Mind Power Math - High School And College Math ((NEW))
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Mind Power Math - High School and College Math
WASHINGTON- There really may be something different about the brains of math-heads. Mathematically gifted teens did better than average-ability teens and college students on tests that required the two halves of the brain to cooperate, as reported in the April issue of Neuropsychology, published by the American Psychological Association (APA).
In the study, a joint effort of psychologists at the U.S. Army Research Institute for the Behavioral and Social Sciences at Fort Benning, Ga. and the University of Melbourne, Australia, researchers studied 60 right-handed males: 18 mathematically gifted (averaging nearly 14 years in age), 18 of average math ability (averaging just over 13), and 24 college students (averaging about 20). Math giftedness seems to favor boys over girls, appearing an estimated six to 13 times more often. It's not known why but prenatal exposure to testosterone is suspected to be one influence due to its selective benefit to the right half of the brain.
The gifted boys were recruited from a Challenges for Youth-Talented program at Iowa State University. Whereas the average Scholastic Aptitude Test (SAT) math score for college-bound high-school seniors is 500 (out of 800), the mathematically gifted boys' average SAT math score in middle school was 620.The boys viewed letter patterns flashed on the left or right sides of a computer screen, and had to indicate whether two patterns matched or not - a simple way of learning how the brain responds to data put before either the left or right visual field, corresponding to processing in the right or left brain because the input generally crosses over to the other side.
In addition, whereas average-ability boys and college students were slower on cooperative trials, which presented letter patterns on both sides of the screen, the math-gifted showed the opposite pattern. They were slower on one-sided trials, but when a task "asked" both sides of the brain to work together, they were considerably faster than the other boys
The study supports the growing notion that the mathematically gifted are better at relaying and integrating information between the cerebral hemispheres. Says co-author Michael O'Boyle, PhD, "It's not that you have a special math module somewhere in your brain, but rather that the brain's particular functional organization - which allows right-hemisphere contributions to be better integrated into the overall cognitive/behavioral equation -- predisposes it towards the use of high-level imagery and spatial skills, which in turn just happen to be very useful when it comes to doing math reasoning."
Article: "Interhemispheric interaction during global-local processing in mathematically gifted adolescents, average-ability youth, and college students," Harnam Singh, Ph.D., U.S. Army Research Institute for the Behavioral and Social Sciences, and Michael W. O'Boyle, PhD, University of Melbourne, Australia; Neuropsychology, Vol. 18, No. 2.
Math anxiety is a nagging fear of or apprehension about math, and it affects the classes college students select and the careers they pursue. As a cognitive scientist, I am concerned that it prevents students who otherwise have the ability to succeed in STEM from doing so. And as president of Barnard College, a school focused on empowering young women, I also worry about the fact that girls and women tend to have more math anxiety and are less confident in their math abilities than boys, which probably helps explain why they continue to be underrepresented in many STEM fields.
Before she was a psychologist at the University of Pennsylvania, Angela Duckworth was a middle school math teacher. As a rookie teacher, she was surprised when she calculated grades. Some of her sharpest students weren't doing so well, while others who struggled through each lesson were getting A's.
In a study of elementary school students, researchers at the Stanford University School of Medicine found that having a positive attitude about math was connected to better function of the hippocampus, an important memory center in the brain, during performance of arithmetic problems.
Educators have long observed higher math scores in children who show more interest in math and perceive themselves as being better at it. But it has not been clear if this attitude simply reflects other capacities, such as higher intelligence.
Upper-Level CoursesThe standard high school mathematics curriculum doesn't demonstrate the true diversity or the true nature of mathematics. Exploring the mathematical landscape beyond calculus, you'll find number theory, complex analysis, algebraic topology, and many other fields that investigate the deep questions raised by seemingly simple ideas. You might encounter situations where multiplication isn't commutative, where a number can have more than one prime factorization, or where a sequence can have more than one limit. Studying these generalizations and abstractions, in addition to being great fun in its own right, helps to shed a surprising amount of light on the "usual" mathematics you know and love.
With immersive research opportunities, supportive & engaged professors, and state-of-the-art lab facilities, Belmont is so much more than a music school. During this summer, high school students can flourish during hands-on pre-college experiences in our College of Sciences and Mathematics (CSM). Our camps are unique because they are developed and taught by our very own faculty, so not only will you receive a nationally-recognized education, but you will also get to become a member of the Belmont community and experience what makes our students thrive!
Camp Purpose: This course will introduce students to higher level mathematics frequently taught after the calculus sequence, focusing on discrete mathematics. While the concepts are challenging, they require little background knowledge and are quite accessible for enthusiastic high school students.
Camp Description:This summer, come learn how to use the power of physics to improve your understanding of some of the physics that goes into designing a car. By applying basic physics principles, such as force and conservation of energy, we will develop a Python-based computational model of the motion of a toy car. We will then test the model and compare experimental results to our theoretical ones. This camp will be a combination of hands on experimentation and mathematical modeling with Python. Come learn what it means to be a scientist or engineer!
In the United States people are more likely to have a fixed mindset about mathematics than any other subject or area of their lives, and the prevalence of fixed mindset thinking is one of the reasons we have widespread failure and math trauma in this country. It is critically important that teachers and students develop growth mindsets; these can be developed at any time in life.
Many of these tasks are shown on the math education resource, youcubed.org. The research on the importance of mindset and struggle suggests strongly that we need math environments in which students are given open tasks and challenging work that causes them to struggle and experience important brain growth. Teachers should support or even reward students for making mistakes so that they feel comfortable doing so. More advice is given on ways to teach math for a growth mindset in my online classes, in the materials on youcubed.org and in Boaler (2016).
An important message that is emerging from neuroscience concerns the damage that is caused when math performance is associated with speed. Many math classes across the United States encourage the idea that the best math students are those who work quickly. When the late mathematician and Fields Medal winner Laurent Schwartz reflected on his childhood, he described his days in school as days when he thought of himself as unintelligent because he was a slow math thinker:
Statistics from the early 2000s (the most recent available) suggest that 31 percent of students with ADHD also have a math disability. This rate is 5 times higher than the general rate of math disabilities, which falls between 6 and 7 percent. Among students with a math disability, roughly 25 percent also have ADHD.
To better understand how math anxiety develops and how to help people who suffer with it, we need to understand what is happening in brain while a person with math anxiety is doing math. One idea is that the human brain can only process a certain amount of information at a time. A system in the brain that allows us to process information is called working memory. Working memory is a part of the human memory system that allows us to remember and think about several things at the same time. This skill is very important for doing math. For example, if a teacher reads out a math problem, the student must hold all numbers in his or her mind, consider the steps needed to solve the problem, and write out the answer at the same time. Researchers think that maybe, when people feel anxious, the math anxiety that they feel is using up some of their working memory, so they do not have enough working memory left to solve the math problem. Maybe the working memory that is being used for the anxiety would have been used for solving the math problem if those people did not feel so anxious . In other words, math anxiety causes students to think and worry about how afraid they feel of math, which occupies the working memory resources that they would otherwise use to do the math problems. This idea that math anxiety uses working memory has been supported by research studies. Importantly, researchers have reported that children who have a high level of working memory do better on math tests than children with a low level of working memory.