Teaching for Understanding (Part 2 => Understanding Goals and Throughlines)

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 second post, I explored my own evolving understanding of what 'understanding' means to me.

I now see understanding as the ability to create a model of cognitive connections between prior and newly acquired knowledge/skills; to recognise relationships and patterns within those webs of connections through practice and effort; and to apply these models and relationships to new situations/problems.

In the third post, I introduced a framework that schools could adopt to take a step towards teaching for the deeper understanding that I wrote about in the second post. The framework is called Teaching for Understand (TfU) and is one that I studied in graduate school. It is built around the following fundamental questions that teachers ask themselves while planning and executing an instructional unit:
  1. What topics are worth understanding? [Generative Topics]
  2. What are the enduring concepts in these topics that need to be understood? [Understanding Goals]
  3. What are the overarching goals that teachers and children want to achieve over the course of the academic year? [Throughlines]
  4. How can teachers help children demonstrate their understanding? [Performances of Understanding]
  5. How can teachers gauge what children understand? [Ongoing Assessment]
In the same post, I went into detail about generative topics by giving concrete examples from different subjects.

In this post, I shall elaborate on understanding goals and throughlines.

Understanding Goals

Teachers' goals are complex and aimed towards satisfying multiple stakeholders (children, parents, school principal etc.) - thus, the TfU framework is likely to be one of several agendas that they are simultaneously focused on. In this light, it is essential that understanding goals be well designed so as to make the planning-teaching-learning-assessment-remediation cycle smooth.

Understanding goals are explicit, actionable statements (not questions) of what children are expected to learn and/or do. These goals define the ideas, processes and relationships that children will grasp through their learning (Wiske, 1998). As an example, take a look at the understanding goals that I wrote for a unit on basic trigonometry.

Understanding goals have to be descriptive and focus on specific concepts within potentially broader topics. This specificity will allow the teacher to scaffold instruction and address breakdowns in conceptual understanding before they can snowball into deep-rooted misconceptions.

This aspect of designing understanding goals to aid scaffolding deserves a deeper exploration. During the learning process, there are two memories in our brain at work - first, a long-term memory where old, familiar knowledge resides and can be called upon when needed; second, a working memory that is trying to process and grapple with new information (Kirschner, Sweller & Clark, 2006).

The working memory has limitations on the amount of load it can handle while learning new concepts and here is where scaffolding comes in. It allows the learner to cognitively process new information in the working memory and then begin to integrate it with existing knowledge in the long-term memory. Scaffolding divides complex tasks by reducing cognitive load through strategies such as having children articulate learning from the sub-tasks, using aids such as the blackboard to emphasise key points and providing children with multiple examples to make learning visible (Hmelo-Silver, Duncan & Chinn, 2007).

To conclude this section, I would like the share the understanding goals that I wrote for my semester project in the course EDU T543 Applying Cognitive Science Research to Learning and Teaching at graduate school. I designed a professional development booklet for first-time online tutors and tried to author it in a way that anyone interested in online tutoring could read the material and understand the elements involved in being a successful online tutor. At the time of working on the project, I had taken over 500 one-to-one sessions as a math online tutor and this helped in combining my experiences with research in structuring the booklet. I divided the fourteen understanding goals into four categories - technology, communication, pedagogy and assessments.

Note how each goal is a descriptive and actionable statement that defines the ideas and elements that the tutor can expect to learn if he/she completes the goal.


The easiest way for a/an teacher/educator to think about throughlines is to ask himself/herself what are the big picture goals that they want to achieve with their learners during their time together - be it in an academic year with students in a school or a week-long training module for adults. Let me illustrate with a few concrete examples.

As a math teacher, one of the throughlines that runs through my instruction is wanting my students to see the logical beauty in mathematics and to systematically approach and break down new problems and concepts through a logical lens. I achieve this through the language that I use while discussing a concept/question; for instance, "Can you see how we were able to logically derive the formula using the basic algebraic identities?" or "Did you notice how all the three methods are different ways of arriving at the same solution?"

In my fourth grade classroom, my co-teacher and I had a lively bunch of 40 children who came from communities where foul language and violence was commonplace. One of the big picture questions that we emphasised throughout the year was "What will I do about it?" The idea behind this was that we wanted our children to not blindly follow the herd and copy the words and actions of others. Our goal was for them to think for themselves and this comes under the ambit of psychological and moral acts that I discussed in this post.

A basketball coach, besides wanting his/her players to improve their skills and the team to work as a more cohesive unit, may want to instill discipline and respect for the game in the players. A driving instructor, besides wanting the new driver to learn how to operate a car, wants him/her drive safely and respect the rules of the road. A history teacher, besides wanting their students to have an understanding of society and past events, may want them to appreciate how a dominant narrative exists in the tales from the past as they are transmitted from generation to generation. All of these are examples of throughlines.

In the next post, I shall discuss the fourth element of the TfU framework that pertains to performances of understanding.


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 Psychologist42(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.

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.

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I read the articles 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. Many of the course examples were drawn from a K-12 context, but the principles apply broadly to life-long learning.