Generalization-Designing Your Lessons for Conceptual Understanding (Part 3)

This post is the third of our blog post series on how to design lessons for conceptual understanding.

Part 1 here

Part 2 here

Strategy 3 : Generalizations

You may have come across Lynn Erickson's diagram on the structure of knowledge.

In my IB workshop's I always like to present the avocado model alongside this diagram when I am talking about facts.

The intention of inquiry-based teaching and conceptually-driven understanding (or Concept-based inquiry- whatever terminology suits your fancy)  is to enable students to make generalizations. In other words, can they transfer their learning to a new context because they have understood what they learnt. 

In order to make generalizations, we need to first plan lessons that help students acquire facts/topics that are interesting  and worth knowing. Bringing in local and global issues that are relevant to the topic help students as they begin to compare the topics and see emerging patterns.

Remember, facts and concepts have a synergistic relationship that help students make the generalizations.

(Hence the argument from some PYP teachers who prefer not to reveal the central idea to students at the beginning of the unit.) You want students to be able to make that generalization which, by the way, is the central idea.

If you use this method (facts- important to know/ a few rich and relevant case studies chosen from local and global environment) in other disciplines, you will help students make generalizations.

Let's see this in a Math classroom.

Present the students with problems that ask the students to find the areas of triangles and rectangles/squares.

Ask them, "What do you notice about the answers?"

We often tell students that the area of a rectangle is L x W and that of a triangle is 1/2  of  L x W. We then give them a worksheet to complete. A student may get everything correct, but did they understand the "why' of the formula?

If, on the other hand,  you allow the students to discover, through inquiry,  by posing the question "What to do notice?" you invite students to make a generalization. Through discovery, the students are able to notice the relationship between a triangle and a rectangle. The  teacher  now has the perfect opportunity  to show consolidate their understanding through a demonstration. These types of lessons make learning stick. Just make sure you refresh their memory with a 5 minute review from time to time throughout the year.

Fold the paper in half to make 2 triangles.

Once you get used to teaching for generalization, you will notice other shapes and look for relationships between them. 

Can you come up with an explanation for the formula of an area of a trapezoid which is 1/2 x h (a+ b)?

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I had so much fun doing this the first time. I'm sure your students will enjoy making sense of the formula. The formula is the generalization.

Language

If you go through your scope and sequence, they are replete with generalizations neatly nestled in the standards/learning outcomes that include subject specific concepts. (micro concepts)

You pick one or two concepts. Determine the success criteria and then go through the process we already discussed. 

What facts and topics will help your students make a generalization?

In order to see how this looks like in a Language-focused classroom,  I've identified a learning outcome from the Ontario Grade 3 Language scope and sequence:

Analyzing Text: C3.3 - analyze various texts, including literary and informational texts, by identifying main and supporting ideas...

• concept 1 (skill-based concept)- analyze
• concept 2- main idea
• concept 3-supporting idea

One way I encourage students to make generalizations is to encourage them to come up with a theme (main idea) of a novel we are reading in class. While reading  "Because of Winn Dixie", for instance, my students used whiteboards to write down the theme of the book as we read a few chapters. For instance, the theme (Yes, you got it! It is a synonym for 'generalization') of the book is :  

Pets helps us deal with loneliness. 

Next, the students gave me evidence from the book as to why they feel this is a theme (concept -analyze). As we continued to read the book, they came across characters that did not like pets. They proceeded to refine their generalization by rewriting the theme on their whiteboards. The fact that they could easily erase their writing, helped some of my students deal with anxiety should their theme be 'wrong'. The teacher's role here would be to ask the students to give evidence and constantly question (analyze) their themes to see if they are always true.

Pets help some people deal with loneliness. 

The clarifier in the form of an adjective 'some' helped my students create a more appropriate generalization. As we continued to read the book, they started coming up with other themes.

So when we moved on to Peter Brown's The Wild Robot, my students were very familiar with finding the main idea - in this case we focused on the theme of the book  - and readily supported our burgeoning theories with evidence from the text. This task of generalization helped my students transfer their learning to a new context.

If you have any great tool to develop this strategy, please do drop in a comment!

-Naini Singh

Research sources:

• Erikson, H. L. (2012). Concept-based teaching and learning. International Baccalaureate Organization.
• Taba, H. (1966). Teaching strategies and cognitive functioning in elementary school children. San Francisco State College.