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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 Structure 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 Purpose 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 communities. 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 circle. 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. ADD IN SAMPLE OF VENN DIAGRAM GET CORRECT SPELLING OF ROBS SCHOOL. 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 Directions: 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 circles? 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 ideas 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