It is common to say that math help us think but all academic subjects rely on thinking. Solving word puzzles, studying, reading, writing an essay, etc are thinking activities. However Math might involve much more thinking activities than other subjects because they concerned primarily with solving problems. The Math vocabulary represents some very powerful ideas.
Our understanding of quantity holds concepts refined over thousands of years (negatives, zero, decimals). Math ideas require extensive thinking to be grasped. Some languages only have words for one, two and many. In those languages the notion of many has never been subdivided and structured.
The notion of quantity has known several developments over the years:
Each quantity can be referred by number words (one, two, three, one hundred and five, one thousand two hundreds and fifty)
The number words can be written with symbols not with letters like lines in the sand. The tally system has a line for each quantity.
Shortcuts are used for large quantities. Romans numerals are then used in this case. Some examples are: V = five, X = ten, C = one hundred.
Emptiness is represented by zero.
The position of a number is a shortcut for another number. Example: 234 = 200+30+4.
Numbers can have very small differences. Examples: 1.1, 1.01, 1.001.
Numbers can be less than nothing. They are called negative numbers and reverse or opposite of another number. Example: negative height is underground. Negative saving is debt.
Numbers can be two dimensional (complex numbers).
Numbers can be very small and still doesn't represent zero.
The concept of numbers has shaped our world during millenia. Numbers were used to describe time in different calendar systems. One of the calendar system was modeled on the number system using the symbols BC and AD. Prices have been set by the stock market in increments of 1/8 until 2000 AD.
The notion of numbers has allowed us to conceptualize many physical ideas. For example the notion of zero allows us to understand the concept of vacuum or emptiness. The notion of negative numbers allows us to understand antigravity and antimatter.
The math vocabulary has shaped our different ways of thinking primarily thanks to the development of the numbers concept. Basic arithmetic is used in various fields of human activity. Multiplication and division which have been difficult concepts to be grasped by scholars for thousands of years are taught to small children in grade school. This is made possible because of better ways to describe quantity. The development of other branches in mathematics such as Geometry, Calculus and Statistics allow us to model and understand better the notions of shape, change and chance.
Interested in tutoring visit New Direction Tutoring Services at www.ndes.wikidot.com to contact me. I can work facetoface or online. You can also leave a message in the comment section of this post.
The purpose of this blog is to teach Math subjects : Calculus, Precalculus, Algebra and Basic Math. It focuses on the learning theories and skills needed in any subject. It educates mostly about the learning skills needed in Math, French, ESL and Spanish and the use of open and web resources for learning.
Wednesday, November 14, 2012
Why do we learn math?
Saturday, July 7, 2012
Why do you have to use the OpenCourseWare?
Let's remind that the OpenCourseWare is made of courses, taught at the high
school or at the university level, that are put on the internet for anyone to
access freely.
access freely.
You can use the OpenCourseWare for several reasons including the following:
1. For your own interest. If you are interested in a particular subject or field you
can use the OpenCourseWare to gain or update your knowledge in that field.
2. To update your skills or knowledge for work. If you are a professional you can
use the OpenCourseWare to review or update your knowledge in a subject or field.
3. To understand concepts you are studying. The OpenCourseWare is used by
many students to help them understand concepts they are studying. If you
are studying mathematics you can find a lot of OpenCourseWare materials to help you
to understand a lot of mathematical concepts.
4. To learn something for a particular subject or task. I heard about someone working on a solar energy project using the OpenCourseWare to help him realizing the project.
5. To supplement/create teaching materials. Educators use the
OpenCourseWare to create courses, enrich the curriculum, etc.
These reasons are based on a study by the OpenCourseWare Consortium.
According to this study the OpenCourseWare is used by Teachers, Students
at the Secondary or high school level, Students at the undergraduate and graduate level, Selflearners, Working professionals, Employers, etc.
The results of the survey by OCW about respondents using OpenCourseWare
are:
46%: to help understand concepts I am studying
31%: to learn something for a specific project or task
23%: supplement/create teaching materials
50%: to update my skills or knowledge for work
59%: for my own interest
7%: other.
A survey of users of OCW materials translated in traditional and simplified
Chinese by researchers at the University of Illinois at UrbanaChampaign revealed similar results.
68%: to extend my professional knowledge
62.8%: to increase knowledge of personal interests
31.4%: to answer questions related to my profession
25.9%: for academic studies
The percentages of these two surveys show that the OpenCourseWare is
mostly used for personal interests, professional knowledge and academic studies.
My interest in different subjects of human and exact sciences led me to create the Open Popular University. I realize also that knowledge cannot be the
prerogative of educational institutions meaning that in order to learn something you have to spend not only a fortune but a huge amount of time and physical energy. Knowledge should be to the disposal of the six billions of humans beings living on the earth and everybody should be able to access and learn that knowledge without any restrictions. The purpose of Open Popular University is to demystify knowledge and make it accessible to anybody provided that you have access to a computer and internet access.
My goal for Open Popular University is that it can become an open and free encyclopedia of courses and knowledge. A lot of resources are needed in order to realize this goal. I am launching a fundraising in order to optimize the site and to continue to add more courses. If you are a reader of this blog and believe in my philosophy of education I am asking for your support by doing the following:
1. Make a donation to www.indiegogo.com/OpenPopularUniversity and ask others to do the same by sharing the link of the fundraising.
2. Like the facebook page of Open Popular University at www.facebook.com/OpenPopularUniversity.
3. Visit the site of Open Popular University at www.openpu.wikidot.com and share the link to others. Feel free to reach me for any questions by writing on the comments section of this blog.
Tuesday, June 19, 2012
Who uses Opencouseware?
In a recent time to learn a subject you can matriculate at an university
in order to attend a class. Depending on the level of the course one
wants to attend one can take a class at a community college or an adult
education center that offers various courses. For example the Boston
Adult Education Center has offered basic and short courses in different
areas for a very long time. Today it is not necessary to spend some
money to attend some courses thanks to the Opencourseware and various
online organizations that offer free courses. One can find a subject in
an opencourseware and find support in a social network like Open study. A
few months ago I launched the project Open Popular University that
has courses in Engineering, Sciences, Math, Human Sciences, etc. In the
section "Resources" are found courses in French. I added a social
network like Open Study to support a course. For certain disciplines
like Civil Engineering I put the whole curriculum like the one offered
by a renowned university with the free courses. In this way someone can
learn an university degree program by oneself. I am presently launching a
fundraising campaign to
raise some funds to optimize the site and add more courses. I am
appealing to my readers to support this project by clicking the link
"fundraising campaign" or clicking the widget on the sidebar of this
blog.
The use of OpenCourseWare is supported by studies of which one originates from Mary Lou Forward, director of Open Courseware Consortium. OpenCourseWare (OCW) and Open Educational Resources (OER) rest on the idea that free and open sharing in education can favor the improvement of teaching and learning around the world. The OpenCourseWare movement was initiated by the Massachusetts Institute of Technology (MIT). Other universities noticing the power of open sharing followed the MIT example. Initially OCW was conceived as a resource for faculty to exchange ideas and course materials. Today OCW supports formal and informal learning and millions of people worldwide are using highquality educational materials for different reasons.
The OpenCourseWare is used by faculty (Professors, Teachers) and students at the university and high school level, selflearners, employers, working professionals and different others. The study of Mary Lou Forward shows that a high percentage of users are not currently involved in formal education as faculty or students. The study uses statistics to show the different reasons people use the opencourseware. University professors and school teachers use the opencourseware to develop their courses. The opencouseware is used for professional development. Some California teachers use the opencourseware of the university of CaliforniaIrvine to help them to prepare for teaching credentials. The African Virtual University provides professional development through the use of the opencourseware. It developed curricula for bachelor of education programs in 5 subjects to prepare teachers. The curriculum is presented in French, Portuguese and English at the African Virtual University (AVU) portal. Opencourseware is also supported by different platforms such as Open study, PeertoPeer university, etc. Many universities and companies put their opencourseware for free and open access. Their opencourseware is organized in different ways. Opencourseware presents different gaps and there ia a need to fill in these gaps. This is what I am trying to do at Open Popular University and I need the support of different interested people.
The use of OpenCourseWare is supported by studies of which one originates from Mary Lou Forward, director of Open Courseware Consortium. OpenCourseWare (OCW) and Open Educational Resources (OER) rest on the idea that free and open sharing in education can favor the improvement of teaching and learning around the world. The OpenCourseWare movement was initiated by the Massachusetts Institute of Technology (MIT). Other universities noticing the power of open sharing followed the MIT example. Initially OCW was conceived as a resource for faculty to exchange ideas and course materials. Today OCW supports formal and informal learning and millions of people worldwide are using highquality educational materials for different reasons.
The OpenCourseWare is used by faculty (Professors, Teachers) and students at the university and high school level, selflearners, employers, working professionals and different others. The study of Mary Lou Forward shows that a high percentage of users are not currently involved in formal education as faculty or students. The study uses statistics to show the different reasons people use the opencourseware. University professors and school teachers use the opencourseware to develop their courses. The opencouseware is used for professional development. Some California teachers use the opencourseware of the university of CaliforniaIrvine to help them to prepare for teaching credentials. The African Virtual University provides professional development through the use of the opencourseware. It developed curricula for bachelor of education programs in 5 subjects to prepare teachers. The curriculum is presented in French, Portuguese and English at the African Virtual University (AVU) portal. Opencourseware is also supported by different platforms such as Open study, PeertoPeer university, etc. Many universities and companies put their opencourseware for free and open access. Their opencourseware is organized in different ways. Opencourseware presents different gaps and there ia a need to fill in these gaps. This is what I am trying to do at Open Popular University and I need the support of different interested people.
Tuesday, May 22, 2012
How to Use Trigonometric Substitution to Integrate
With the trigonometric substitution method, you can do integrals containing radicals of the following forms (given a is a constant and u is an expression containing x):
You’re going to love this technique … about as much as sticking a hot poker in your eye.
Before you look at how trigonometric substitution works, here are some mnemonic tricks to help you keep this method straight. Remember, with mnemonic devices, silly (and vulgar) works. First, this involves three trig functions, tangent, sine, and secant. Their initial letters, t, s, and s, are the same letters as the initial letters of the name of this technique, trigonometric substitution. Pretty nice, eh?
Okay, this sin/ass mnemonic is admittedly pretty weak. If you can come up with a better mnemonic, use it!
Now, ready to do a problem?

Draw a right triangle—basically a SohCahToa triangle—wherea SohCahToa triangle is shown in the following figure.

Solvethen differentiate, and solve for dx.

Find which trig function is represented by the radical over the aand then solve for the radical.Look at the triangle in the figure. The radical is the hypotenuse and a is 2, the adjacent side, so

Use the results from Steps 2 and 3 to make substitutions in the original problem and then integrate.

Substitute the x expressions from Steps 1 and 3 back in forYou can also get the expressions from the triangle in the above figure.
http://www.dummies.com/howto/content/howtousesinesubstitutiontointegrate.html
Saturday, May 5, 2012
Some quotes that can help you move ahead in life
If you need some motivation to move ahead in your life today,
try out one of these 20 encouraging quotes to get your day started.
“Twenty years from now you will be more disappointed by the things that you didn’t do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover.”
 Mark Twain
“Get going. Move forward. Aim High. Plan a takeoff. Don’t just sit on the runway and hope someone will come along and push the airplane. It simply won’t happen. Change your attitude and gain some altitude. Believe me, you’ll love it up here.”
 Donald Trump
“I took a deep breath and listened to the old brag of my heart. I am, I am, I am.”
 Sylvia Plath
“Opportunity is missed by most people because it is dressed in overalls and looks like work.”
 Thomas A. Edison
“I decided, very early on, just to accept life unconditionally; I never expected it to do anything special for me, yet I seemed to accomplish far more than I had ever hoped. Most of the time it just happened to me without my ever seeking it.”
 Audrey Hepburn
“Knowledge has to be improved, challenged, and increased constantly, or it vanishes.”
 Peter Drucker
“If you don’t pay appropriate attention to what has your attention, it will take more of your attention than it deserves.”
 David Allen
“I’d rather be a failure at something I love than a success at something I hate.”
 George Burns
“The miracle is not that we do this work, but that we are happy to do it.”
“Learn from yesterday, live for today, hope for tomorrow. The important thing is not to stop questioning.”
 Albert Einstein
“I find hope in the darkest of days, and focus in the brightest. I do not judge the universe.”
 Dalai Lama
“Character cannot be developed in ease and quiet. Only through experience of trial and suffering can the soul be strengthened, ambition inspired, and success achieved.”
 Helen Keller
“And no, we don’t know where it will lead. We just know there’s something much bigger than any of us here.”
 Steve Jobs
“Real integrity is doing the right thing, knowing that nobody’s going to know whether you did it or not.”
 Oprah Winfrey
“Talent is cheaper than table salt. What separates the talented individual from the successful one is a lot of hard work.”
 Stephen King
“Big jobs usually go to the men who prove their ability to outgrow small ones.”
 Ralph Waldo Emerson
“If they can make penicillin out of mouldy bread, they can sure make something out of you.”
Muhammad Ali
“Never give up, for that is just the place and time that the tide will turn.”
 Harriet Beecher Stowe
“It is by going down into the abyss that we recover the treasures of life. Where you stumble, there lies your treasure.”
 Joseph Campbell
“In essence, if we want to direct our lives, we must take control of our consistent actions. It’s not what we do once in a while that shapes our lives, but what we do consistently.”
 Tony Robbins
Wednesday, April 25, 2012
Why find a personal tutor?
Employing a private tutor was once the preserve of the prosperous few. These days, private teaching is a support available much more widely than any other time. People searching for private instructors have better choices along with personalized help available for learners in a lot of different subjects.
Private tutoring can consist of a specialist teacher attending the actual learners home. Using the growth of the net and high speed broadband, private teaching can also be available online. Several private instructors use a combination of individualized tutoring given on the students home (or any other mutually decided location) along with the possibilities that online studying offers.
Precisely why find a nonpublic tutor?
Educational institutions, schools, colleges and universities obviously teach peeople. Sometimes it really is individual consideration that really helps make the difference. The effectiveness of onetoone tutoring, the foundation of nearly all private educating, should never be overlooked. Its not hard to discover why private instructing can be so successful. An experienced instructor will be able to identify where a student has expertise gaps or difficulties
Private teaching can be particularly useful for kids, young learners and adults. The increase of online tutoring has had help to millions of individuals..
Private teaching online
For many millions of individuals,, private teaching over the internet can be a lifeline. .
From homework assistance to more particular subject teaching or test prep, personal teaching can create a big difference to educational and also career outcomes. In a competing world where qualifications and also achievement count, private tutoring is an option well worth thinking about.
For private tutoring visit New Directions Tutoring Services at www.ndes.wikidot.com
Article source site URL www.personalizedchristmas.net
Thursday, April 12, 2012
Study Skills for Success: Study Smarter, not Harder
Far too many people study harder rather than smarter and end up burning out. Sitting and passing exams is supposed to get you ahead in life – not make you tense and a nervous wreck.
With simple and effective techniques you can massively increase your ability to pass exams. Here are a few tips to get the most out of your study time.
Use lots of color. Using color in note taking and study will increase your ability to remember and recall information. It makes your notes more exciting to reread and learn.
Use felt pens of different thicknesses, colored pencils and crayons. Use your favorite colors, highlight key information, and make notetaking fun.
Talk about the information as much as possible. When you say information out loud, it is reinforced in the brain. Have you ever asked someone to remind you to do something? Do they usually need to remind you? Not usually. When you say something out loud it comes out of your mouth and back into the brain through your ears. Talk about the information you are learning to yourself, friends, family, or even the dog! Just say it out loud.
Study at “my best thinking time.” Are you a morning, afternoon or late night person? Study when you are most alert. If you prefer to stay up late at night, study at this time. One of the worst times to study is the one hour after school. Take time to refresh and relax before doing homework or study.
Study the information you don’t know. This may sound obvious and is a major key to successful study. Take out old test and exam papers and learn the information you got wrong. When you get your test marks back, celebrate if you have a pass mark. However it is the questions you got wrong that are the most important to learn. This is how you will improve.
Study for 20 minutes with 5minute breaks. Having short study times increases the retention of information and avoids the brain ‘chunking out’ or forgetting. During a five minute break, eat brain food, get some fresh air, or do some quick exercise to keep the blood and oxygen flowing to the brain. Always leave your study environment during this fiveminute break to give the brain some variety and a change of focus.
Frame important information. Putting a frame around information makes the brain focus within the frame and can raise comprehension. This is such a simple strategy and works. If you are a doodler and often draw all over the page when listening or thinking, doodle frames around the edge of the page – it will increase your ability to recall and remember the information within the frame.
Review your notes one day after learning them. Reviewing or periodic revision of material is needed to reactivate the stored memories and prevent information from being buried under other data. The more recent, regular, and fun the review is the easier it will be to recall. Research shows if you go over your notes the next day, your recall can stay at up to ninety percent, however waiting three days before you revisit your notes drops recall down to thirty percent
http://www.lifebound.com/blog/educators/studyskillsforsuccessstudysmarternotharder/
For tutoring in Math, French and Spanish visit www.ndes.wikidot.com
http://www.lifebound.com/blog/educators/studyskillsforsuccessstudysmarternotharder/
For tutoring in Math, French and Spanish visit www.ndes.wikidot.com
Thursday, April 5, 2012
How to Find the Volume of a Shape Using the Washer Method
Geometry tells you how to figure the volumes of simple solids. Integration enables you to calculate the volumes of an endless variety of much more complicated shapes. If you have a round shape with a hole in the center, you can use the washer method to find the volume by cutting that shape into thin pieces. Each slice has a hole in its middle that you have to subtract. There’s nothing to it.
Here you go.
A sideways stack of washers — just add up the volumes of all the washers.
Just think: All the forces of the evolving universe and all the twists and turns of your life have brought you to this moment when you are finally able to calculate the volume of this solid — something for your diary. So what’s the volume?
 Determine where the two curves intersect.So the solid in question spans the interval on the xaxis from 0 to 1.
 Figure the area of a crosssectional washer.In the above figure, each slice has the shape of a washer so its area equals the area of the entire circle minus the area of the hole.The area of the circle minus the hole iswhere R is the outer radius (the big radius) and r is the radius of the hole (the little radius).
 Multiply this area by the thickness, dx, to get the volume of a representative washer.
 Add up the volumes of the washers from 0 to 1 by integrating.
Focus on the simple fact that the area of a washer is the area of the entire disk,
minus the area of the hole,
When you integrate, you get
This is the same, of course, as
which is the formula given in most books. But if you just learn that by rote, you may forget it. You’re more likely to remember how to do these problems if you understand the simple bigcircleminuslittlecircle idea.
Source: www.dummies.com
Labels:
Calculus,
math learning,
volume of a shape
Thursday, March 29, 2012
Differential & Integral Calculus, Lec 1, Math 31A, UCLA
In this video of a math course at the university of California at Los Angeles are simply defined the notions of differential and integral calculus, slope and limit. Simply put, the differential calculus is the calculation of the rate of change and the integral calculus defines the accumulation of change. The equation of the derivative of a function tells you how this function changes meaning when it increases and when it decreases. The integral calculus tells how much changes happen. The velocity of a car can be represented by the equation of a derivative. This function derivative tells you when the velocity increases, decreases and when the car comes to a stop. The integral gives the distance traveled by the car in absolute value of course.
For more calculus courses contact me at www.ndes.wikidot.com
For more calculus courses contact me at www.ndes.wikidot.com
Evaluating integrals using area interpretation
Since the integral is an area under curve its calculation can be done without calculating the antiderivative but rather by calculating the areas under curve. This is what this video shows
Wednesday, March 28, 2012
AP Calculus AB: Revolving Solids Known Cross Sections
This is a problem concerning the volume of a solid with known cross section. The calculation of the volume is found in three steps:
1) Express the area of the cross section as a function of a variable
2) Find the limits of integration
3) Integrate the function
The cross section can be a triangle, a square, rectangle, washer, etc. A washer has the shape of a disk with a circular region cut out from its center. Its area is found by subtracting the area of the inner circle from the area of the bigger circle.
For calculus tutoring online or facetoface contact me at www.ndes.wikidot.com
1) Express the area of the cross section as a function of a variable
2) Find the limits of integration
3) Integrate the function
The cross section can be a triangle, a square, rectangle, washer, etc. A washer has the shape of a disk with a circular region cut out from its center. Its area is found by subtracting the area of the inner circle from the area of the bigger circle.
For calculus tutoring online or facetoface contact me at www.ndes.wikidot.com
Saturday, March 24, 2012
Definition of some basic math words and expressions
In every body of knowledge the definition of words is important. Here is the definition of some basic words and expressions used in math.
Mathematics (math) is the study of numbers, quantities, shapes, and space using mathematical processes, rules, and symbols. There are many branches of mathematics and a large vocabulary associated with this subject.
Here are some math words and terms you will likely come across but may not know their precise meanings.
Algorithm A stepbystep mathematical procedure used to find an answer.
Coefficient A number that multiplies a variable. For example, 9 is the coefficient in 9x.
Denominator The bottom number in a fraction. The denominator represents the number of parts into which the whole is divided. For example, 6 is the denominator in the fraction .
Equation A mathematical statement used to show that two expressions are equal. It contains an equals sign. For example, 16  9 = 7 (the expression 16  9 and the expression 7 are equal).
Greatest Common Factor (greatest common divisor) The largest number that will divide two or more other numbers equally. For example, the greatest common factor of 32 and 48 is 16.
Improper Fraction (mixed fractions) A fraction that has a larger numerator than denominator. For example, is an improper fraction.
Inverse Operations Opposite or reverse operations. Addition and subtraction are inverse operations, as are multiplication and division.
Negative Number A number that is less than zero. A minus sign is used to show that a number is negative. For example, 12 is a negative number.
Numerator The top number in a fraction. The numerator represents the number of parts of the whole. For example, 5 is the numerator in the fraction .
Ordinal Number A number that shows place or position, as in 2nd place.
Positive Number A number that is greater than zero. While a minus sign is used to signify a negative number, the absence of a minus sign signifies a positive number.
Prime Number A number that can be divided evenly only by itself and 1. For example, 7 is a prime number.
Square Number A number that results from multiplying another number by itself. For example, 49 is the square of 7 (7 x 7 = 49).
Square Root of a Number A number that is multiplied by itself to produce a square number. For example, 7 is the square root of 49. It is designated by the symbol √.
Variable A quantity that can change or vary, taking on different values. It is typically represented by a letter of the alphabet. For example x is the variable in 9x (x can be any number that is being multiplied by 9).
These are just some of the many words and terms found in mathematics. It is important to know the meanings of words and terms you will encounter as you progress through the study of math.
Mathematics (math) is the study of numbers, quantities, shapes, and space using mathematical processes, rules, and symbols. There are many branches of mathematics and a large vocabulary associated with this subject.
Here are some math words and terms you will likely come across but may not know their precise meanings.
Algorithm A stepbystep mathematical procedure used to find an answer.
Coefficient A number that multiplies a variable. For example, 9 is the coefficient in 9x.
Denominator The bottom number in a fraction. The denominator represents the number of parts into which the whole is divided. For example, 6 is the denominator in the fraction .
Equation A mathematical statement used to show that two expressions are equal. It contains an equals sign. For example, 16  9 = 7 (the expression 16  9 and the expression 7 are equal).
Greatest Common Factor (greatest common divisor) The largest number that will divide two or more other numbers equally. For example, the greatest common factor of 32 and 48 is 16.
Improper Fraction (mixed fractions) A fraction that has a larger numerator than denominator. For example, is an improper fraction.
Inverse Operations Opposite or reverse operations. Addition and subtraction are inverse operations, as are multiplication and division.
Negative Number A number that is less than zero. A minus sign is used to show that a number is negative. For example, 12 is a negative number.
Numerator The top number in a fraction. The numerator represents the number of parts of the whole. For example, 5 is the numerator in the fraction .
Ordinal Number A number that shows place or position, as in 2nd place.
Positive Number A number that is greater than zero. While a minus sign is used to signify a negative number, the absence of a minus sign signifies a positive number.
Prime Number A number that can be divided evenly only by itself and 1. For example, 7 is a prime number.
Square Number A number that results from multiplying another number by itself. For example, 49 is the square of 7 (7 x 7 = 49).
Square Root of a Number A number that is multiplied by itself to produce a square number. For example, 7 is the square root of 49. It is designated by the symbol √.
Variable A quantity that can change or vary, taking on different values. It is typically represented by a letter of the alphabet. For example x is the variable in 9x (x can be any number that is being multiplied by 9).
These are just some of the many words and terms found in mathematics. It is important to know the meanings of words and terms you will encounter as you progress through the study of math.
Wednesday, March 14, 2012
New technologies can help physically challenged and diverse learners learn math
Every mathematics teacher wants to be able to help their students learn more math and learn math better. The typical mathematics classroom contains a diverse range of students who differ in their readiness to learn. Quality mathematics teachers seek new strategies to reach their students and help them grow.
Differences in learning occur for a variety of reasons. Some students may have academically encouraging homes. Some students may have academic learning disabilities. Other students may have physical differences. And just as with physical growth, some students may simply grow in their mathematical abilities at different rates.
Regardless of the reason, mathematics educators often strive to find tools and resources to help meet individual student needs and differentiate instruction. Handheld, mobile technologies may offer just the means to do that. As this recent article from SmartPlanet, details there are new opportunities for the visually impaired learner using “haptic” technology.
Haptic means relating to the sense of touch. Through a research project at Vanderbilt University, an android app is being developed to help learners who have difficulties with their vision to learn mathematics – a subject where visual data such as graphs, charts, and symbols are relied upon for communication.
Many learn better through doing rather than speaking or hearing. Mathematics can be difficult to teach to these learners. In addition to assisting the visually impaired, such technology may open the door for the kinesthetic learner. With handheld devices becoming downright commonplace, this seems like an opportunity with a lot of promise.
http://blog.lexile.com/category/innovativepractices/
Differences in learning occur for a variety of reasons. Some students may have academically encouraging homes. Some students may have academic learning disabilities. Other students may have physical differences. And just as with physical growth, some students may simply grow in their mathematical abilities at different rates.
Regardless of the reason, mathematics educators often strive to find tools and resources to help meet individual student needs and differentiate instruction. Handheld, mobile technologies may offer just the means to do that. As this recent article from SmartPlanet, details there are new opportunities for the visually impaired learner using “haptic” technology.
Haptic means relating to the sense of touch. Through a research project at Vanderbilt University, an android app is being developed to help learners who have difficulties with their vision to learn mathematics – a subject where visual data such as graphs, charts, and symbols are relied upon for communication.
Many learn better through doing rather than speaking or hearing. Mathematics can be difficult to teach to these learners. In addition to assisting the visually impaired, such technology may open the door for the kinesthetic learner. With handheld devices becoming downright commonplace, this seems like an opportunity with a lot of promise.
http://blog.lexile.com/category/innovativepractices/
Tuesday, March 6, 2012
Instruction for masses knocks down campus walls
The pitch for the online course sounds like a latenight television ad, or maybe a subway poster: “Learn programming in seven weeks starting Feb. 20. We’ll teach you enough about computer science that you can build a Web search engine like Google or Yahoo.”
But this course, Building a Search Engine, is taught by two prominent computer scientists, Sebastian Thrun, a Stanford research professor and Google fellow, and David Evans, a professor on leave from the University of Virginia.
The big names have been a big draw. Since Udacity, the forprofit startup running the course, opened registration on Jan. 23, more than 90,000 students have enrolled in the searchengine course and another taught by Mr. Thrun, who led the development of Google’s selfdriving car.
Welcome to the brave new world of Massive Open Online Courses — known as MOOCs — a tool for democratizing higher education. While the vast potential of free online courses has excited theoretical interest for decades, in the past few months hundreds of thousands of motivated students around the world who lack access to elite universities have been embracing them as a path toward sophisticated skills and highpaying jobs, without paying tuition or collecting a college degree. And in what some see as a threat to traditional institutions, several of these courses now come with an informal credential (though that, in most cases, will not be free).
Consider Stanford’s experience: Last fall, 160,000 students in 190 countries enrolled in an Artificial Intelligence course taught by Mr. Thrun and Peter Norvig, a Google colleague. An additional 200 registered for the course on campus, but a few weeks into the semester, attendance at Stanford dwindled to about 30, as those who had the option of seeing their professors in person decided they preferred the online videos, with their simple views of a hand holding a pen, working through the problems.
Mr. Thrun was enraptured by the scale of the course, and how it spawned its own culture, including a Facebook group, online discussions and an army of volunteer translators who made it available in 44 languages.
“Having done this, I can’t teach at Stanford again,” he said at a digital conference in Germany in January. “I feel like there’s a red pill and a blue pill, and you can take the blue pill and go back to your classroom and lecture your 20 students. But I’ve taken the red pill, and I’ve seen Wonderland.”
Besides the Artificial Intelligence course, Stanford offered two other MOOCs last semester — Machine Learning (104,000 registered, and 13,000 completed the course), and Introduction to Databases (92,000 registered, 7,000 completed). And this spring, the university will have 13 courses open to the world, including Anatomy, Cryptography, Game Theory and Natural Language Processing.
“We’re considering this still completely experimental, and we’re trying to figure out the right way to go down this road,” said John Etchemendy, the Stanford provost. “Our business is education, and I’m all in favor of supporting anything that can help educate more people around the world. But there are issues to consider, from copyright questions to what it might mean for our accreditation if we provide some official credential for these courses, branded as Stanford.”
Mr. Thrun sent the 23,000 students who completed the Artificial Intelligence course a PDF file (suitable for framing) by email showing their percentile score, but not the Stanford name; 248 students, none from Stanford, earned grades of 100 percent.
For many of the early partisans, the professed goal is more about changing the world than about making money. But Udemy, a startup with backing from the founders of Groupon, is hoping that wide use of its site could ultimately generate profits. And Mr. Thrun’s new company, Udacity, which is supported by Charles River Ventures, plans to, essentially, monetize its students’ skills — and help them get jobs — by getting their permission to sell leads to recruiters.
“We’re going to have detailed records on thousands of students who have learned these skills, many of whom will want to make those skills available to employers,” said Mr. Evans, the Virginia professor. “So if a recruiter is looking for the hundred best people in some geographic area that know about machine learning, that’s something we could provide, for a fee. I think it’s the cusp of a revolution.”
On Feb. 13, the Massachusetts Institute of Technology, which has been posting course materials online for 10 years, opened registration for its first MOOC, a circuits and electronics course. The course will serve as the prototype for its MITx project, which will eventually offer a wide range of courses and some sort of credential for those who complete them.
The Georgia Institute of Technology is running an experimental twosemester MOOC, known as Change 11, a freefloating forum that exists more in the online postings and response of the students — only two of whom are getting Georgia Tech credit — than in the formal materials assigned by a rotation of professors. Next year, Richard DeMillo, director of Georgia Tech’s Center for 21st Century Universities, hopes to put together a MOOSe, or massive open online seminar, through a network of universities that will offer credit.
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Saturday, March 3, 2012
Girl's verbal skills make them better at math study
A study published in the journal Psychological Science suggests that the learning of mathematical concepts or mathematical terms is very important in learning math. The misconception about girls and boys learning math is that girls are less proficient in math than boys because of their verbal skills. In fact it might happen that certain girls might not have the ability to reflect enough in order to apply their verbal skills in the understanding of math. Moreover it is false to state that boys are better than girls in math. Is this statement based on preconceptions or studies?. What studies ever prove that? Even if these studies might exist it would be limited because of the worldviews or perceptions of those who did them. It is also important to know that a study never proves something true at a very high percentage. It might happen that certain conditions produce such or such results and if those conditions change the results change also. It has been repeated over and over for eons that boys are better than girls in math. Is that certain conditions common to the human race everywhere in the planet make that to happen and if those conditions reverse boys and girls equally learn math or the girls learn better than boys. One of the conditions is that educators think that learning is a conditioning process. This conditioning is rather artificial than natural. In artificial conditioning also called operant conditioning the conditions are created to produce certain actions. you are forced to learn something because of the results that this learning might produce. You might get punished if you don't learn or you might be rewarded if you learn. In these conditions you never have a natural motivation to learn the subject. These conditions deprive the learner of the joy of learning. He is forced to learn because of the consequences of not learning that might happen. In this anxious situation it happens that learning doesn't occur fully. Several scenarios might happen. One doesn't understand anything. One learns some parts of the subject. One learns all the subject just to avoid the consequences and forgets what was learned later. It is also interesting to know that educators don't teach students how to learn and why they have to learn a subject. The importance of learning the terms or concepts is necessary in any subject. The ability to represent mentally the concepts and to progress gradually in the process of learning is also important. It is quite evident that the girls mastering this process had the ability to perform better than boys in this study,
While boys generally do better than girls in science and math, some studies have found that girls do better in arithmetic. A new study published in Psychological Science, a journal of the Association for Psychological Science, finds that the advantage comes from girls’ superior verbal skills.
While boys generally do better than girls in science and math, some studies have found that girls do better in arithmetic. A new study published in Psychological Science, a journal of the Association for Psychological Science, finds that the advantage comes from girls’ superior verbal skills.
“People have always thought that males’ advantage is in math and spatial skills, and girls’ advantage is in language,” says Xinlin Zhou of Beijing Normal University, who cowrote the study with Wei Wei, Hao Lu, Hui Zhao, and Qi Dong of Beijing Normal University and Chuansheng Chen of the University of CaliforniaIrvine. “However, some parents and teachers in China say girls do arithmetic better than boys in primary school.”
Zhou and his colleagues did a series of tests with children ages 8 to 11 at 12 primary schools in and around Beijing. Indeed, girls outperformed boys in many math skills. They were better at arithmetic, including tasks like simple subtraction and complex multiplication. Girls were also better at numerosity comparison — making a quick estimate of which of two arrays had more dots in it. Girls outperformed boys at quickly recognizing the larger of two numbers and at completing a series of numbers (like “2 4 6 8″). Boys performed better at mentally rotating threedimensional images.
Girls were also better at judging whether two words rhymed, and Zhou and his colleagues think this is the key to their better math performance. “Arithmetic and even advanced math needs verbal processing,” Zhou says. Counting is verbal; the multiplication table is memorized verbally, and when people are doing multipledigit calculations, they hold the intermediate results in their memory as words.
“Better language skills could lead to more efficient verbal processing in arithmetic,” Zhou says. He thinks it might be possible to use these results to help both boys and girls learn math better. Boys could use more help with verbal strategies for learning math terms, while girls might benefit from more practice with spatial skills.
I would add to the conclusion of this study that educators apply the three steps of the learning process: learning of terms, pictorial representation of concepts and step by step mastery of the elements to be learned. In this way verbal and spatial skills will be developed both in girls and boys. Then with certain variations in the mastery of these skills there will not be polarization of this set of skills by both genders.
Saturday, February 4, 2012
Free math course
This is a free math course offered by Yves Simon, certified and experienced math educator. For tutoring online and facetoface, teaching online and facetoface in the following subjects: Math, ESL, French and Spanish visit New Direction Education Services at www.ndes.wikidot.com
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