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Montessori Cognitive Power Point
- 1. The Montessori Model
- 2. Real world problem: There is an evolving realization and consensus that our current educational system is no longer meeting the needs of today’s children.
- 3. In international rankings, our students came in at 23rd in science (out of 30 ) and 16 th in math, especially in the area of application of information . Further, there are reported shortages in the US in fields of applied sciences, and projections that these shortages will continue as fewer students sign up for classes in engineering and other “hard sciences.” Howard Gardner of Harvard tells us: “ Many schools have fallen into a pattern of giving kids exercises and drills that result in their getting answers on tests that look like understanding. Most students, from as young as those in kindergarten to students in some of the finest colleges in America do not understand what they've studied, in the most basic sense of the term.”
- 4. Is there a way to explain what might be happening?
- 6. to use cognitive science to explain our current educational problems… as well as to propose solutions. Knowing that children are sensorial learners, and that humans need to encode stimuli with many retrieval cues (in order to process and use information)…we can try
- 7. Proposal : Use Montessori pedagogies that address the changes to the modern lives of children, and are consistent with leading cognitive theories of learning, memory, and application.
- 8. Children’s House Sensorial Language Practical Life Math Cultural
- 9. Children’s House Letter recog/ Care of indoors Math Cultural + - x / sq- cubes Sensorial The five senses Attributes of geometry Care of the person Care of outdoors Practical Life Handwriting Word blg/ grammar Language Mathematics 1-10, 1- 9,999 Properties/ frac Cultural Arts, Sciences Cultures, Time Cultural Arts, Sciences Cultures, Time
- 10. Sensorial The five senses Attributes of geometry Arts, Sciences Cultures, Time Cultural Arts, Sciences Cultures, Time Length, width, height Depth, circumference Shapes - circles, rectangles, triangles (sides-equilateral, isosceles, scalene, and angles-right, acute, obtuse) polygons (pentagon, hexagon, heptagon, octagon, nonagon, decagon) and curvilinear shapes (oval, ellipse, trefoil, quatrefoil) Volume -geometric solids (cube, rectangular prism, cone, ovoid, ellipsoid, square based pyramid, triangular based pyramid, etc.) Trigonometry- constructing other geometric shapes (hexagons, trapezoids, parallelograms and other triangles) out of different triangles (in preparation for trigonometry). Algebra - Use geometric attributes to discover algebraic concepts Vision (color discrimination), Auditory (pitch, gradation), Tactile (rough-smooth, stereognostic senses), Olfactory (smelling bottles), Taste (bitter, sweet, etc.) Art -artistic expression, art history, Geography - Land, water, continents, oceans, landforms (lake, island, isthmus strait, peninsula, gulf, etc.) and waterways (oceans, etc.) Zoology - Vertebrates/parts of a fish, amphibian, reptile, bird mammal, invertebrates, insects Botany - parts of a plant, flower, leaf, identifications, shapes, margins Cultures flags, art, clothing, costumes, food, traditions, clothing and transportation, money , Time- Year, month, day, hour, minutes
- 12. Children need organized learning environments and educational materials that provide enriching meaningful experiences to support their cognitive development.
- 13. Our earth has LAND and WATER , and is surrounded by a blanket of air We call the large masses of land “continents.” We call the large bodies of water “oceans” We can learn the names of the continents and oceans.
- 17. Working Memory The visio-spatial sketchpad, the phonological loop, and procedural memory
- 20. Subvocal
- 23. Research
- 24. The video mentioned Lillard’s research model. The most difficult factor to parse out in educational research is parental influence. The question becomes: “Are parents who make the effort to enroll their children in Montessori schools generally more likely to know about child development, and therefore would be providing optimal learning environments for their children both in and out of the classroom anyway”? Lillard’s study- used a lottery system. Parents did not know in advance, and could not influence, which school their children attended. Socioeconomic conditions, and other factors were all similar. Outcomes: Students showed significantly differences in creative writing skills, exhibited greater social skills, had better coping skills, more positive outlooks on life, and higher academic scores in many areas.
- 25. I know for a fact that without this school and my teachers, I would never have had the courage to explain the process of how a Proton Exchange Membrane Fuel Cell works in front of a national panel of engineers.” ~Lara K. (7 th grade) Anecdotal evidence: Montessori schools have been consistent top winners in Future Cities engineering competitions, as well as the Geo (Geography) Bee. Clark Montessori was in the top three schools in the recent nationwide Race to the Top campaign.
- 27. Famous Alumni Sergey Brin & Larry Page , Founders of Google Jimmy Wales , Creator of Wikipedia Jeff Bezos , Financial Analyst, Founder of Amazon Will Wright , Video Game Designer and Creator of SimCity, The Sims George Clooney , Actor Gabriel Garcia Marquez , Nobel Prize winner for Literature Peter Drucker , entrepreneur and business management expert Jacqueline Kennedy Onassis , Editor, Former First Lady (John F. Kennedy) T. Berry Brazelton , Pediatrician and author Sean Combs , Music producer Anne Frank , Author of The Diary of Anne Frank Dakota Fanning -Actress Prince William and Prince Harry, British Royal Family Julia Child , Chef, star of many TV cooking shows, and author Melissa Gilbert and Sarah Gilbert, Actresses Katherine Graham , Owner/Editor of The Washington Post John Cusak and Joan Cusak , actors Friedensreich Hundertwasser , Austrian painter/Architect
- 28. Conclusion : Dr. Montessori travelled the world and discovered that “children naturally have the same drive to develop in a cognitive sense as they do in a physical sense. The desire of an elementary student to master equivalent fractions can be just as strong as the desire of the infant to crawl…unless the desire has been diminished by the circumstances of the child’s life.” In the 21st century, we can support those drives by intentionally creating responsive environments that meet the natural needs of our curious, social, and growing children. THE END
- 29. Print out “notes” underneath if you want a hardcopy script of the presentation. You are free to add any information to personalize this power point for your individual school. This can be used for educational purposes ONLY under the “fair use” copyright laws. Copyrights have not been purchased for all photos.
- 30. References Baddeley, A. (2002). Is working memory still working?. European Psychologist , 7 (2), 85-97. Clements, Rhonda. (2004). An Investigation of the Status of Outdoor Play Contemporary Issues in Early Childhood, Volume 5, Number 1, 2004 Durr, Patricia. (2008). Children’s Environment and Health Strategy for the UK The Children’s Society Response, June, 2008 November, 2010 http://www.childrenssociety.org.uk/resources/documents/Policy/7670_full.pdf Glod, Maria. U.S. Teens Trail Peers Around World on Math-Science Test. The Washington Post. December 5, 2005 Lillard, Angeline & Nicole, Else. (2006) Evaluating Montessori Education. Science, Volume 313, September 29, 2006 < http://www.montessori- ami.org/research/ScienceLillard060929.pdf> Matthews, Christine (2010) Foreign Science and Engineering Presence in U. S. Institution and the Labor Force. The Congressional Research Service . Washington, DC Quinette, P., Guillery, B., Desgranges, B., de la Sayette, V., Viader, F., & Eustache, F. (2003). Working memory and executive functions in transient global amnesia. Brain: A Journal of Neurology , 126 (9), 1917-1934. doi:10.1093/brain/awg201. Whitley, Peggy (2008). The Lone Star College- Kingwood Library website. American Cultural History 1900-1909. <http://kclibrary.lonestar.edu/decade00.html>
Notas del editor
- Welcomes and Introduction
- (On the slide) Real world problem: There is an evolving realization and consensus that our current educational system is no longer meeting the needs of today’s children.
- In International Rankings, we didn’t do so well! We ranked 23rd out of 30 in science and 16th in Math. There is also a shortage of students enrolling in science, math and engineering. That isn’t good considering we are in The Technology Age! Howard Gardener of Harvard tells us: Many schools have fallen into a pattern of giving kids exercises and drills that result in their getting answers on tests that look like understanding. Most students, from as young as those in kindergarten to students in some of the finest colleges in America do not understand what they've studied, in the most basic sense of the term.” Pic from google images
- (read slide) Is there a way to explain what might be happening?
- What CHANGED? Family size , and the number of children in neighborhoods - Only a few years ago, it was not uncommon to have 6- 10 children per family. This meant that sidewalks were full of children riding their bikes and exploring their world. There was strength in numbers, and children were safe because there were always playmates that could go for help, or to keep them company. Family structure and time with adults - Older children helped to take care of young ones. This meant chores. Family businesses or farms meant children could imitate their parents and learn skills as they worked alongside each other. The amount of time children spend playing and designing their own time . Without modern technological devices, children created games, climbed trees, followed grasshoppers, built forts, and spent long hours deciding how to use their time. The size of the space a child can freely explore on their own. According to researchers, the area a child can travel on his or her own has decreased by 90 % in the space of ONE GENERATION. The type of activities (now mostly passive and indoors). 96% of parents report their children spend long hours in front of TV sets, computers or videos. Many even watch tv in the car now.
- Knowing that children are sensorial learners, and that we need to encode learning with many retrieval cues (in order to process and use formation)…we can try to use cognitive science to explain our current educational problems… as well as to propose solutions. Our children are sensorial learners (they educate themselves using touch, taste, vision, sound and smells). Their brains are not like ours…so what THEY need to learn is DIFFERENT from what we need.
- According to Rosch, Mervis, et al., organizing information allows us to categorize, memorize, and refine our understanding of concepts. Using their hierarchy, the “Superordinate level” denotes the broad category, the “basic level” describes a group category and subordinate categories are specific exemplars. In other words, (broad) ANIMALS > (basic) DOG > (subordinate) German shepherd or poodle. In the Montessori classroom, the Superordinate Categories are: Practical Life, Sensorial, Math, Language and Cultural.
- On the shelves in each level, are their “basic” categories. Lessons for the Five Senses can be found on the Sensorial shelf, for example.
- And here we break it down even further to the subordinate categories. For example, on the Sensorial shelves, there are lessons for the 5 senses: Vision - these lessons are broken down into color recognition, identifying shades of color, magnified vision, using binoculars (distance and depth perception), etc. For the Auditory sense, there are AMAZING materials that teach pitch, scales, loud and soft gradation of sounds, for the sense of touch there are TACTILE lessons that teach rough and smooth, sterognostic memory bags (using “feel” to recognize items)….etc (see slide). Once we have learned to recognize individual attributes, we use our senses to experience LENGTH, WIDTH, HEIGHT, DEPTH, CIRCUMFERENCE, SHAPES, VOLUME… Then we combine shapes (triangles for example) to make other shapes and to see how things fit together. We also use our observations of geometric attributes to discover algebraic concepts in three dimensions (with the binomial and trinomial cubes). ------- Under the basic category CULURAL, you’ll find the subordinate categories of Art and Art history, geography, Geology, Zoology, Botany, Biology, Cultures (humanities) and Time, for example
- With all of those materials available to students, one might think the classroom would cluttered or over-stimulating. But instead, the classrooms are very homelike and quite cozy. There is a place for everything, and everything in its place! Montessori classrooms are called Children’s Houses. Shelves are used to create “different rooms”, and there is also a kitchen space and a living room area. Instead of a teacher at the front of the classroom taking an entire group of children through a curriculum in unison, children have access to all of the educational the materials that make up the curriculum…and the teacher helps children to master each area of study. In the Montessori model, the three classroom components (teacher, student, curriculum) have simply been rearranged. The materials are placed on the shelves in order of a single isolation of difficulty. You can “read” the shelves like a book! You start with introductory lessons in the top left hand corner and by the time you reach the last material in the lower right hand corner, you have mastered the curriculum in that subject (with no gaps in instruction).
- We can use the globe to help illustrate the idea of using an isolation of difficulty (incremental changes in the materials) as a way to convey information.
- The first globe presented to children uses fine sandpaper to tactilely represent the general location of land and water on the planet. Then we say “ our earth has land and water, and is surrounded by a blanket of air.” The second globe is used to impart the lesson that we call the large masses of land “continents” and the large bodies of water are called “oceans.” This globe is smooth, but the “continents” are raised to distinguish their locations. The third globe has raised areas AND is color coded, so that we can isolate specific areas and learn the names of the continents.
- But that’s not all! We use the globes to point out that we can only see side at a time. And we express the difficulty of having to carry a round ball with us (it won’t fit in our pockets!) …so we introduce the concept of a 2D map and compare the two. We then break it down into maps of each continent (with countries and capitals). Landforms are also introduced, as well as the biomes, animals, plants, people, architecture, money, dress, art, traditions, flags, transportation, etc. that might be found each place. But even that’s NOT ALL!
- Each lesson in the classroom also has several procedural steps to follow. Here you see: 1. A boy choosing to wash a table. 2. He gets out the mat to protect the floor from drips of water. 3. He lays out his materials in order (much like a doctor, plumber, or any professional) so they will be ready for efficient use. In this case, the brush and soap are used to WASH, the sponge to RINSE, and the towel to DRY. 4. He goes to the sink and fills up a pitcher of water. Then he pours the water into the bucket. 5. He asks a friend to help him carry a table safely in the classroom. 6. He wets his brush, loads it with soap, and begins. 7. Using a cursive e motion, he starts at the top left corner and goes across to the other side of the table. He repeats this across, across, across until the table top has been thoroughly scrubbed. 8.Then he washes the table legs. 9. He wets the sponge, and uses it to remove soap suds (rinsing in bucket as needed). 10. Dries the table. 11. Gets a friend to help him to return the table to its spot. 12. Empties the dirty water into the sink. 13. Dries the floor mat, white underlay, pitcher. 14. Rolls up underlay and replaces all the dried supplies back into the bucket (refreshing with a dry towel and putting the wet towel in the laundry basket). 15. Carries back to the shelf. 16. He returns the work back to its place on the shelf, in good order and ready for the next person.
- While it might seem like there is a lot to remember, the main focus of the classroom is DISCOVERY, FRIENDSHIP, and FUN. Multi aged groupings allow older students to help younger ones. This reinforces academic concepts, provides leadership opportunities, allows for indirect observation, and promotes a sense of community.
- An important idea in the area of “application of knowledge” is Alan Baddeley’s theory of procedural working memory. This theory posits that we have a vast storage of implicit knowledge, which might be described as our accumulated experiences of cause and effect information. This internalized memory allows us to understand if/then relationships (IF I do this, THIS will occur as a result), helps us to know how to attempt to accomplish a task, and to understand what actually works in the real world. Our procedural memories give us the information we need to take successful action in APPLYING semantic knowledge (facts and figures). It is THIS ability, that allows our students to understand what they are studying in order to be able to APPLY information to solve real world problems.
- In Baddeley’s working memory model, our minds make use of two separate channels to process information. We create or remember visual images… AND we have an auditory channel for words and sounds. Montessori makes use of both channels. Introductory lessons are given using live or real world examples. Then 2D representations like puzzles, charts, cards, and outlines are given over time. This allows us to attach language with incrementally increasing complexity.
- Here is another example of tying visual representations to language, using the geometric solids. First, the solids are placed in a covered basket. Using only their hands to feel the shapes, children pull out the shapes one at a time. Language is given for the shape they revealed. Next, we do it in reverse. We will ask if the child can use their hands to find a “cube.” The child reaches under the cloth and feels the shapes until they have found the one that has the attributes of a cube. Then 2D cards and charts are introduced, further attaching language to the 2D and 3D images (cube, rectangular prism, square and triangular based pyramids, cylinder, sphere, ovoid, and ellipsoid). Children LOVE big words! Think supercalifragilisticexpalidocious !
- This representation of Baddeley’s working memory model includes a graphic for the importance of rehearsal (repetition) in all areas. In the phonological loop, we use subvocal (or inner) speech to help us think through problems, remember information, as primers for retrieval (spreading activation into levels of categories), and to plan ahead. Alexander Luria, and many modern day theorists, agree that “inner speech” strengthens the brain’s central executive functions. He insists that helping children to talk through their activities and the steps to problem solving is the key to higher level learning and mental organization… as well with helping them learn to function independently and manage their own behavior. In Montessori classrooms, students use all three modalities and talk themselves through the procedural steps of each lesson, while using their visual and other senses to have an episodic experience to reinforce semantic information.
- Here is an interesting example of how these ideas are put together in the area of mathematics. In the top left, you can see 1 unit, 1 ten bar, 1 hundred square, and 1 thousand cube (place values). Similarly, you can easily show that the ten bar is 10 units, that the hundred square is 10 ten bars, that the hundred square is 10 tens, and that the 1000 cube is a stack of 10 hundred squares. Attach the written expression. When you change the amount, the written expression reflects that (but there are a lot of extra zeros). Its easier to read and write our numbers when we let them tell us how units, tens, hundreds, thousands ..that we have. And it saves space! And we don’t have to keep making up new names for numbers. Every time we get to ten…we start a new row and count to ten again. The top right picture shows how numbers grow, and reaffirms the learning. The bottom left picture takes the concept to 1 MILLION. You can see the 1 tiny green unit, the 1 small blue tens bar, the 1 red hundred square, the 1 green thousand cube, the 1 blue ten thousand bar, the1 red hundred thousand square, and the finally the 1 large green million cube. Again, you can easily see (and prove to the child) that each hierarchy is a collection of 10 of the preceding amounts.
- Is there support for the efficacy of the Montessori model? Lets watch what Dr. Steven Hughes has to say. (Stop at 2 : 29 ) for presentation purposes so it will not be too long
- The video mentioned Lillard’s research. This is because it is almost impossible to parse out parental influence. The question becomes “are parents who enroll their children in Montessori schools generally more likely to know about development, and willing to provide optimal learning environments both in and out of the classroom”? Lillard study- Lottery system. Parents did not know, and could not influence, which school their children attended. Socioeconomic conditions were similar. Outcomes: Students showed more creativity, Better social skills, more positive outlooks, and higher academic scores in many areas.
- This slide tells about the outcomes when using Montessori in an inner city school:
- I won’t read all of these names, but the first few are pretty interesting! Sergey Brin & Larry Page , Founders of Google Jimmy Wales , Founder of Wikipedia Jeff Bezos , Financial analyst, founder of Amazon Will Wright , Video Game designer and Creator of SimCity, The Sims George Clooney , actor Montessori graduates seem to do pretty well for themselves! Montessori also has had a big list of supporters from Mr. Rogers to Thomas Edison.
- The End
- COGNATIVE PRESENTATION The Montessori Model SLIDE 1 Introduction SLIDE 2 (On the slide) Real world problem: There is an evolving realization and consensus that our current educational system is no longer meeting the needs of today’s children. SLIDE 3 In International Rankings, we didn’t do so well! We ranked 23 rd out of 30 in science and 16 th in Math. There is also a shortage of students enrolling in science, math and engineering. That isn’t good considering we are in The Technology Age! Howard Gardener of Harvard tells us: Many schools have fallen into a pattern of giving kids exercises and drills that result in their getting answers on tests that look like understanding. Most students, from as young as those in kindergarten to students in some of the finest colleges in America do not understand what they've studied, in the most basic sense of the term.” SLIDE 4 (read slide) Is there a way to explain what might be happening? SLIDE 5 What’s CHANGED? Family size , and the number of children in neighborhoods - Only a few years ago, it was not uncommon to have 6- 10 children per family. This meant that sidewalks were full of children riding their bikes and exploring their world. There was strength in numbers, and children were safe because there were always playmates that could go for help, or to keep them company. Family structure and time with adults - Older children helped to take care of young ones. This meant chores. Family businesses or farms meant children could imitate their parents and learn skills as they worked alongside each other. The amount of time children spend playing and designing their own time . Without modern technological devices, children created games, climbed trees, followed grasshoppers, built forts, and spent long hours on their own. The size of the space a child can freely explore on their own. According to researchers, the area a child can travel on his or her own has decreased by 90 % in the space of ONE GENERATION. The type of activities (now mostly passive and indoors). 96% of parents report their children spend long hours in front of TV sets, computers or videos. Many even watch tv in the car now. SLIDE 6 (read or paraphrase slide) Knowing that children are sensorial learners, and that we need to encode learning with many retrieval cues (in order to process and use formation)…we can try to use cognitive science to explain our current educational problems… as well as to propose solutions. Our children are sensorial learners. Their brains are not like ours…so what THEY need to learn is DIFFERENT from what we need. SLIDE 7 (read from slide) One Proposed Solution: Montessori education SLIDE 8 According to Rosch, Mervis, et al., organizing information into hierarchies allows us to categorize, memorize, and refine concepts. The “Superordinate level” denotes the broad category, the “basic level” describes a group category and subordinate categories are specific examplars. In other words, animals >dogs > German shepherd. In the Montessori classroom, the Superordinate Categories are: Practical Life, Sensorial, Math, Language and Cultural. SLIDE 9 On the shelves in each category are their basic categories. As you can see, under SENSORIAL, you would find lessons concerning use of the five senses…and, in turn you will find opportunities to put those to work to sense the presence and attributes of the shapes we find in the world around us. Under the basic category of Cultural, we find the Arts, Sciences, Humanities, and Time SLIDE 10 Here we break it down even further to the subordinate categories. For example, under Vision-there are lessons that teach color recognition, shades, magnifying glasses, binoculars, etc. under Auditory, there are AMAZING materials that teach pitch, scales, loud and soft gradation of sounds, TACTILE lessons that teach rough and smooth, employ sterognostic senses (using feel to recognize items)…. Then we use these senses to look at LENGTH, WIDTH, HEIGHT, DEPTH, SHAPES, CIRCUMFERENCE, VOLUME, Then we combine shapes (triangles for example) to make other shapes and to see how things fit together. We also use our observations of geometric attributes to discover algebraic concepts in three dimensions (with the binomial and trinomial cubes). Under the basic category CULURAL, you’ll find Art and Art history, geography, Geology, Zoology, Botany, Biology, Cultures (humanities) and Time. With all of those materials available to students, one might think the classroom would cluttered or over-stimulating. SLIDE 11 … ..But instead, the classrooms are very homelike and quite cozy. There is a place for everything, and everything in its place! Montessori classrooms are called Children’s Houses. Shelves are used to create “different rooms”, and there is also a kitchen space and a living room area. Instead of a teacher at the front of the classroom taking an entire group of children through a curriculum in unison, children have access to all of the educational the materials that make up the curriculum…and the teacher helps children to master each area of study. The three classroom components have been rearranged. The materials are placed on the shelves in order of a single isolation of difficulty. You can “read” the shelves like a book! You start with introductory lessons in the top left hand corner and by the time you reach the last material in the lower right hand corner, you have mastered the curriculum in that subject (with no gaps in instruction). SLIDE 12 (read slide) Children need organized learning environments and educational materials that provide enriching meaningful experiences to support their cognitive development. We can use the globe to help illustrate the idea of using an isolation of difficulty (incremental changes in the materials) as a way to convey information. SLIDE 13 The first globe presented to children uses fine sandpaper to tactilely represent the general location of land and water on the planet. Then we say “our earth has land and water, and is surrounded by a blanket of air.” We call the large masses of land “continents.” We call the large bodies of water “oceans.” The next globe is smooth, but the “continents” are raised to distinguish their locations. The third globe has raised areas AND is color coded, so that we can isolate specific areas and learn the names of the continents. SLIDE 14 But that’s not all! We use the globes to point out that we can only see side at a time. And we express the difficulty of having to carry a round ball with us (it won’t fit in our pockets!) …so we introduce the concept of a 2D map and compare the two. We then break it down into maps of each continent (with countries and capitals). Landforms are also introduced, as well as the biomes, animals, plants, people, architecture, money, dress, art, traditions, flags, transportation, etc. that might be found each place. But even that’s NOT ALL! SLIDE 15 Each lesson also has several procedural steps to follow. Each lesson in the classroom also has several procedural steps to follow. Here you see: 1. A boy choosing to wash a table. 2. He gets out the mat to protect the floor from drips of water. 3. He lays out his materials in order (much like a doctor, plumber, or any professional) so they will be ready for efficient use. In this case, the brush and soap are used to WASH, the sponge to RINSE, and the towel to DRY. 4. He goes to the sink and fills up a pitcher of water. Then he pours the water into the bucket. 5. He asks a friend to help him carry a table safely in the classroom. 6. He wets his brush, loads it with soap, and begins. 7. Using a cursive e motion, he starts at the top left corner and goes across to the other side of the table. He repeats this across, across, across until the table top has been thoroughly scrubbed. 8.Then he washes the table legs. 9. He wets the sponge, and uses it to remove soap suds (rinsing in bucket as needed). 10. Dries the table. 11. Gets a friend to help him to return the table to its spot. 12. Empties the dirty water into the sink. 13. Dries the floor mat, white underlay, pitcher. 14. Rolls up underlay and replaces all the dried supplies back into the bucket (refreshing with a dry towel and putting the wet towel in the laundry basket). 15. Carries back to the shelf. 16. He returns the work back to its place on the shelf, in good order and ready for the next person. SLIDE 16 While it might seem like there is a lot to remember, the main focus of the classroom is DISCOVERY, FRIENDSHIP, and FUN. Multi aged groupings allow older students to help younger ones. This reinforces academic concepts, provides leadership opportunities, allows for indirect observation, and promotes a sense of community. SLIDE 17 An important idea in the area of “application of knowledge” is Alan Baddeley’s theory of procedural working memory. This theory posits that we have a vast storage of implicit knowledge, which might be described as our accumulated experiences of cause and effect information. This internalized memory allows us to understand if/then relationships (IF I do this, THIS will occur as a result), helps us to know how to attempt to accomplish a task, and to understand what actually works in the real world. Our procedural memories give us the information we need to take successful action in APPLYING semantic knowledge (facts and figures). It is THIS ability, that allows our students to understand what they are studying in order to be able to APPLY information to solve real world problems. SLIDE 18 In Baddeleys model, our minds make use of two separate channels to process information. We create or remember visual images and properties AND we have an auditory channel for words and sounds. Montessori makes use of both channels. Introductory lessons are given using live or real world examples. Then 2D representations like puzzles, charts, cards, and outlines are given over time. This allows us to attach language while incrementally increasing complexity. SLIDE 19 Here is another example, using geometric solids. First, the solids are placed in a covered basket. Using only their hands to feel the shapes, children pull out the shapes one at a time. Language is given for the shape as they are revealed. Next, we do it in reverse. We will ask if the child can use their hands to find a “cube.” The child reaches under the cloth and feels the shapes until they have found the one that has the attributes of a cube. Then 2D cards and charts are introduced, further attaching language to the 2D and 3D images (cube, rectangular prism, square and triangular based pyramids, cylinder, sphere, ovoid, and ellipsoid). Children LOVE big words! Think supercalifragilisticexpalidocious ! SLIDE 20 This newer representation of Baddeley’s working memory model includes a graphic for the importance of rehearsal in all areas. In the phonological loop, we use subvocal (or inner speech) to help us think through problems, remember information, as primers for retrieval (spreading activation) and to plan ahead. Alexander Luria, and many modern day theorists, say that “inner speech” strengthens the brain’s central executive functions. He insists that helping children to talk through their activities and the steps to problem solving is the key to higher level learning and mental organization… as well with helping them learn to function independently and manage their own behavior. In Montessori classrooms, students talk themselves through the procedural steps of each lesson, while using their visual and other senses to have an episodic experience to reinforce semantic information. SLIDE 21 So here is an interesting example of how these ideas are put together in the area of mathematics. In the top left, you can see 1 unit, 1 ten bar, 1 hundred square, and 1 thousand cube (place values). Similarly, you can easily show that the ten bar is 10 units, that the hundred square is 10 ten bars, that the hundred square is 10 tens, and that the 1000 cube is a stack of 10 hundred squares. Attach the written expression. When you change the amount, the written expression reflects that (but there are a lot of extra zeros). Its easier to read and write our numbers when we let them tell us how units, tens, hundreds, thousands ..that we have. And it saves space! And we don’t have to keep making up new names for numbers. Every time we get to ten…we start a new row and count to ten again. The top right picture shows how numbers grow, and reaffirms the learning. The bottom left picture takes the concept to 1 MILLION. You can see the 1 tiny green unit, the 1 small blue tens bar, the 1 red hundred square, the 1 green thousand cube, the 1 blue ten thousand bar, the1 red hundred thousand square, and the finally the 1 large green million cube. Again, you can easily see (and prove to the child) that each hierarchy is a collection of 10 of the preceding amounts. SLIDE 22 Video (youtube) STOP AT 2 :29 SLIDE 23 (read slide) Research SLIDE 24 The video mentioned Lillard’s research. This is because it is almost impossible to parse out parental influence. The question becomes: “Are parents who make the effort to enroll their children in Montessori schools generally more likely to know about child development, and therefore would be providing optimal learning environments for their children both in and out of the classroom anyway”? Lillard’s study- used a lottery system. Parents did not know in advance, and could not influence, which school their children attended. Socioeconomic conditions, and other factors were all similar. Outcomes: Students showed significantly more creative writing skills, exhibited greater social skills, had better coping skills, more positive outlooks on life, and higher academic scores in many areas. Slide 25 (Of note, Montessori schools have been consistent top winners in the national Future Cities engineering competitions for the last several years!) SLIDE 26 Other Anecdotal evidence : Montessori in an inner city school: East Dallas Community School:67% from families living at or below poverty level 49% are learning English as a second language In a neighborhood where the high school graduation rate is less than 50%, 94% of our third-grade alumni have graduated from high school ; 88% of those have gone on to college. 100% of our public charter school students have passed the high stakes state reading competency tests. According to a ten-year study of standardized test scores (1993-2003), EDCS students' average scores were in the top 36% nationwide in reading and math. In 2009, EDCS was awarded Gold Performance acknowledgments in both reading and math by the State of Texas. Once again in 2010, the EDCS Charter School was rated as exemplary . H. Ross Perot proposed using this program as our national model for public schools during his presidential campaign in the 1980s. SLIDE 27 (show fast) I won’t read all of these names, but the first few are pretty interesting! Sergey Brin & Larry Page , Founders of Google Jimmy Wales , Creator of Wikipedia Jeff Bezos , Financial analyst, Founder of AMAZON Will Wright , Video Game designer and Creator of SimCity, The Sims George Clooney , actor (more on the slide) Montessori graduates seem to do pretty well for themselves! SLIDE 28 Conclusion : Dr. Montessori travelled the world and discovered that “children naturally have the same drive to develop in a cognitive sense as they do in a physical sense. The desire of an elementary student to master equivalent fractions can be just as strong as the desire of the infant to crawl…unless the desire has been diminished by the circumstances of the child’s life.” In the 21st century, we can support those drives by intentionally creating responsive environments that meet the natural needs of our curious, social, and growing children. THE END