Teaching for Understanding (Part 1 => Generative Topics)

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.

Outline of the framework

The teaching for understanding (TfU) framework describes a cyclical, reflective and non-linear process (Wiske, 1998) that teachers and children engage in with the goal of developing a deeper understanding of concepts. The TfU framework 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]

Each element of the TfU framework invokes the other and adds more nuance to it (Wiske, 1998). For example, a clear articulation of what constitutes good performances of understanding helps both teachers and students clarify understanding goals. 

In this post, I shall explore generative topics in more detail.

Generative Topics

Generative topics are those that are central to a subject or discipline while being accessible and interesting to teachers and children (Wiske, 1998). These topics are connectable to other concepts within and across the discipline and build children's structural knowledge i.e. the way they organise and make meaning of links between concepts in their long term memory (Grotzer, 2002).

One key feature of generative topics is that they include bottleneck concepts - concepts that are fundamental to understanding higher concepts in the discipline. For example:

• children comprehending the need for variables and knowing what they can represent is foundational to algebra;
• children understanding the role that perspective plays in deciding how a story is presented in history is essential to making sense of any historical event;
• children grasping the idea of matter in chemistry and the work of different scientists in building that bank of knowledge is key to them appreciating any chemical reaction;
• children learning the strategies of making inferences in English so that they can analyse any poem or text.

T. Grotzer (classroom discussion, February 2, 2018) emphasised that generative topics should pique both the teacher's and child's interests. In some cases, these topics can be centred around an intentional tension where a child's existing knowledge is insufficient to tackle a new problem/situation which, in turn, prompts him/her to want to learn (Strike & Posner, 1985). For instance, taking 5 from 3 requires children to move beyond their existing knowledge of whole numbers into the world of negative numbers.

Inviting children to explore implications of what they are learning can further engage them. For example, instead of simply asking "what causes day and night?", how about have children ponder the following...?

Or, instead of asking "what base number system do we commonly use?", how about asking "what will change if we change the base of our number system?" or "why is zero important?"

Or, instead of ordering children to follow the school rules, how about asking them "how would our school be different if we didn't have rules?"

Or, instead of "what does a cartographer do?", ask them "how does a cartographer's choice impact our view of the world?" along with showing them these images...

Image source: https://i0.wp.com/geoawesomeness.com/wp-content/uploads/2017/04/Map-projections-net-comparison-1.png?resize=640%2C328&ssl=1

I would like to outline some tips that I learned at graduate school about framing generative topics. Take a look at the infographic below that uses the map example. One or more of these questions can be used as the basis for exploration.

Clearly, it is important to frame the topic in a manner that asks probing questions of the learner to draw him/her into the topic.

I would like to end by touching upon a facet of generative topics that is subtle yet vital - culture.

Culture tends to be subjected to harsh stereotypes with those different from the majority (or perceived 'normal') viewed as deficient (Nasir et al., 2006). Thus, a teacher should be conscious of potential biases that may unknowingly creep in and carefully frame generative topics contextualised to his/her class while accounting for the diversity in the classroom - be it economic, ethnic, religious or social. The existing knowledge that children bring from out-of-school settings should be leveraged wherever possible. For instance:

• a unit on decimals and percentages can be learned through family budgeting;
• a unit on weather could be connected to their own observations about the weather in their town;
• a unit on historical artifacts could start by asking children to consider objects in their family that have been passed down from generation to generation;
• a unit on proportions can be learned through recipes and cooking;
• a unit on compound and mixtures in chemistry can be linked to ingredients in common household foods;
• a unit on careers can have one parent come into the classroom each week to talk about their jobs and how they got into their field of work.

Linking concepts in this way can create a more relatable and emotional experience for the child that is tied to their lives; after all, learning is more than simply memorising facts associated with a body of knowledge...

In the next post, I will write about the second and third points of the framework viz. understanding goals and throughlines.

References

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

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.

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.

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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.