I have a student that knows the math content being presented in class but always hesitates when he is solving problems and lacks self-confidence. It made me think about what is math anxiety, what causes it, and most importantly how to overcome it.
What is Math Anxiety?
Math anxiety or fear if math is actually quite common. Math anxiety is similar to stagefright. Why does someone suffer from stagefright? Fear of something going wrong in front of a crowd? Fear of forgetting the lines? Fear of going completely blank? Fear of being judged poorly? Math anxiety conjures fear of some type. The fear that one won't be able to do the math or the fear that it's too hard or the fear of failure which often stems from having a lack of confidence. For the most part, math anxiety is the fear about doing the math right, our minds draw a blank and we think we'll fail and of course the more frustrated and anxious our minds become, the greater the chance for drawing blanks. Added pressure of having time limits on math tests and exams also cause the levels of anxiety to grow for many students.
Where Does Math Anxiety Come From?
Usually math anxiety stems from unpleasant experiences in mathematics. Typically math phobics have had math presented in such a fashion that it led to limited understanding, Unfortunately, math anxiety is often due to poor teaching and poor experiences in math which typically leads to math anxiety. Many of the students I've encountered with math anxiety have demonstrated an over reliance on procedures in math as opposed to actually understanding the math concepts. When one tries to memorize procedures, rules, and routines without much understanding, the math is quickly forgotten and panic soon sets in. Think about your experiences with one concept - the division of fractions. You probably learned about reciprocals and inverse. In other words, "It's not yours to reason why, just invert and multiply". Well, you memorized the rule and it works. Why does it work? Do you really understand why it works? Did anyone ever use pizza or math manipulatives to show you why it works. Did anyone ever make the connection to the commutative or distributive laws? Or did they relate the algorithm to whole numbers? It not, you simply memorized the procedures and that was that. Think of math as memorizing all the procedures - what if you forget a few?
Therefore, with this type of strategy, a good memory will help, but, what if you don't have a good memory? Understanding the math is critical. Once students realize they can do the math, the whole notion of math anxiety can be overcome. Teachers and parents have an important role to ensure students understand the math being presented to them.
Myths and Misconceptions - None of the following are true!
You're born with a math gene, either you get it or you don't.
Math is for males, females never get math!
If the logical side of your brain isn't your strengtht, you will never do well in math.
Math is a cultural thing, my culture never got it!
It's hopeless, and much too hard for average people.
There's only one right way to do math.
Overcoming Math Anxiety
1. A positive attitude will help, positive attitudes come with quality teaching for understanding which often isn't the case with many traditional approaches to teaching mathematics.
2. Ask questions, be determined to "understand the math". Don't settle for anything less during instruction. Ask for clear illustrations and for demonstrations or simulations.
3. Practice regularly, especially when you are having difficultly.
4. When total understanding escapes you, hire a tutor or work with peers that understand the math. You can do the math, sometimes it just takes a different approach for you to understand some of the concepts.
5. Don't just read over your notes - do the math. Practice the math and make sure you can honestly state that you understand what you are doing.
6. Be persistent and don't over emphasize the fact that we all make mistakes. Remember, some of the most powerful learning stems from making a mistake.
Find out more about the myths of doing math and you too will overcome math anxiety. And, if you think making mistakes it a bad thing, look again. Sometimes the most powerful learning stems from making mistakes!
Friday, November 22, 2013
Sunday, November 17, 2013
What is Wrong With Charter Schools?
There are two local school districts considering charter schools and there have been discussions about instituting a voucher system. Recently a local newspaper published a column written by one founders of one of the proposed charters and a letter written to the editor by a parent. Both articles are riddled with misinformation.
There are many innovative public schools all around the country. I personally have had the good fortune to have taught in such schools and have worked with many progressive educators. As nice as independent schools are, and I have visited many, they cannot afford to serve the poor to more than a token extent, and so are therefore, elitist. And I do not agree that you should be free to educate students however you want. I believe in public responsibility, and how you educate children matters to society as a whole not just to you or the child. That's where I align myself with thinkers like John Dewey; there is a balance in a democratic society between the freedom of the individual and responsibility to society. Where to draw the line is complex, but it needs to exists. Drawing that line is part of the democratic process.
The rhetoric behind vouchers is that if everyone had vouchers parents could select the best school for their child instead of being forced to go to "government schools".
Where does such logic fall apart? There are two main logistical reasons it is really a false promise. One is economic and the other is the question of who gets to choose.
The private schools that the elite send their children to cost tens of thousands of dollars a year to attend. I looked up a few private schools and tuition ranged from $20,000 to well over $30,000, more than many private colleges. And the actual amount they spend per pupil is well over the tuition since they raise lots of extra money from alumni. They also tend to pay their non-unionized teachers significantly less than public schools.
Since at best the voucher proposals I have seen only pay a small fraction of that, these vouchers will leave the recipients with few real choices without putting out a lot more money. I do not think the public is going to go for vouchers of $20,000+ and have never even heard such figures discussed. It they did, the public education budgets would soar. And those already in private schools would and should claim they should get the subsidies too. What it would do in effect, at the rates being proposed, is subsidize the middle class and the rich to abandon public schools and send their children of private schools, and while leaving such choices out of reach financially for the poor.
The other issue is who chooses. Most private schools have selective admission, and limited space. Since unlike public schools they get to choose their students, even if the voucher fully paid for them (which of course it will not), they would still most likely cream the easiest students to teach, leaving the more difficult to teach children to the public schools.
These two factors in combination would end up subsidizing private schools and the middle and upper class families at the expense of public schools and the poor that are left in them. This would further segregate our schooling system into the haves and the have-nots.
Since I have never heard voucher proponents either suggest that vouchers should be at the levels necessary to have them cover the full cost of most private schools, nor to force private schools to take those children, I find their arguments disingenuous.
Charter schools, in theory at least, get around both of the above limitations. There is no tuition; schools receive the same funding as other public schools, and (at least in California) schools cannot select the students. (In reality, though, they often find ways of using other means to "encourage" and "discourage" certain types of students) So, is this not a solution?
Why I still do not favor even this is that it fundamentally changes the purpose of public schools. Traditionally we have considered the education of the next generation to be a concern of society as a whole. In fact, virtually every society has considered this to be true throughout history. For this reason, locally elected school boards have governed our public schools.
Charter schools and voucher systems make schooling a private consumer choice. In the charter and voucher systems consumers choose among the choices offered them, but have no guaranteed right to have a say about the schooling other than making that choice. Those who do not have children in school have no say at all. Private schools are run privately, and do not have to answer to the public. Charter schools usually have to answer for test scores and financial responsibility, but even there it is to the state and not in any direct way to the local public. While charter schools have governing boards, they select their own members of those boards. This gives control of the content of schooling to those who run the schools, often for-profit concerns, but even if not, private concerns of some sort. While our government is not perfect, should I really trust those who have private agendas and do not have to answer to the public to decide the how and what of our next generation's schooling? Public school boards are elected, and have open meetings: private schools do not have to. Even if the charters do have open meetings, they are often run by national organizations and so are inaccessible and would probably just say, "Don't send your child here if you don't like our agenda".
Charters and vouchers are about redefining the public as consumers rather than citizens, which is part of a larger corporate agenda to destroy public institutions and limit the power of the public.
For the above (and other) reasons, I see truly public schools as the only answer for those committed to a democratic society.
Read between the lines the implication that anything government does must be poor quality. Yet since parents in the suburbs and rich areas are perfectly happy with their public schools, why is it only the public schools that poor kids go to that seem to be failing? "Government" schools for the rich and middle class are fine it seems-as long as they do not have to share them with the poor.
There are many innovative public schools all around the country. I personally have had the good fortune to have taught in such schools and have worked with many progressive educators. As nice as independent schools are, and I have visited many, they cannot afford to serve the poor to more than a token extent, and so are therefore, elitist. And I do not agree that you should be free to educate students however you want. I believe in public responsibility, and how you educate children matters to society as a whole not just to you or the child. That's where I align myself with thinkers like John Dewey; there is a balance in a democratic society between the freedom of the individual and responsibility to society. Where to draw the line is complex, but it needs to exists. Drawing that line is part of the democratic process.
The rhetoric behind vouchers is that if everyone had vouchers parents could select the best school for their child instead of being forced to go to "government schools".
Where does such logic fall apart? There are two main logistical reasons it is really a false promise. One is economic and the other is the question of who gets to choose.
The private schools that the elite send their children to cost tens of thousands of dollars a year to attend. I looked up a few private schools and tuition ranged from $20,000 to well over $30,000, more than many private colleges. And the actual amount they spend per pupil is well over the tuition since they raise lots of extra money from alumni. They also tend to pay their non-unionized teachers significantly less than public schools.
Since at best the voucher proposals I have seen only pay a small fraction of that, these vouchers will leave the recipients with few real choices without putting out a lot more money. I do not think the public is going to go for vouchers of $20,000+ and have never even heard such figures discussed. It they did, the public education budgets would soar. And those already in private schools would and should claim they should get the subsidies too. What it would do in effect, at the rates being proposed, is subsidize the middle class and the rich to abandon public schools and send their children of private schools, and while leaving such choices out of reach financially for the poor.
The other issue is who chooses. Most private schools have selective admission, and limited space. Since unlike public schools they get to choose their students, even if the voucher fully paid for them (which of course it will not), they would still most likely cream the easiest students to teach, leaving the more difficult to teach children to the public schools.
These two factors in combination would end up subsidizing private schools and the middle and upper class families at the expense of public schools and the poor that are left in them. This would further segregate our schooling system into the haves and the have-nots.
Since I have never heard voucher proponents either suggest that vouchers should be at the levels necessary to have them cover the full cost of most private schools, nor to force private schools to take those children, I find their arguments disingenuous.
Charter schools, in theory at least, get around both of the above limitations. There is no tuition; schools receive the same funding as other public schools, and (at least in California) schools cannot select the students. (In reality, though, they often find ways of using other means to "encourage" and "discourage" certain types of students) So, is this not a solution?
Why I still do not favor even this is that it fundamentally changes the purpose of public schools. Traditionally we have considered the education of the next generation to be a concern of society as a whole. In fact, virtually every society has considered this to be true throughout history. For this reason, locally elected school boards have governed our public schools.
Charter schools and voucher systems make schooling a private consumer choice. In the charter and voucher systems consumers choose among the choices offered them, but have no guaranteed right to have a say about the schooling other than making that choice. Those who do not have children in school have no say at all. Private schools are run privately, and do not have to answer to the public. Charter schools usually have to answer for test scores and financial responsibility, but even there it is to the state and not in any direct way to the local public. While charter schools have governing boards, they select their own members of those boards. This gives control of the content of schooling to those who run the schools, often for-profit concerns, but even if not, private concerns of some sort. While our government is not perfect, should I really trust those who have private agendas and do not have to answer to the public to decide the how and what of our next generation's schooling? Public school boards are elected, and have open meetings: private schools do not have to. Even if the charters do have open meetings, they are often run by national organizations and so are inaccessible and would probably just say, "Don't send your child here if you don't like our agenda".
Charters and vouchers are about redefining the public as consumers rather than citizens, which is part of a larger corporate agenda to destroy public institutions and limit the power of the public.
For the above (and other) reasons, I see truly public schools as the only answer for those committed to a democratic society.
Read between the lines the implication that anything government does must be poor quality. Yet since parents in the suburbs and rich areas are perfectly happy with their public schools, why is it only the public schools that poor kids go to that seem to be failing? "Government" schools for the rich and middle class are fine it seems-as long as they do not have to share them with the poor.
Friday, November 8, 2013
When Will I Ever Use This Stuff?!
When will I ever use this stuff?!
I have been in education for forty years and the statement I hear over and over again with regards to math is something I'm sure you have heard too. It I've heard it once, I've heard it thousands of times: "When will I ever use this stuff".
All too often, students who make this statement are referring to the actual concept they are learning; whether it be Pythagorean's Theorem, long division, multiplication of polynomials, properties of polygons, the Power Rule, or what have you, their comment is usually based on the specific math topic. I related what they are learning to "real- life" examples, and or course, I tell them they are also actually applying and deepening many life long skills that will benefit them for the rest of their lives. Skills that include but are not limited to: analyzing, making connections, problem solving, looking for patterns, proving, thinking, understanding and persistence. Math is an opportunity gateway, it opens doors and without it, it often closes doors. However, if in fact math isn't for you and you have a goal or career that doesn't require university math, here's some of the everyday math that you'll need, hence this article is for you.
Everyday Math
First of all, before I generate this list of what I believe to be helpful math for everyone to know for day to day living, it's only my opinion and may differ from the opinions of others.
Percent
Percent is a concept that is used regularly. What is the percent of deductions of your gross pay? This helps you calculate your net pay or potential pay. Sales are often based on percent, what is 20, 30, or 40 percent of a number? Percent is used in loans, investment and mortgages. You need to understand enough about percent to use a calculator correctly. Percent is used to calculate simple and compound interest. Percents are used in services to calculate sales tax and tips. You should be able to use mental math for some percent computations and the calculator for others.
Four Operations
The four operations refers to adding, subtracting, dividing, and multiplying and are sometimes referred to as arithmetic. I think this concept is self explanatory. We use the four operations for mental math in grocery stores, bill payment, recipes, etc. You should know the basic multiplication facts and you should know when and how to add, subtract, divide and multiply fluently mentally and with a calculator.
Measurement
Understanding the various units of measure that we are exposed to each day is vital to making decisions based on this information. When you go into the carpet store to consider a purchase and the store clerk tells you the carpet is 4.50 per square yard, you need to have an understanding of what your room measurements of 12 feet by 16 feet means in terms of the unit of measure, square yards. Think in terms of following a recipe. If you do not understand the various units of measure for dry goods such as flour, then you can make a mess out of baking. Measurement recognition and understanding is a daily occurrence. Even if you need an online converter or calculator for conversions, a basic understanding of measurement is helpful.
Estimation
Estimation is a basic skill we use so much in our daily lives that we never think about it. Estimation is not a guess; it is a calculation based upon specific information and often referred to as an "educated guess".You estimate what time you have to get up in the morning to do all the tasks needed before you head off to school or work. You estimate how long it will take you to your homework. I'm sure you can think of countless examples.
Charts, Graphs and Data
Visual representation of information is commonplace in modern living. Graphs and charts are used to reduce the amount of textual explanation that many comparisons require. With the advent of the internet, it's imperative that we have the ability to look at a graph and see the weight of the data points individually while having an idea as to the trend the data exhibits. Basic to extremely complex information can be portrayed using charts such as scatter plots in terms we understand. It's helpful to be able to interpret pie charts, and line bar graphs.
Problem Solving
Problem solving is a daily skill. Being able to use the basic math mentioned here and apply it to problem solving situations is key. In other words, knowing what math to use to solve basic problems. Examples of this are in doubling a recipe, halving a recipe, calculating how much tile is needed id a room of various sizes, balancing check books, calculating time lapses and distances for trips along with various money situations/financial literacy.
It can be difficult to determine the daily math one needs in everyday life and much depends on ones responsibilities in life, however, having a grasp on the above certainly helps. And, taking steps to improve your math skills is always a great idea. Knowing math helps us understand the world and empowers our ideas.
I have been in education for forty years and the statement I hear over and over again with regards to math is something I'm sure you have heard too. It I've heard it once, I've heard it thousands of times: "When will I ever use this stuff".
All too often, students who make this statement are referring to the actual concept they are learning; whether it be Pythagorean's Theorem, long division, multiplication of polynomials, properties of polygons, the Power Rule, or what have you, their comment is usually based on the specific math topic. I related what they are learning to "real- life" examples, and or course, I tell them they are also actually applying and deepening many life long skills that will benefit them for the rest of their lives. Skills that include but are not limited to: analyzing, making connections, problem solving, looking for patterns, proving, thinking, understanding and persistence. Math is an opportunity gateway, it opens doors and without it, it often closes doors. However, if in fact math isn't for you and you have a goal or career that doesn't require university math, here's some of the everyday math that you'll need, hence this article is for you.
Everyday Math
First of all, before I generate this list of what I believe to be helpful math for everyone to know for day to day living, it's only my opinion and may differ from the opinions of others.
Percent
Percent is a concept that is used regularly. What is the percent of deductions of your gross pay? This helps you calculate your net pay or potential pay. Sales are often based on percent, what is 20, 30, or 40 percent of a number? Percent is used in loans, investment and mortgages. You need to understand enough about percent to use a calculator correctly. Percent is used to calculate simple and compound interest. Percents are used in services to calculate sales tax and tips. You should be able to use mental math for some percent computations and the calculator for others.
Four Operations
The four operations refers to adding, subtracting, dividing, and multiplying and are sometimes referred to as arithmetic. I think this concept is self explanatory. We use the four operations for mental math in grocery stores, bill payment, recipes, etc. You should know the basic multiplication facts and you should know when and how to add, subtract, divide and multiply fluently mentally and with a calculator.
Measurement
Understanding the various units of measure that we are exposed to each day is vital to making decisions based on this information. When you go into the carpet store to consider a purchase and the store clerk tells you the carpet is 4.50 per square yard, you need to have an understanding of what your room measurements of 12 feet by 16 feet means in terms of the unit of measure, square yards. Think in terms of following a recipe. If you do not understand the various units of measure for dry goods such as flour, then you can make a mess out of baking. Measurement recognition and understanding is a daily occurrence. Even if you need an online converter or calculator for conversions, a basic understanding of measurement is helpful.
Estimation
Estimation is a basic skill we use so much in our daily lives that we never think about it. Estimation is not a guess; it is a calculation based upon specific information and often referred to as an "educated guess".You estimate what time you have to get up in the morning to do all the tasks needed before you head off to school or work. You estimate how long it will take you to your homework. I'm sure you can think of countless examples.
Charts, Graphs and Data
Visual representation of information is commonplace in modern living. Graphs and charts are used to reduce the amount of textual explanation that many comparisons require. With the advent of the internet, it's imperative that we have the ability to look at a graph and see the weight of the data points individually while having an idea as to the trend the data exhibits. Basic to extremely complex information can be portrayed using charts such as scatter plots in terms we understand. It's helpful to be able to interpret pie charts, and line bar graphs.
Problem Solving
Problem solving is a daily skill. Being able to use the basic math mentioned here and apply it to problem solving situations is key. In other words, knowing what math to use to solve basic problems. Examples of this are in doubling a recipe, halving a recipe, calculating how much tile is needed id a room of various sizes, balancing check books, calculating time lapses and distances for trips along with various money situations/financial literacy.
It can be difficult to determine the daily math one needs in everyday life and much depends on ones responsibilities in life, however, having a grasp on the above certainly helps. And, taking steps to improve your math skills is always a great idea. Knowing math helps us understand the world and empowers our ideas.
Friday, November 1, 2013
Online Resources: There are a number of websites that provide help with mathematics
This week I am sharing some links to excellent websites that provide help with math.
Online Resources:
* http://kahnacademy.org - this site contains hundreds of topic specific videos and example problems.
* http://www.purplemath.com
* http://math.com
* http://mathforum.org/dr/math
* http://nlvm.usu.edu/en/nav/vlibrary.html - National Library of Virtual Manipulatives
Online Resources:
* http://kahnacademy.org - this site contains hundreds of topic specific videos and example problems.
* http://www.purplemath.com
* http://math.com
* http://mathforum.org/dr/math
* http://nlvm.usu.edu/en/nav/vlibrary.html - National Library of Virtual Manipulatives
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