I guess the best way to explain this is that according to the information that you know, how do you think neuroscientific research findings and recent discoveries regarding how the brain learns support differentiation in the classroom, how insights into the learning process affirm the importance of differentiation, and how may the research findings be translated into specific teaching strategies used in the classroom. For example, in my findings the brain may work like this. To most people, mathematics is about calculating numbers. Some may even expand the definition to include the study of quantity (arithmetic), space (plane and solid geometry), and change (calculus). But even this definition does not encompass the many areas where mathematics and mathematicians are found. A broader definition of mathematics comes from W. W. Sawyer. In the 1950s, he described mathematics as the classification and study of all possible patterns. He explained that pattern was meant to cover almost any kind of regularity that can be recognized by the mind (Sawyer, 1982).Other mathematicians who share Sawyers view have shortened the definition even further: Mathematics is the science of patterns. Devlin (2000) not only agrees with this definition but has used it as the title of one of his books. He explains that patterns include order, structure, and logical relationships and go beyond the visual patterns found in tiles and wallpaper to patterns that occur everywhere in nature. For example, patterns can be found in the orbits of the planets, the symmetry of flowers, how people vote, the spots on a leopards skin, the outcomes of games of chance, the relationship between the words that make up a sentence, and the sequence of sounds we recognize as music. Some patterns are numerical and can be described with numbers, such as voting patterns of a nation or the odds of winning the lottery. But other patterns, such as the leopards spots, are visual designs that are not connected to numbers at all.Devlin (2000) further points out that mathematics can help make the invisible visible. Two thousand years ago, the Greek mathematician Eratosthenes was able to calculate the diameter of Earth with considerable accuracy and without ever stepping off the planet. The equations developed by the eighteenth-century mathematician Daniel Bernoulli explain how a jet plane flying overhead stays aloft. Thanks to Isaac Newton, we can calculate the effects of the unseen force of gravity. More recently, linguist Noam Chomsky has used mathematics to explain the invisible and abstract patterns of words that we recognize as a grammatical sentence.If mathematics is the science of patterns and if visible and invisible patterns exist all around us, then mathematics is not just about numbers but about the world we live in. If that is the case, then why are so many students turned off by mathematics before they leave high school? What happens in those classrooms that gives students the impression that mathematics is a sterile subject filled with meaningless abstract symbols? Clearly, educators have to work harder at planning a mathematics curriculum that is exciting and relevant and at designing lessons that carry this excitement into every days instruction.I will leave the discussion of what content to include in a Pre K to 12 mathematics curriculum to experts in that area. My purpose here is to suggest how the research in cognitive neuroscience that we have discussed in the previous chapters can be used to plan lessons in mathematics that are more likely to result in learning and retention.Resources:
Devlin, K. (2000). The math gene: How mathematical thinking evolved and why numbers are like gossip. New York: Basic Books.Research is continually making progress in discovering new and remarkable things about the functions, the organization, and the responsibilities of the brain. The more research progresses in this area, the more likely the findings can be used in educational programs, training, and policies that take advantage of what it found in laboratory research. Through technology and the use of CT scan and MRI Scans, researchers have been able to glance inside the brain to see what the brain is doing when specific things are happening in our lives. For example: When you hear a sound, catch a whiff of your favorite scent, or look at vibrant colors, what part of the brain reacts? What about when you are doing something complicated like talking on the phone, driving a car, or reading a book – which part of the brain responds and how does it respond to the action(1)?The optimal time for the brain is during the first decade of life, the brain has the ability to change and compensate; therefore, this is a critical time for teachers to use differentiation in the classroom in order to optimize the learning potential (2). Research shows that the brain is continually learning and absorbing. A persons genetic makeup, nutrition, care, surroundings, stimulation, and teaching, whether provided or withheld contribute to how the brain develops. Because each child learns at a different rate, respecting each student by allowing every student to use the essentials in ways that require complex thought and problem solving helps to support differentiation in the classroom. Flexible grouping could also help in this area. By grouping students together that are working on the same level will help those students to work together to learn and understand the material instead of using memorization to recall the information at the time of test or assessment. This also helps to support differentiation in the classroom. Another area that can help to support differentiation in the classroom environment and help students is the classroom environment itself. The classroom environment needs to be stimulating for a childs brain to encourage growth and learning (1).When teachers understand the learning process it enables them to look at the individual students, instead of the class as a whole, and determine which area the student could use the most help. Differentiation in the classroom looks at the child as an individual and allows the teacher to create an ultimate learning environment that works to teach the child to the best of the teachers ability. Research shows that a child learns more by brain stimulation and exposure to a variety of learning experiences such as music, blocks, talking to the child, patterns in which to count and sort, shapes, colors, and numbers. This information can assist teachers when creating the lesson plans which they use to teach the children. Research shows that a variety of things stimulate the brain and these things should be used in the classroom setting. For example, if color stimulates a persons mood and feelings, it must stimulate some part of the brain to trigger these types of emotions (3).According to Elena Mannes, scientists have found that music stimulates more part of the brain than any other human function. She goes on to say that music has the possibility to help people with neurological deficits by the use of a therapy technique known as melodic intonation therapy. This type of therapy uses music to persuade parts of the brain to take over for the areas of the brain that may be damaged; therefore, it has the potential to help patients regain their ability to speak. Music speaks to people in various ways, it can brings on emotions, feelings, calmness, and can bring back memory of times long gone (4).References:
(1) http://nichcy.org/schoolage/effective-practices/brain101(2) http://childcareaware.org/parents-and-guardians/resources/additional-resources/rethinking-the-brain(3) http://psychology.about.com/od/sensationandperception/a/colorpsych.htm(4) http://www.npr.org/2011/06/01/136859090/the-power-of-music-to-affect-the-brain.

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