Math Education are we instructing the right part of the brain?

Some Interesting Websites
 Forvo is the largest pronunciation guide in the world. Ever wondered how a word is pronounced?  Ask for that word or name, and another user will pronounce it for you. You can also record your own pronunciations.
 VPike will fascinate kids and adults alike.  When you enter an address you will see a picture of that place. 
10 Cool Math Sites contains ten math sites for students of all ages, as well as teachers.  There are websites for everything from basic flash cards to game theory. 

Articles on Math Education
 A A-Maze-ing Approach to Math by Barry Garelick in Education Next
'Algebra-for-all' Approach Fount to Yield Poor Results by Debra Viadero Education Week
 West Brain, East Brain by Sharon Begley in Newsweek
Number Wars: School Battles heat Up Again in the Traditional versus Reform-Math Debate  by Linda Baker in Scientific American

Thoughts From Yrisarri
I recently read an article that asks whether or not a math teacher should have a degree in mathematics.  That depends a great deal upon what level is being taught and the amount of math study the teacher has completed.  It is probably a good requirement for a high school teacher with classes in upper level math because of the need for depth of knowledge needed to transmit not only the information but a love of the subject.  I have encountered many math teachers with minimum exposure to math who have been assigned to teach teach math at the middle or high school level.  Needless to say, these teachers are frequently ineffective because they don't know math. There are also many people who know about math but don't necessarily understand how to work with children.  It seems that this problem of math aptitude for the teacher has some real solutions.  The problem however, is deeper than who has a degree and who does not have a degree in math.

The most important skill of any teacher, including the math teacher, is to motivate the students, provide the student with the proper challenge, and explain what they do not understand.  Unfortunately we seem to have a culture in which many people admit they do not understand math or just do not see why it is important to their life.  Elementary teachers reflect the society they represent and many do not understand the relationship between math and problem solving and are unable to motivate their students to want to learn math.  These teachers end up teaching math as a language by having their students solve and memorize equations.  Even if the student is motivated to learn math that is only a small part of learning mathematics .

An interesting study of east vs. west mathematical thinking demonstrates the difference in the ways each culture is taught math.  Using brain scans to determine what part of the brain an individual uses when confronted with a math problem the researchers found differences between eastern and western use of the brain.  Asian brains generally used the spatial/visual portions of the brain while their western counterparts depended upon the language area of their brain.

I spent a number of years in Asian cultures and my experience leads me to believe that a difference between how we learn math may contribute to the difference in how our brains treat math problems.  In the U.S.  we jump immediately to abstract concepts when teaching math.  The use of graphical representations runs counter to a child’s intuitive knowledge about math.  All kids know that three cookies on the plate are preferable to one cookie.  But, when we put the number 3 and the number 1 in writing and begin talking about what they mean, we have moved beyond the concrete operations the child needs to fully conceptualize what we are talking about.

The Japanese use the abacus to learn math.  I vividly remember young children doing math operations on the abacus much faster and more accurately than I could with pencil and paper.  When their students begin solving equations in all four areas of math using a concrete model, our students are memorizing math tables of graphical representations.  I believe this helps to explain why Asians use visual/spatial areas of their brain and we tend to think in terms of language.  I also recall that most Japanese students knew their "math facts" because of repetition on the abacus.

The aversion to math in our culture is often echoed by middle school children and their chants of “boring” and “I’ll never use this”.  This is not something they thought of on their own.  Frequently you hear their parents say exactly the same thing when you discuss their child's problem with math.  We need math teachers who can counter this national aversion to math by demonstrating and relating the subject to daily life and who understand that math is a way of thinking more than a specific operation.  They also need to motivate children by their teaching to want to learn math.     

Teachers do not necessarily need math degrees but they do need to understand and value math at various levels based upon the level they teach.  However, nothing will change unless there is a paradigm shift in our country.  As long as we do more of the same thing in our math instruction, our children will not want to learn math because it seems boring and useless to them.  It is going to require a commitment from the teachers to learn a different way of thinking about the purpose of math and giving our students positive messages about their ability to think in mathematical ways.

National Standards

Common Core
The National Governors Association and Council of Chief State School Officers released the first official draft of the Common Core State Standards Initiative and will be accepting feedback on the draft until October 21, 2009. This initiative is a set of Core Standards for college and career readiness in maths and language arts. Arne Duncan, the Secretary of Education, has applauded this initiative and stated, "There is no work more important than preparing our students to compete and succeed in a global economy, and it is to the credit of these states that this work is getting done.” I am not opposed to national standards that are process oriented but believe that the problems these standards propose to solve are systemic in our culture not failures caused by the schools. It is more important to address the skills of living in our culture and motivating children to love learning before we set standards that address the problems of universities and career development.

In his article entitled National Subject-Matter Standards? Be Careful What You Wish For Marion Brady wrote “ It will fail for the same reason the No Child Left Behind Act failed—because it will be driven by data derived from simplistic tests keyed to simplistic standards keyed to a simplistic, dysfunctional, obsolete, 19th-century curriculum.” I agree with his assessment of national standards when viewed as a core of knowledge. Standards for college bound students can be controlled by universities. If they have higher expectations, students will meet them. Those who truly want to go to college work hard to achieve their dreams.

A reading of the standards led me to think that we are trying too hard to quantify what we learn as opposed to how we learn. Most of the standards have been in place in our schools for a long time. I guess that pulling them together into a list is a good idea but, I am not sure it is necessary. The standards for world wide competition can be met if we devise an education system of cooperation that individualizes skill development, teaches problem solving and how to find answers to questions. These are skills needed to succeed in the 21st century.

I fear that common core standards will lead us to spend more time teaching a common core of knowledge rather than those skills students will need for the future. I can’t help but think about a video I saw where a teacher was working with a group of elementary students who were developing a project. As she questioned them about their project they would pull out their mobile devices and look up the information they needed to answer the questions and fully develop the project. This points out that the common core of knowledge needed for any project is available to anyone who can use today's technology and knows how to ask the right questions.

The standards that are being developed do not, in my opinion, address the primary aim of our schools. A set of common standards should address the notion of literacy, citizenship and problem solving skills you need in life. Our present aim to send everyone to college is unrealistic just like our expectations in No Child Left Behind. Not everyone is going to go to college or begin a career when they are 18. It seems to me that as our population ages, childhood should be extended to provide life experiences and some time for fun. We are all going to work for 30 or 40 years. Let’s ease up on our kids and let them explore the possibilities of life and develop lifelong learning and coping skills before going to work.

The core standards being developed are more of the same stuff we have been doing since the 19th century. We need some ideas for the 21st century!!

Some Sites of Interest
Flowing Data is a website all about visualizing data so that it can be used. You can't visualize it if you don't find it. A problem I encountered time and again with students doing research was there total reliance on Google for information. It is a fine search engine but there are other places to go. Flowing Data's 30 Resources to Find the Data You Need could be helpful to extend a student's understanding of how to find informtion.

Fighting Drug Use
Teachers frequently encounter adolescent attitudes towards drugs and alcohol that are based upon popular culture's view of their use rather than facts. I was always looking for ways to try to convince my students that children's brains are growing and the use of drugs and alcohol can be detremental to them. They were frequently skeptical. Here are two sites that have some information about the effects of drugs and alcholol on the teenage brain from Scientific American Online:

Marijuana Hurts Some and Helps Others and Is Bad Judgment the Cause and Effect of Adolescent Binge Drinking have some useful information for teenagers.