Optical Illusions in Mathematics and Reading Kenton Middle School 7th Grade Study Skills Amanda Ritzler ritzlera@kentoncityschools.org Co-Presenters today: Jenifer Stauffer - Elementary Educator Robin Hughes -KMS Technology Teacher Goals for this presentation today… 1. Build interest about optical illusions. 2. Show how illusions relate to math and reading. 3. Create an atmosphere where each child can learn at his or her own pace and ability. 4. Differentiate instruction using 21st technology. 5. Give teachers the standards used to combine reading and math (Content Skills) in order to create a well rounded educational experience. 6. Have FUN with your students. Building interest and addressing the Student Goals Have students research on the internet how math relates to our everyday lives through studying optical illusions. Ask the students how perception can change the way we can see objects? When we see an illusion, is it math related? Does the brain use prior knowledge and information when perceiving pictures? Technology ideas that can be used for this project… 1. Google Docs 2. PowerPoint 3. Blogging/Moodle/Social Networking 4. E-mail 5. Inspiration 6. Movie 7. Animation techniques January 8, 2007 By:Alysha Coulson Does this image appear to be an impossible Triangle? Penrose Impossible Triangle This triangle appears to be impossible, But it isn’t because a man made this illusion to make it appear to look impossible to trick your mind and eyesight. This image was made out of paper. He connected the sides in 3-D form to make it an illusion. •Can you feel the "motion" of the image?…… •There is an exact number of squares, but while your trying to count them your eyes and brain are trying to work together to read the image. • Your eyesight gets blurry so you can’t count the exact number of squares! Look carefully at any of the white dots in the grid below. How many black or grey dots can you see elsewhere in the grid.? Look again! •You can’t see any black or grey dots. •You’re seeing things in the illusion because there is so much black in it and only a little white. •This makes your eyes see it blend together when you are focusing on the illusion. •The blending is making you see grey from where the black and white blend together. This one will make you dizzy. Try focusing on just the center circle while moving your head. Did it work? This illusion should have made you dizzy from focusing on the center of the object while the other part of the object is appearing to go around the other way as you turn your head. Are the cubes moving backward and forward? No, nothing in this illusion is moving. But the cubes are getting smaller, as it appears the cubes are moving in and out of the object. The cubes were made to look like they are moving so the ones around the outside of the page are larger and as they get closer to the middle they are reducing! Stare at the four black dots in the center of the image for 30 - 60 seconds. Then quickly close your eyes and look at something bright (like a lamp or a window with sunlight coming through it). You should see a white circle with an image inside it. ADVANCE ARE THE SPIRALS ROTATING? These spirals should appear to move! As you look at the spirals, they will appear to move. This is called "illusory movement" and the same technique has been explored. Move your head close to the screen. Do the perfect blue cubes appear to be distorted? Absolutely... this is due to the black figurations in the back moving and twisting it in your mind. But they are really perfectly cubed. What an eye trick! Terms… Image-An optical counterpart or appearance of an object, as is produced by reflection from a mirror, refraction by a lens, or the passage of luminous rays through a small aperture and their reception on a surface. Grid-A network of horizontal and perpendicular lines, uniformly spaced, for locating points on a map, chart, or aerial photograph by means of a system of coordinates. Object-Anything that is visible or tangible and is relatively stable in form. Inspiration From the Inspiration website: “Inspiration's integrated diagramming and outlining environments work together to help students comprehend concepts and information. Educators use Inspiration to customize instruction, achieve standards, assess student progress and energize learning.” Inspiration Visual Thinking and Learning Learning to think. Learning to learn. These are the essential skills for student success in every curriculum area and academic pursuit. Visual Learning Techniques Data Literacy Suggested Reading About Visual Thinking and Learning Visual thinking and learning utilize graphical ways of working with ideas and presenting information. Research in both educational theory and cognitive psychology tells us that visual learning is among the very best methods for teaching students of all ages how to think and how to learn. Inspiration Concept Map OPTICAL ILLUSIONS (Visual Phenomena) -Hyper Links -Direct students The Body Fun Pictures and Puzzles - Everyone has the same resources -independent learning Mathematical Concepts and Optical Illusion Vocabulary Artistic Illusions Anim ate d proof of Pythagore an Therom Try this Be ginne r activity be low Vision Basic Patterning W hy do we se e illusions? Ge ome try --differentiated work Te sse lation Activity Spatial Ability Through Inte ractive Image ry How do e yes form image s? Diagram of the Brain Color Visual learning helps students: * Make abstract ideas visible and concrete * Connect prior knowledge and new concepts * Provide structure for thinking, writing, discussing, analyzing, planning and reporting * Focus thoughts and ideas, leading to understanding and interpretation. What do your students know about optical illusions? Discuss with the class the basics of optical illusions in Mathematics and their background knowledge. Have students write down some questions that they would like answered about optical illusions at the end of this project. Share past projects and books on optical illusions to build interest and give concrete examples on how they relate to Mathematics. Research Questions The students can use these questions as to guide them in their RESEARCH efforts. They are open ended and can have many different answers. I provide a folder with sites, topics and resources in my shared folder. If you do not have a shared folder; then an email can be sent to your students with the links attached. 7th grade minds at work…. STUDENT CHECKLIST 1-2 days to explore and bookmark sites Complete the research/question packet Write a 1-2 page paper Draw diagrams of the eye, brain and correlations (use mathematical terms such a reflection,angles, distance… etc.) Explain to the class how your brain and eyes work together to see an illusion. (Do they really work together? Or… Do they play tricks on each other?) Create a final presentation (Googles Doc,Power point, movie or Inspiration) to present to the Class. It will be used to learn Mathematical terms and concepts) Requirements for optical illusion project Choose from the following kinds of presentations: Googles Doc PowerPoint Presentation Movie Inspiration Concept Map List and define 5 to10 Mathematical terms used within your project. FINAL PRESENTATION Title page with your name and date At least 5 or more Optical Illusions At least 5 or more summaries of the above illusions. (What should we see?) Highlighted math terms and definitions Creative style and personality Informational ( summaries, descriptions…) Connecting Mathematics with Reading Oral Presentation Students use the computer, TV and/or the Smart Board to present their projects to the class. The students are engaged and interacting with the student presenter… The class takes notes and records on their own new vocabulary they have learned. Rotate-To cause to turn around an axis or center point; revolve. Figure-Form or shape, as determined by outlines or exterior surfaces: to be round, square, or cubical in figure. Figuration-The resulting figure or shape. Cube-A solid bounded by six equal squares, the angle between any two adjacent faces being a right angle. Spirals-A three-dimensional curve that turns around an axis at a constant or continuously varying distance while moving parallel to the axis. Reducing-To bring down to a smaller extent, size, amount, number, etc. 3-Dimensional-Involving or relating to three dimensions or aspects; giving the illusion of depth; "lifelike three-dimensional characters." QuickTime™ and a decompressor are needed to see this picture. ttfn…rofl…ttyl…r u jk ?…g2g…brb… ta ta for now…rolling on the floor laughing…talk to you later… got to go…be right back…Are you just kidding? QuickTime™ and a decompressor are needed to see this picture. VOCABULARY WALL Just to name a few…. Ambiguous rotate perceive Movement pattern transform Symmetry arch intercept Distorted net parallel Bisector angles transparent Flip tile ascend Conform similar shadow Tessellations Preparation for you before we go over all the Curriculum Standards. Here are a few cute cartoons before I talk to you about the ins and outs of the standards, benchmarks and curriculum guides from the state of Ohio. Does this describe your life as an educator? And of course… curriculum standards to read and apply to our lessons. Do you ever feel like this? Have you ever felt this pressed for time? Did you know your brains can read a passage even when the letters are in a different order? HOW DOES YOUR BRAIN DO IT? Try to read the handout quietly to yourself for the answer. Curriculum Benchmarks, Indicators, and Standards A Context Acquisition of Vocabulary Clues and Text structures to determine the meaning of new vocabulary. B E Infer word meanings by examining relationships of analogical statements. Apply knowledge of roots and affixes to determine meaning of complex subject area words. Curriculum Benchmarks, Indicators, and Standards Reading Applications, Informational, and Technical Persuasive Text C Analyze whether graphics supplement textual information and promote author’s purpose. Persuasive Text E Utilize multiple resources to critique the various ways authors develop their ideas. Curriculum Benchmarks, Indicators, and Standards Writing Process A Formulate writing ideas and identify a topic appropriate to the purpose and the audience. B Organize and apply appropriate pre-writing tasks. C Use revision strategies to improve the style, variety of sentence structure,clarity of controlling idea, logic, effectiveness of word choice and transitions between paragraphs, passages and ideas. D Edit to improve sentence fluency, grammar and usage. E Apply tools to judge the quality of writing. F Prepare writing for publication that is legible, follows an appropriate format and uses techniques such as electronic resources and graphics. Curriculum Benchmarks, Indicators, and Standards Research A Formulate open-ended research questions suitable for investigation and adjust questions as necessary while research is conducted. B Evaluate the usefulness and credibility of data and sources. C Organize information from various resources and select appropriate sources to support central ideas, concepts and themes. D Use style guides to produce oral and written reports that give proper credit for sources. E Communicate findings, reporting on the substance and process orally, visually in writing or multimedia. Curriculum Benchmarks, Indicators, and Standards Communication, Oral and Visual A Use a variety of strategies to enhance listening comprehension. C Evaluate the content and purpose of the presentation by analyzing language and delivery choices made by the speaker. D Demonstrate an understanding of effective speaking by selecting appropriate language and adjusting presentation techniques. E Give informational presentations that present ideas in a logical sequence,include relevant facts and details from multiple sources and use a consistent organizational structure. F & G Controlling ideas or thesis; give presentations using a variety of delivery methods, visual displays, and technology. Math Standards Geometry and Spatial Sense 1, 2, 5,& 6 Patterns, Functions and Algebra 2, 7, 14 & more And other Science and Technology standards With all of these standards.. We can proudly say…. Why does this happen? Comprehension is important! These are people of courage... General Rubric for Project 4 The student fully achieves all mathematical and project goals. The presentation demonstrates clear thinking and explanation. All work is complete and correct. 3 The student substantially achieves the mathematical and project goals. The main thrust of the project and the mathematics behind it is understood., but there may be some minor misunderstanding of content, errors in computation, or weakness in presentation. 2 The student partially achieves the mathematical and project goals. A limited grasp of the main mathematical ideas or project requirements is demonstrated. Some of the work may be incomplete, misdirected, or unclear. 1 The student makes little progress toward accomplishing the goals of the project because of lack of understanding or lack of effort. 1/6/09 By: Collin Roll Circles in optical illusions can make an object look like it is rotating.. Lines can appear to make an illusion look as if it is disproportioned with the mix of colors. This illusion is creating the effect of letters and numbers. Which can you see? This illusion creates an illusion of 3D or 3dimentional. It means that there is the view of something realistic. People can be hypnotized by an illusion. One that is created with circles can look as if they are rotating when they are really not moving at all. The End Optical Illusions By: Graham Reese 01/05/09 Optical Illusions Optical illusions are pictures that are visually perceived to be something that they aren’t. Optical Illusions Circles are a very important part of an optical illusion. They can create the illusion that a picture is spinning or tilting irregularly. Above: Which of the center dots are bigger? This illusion makes the circles look like they are spiraling. Right: The circle appears to be facing 2 directions. Optical Illusions Line segments are also important. They might seem to bend, but are straight. The illusions above all make the line segments look like they are not straight. Optical Illusions Another important object of optical illusions is the color of an object. Above: The color of the boat’s sail is the same color as the sky, giving the boat the ability to transform from the sky. Left: The color of the people’s robes is the same as the water,giving them the illusion of being water. The End http://www.michaelbach.de/ot/ http://www.moillusions.com/ Geometry Illusions http://www.palmyria.co.uk/illusio ns/illusions.htm http://www.coolopticalillusions.com/ http://www.archimedeslab.org/Gallery/new_optical_illusions/index.htm l http://www.wyrmcorp.com/galleries /illusions/index.shtml http://www.colorcube.com/illusions/ illusion.htm