Some helpful ways in the study of math

Being successful in math implies the practice of some proven learning skills that make sense and that apply to any subject. It involves also a certain behavior and some helpful tools for learning. It is understandable that if doing some things makes you successful, not doing them make you unsuccessful. In this article I am writing about some tips for learning math successfully and that may lead to success by applying them.

I am going to state these proven skills mentioned above and then I will give some tips that fall in line with these universal learning skills. These skills resume to three:

1. Reality of concepts. The more concrete a concept is the more it can be learned. Concepts can be clarified and made easy to understand by using pictures or the real object that is being learned. Math use symbols and shapes. So this visual imagery can help in the study of math. In some situations some concrete tools can be used to facilitate the understanding of concepts. For example one can divide a pizza in several slices to make it easy to understand fractions. For example if you divide a pizza into eight equal slices each slice represents a fraction of the actual pizza or 1/8 of the pizza unit.
2. Respecting the order of sequences. We know how the structure of the 4 basic operations is interrelated. It is impossible to just start to learn addition and to move to the learning of division since doing a division involve multiplying and subtracting. Subtracting itself implies knowing how to add. The learning of the 4 basic operations have to be sequential: first addition, then subtraction, multiplication and division.
3. Understanding words    Knowing the vocabulary used in every discipline is important in the learning of that discipline. Knowing the definitions of math words is important in being successful in math. Math is built on fundamental words, propositions, axioms, theorems. It is essential to know this structure in order to be successful in math.

Some things to know in order to be successful in math

These tips involve some learning tools, the skills mentioned above and an approriate behavior

1. Math can't be learned by listening only to lectures or videos. Learning involves using some tools like seeing, listening, reading, writing and doing. It has been said in regular educatiion that too much lecturing is not good for learning. While open education that includes online education tries to be innovative and  to remedy the traditional closed system of education it is regrettable to see the same practices repudiated are being promoted in online or open education. For example most of online course providers promote exclusively watching videos as the only tool for learning. While short videos can be useful to learn something but the content can be forgotten quickly and there is no way of getting back to some concepts explained in the video without re-watching it  entirely. Taking notes that one can review later while watching the video is important. Some videos have transcripts that may help. Reading and practicing are the most important skills in learning math. Reading allows to review and master the concepts. You can't expect to know math without knowing the concepts. Reading and studying are ways that allow to master the concepts. Concepts can't be mastered by just listening to lectures. Concepts need to be reviewed in order to master them completely. That is the reason why they have to be written in order to be read, studied and reviewed. Lectures can be an easy  introduction and a motivating factor in learning a concept. Math has also to be practiced constantly in order to master it.
2. Math is a sequential subject. Concepts learned in a given day are based on concepts learned previously. It's important to learn the concepts of each lesson successfully and do the related assignments. Craming before a test or an exam isn't productive. If there are concepts that you don't master or if your performance is poor it is recommended to get some help as soon as possible.
3. Math is a complex subject. Math require to spend more time time studying than what is required in other subjects. The reason is math involve a lot of time practicing  in order to master it.
4. Memorization alone doesn't work in math. Concepts have to be understood before being memorized. It is important to learn the procedures to solve problems. After learning the concepts, definitions, rules and theorems it is important to know how these are applied to solve problems. Solving a problem involves a step by step procedure. This procedure is applied in the examples and problems solved in the book or during a lesson. Once you know the concepts and procedures you can apply them to the solution of other problems.
5. Learn the math vocabulary. Math words have a different meaning than in other contexts. That is the reason why it is important to learn the vocabulary. For example the word volume in math refers to the amount of space within a solid figure while in another context it has a different meaning.
6. Math can make students anxious. Students can feel anxious as a result of having to learn math. It is essential that students develop confidence in themselves in order to overcome the feeling of anxiety. One way to develop this confidence is to master the theoretical and practical aspect of math. One can say instead that this confidence arises by practicing math a lot and very often.

Interested in math lessons and tutoring face-to-face and online visit my site New Direction Education Services at  www.ndes.wikidot.com and click the contact button. There you can connect with me by liking the Facebook page of New Direction Education Services and follow the Google+ page as well. You can also suscribe to this blog to receive articles like this. You can find different ways to connect me as well in the left side of this blog

Introduction to the notion of limits

Dear readers,

You may have noticed that I haven't blogged during a few months. I redirect the focus of this blog on teaching and tutoring about Math, ESL (English as a Second Language), French and Spanish. The future posts will be centered about teaching math, learning skills and the use of web technologies for teaching and learning. I'll be offering also some free math courses . For now I am publishing some parts of a Course on limits that I will offer entirely free the next time. If you are a learner who needs tutoring or a private course face-to-face or online in Math, ESL, French and Spanish visit my website New Direction Education Services at www.ndes.wikidot.com. If you know someone who needs these services please refer them to the site I just mentioned. In this post on the "Introduction to the notion of limits" I share two resources: a video introducing the "Notion of limits" and three methods for calculating a limit.

Video Introduction

Introduction to the notion of limit

     

An online course on limits

Mathematics play an important role in human activities. They are used from simple everyday activities such as personal budgeting, checkbook balancing, groceries shopping to more complicated disciplines such as Economy, Science, Computers, Engineering, etc. The buildings we live in, the roads we use, the computers, cellphones, tablets, televisions, etc are designed by people who know math. Calculus is an important branch of mathematics used in various disciplines taught at the college level. The notions of limits are fundamental in understanding some very important notions in Calculus such as Continuity, Derivation and Integrals. I have designed the "Notion of limits" course for high school students taking AP Calculus or who will take it. It is also designed for students at the college level who needs a remediation course.

Students taking this course will have several benefits:
1. They can ask questions that will be answered by the Instructor
2, They have the possibility to interact with other students in online discussions
3. Online discussions are monitored by the Instructor
4. One on one tutoring is available for students who need it.

The instruction process for this course is designed in the following manner:
1. Students will watch an introductory video
2. They will have to do some guided assignments
3. They will have to solve problems based on these assignments.

Courses in Basic Algebra, Algebra I, II, Geometry, Trigonometry, Pre-Calculus and math for adults are also available. Other online courses in French, Spanish, ESL are available on demand. Online and face-to-face tutoring are also available in these subjects.For more information visit New Direction Education Services at www.ndes.wikidot.com. If you are reading this blog post and know someone who might be interested in this course, other courses and services please share this post with them. Here is the course link: Notion of limits

   

Scientists unravel how kids learn math, first grade abilities key to skills later on

By Lauran Neeergaard, The Associated Press.

WASHINGTON – We know a lot about how babies learn to talk, and youngsters learn to read. Now scientists are unraveling the earliest building blocks of math — and what children know about numbers as they begin first grade seems to play a big role in how well they do everyday calculations later on.

The findings have specialists considering steps that parents might take to spur math abilities, just like they do to try to raise a good reader.

This isn’t only about trying to improve the nation’s math scores and attract kids to become engineers. It’s far more basic.

Consider: How rapidly can you calculate a tip? Do the fractions to double a recipe? Know how many quarters and dimes the cashier should hand back as your change?

About 1 in 5 adults in the U.S. lacks the math competence expected of a middle-schooler, meaning they have trouble with those ordinary tasks and aren’t qualified for many of today’s jobs.

“It’s not just, can you do well in school? It’s how well can you do in your life,” says Dr. Kathy Mann Koepke of the National Institutes of Health, which is funding much of this research into math cognition. “We are in the midst of math all the time.”

A new study shows trouble can start early.

University of Missouri researchers tested 180 seventh-graders. Those who lagged behind their peers in a test of core math skills needed to function as adults were the same kids who’d had the least number sense or fluency way back when they started first grade.

“The gap they started with, they don’t close it,” says Dr. David Geary, a cognitive psychologist who leads the study that is tracking children from kindergarten to high school in the Columbia, Mo., school system. “They’re not catching up” to the kids who started ahead.

If first grade sounds pretty young to be predicting math ability, well, no one expects tots to be scribbling sums. But this number sense, or what Geary more precisely terms “number system knowledge,” turns out to be a fundamental skill that students continually build on, much more than the simple ability to count.

What’s involved? Understanding that numbers represent different quantities — that three dots is the same as the numeral “3” or the word “three.” Grasping magnitude — that 23 is bigger than 17. Getting the concept that numbers can be broken into parts — that 5 is the same as 2 and 3, or 4 and 1. Showing on a number line that the difference between 10 and 12 is the same as the difference between 20 and 22.

Factors such as IQ and attention span didn’t explain why some first-graders did better than others. Now Geary is studying if something that youngsters learn in preschool offers an advantage.

There’s other evidence that math matters early in life. Numerous studies with young babies and a variety of animals show that a related ability — to estimate numbers without counting — is intuitive, sort of hard-wired in the brain, says Mann Koepke, of NIH’s National Institute of Child Health and Human Development. That’s the ability that lets you choose the shortest grocery check-out line at a glance, or that guides a bird to the bush with the most berries.

Number system knowledge is more sophisticated, and the Missouri study shows children who start elementary school without those concepts “seem to struggle enormously,” says Mann Koepke, who wasn’t part of that research.

While schools tend to focus on math problems around third grade, and math learning disabilities often are diagnosed by fifth grade, the new findings suggest “the need to intervene is much earlier than we ever used to think,” she adds.

Exactly how to intervene still is being studied, sure to be a topic when NIH brings experts together this spring to assess what’s known about math cognition.

But Geary sees a strong parallel with reading. Scientists have long known that preschoolers who know the names of letters and can better distinguish what sounds those letters make go on to read more easily. So parents today are advised to read to their children from birth, and many youngsters’ books use rhyming to focus on sounds.

Likewise for math, “kids need to know number words” early on, he says.

NIH’s Mann Koepke agrees, and offers some tips:

—Don’t teach your toddler to count solely by reciting numbers. Attach numbers to a noun — “Here are five crayons: One crayon, two crayons…” or say “I need to buy two yogurts” as you pick them from the store shelf — so they’ll absorb the quantity concept.

—Talk about distance: How many steps to your ball? The swing is farther away; it takes more steps.

—Describe shapes: The ellipse is round like a circle but flatter.

—As they grow, show children how math is part of daily life, as you make change, or measure ingredients, or decide how soon to leave for a destination 10 miles away,

“We should be talking to our children about magnitude, numbers, distance, shapes as soon as they’re born,” she contends. “More than likely, this is a positive influence on their brain function.”

Interested in tutoring and courses in Math, French, ESL (English as a Second Language), Spanish visit New Direction services at www.ndes.wikidot.com and click the contact button  at the top of the site to contact me. 

Why do we learn math?

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 face-to-face or online. You can also leave a message in the comment section of this post.  

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.

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, Self-learners, 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 Urbana-Champaign 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/Open-Popular-University 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.

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 high-quality educational materials for different reasons.

The OpenCourseWare is used by faculty (Professors, Teachers) and students at the university and high school level, self-learners, 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 California-Irvine 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, Peer-to-Peer 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.