside it. I collected these at different points of the course, reviewed them and made notes about each child before returning the books. When possible, I gave specific feedback to the children then and there and/or to their parents when I spoke to them on open day.

Second, the planning and execution of the open day. I observed how the group of 7 children who were randomly assigned to my course went about deciding what the stall would contain. This revealed their key takeaways, the puzzles that had the most lasting impressions and the elements of the course that they thought they must convey/present to their parents. While they were setting up the stall, I spoke with each of them to better understand why they included a particular element and what were their learnings from that puzzle/part of the course.

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That concludes the series on understanding. Frankly, I had no idea that the gap between the first and last post would be about one and a half years! 😅

Please do share the series with teachers and educators who you think would be interested in learning about the framework.

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Grotzer, T.A. (2002). Expanding our vision for educational technology: Procedural, conceptual, and structural knowledge. Educational Technology Magazine, March-April edition, pp. 52-59.

Hmelo-Silver, C.E., Duncan, R.G. & Chinn, C.A. (2007) Scaffolding and Achievement in Problem-Based and Inquiry Learning: A Response to Kirschner, Sweller, and Clark (2006) Educational Psychologist, 42(2), pp. 99-107.

Kirschner, P.A., Sweller, J. & Clark, R.E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), pp. 75-86.

Nasir, N.S., Rosebery, A.S., Warren, B. & Lee, C.D. (2006). Learning as a cultural process: Achieving equity through diversity. In R.K. Sawyer (Ed.) The Cambridge Handbook of the Learning Sciences. New York, NY: Cambridge University Press, pp. 489-504.

Simmons, R. (1994). The horse before the cart: Assessing for understanding. Educational Leadership, 51(5), pp. 22-23.

Strike, K.A. & Posner, G.J. (1985). A conceptual change view of learning and understanding. In L.H.T. West & A.L. Pines (Eds.), Cognitive structure and conceptual change. New York: Academic Press, pp. 211-231.

Wiske, M.S. (1998). What is Teaching for Understanding? In M.S. Wiske (Ed.) Teaching for Understanding: Linking Research with Practice. San Francisco, CA: Jossey-Bass, pp. 61-86.

Wolf, K. & Stevens, E. (2007). The role of rubrics in advancing and assessing student learning. The Journal of Effective Teaching, 7(1), pp. 3-14.

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I read the article quoted in this essay as part of the course EDU T543 Applying Cognitive Science Research to Learning and Teaching at the Harvard Graduate School of Education. The course was intended for those who wanted to develop thoughtful instructional designs for learning. These designs could be in the form of traditional lesson plans or in forms for a variety of other contexts, formal or informal, including massive open online courses (MOOCs), online learning, computer programs and so on.


  1. There are two learning topics that I have started to feel can be used at most ages. One is basic Arduino usage and the other is making fractals. Both help develop a flow of logic and making abstract connections to known rules. It seems similar to how you use puzzles and I am considering how I can combine them.


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