Chapter Six Venn Diagrams as an Instructional Tactic by sdfsb346f


									Chapter Eight: Venn Diagrams as Instructional Tactics

Key Questions: Does student thinking improve when they integrate Venn Diagrams into
other graphic organizers? Can you find one study that proves you’re right or wrong?

In this chapter the practical application of Venn Diagrams is explored through first describing
the structure of Venn Diagrams and then why to employ them. That is followed by a brief
history of how they evolved. From there, examples of Venn Diagrams are provided which
students in elementary and secondary classrooms completed. Some of the examples will
illustrate how Venn Diagrams have been merged with other graphic organizers. Note that the
examples get somewhat more complex as you move through the chapter. Sample lessons are
also provided after the examples to illustrate how Venn Diagrams weave into the process of a
lesson or unit of study. At the end of the chapter research findings or suggestions for research
are provided.

Venn Diagrams

   Venn Diagrams involve circles or ellipses constructed to form the following positions.

   a. no overlap                      b. two overlapping            c. three overlapping

   d four overlapping                        e. circles inside each other

   The structure of Venn Diagrams usually involves the placing of circles or ellipses in
   various configurations to illustrate the relationship or lack of relationship between two to
   four concepts. That said, some students use other geometric shapes. Venn Diagrams
   involve a minimal use of words so are efficient in terms of succinctly illustrating
   relationships. ESL students find them useful to show their thinking, as they do not have to
   use sentences.
Venn Diagrams: Their Application in Education

Below are examples of learning outcomes that would connect to the use of Venn Diagrams to
demonstrate student learning.

Grade Three: Urban and Rural Communities – compare transportation in urban and rural

Grade Six: First Nation Peoples – compare key social and cultural characteristics of Algonquian
and Iroquoian groups (e.g., language, agriculture and hunting; governance, matriarchal,
patriarchal societies; arts; storytelling, trade; etc.)
Venn Diagrams: A Brief History of Their Application in Education
Gideon Chamel, a student in one of my graduate students took the time to inquire into the history
of Venn Diagrams. What follows is a summary of what he found. In 1274, the earliest known
attempt to employ geometrical diagrams for the purpose of discovering mathematical truths was
accomplished by a person by the name of Lull. In one of his drawings he employed four
overlapping circles individually representing the ideas of ‘essence’, ‘truth’, ‘unity’, and
‘goodness’. The overlapping illustrating how these concepts existed within one another. Lull’s
work influenced others in the 16th Century such as Leibniz who used them to clarify the
imperfections in Aristotle’s work. George Boole employed them in the early 1800’s and pushed
their use into the area of algebra. Today, Boolean Algebra forms the basis upon which modern
computers function. In 1880 John Venn built on Boole’s work and pushed the application of
two, three, and four circles overlapping to illustrate the multiple combinations of classes. The
diagrams now bear his name.

Venn Diagrams: Examples
Getting Students Started
As stated previously, Venn Diagrams push the analysis level of thinking. Analysis, at the simplest
level may involve identifying and being able to explain in your own words how two or more things are
alike and different. The more deeply you understand the essence of something, the more detailed the
analysis. That implies that Venn Diagrams completed by students are only as powerful as their depth
of understanding. Venn Diagrams on their own simply provide the invitation; the students have to
provide the grist. If the teacher has not engaged students in inquiring deeply into the issues or
concepts being analyzed, then the Venn Diagrams will not be that academically powerful.

How do we get students involved in ‘analysis?’ One of the best approaches is to employ Bruner’s
process known as Concept Attainment (showing Yes and No examples of a concept). Given this is
how our parents taught all of us to understand concepts when we were little kids, it would seem that
this process would be a wise place to start. For more information on Concept Attainment, see pages
in this book and read Chapter Eight in Beyond Monet: The Artful Science of Instructional Integration
(Bennett & Rolheiser, 2001);

How did your mother or father assist you to grasp the idea of ‘hot?’ My guess is that they said the
word ‘hot’ before or after you felt or tasted something hot. You put those instances together and
‘induced’ or ‘concluded’ what the word ‘hot’ implied. The same happened with ‘cold.’ Think of how
you learned the difference between a car and truck. Below you see a data set illustrating the difference
between ‘ridicule’ and ‘sarcasm.’ Two concepts or terms we apply but don’t really understand in
terms of how they are the same and how they are different. One key component cannot be determined
with just the use of words. What is it?

Side A: Ridicule                                     Side B: Sarcasm

a. You’re such a jerk!                           a. You’ll win a prize in that outfit!
b. You look ridiculous in that outfit.           b. Who cut your hair?
c. There is stupid and then there is stupid.     c. Great answer Einstein.
d. You have the mind of an ant!                  d. I can see that exercising has really helped.
e. Hey, four eyes.                               e. So who taught you to dance? Fred Astaire?
f. Dumbo, you fail the exam again!               f. Wish I had your brains.

Testers: Where would these fit? Do any fit in between?
1. Don’t put your mouth near a magnet.
2. When they gave out brains, you thought they said trains and you’re a million miles away.
3. With friends like you, who needs enemies.
4. How long have you been like this?
5. No such thing as a wrong answer; but if there was, that would be it.
6. I can tell Michael Jordan will be seeking you out.

What Venn Diagram best illustrates their relationship? (Draw the three types)
Starting Primary Kids with Venn Diagrams

Below is an example from a Grade One classroom.

This diagram shows how one teacher introduced her students to the process of Venn
Diagrams. The students first read the story Strega Nona Meets Her Match. They then
identified what they knew about the two witches. The teacher then typed their answers,
cut them up into strips and then the students pasted where they thought each idea fit.
The picture of the witches helped the students decide where they fit.

Below is how this is slowly adapted to Venn Diagrams. Note: the use of the diagrams
to assist students to remember.
Starting with Primary Students continued…

Using Hula Hoops

Most primary teachers employ Hula Hoops to assist students with classifying their ideas. One teacher
employed Hula Hoops (placed beside each other but not touching) to complete a Concept Attainment
data set to introduce her grade one students to the concepts of Plastic and Metal. She placed items of
each in two respective Hula Hoops. Once most students had an idea, she gave each one an object.
They had to decide whether it fit into the Red or the Blue hoop. Students took turns coming up and
placing their object in one of the two hoops. One boy had a pair of scissors; a girl a ball that wa s half
plastic and half metal. The hoops were placed so that they were close together but not overlapping.
When it was this boy’s turn, he came up and looked for about 30 seconds, he then placed the scissors
so that the metal part was laying on one hoop and the plastic on the other hoop. The girl took about
the same amount of time; the hoops were not close enough for her to place the ball on both
simultaneously. Finally, she reached down, lifted on Hula Hoop over the other, like in the diagram
below, and placed the ball in the middle. This was her first experience with Venn Diagrams; so, in
one way, she invented that configuration.

The important point here is to make sure all students can explain why each item belongs in each hoop.

Using Ropes Joined to Form a Circle

This teacher used these in the gym to take more of a bodily kinesthetic approach to Venn Diagrams.
That said, the ‘ropes’ can be employed in the room if you have enough space. Students were given
objects and they had to come and stand in one of the two hoops based on the criteria for each hoop.
She then used three ‘ropes’ to have them compare and contrast objects. The picture below illustrates
what was done.
Beginning Venn Diagrams in Kindergarten: A Lesson in a Classroom in Western Australia

This is a lesson I taught at Coolingup Primary School in Western Australia. The students had been
studying farm animals and zoo animals. They had also studied where zoo animals lived. The teacher
asked me to complete a lesson that would introduce students to Venn Diagrams in order to explore
how zoo animals and farm animals are the same. Below is an example of one of the Venn Diagrams.

Mental Set/Input/Modeling: Think to yourself please. What animals would I see if I visited a zoo?
(Note: the students have done extensive work in this area and had all visited the zoo in Perth.). Find a
partner and do a Think Pair Share. (These students were very skilled at doing Think Pair Share and
immediately found a partner and sat facing that partner with knees touching.)

I then randomly called on them to share and recorded their ideas (printed word with a drawing of the
animal) on a large Venn Diagram constructed on a white board. Each circle was a different colour. I
placed their ideas into one of the circles and had them read the words (they followed the line from the
word to the picture). (It was a bit embarrassing not being able to spell some of the names;
orangoutang or orangeatang or however you spell it proved particularly tough – applying my
knowledge of phonetics was of little use.)

Input/Modelling Continued: Now think of animals you would find on a farm. (The students had also
visited a farm.) I repeated the Think Pair Share and collected their ideas and put them in the other

Input/Check for Understanding: I then told them that the next part would be the hardest. They were
going to have to tell me how zoo animals and farm animals are the same. As a check for
understanding, I first had them tell me how trucks and cars are the same. They said they had doors
and wheels etc. I then went back and had them do a Think Pair Share on farm and zoo animals and
how they were the same. I then randomly called on them to share and I drew the idea and printed it in
the overlapping part of the Venn Diagram.

Practice/Modeling (applying the Venn Diagram): The teacher had created large Venn Diagrams on
white paper and the students now went back to their tables and with a partner, completed the Venn
Diagram. One person did farm animals; the other zoo animals. One group had three so the third
person did what they had in common. As they worked I held up their work to show others.

Given they finished at different rates, when they were finished, they moved into their centre work and
this ended my part of the lesson. Below is an example of one of the students Venn Diagrams. You can
see more on the Web page.

Directions for Completing a Venn Diagram in a Place Mat*

Academic Task: Students, in small cooperative groups, will compare and contrast
rational and irrational numbers employing Place Mat, Lettered Heads*, Between Group
Share*, the Johnsons’ 5 Basic Elements* and a Venn Diagram.

Collaborative Task: Equal Voice

      1. Students are placed in groups of 3 or 4
      2. Students letter off A, B, C, and D (Lettered Heads)
      3. Student C comes and gets a piece of paper for the Place Mat
      4. Each student takes out a pen or pencil
      5. Student A draws the Place Mat
      6. Complete a T-Chart on the social skill of Equal Voice
      7. Each student constructs the Venn Diagram
      8. Each student then fills in their Venn Diagram
      9. When finished, they rotate to check to see each others ideas
      10.They now complete a group Venn Diagram in the Middle (person B draws)
         Note that one person will be randomly selected from each group to share with
         another group. Make sure you are all ready to share.
      11. Now do a Between Group Share*
      12. Each group processes how well they functioned as a group in terms of the
         social skill of ‘equal voice.’

Sample of what the Venn Diagram looks like at the end of this activity.
Venn Diagrams Merged with Other Graphic Organizers

Below is an example of two Fish Bones integrated within a Venn Diagram. In this
grade 7 class, the students were discussing the protagonist and the antagonist and
their respective characteristics. In the middle of the Venn Diagram, the students
compare the characteristics of the protagonist and the antagonist.

How could you apply this to explore the Regions of Canada, Types of
Government, Types of Energy, Myths and Legends? Could you overlap three

Insert the student example

On the following page is a blank form.
Venn Diagrams Employed ‘IN’ and ‘AS’ Place Mats
Venn Diagram: Sample Lessons

Grade: Six Social Studies
Topic: Global Responsibility

Background information: the students had previously inquired into rights and responsibilities,
as well as, needs and wants.

Mental Set: Review of previous learning. The students were asked to think back on what is
meant by needs and wants. They were then asked to do a Think Pair Share. Four students were
selected to respond to share and give examples of wants and needs.

Input: the students were told that they were going to explore two ideas that connect to what they
had been studying about wants and needs with a specific focus on responsibilities. The teacher
then employed Bruner’s Concept Attainment Strategy.

Concept Attainment
Phase One - Focus Statement: I am going to put ideas on the left side (Side A) and on the right
side (Side B). They both have something to do with responsibility; however, the ideas on the
right are different from the ideas on the left. (Note: the data set is on the opposite page.)

Phase Two – Sharing their Hypotheses: After reading the examples on the board and the
newspaper clippings, the students discussed with their partners what they think each side had in
common. These were written on the board. They then shared the journey their minds went on as
they explored the examples. Following that they created their Venn Diagrams.

Phase Three – Application/Making Connections: The students were asked to decide who was
more globally responsible in these two situations.

Situation A: A man and women who have 100 000 dollars in the bank write a check for 1000
dollars and give it to the Red Cross.

Situation B: A boy and girl spend all day Saturday cutting lawns and they gave all the money
(32 dollars) to the Red Cross.

They then had to individually and privately score themselves on a scale of 1 to 10; one meaning
taking no responsibility and 10 meaning taking extensive responsibility. They then discussed if
one could be globally responsible if they did not feel a sense of loss regarding what they had to
give -- in terms of time or material possessions or money etc. Las they took the two situations
above and decided which situation had the potential to have the biggest effect; they then
discussed global responsibility and global impact.
Data Set: Global versus Local Responsibility

Side A                                                 Side B
Students raised money to send to the         Students raised money to help build
Red Cross to help the people in Sri          a playground in their community
Lanka.                                       park.
A girl in Prince Edward Island saved         The boy scouts had a bottle drive to
her allowance for three weeks and            help fund a clean-up program in a
gave it to World Vision to help the          local creek.
kids in Indonesia who lost their
homes and families to the Tsunamis.
The local Chinese community in               City council has donated one-million
Toronto had a clothing drive to              dollars towards building a shelter for
collect clothing to send to the              the homeless.
earthquake victims in China.

Now the teacher shared Newspaper Clippings for each side – three for each side. An
example of each is provided below.

Students were then asked to think what they had in common and to then share with their
partner. Their ideas were collected on the board. The sides were then labeled (this came
out in their sharing) Global Responsibility and Local Responsibility. They then
completed a Venn Diagram comparing and contrasting the two. The Venn Diagram is on
the following page.
Venn Diagram Rubric

Criteria           Level One          Level Two           Level Three        Level Four
applying the       does not select    selects the         selects the        selects the
different          the correct        correct config.,    correct config.,   correct config.,
configurations     configuration      but does not        and for the most   and accurately
                   and struggles      accurately apply    part accurately    applies it
                   to apply it        it                  applies it

selecting and     insufficient        some of the key     most of the key    all of the key
accurately        number of ideas     ideas selected      ideas selected     ideas selected
applying the      selected
correct number of
placing the idea   few if any of      some of             most of            all of those
precisely          those selected     those selected      those selected     selected are
                   are accurately     are accurately      are accurately     accurately
                   placed             placed              placed             placed
integrating with   does not           thinking about      starting to        thoughtfully
other graphic      integrate other    integrating other   integrate other    integrates other
organizers when    graphic org.       graphic org.        graphic org.       graphic org.,
appropriate        when integrating   needs assistance    may need a         when
                   them is possible   thinking through    bit of coaching    appropriate
                                      how this could
                                      be done
Venn Diagrams: Research Findings/Suggestions

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