This differentiation technique is called “Concentric Circles”. You use it to move students up and down the ladder of abstraction, applying a single idea in multiple contexts.

# Differentiation TechniqueThe Spectrum Of Abstraction

## Read The OverviewMoving Between the Specific and Abstract

When differentiating, it's helpful to note where on the "spectrum of abstraction" your content lies. Then, see what happens when you move that content to be more abstract or more specific. It often unlocks lots of new opportunities for thinking.

## Specific Examples of “The Spectrum Of Abstraction”

## Analyzing Prefixes and Suffixes

Instead of just memorizing what a bunch of morphemes mean, we’re looking broadly, exploring patterns, finding unexpected similarities and weird differences.

## Use Universal Themes to Make Fractions Interesting

What if we used a universal theme to guide our study of fractions? These *very* big ideas get students thinking about fractions in a new way.

## Combining Depth and Complexity Prompts into a Generalization

Let’s start with a puzzlement, ask kids to generate an abstract statement, and then find evidence that their statement works across several different areas.

## Concept Formation: A Model for Inductive Thinking

Here’s are the steps for running an inductive lesson based on Hilda Taba’s model of Concept Formation. Plus a sample lesson about the Nile River.

## The Surprises Within a Triangle’s Angles

Discovering what is interesting and unexpected about a triangle’s angles. What twists have I unintentionally spoiled for my students over the years?

## Encourage Curiosity With Calculators

It’s easy to fall in love with chasing the newest technology to use in the classroom. But sometimes, the perfect tool is a plain old calculator. We’ll be using this tool to develop curiosity about math.

## Creating A Class Motto

Using Hilda Taba’s model of inductive thinking, use your students’ prior knowledge to develop a statement about expected class behavior.

## Inductive Thinking in Spelling and Vocabulary

Let’s look at a couple ways to bring inductive thinking into word studies. We’ll examine simple plural rules all the way up to etymology of foreign words in English.

## Math Game: The Game of 100

The Game of 100 is a simple game requiring no supplies, yet it opens up a rich world of exploring strategy and a little mental math.

## Differentiate Math with Inductive Learning

With inductive learning, we still define terms, explain rules, and practice, but the order is different. We’re harnessing gifted students’ natural abilities to enhance our lessons.

## Climbing Bloom’s Taxonomy In Science

Science should be more than memorizing facts. Let’s spice it up and push our students from the doldrums of remembering to the soaring heights of evaluation. While it’s true that this will take longer than just following a textbook, we’re not just teaching facts, we’re equipping students with the ability to make well-informed judgements.

## Coats of Arms, Seals, and Other Heraldry

Symbolic seals, crests, and coats of arms are a common concept across cultures. From the simplicity of Japanese mon to the regality of English coats of arms all the way to America’s Great Seal, humans around the world create graphical representations of themselves.

## Multiple Perspectives: Right And Wrong At The Same Time?

It’s essential to teach our students to think flexibly and consider multiple points of view. Flexible thinking leads to product innovation, diplomacy between nations, and advances in science. School, however, often encourages students to settle into a “one right answer” mindset.

## Inductively Evaluate Website Reliability

Last time, we discussed a few ways to help students search Google. Google helps us find related websites, however its ranking system does not necessarily return the most reliable pages. The final step requires our human mind to make difficult decisions that computers can only approximate. Simply choosing the top result is not enough. We must teach our students to *evaluate* websites.

## Analyzing Suffixes Inductively

The year opens with a vocabulary skill analyzing “Suffixes: -ful, -less, -ly.” I adjusted this lesson to examine how these suffixes change the part of speech of words, rather than the meaning.

## An Inductive Exploration of Linear Graphs

Let’s play with linear graphing! First, don’t set this up as a direct instruction lesson. That wouldn’t be playing. Instead, capitalize on your students’ ability to think inductively and recognize patterns. Set up a situation where they can construct their own meaning.

## Exploring Circumference With Famous Circles

Remembering the formulae for area and circumference of a circle is often a challenge for students due to their surface similarities as well as the additional confusion of radius and diameter. I like to tackle them one at a time and give students a chance to explore the origin of each formula. Let’s look at circumference today by utilizing some famous circles from around the world… and beyond!

## All About Character Archetypes

Another example of “structure that increases creativity” is character archetypes. An archetype, according to Wikipedia, is “an original model of a person, ideal example, or a prototype upon which others are copied, patterned, or emulated.” Let’s use an inductive lesson to teach our students about these literary tools.

## Patterns In Writing I: Introduction

Take a break from teaching the details of writing and examine narrative writing from a larger perspective. How can structure increase creativity in writing? Take your gifted writers on a journey through common patterns in narrative writing.

## The Original Puzzlement: A Zoetrope

As teachers, I spend a ton of time searching for inspiration to enliven my lessons. But sometimes, inspiration hits as soon as you leave the desk and books behind. Friday my wife and I took a trip to Disneyland and saw this unbelievable (literally, it seems like magic) intersection of art & technology.

## Concept Attainment: A Model for Inductive Thinking

The first grammar lesson in our reading program is titled “types of sentences.” Nothing excites gifted 11 year olds less than watching me explain the difference between interrogative and declarative sentences. This year, rather than teach the lesson using direct instruction, I used another model of instruction: concept attainment.

## Introducing Universal Themes and Generalizations

Generalizations, big ideas, abstractions, universal themes… they are designed to help our gifted students learn. However, what I didn’t realize was that they would help me teach!

## Movie Previews and Poems’ Tones

In California, both Third and Sixth grade teachers are required to teach students to recognize elements that contribute to the tone of a written piece. I struggled with this abstract concept before landing on an engaging tool to help express the meaning of tone: movie previews.

## Building Confidence in Speaking Skills

When preparing your students for standardized tests, those little standards labeled Speaking And Listening can easily slip by the wayside. And yet, is there any skill more important in landing a job, surviving social engagements, or being a successful leader than confident oral language skills? Teach your students to analyze great speeches to become better public speakers themselves.