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Representation-Design Your Lessons for Conceptual Understanding (Part 2)

 

Strategy 2 - Representation




    Source: ibo.org

In this post, I will flesh out yet another research based strategy - Representation.  
Check out my first post of this series here:  Part 1

Think of a concept, an idea. How many different ways can you represent it?

First of all, before you can expect your students to show their understanding in different ways, don't forget to model it.
For example, as you teach students the concept of subtraction, show them a variety of ways to get to the answer.

Math
Let us take 600 - 148 for instance.


One way to solve this would be:



Another representation would be to draw using place value blocks.



And then of course, there is the basic algorithm which is great for students who have a good conceptual understanding of the concept of  "subtraction."
It is a quick and efficient method to get to the answer.

    600
-  148
    ______


I understand the importance many teachers place on this last method, yet I have found, as I confer with my students, that this method does not necessarily reflect conceptual understanding of subtraction. They go through the motions on borrowing over and over again. It is messy.  You may even notice misconceptions-which, now, is valuable data. 



There is another way to represent the subtraction problem but this time, you invite students to become more number fluent. 



  599  (600-1)  - 148  =  151   (+1) 
                                                                        
                                                                            

This becomes so much more easy to solve! The students are developing number fluency as they play around with numbers in order to make a problem more manageable. 


Social Studies

In the middle of a unit of study, identify a few related concepts that you have introduced to your students

traders, environment, indigenous people,  survival

Print these words onto hexagons and ask students to represent their understanding in any way they like.
The great thing about this task is that it is open-ended and allows for different representations. Students have to explain why they connected one hexagon to another. It allows them to appreciate and value the many ways of talking about a unit of study using concepts. I also love the fact that each hexagons allows the students to make 6 different connections with a concept if required.

As an IB practitioner, this is where you step in. Question each group about their connections. Ask them to give reasons. Allow groups to discuss their representations with one another. In some of my school visits, I have come across some of these hexagons on the walls. They do look pretty but  on closer inspection, I have noticed many connections that do not make sense. They seem to have gone unnoticed.


I use the Pam Hook's webiste to generate hexagons.  I type in the concepts I want and then print them out.
You can differentiate this task by reducing the number of hexagons, focusing on the few key ideas you want your students to flesh out.

It is usually easy to use this strategy in Math.  How can we represent concepts in other disciplines?

Science/Ecosystems

You want to see how well your students have understood the concept of "interaction".

Or

Language/Biography
You are teaching your students all about role models and you want them  show you what they have understood by the word "hurdle". 

A way of representing these concept would be through use of loose parts. In my workshops, whenever I ask my participants (adults) to use everyday objects (fabric, sticks, leaves, bottle tops, buttons, wire) to show their understanding of a concept, they absolutely love the challenge. This task is a lot of fun as it not only challenges your thinking, it is also very tactile in nature. Touching different objects and thinking of their purpose in different ways seldom fails to hook the student. The theory of loose parts stems from architect Simon Nicholson (1971) who wrote about the benefits of a loose parts environment to child development.  He identifies loose parts as “all the things that satisfy ones curiosity and give us the pleasure that results from discovery and invention.” Of course, in this case, we are tweaking it slightly to use it as an assessment to see how the students use the loose parts and connect them to a concept through their representation.


Using visible thinking routines are also a great way to show learning in various ways:

Chalk Talk

Colour Symbol Image





There are so many other methods of representation, and I barely scratched the surface. However, I hope it got you thinking of how you can utilize this strategy in your classroom.



- Naini Singh

Research sources:

Kilpatrick et. al. (2001) Pearson et al. (2015) Dijkstra et al. (2019)

PZ’s Thinking Routines Toolbox | Project Zero. (n.d.). https://pz.harvard.edu/thinking-routines

Simon Nicholson  (1971) https://media.kaboom.org/docs/documents/pdf/ip/Imagination-Playground-Theory-of-Loose-Parts-Simon-Nicholson.pdf

PZ’s Thinkin

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