The purpose of this blog is to teach Math subjects : Calculus, Pre-calculus, Algebra and Basic Math. Now it focuses on Higher Math. You can also find posts on learning theories, study skills and web resources for learning.
I am adding a few comments about the article: Not a math person: "how to remove obstacles to learning math" written by Katrina Schwartz and published in the online magazine Mind/Shift concerning the pedagogical techniques to remove obstacles in learning math. The author of the article wrote: "Neuroscience research is now showing a strong connection between the attitudes and beliefs students hold about themselves and their academic performance". Our brain is the command center of our physical, emotional, mental and spiritual life. The brain stores also a lot of information recorded consciously or unconsciously. It interprets our surrounding reality and draws its conclusions. One type of conclusions is "the beliefs and attitudes" mentioned in the quote. Our beliefs and attitudes strongly influence our actions and personality. If students believe they can't do math it's obvious that they are not going to make any efforts in order to learn the subject. Their actions will reflect negative views or attitudes about learning math. The beliefs and attitudes originate from the student himself and his social and educational environment. If the social environment including the family cannot do much about developing positive attitudes about learning math this is the role of the school system to favor the development of attitudes and beliefs necessary for learning math. Not only the math teacher develops techniques to help students to learn the subject but he encourages students to "like" the subject. I use the word "like" instead of any other complicated word because I found when a student likes a subject he tends to make efforts in order to perform strongly at it. "Neuroscientists now know that the brain has the abilities to grow and shrink". The fact that our brain grows simply means that we are able to use the brain to think, reflect and solve our problems. We know that every individual uses his brain to live. When we think for a certain period of time about something we solicit the brain's resources in order to help us in order to solve problems. We use a great portion of the "working memory" of our brain to the solution of these problems. However we need to use the brain resources and the "working memory" effectively. Background knowledge helps us to free some parts of the working memory in order to move quickly in the solution of problems. In fact a study done about the strong performance of chess players shows that the memorization of different chess positions helps players to think quicker and gain advantages on their competitor. The background knowledge is important in performing math. Background knowledge is the knowledge of facts and theories so that we don't have to demonstrate them each time we encouter them. The fact that we know the multiplication tables allow us to do the multiplication of different large numbers instead of figuring out each time the multiplication of single numbers. There are math problems that are so complicated that we have to know the method of solutions and the formulas instead of figuring out each time how to solve the same type of problems. Background knowledge of math theories help us to solve complicated math problems. A complicated and abstract subject like math cannot be mastered without knowing its theories. The other technique mentioned in the article is about visualization. Visualization allows to visualize a fact, theory, etc. It helps to figure out something more clearly. It is a tool. It doesn't substitute the knowledge of the subject. Here is an excerpt of the article:
Stanford math education professor Jo Boaler spends a lot of time worrying about how math education in the United States traumatizes kids. Recently, a colleague’s 7-year-old came home from school and announced he didn’t like math anymore. His mom asked why and he said, “math is too much answering and not enough learning.”
This story demonstrates how clearly kids understand that unlike their other courses, math is a performative subject, where their job is to come up with answers quickly. Boaler says that if this approach doesn’t change, the U.S. will always have weak math education.
“There’s a widespread myth that some people are math people and some people are not,” Boaler told a group of parents and educators gathered at the 2015 Innovative Learning Conference. “But it turns out there’s no such thing as a math brain.” Unfortunately, many parents, teachers and students believe this myth and it holds them up every day in their math learning.
There’s no such thing as a math brain.’Jo Boaler, Stanford professor of math education
“We live in a society with lots of kids who don’t believe they are good at math,” Boaler said at an Education Writers Association conference. “They’re put into low groups; they’re given low-level work and their pathway has been set.” But math education doesn’t have to look like this.
Neuroscience research is now showing a strong connection between the attitudes and beliefs students hold about themselves and their academic performance. That’s a departure from the long-held traditional view that academic success is based only on the quality of the teacher and curriculum. But researchers like Carol Dweck, Camille Farrington and David Yeager have shown repeatedly that small interventions to change attitudes about learning can have an outsized effect on performance.
Neuroscientists now know that the brain has the ability to grow and shrink. This was demonstrated in astudy of taxi drivers in London who must memorize all the streets and landmarks in downtown London to earn a license. On average it takes people 12 tries to pass the test. Researchers found that the hippocampus of drivers studying for the test grew tremendously. But when those drivers retired, the brain shrank. Before this, no one knew the brain could grow and shrink like that.
“We now know that when you make a mistake in math, your brain grows,” Boaler said. Neuroscientists did MRI scans of students taking math tests and saw that when a student made a mistake a synapse fired, even if the student wasn’t aware of the mistake. “Your brain grows when you make a mistake, even if you’re not aware of it, because it’s a time when your brain is struggling,” Boaler said. “It’s the most important time for our brains.”
A second synapse fires if the student recognizes his mistake. If that thought is revisited, the initial synapse firing can become a brain pathway, which is good for learning. If the thought isn’t revisited, that synapse will wash away.
A recent study of students with math learning disabilities found in a scan that their brains did behave differently from kids without the disability. “What they saw was the brain lighting up in lots of different areas while working on math,” Boaler said. The children were recruiting parts of the brain not normally involved in math reasoning.
The researchers tutored the group of students with math disabilities for eight weeks using the methods Boaler recommends like visualizing math, discussing problems and writing about math. At the end of the eight weeks, they scanned their brains again and found that the brains of the test group looked just like the kids who did not have math disabilities. This study shows that all kids can learn math when taught effectively. Boaler estimates that only 2 to 3 percent of people have such significant learning disabilities that they can’t learn math at the highest levels.
People who learned math the traditional way often push back against visual representations of math. That kind of thinking represents a deep misunderstanding of how the brain works. “When you think visually about anything, different brain pathways light up than when we think numerically,” Boaler said. The more brain pathways a student engages on the same problem, the stronger the learning.
An example of many ways to visually represent 18*5 (Jo Boaler/YouCubed) (to be continued)
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Success skills in school and learning fall in different categories such as: study skills, organization, environment, etc. In this post I will develop four important skills for success in learning and one to avoid.
1. Study skills
Success in study require the ability to use some skills to master the subject. These skills are related to some reading and study techniques. Reading skills are important for success in study. Reading begins before study. In the reading phase some techniques are used such as previewing, skimming, scanning, etc, In the previewing phase one seeks to get a panoramic view of the material without reading the details. One looks at the title, headings, subheadings, pictures of a single piece of the study material. Then one reads the introduction, the first sentence of each paragraph and the conclusion. These techniques are not easy to use especially when one is accustomed in reading line by line. In acquiring the general view one can sketch an outline with the main points of the subject. Once one has finished with the general view one starts by reading the full text. This reading is active since it involves different activities such as outlining important details, thinking, reflecting, etc. The last phase consists in memorizing the important details of the subject.
2. Organization
A calendar is important in order to find time to study. Everyone in school or not has different daily activities. It is important to schedule these activities in order to find time for study, If you are a student in grade school or at the university your time is divided in different blocks of activities, Classes take the majority of the time in school. Extra curricular activities and social events are also included in the school time. There are also personal activities outside the school. For adults who are in school they are very busy and share their time between work, personal activities and family responsibilities. One can use online calendars such as Google calendar to manage time for different activities. There are also some apps for reminders such as Google keep to remind about different activities. Students can use these reminders or hard and computer sticky notes to remind about textbook pages, assignments, etc. Google keep can also be used to take some notes.
3. Disconnection
Disconnect from the internet is the most difficult thing to do since the internet is also used for classwork. In addition one is addicted to social medias, emails and text messages. One has to set the rule that when it's time to study one has to avoid logging in these things. One can set a time for study and another time for the internet to avoid doing both at the same time.
4. Environment
Finding one's convenient environment is important. There are two elements in the environments: the place to study itself and the absence or not of complete quietness. A quite place such as the library or home place reserved especially for study is important. One should avoid to be bothered by other people, telephone, television, etc. If other people are doing other activities that prevent you from concentrating while you are studying this can distract you. If they ask you to do some things you lose time in your study. It doesn't mean that you can't interrupt your study to do some important things for someone else. But these things have to be really important and you are the sole person who can help in time and place. Some people like to learn while they listen to music, Others prefer not, The choice depends on your preferences. You can't study while watching the television, answering phones, sending text messages and logging in social medias. You decrease considerably the time dedicated to study and your concentration when you study and do these things at the same time. Observe the Ecclesiastes principle that says there is a time for each thing.
5. Cramming
Cramming is the process of studying material that one hasn't studied before an examination. Study should be a daily activity. It extends over a certain period of time if one wants to master the material. It involves also constant reviewing. Mastering a certain amount of materials that one hasn't had the opportunity to digest during times where the study of materials is allotted can be hard to do. This requires the display of a considerable amount of energy and can lead to exhaustion.
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An article titled "Kids'brains reorganize when learning math", appeared in Associated Press in August 2014, describes the role of the long-term memory in the improvement of the learning of addition by kids. The article doesn't describe specifically what happens in the kid's brain when they automatically answer a question to a simple addition without counting on their fingers. However there are key elements in the article related to the role of the kids' brain in learning math and how this could help in learning math better. The discoveries are also related to the chid's cognitive development specifically how memories are recorded and retrieved in the brain.
The scientists scanned the kids' brain to study how they were able to transition from counting to their fingers to simply answer a question related to a simple addition. They repeated the study a year later and did the same experiment in adolescents and adults. The results of the study are:
At some point kids makes the transition from counting from their fingers to automatically answer a question related to a simple addition. If they make this transition well their performance in the future learning of math will improve.
Older kids are able to do the simple addition quicker than the younger. In other words performance increases with age.
Being able to retrieve simple math addition in the memory helps kids to learn new math concepts. In other words this process allows children to use free space in the work memory in order to learn new math concepts.
This retrieval process improves the ability of the hippocampus which is the region of the brain where new memories come in before being transferred in long term memories.
The implications of this study are important in learning math and in learning in general. It stresses the importance of the use of memory in learning math. Learning uses long-term memory as a storage where different concepts can be retrieved when one learns new things or things related to the previous concepts. Imagine that you are not able to remember your telephone number. For this reason you either write it somewhere or save it in your telephone memory. It would be annoying to loook for this number each time you have to dial it, However if you are able to remember the telephone number dial it each time becomes easier. In fact the use of our memory is a natural process in living. There are many things that are transferred in the long term memory without our conscious will. Once certain things are stored in the long term memory the retrieval becomes automatic after performing certain actions related to the information stored. When you learn to drive a car you store certain information in the brain. Once you know how to drive the car the retrieval information related to driving becomes automatic. You don't have to consciously remember the driving information.
One tends to think that learning math is simply related to thinking and solving problems only. The role of the memory is important in these processes. We retrieve procedures, theorems, rules, etc in the memory in order to learn new concepts and solve problems. One would think that in using the memory one would record things without understanding them. Quite the contrary when you understand something you can better store it in the long term memory and retrieve it from there. The long term memory is where you store things that are important to you. Sometimes things are stored verbatim when it's necessary, For example you store formulas verbatim so that they can be retrieved for future use. Other times only representations of things are stored in the long memory. These representations are not exactly a reproduction of the reality but a way for you to figure them out. Learning involves processes in the brain. It is important to understand these processes to improve learning.
Source: http://www.deseretnews.com/article/765658477/Kids-brains-reorganize-when-learning-math-skills.html Interested in learning to use effective study skills? For free tutoring by email fill out this form:Free Tutoring by Email . For paid tutoring and courses visit New Directions Education Services atwww.ndes.wikidot.com
Studying effectively requires some good strategies. The acronym A.S.P.I.R.E allows to remember these strategies. "A" stands for "Approach/Attitude/Arrange". "S" stands for "Select/Survey/Scan". "P" stands for "Piece together the parts". "I" stands for "Investigate/Inquire/Inspect". "R" stands for "Re-examine/Reflect/Relay". "E" stands for "Evaluate/Examine/Explore".
A: Approach/attitude/arrange
Approach your studies with a positive attitude
Arrange your schedule to eliminate distractions
S: Select/survey/scan
Select a reasonable chunk of material to study
Survey the headings, graphics, pre- and post questions to get an overview
Scan the text for keywords and vocabulary: mark what you don’t understand
P: Piece together the parts:
Put aside your books and notes
Piece together what you've studied, either alone, with a study pal or group: summarize what you understand.
I: Investigate/inquire/inspect:
Investigate alternative sources of information you can refer to: other text books, websites, experts, tutors, etc.
Inquire from support professionals (academic support, librarians, tutors, teachers, experts,) and other resources for assistance
Inspect what you did not understand.
R: Reexamine/reflect/relay Reexamine the content | Reflect on the material | Relay understanding
Reexamine: What questions are there yet to ask? Is there something I am missing?
Reflect: How can I apply this to my project? Is there a new application for it?
Relay: Can I explain this to my fellow students? Will they understand it better if I do?
E: Evaluate/examine/explore:
Evaluate your grades on tests and tasks: look for a pattern
Examine your progress: toward achieving your goals
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In a new study published in the journal Child Development, Florida International University Professor Zahra Hazari found that interest and recognition can help a student become a "math person" and pursue a STEM career.
Math isn't exactly every student's favorite subject, but
those who have an affinity for it aren't necessarily born a "math
person," as one might think.
"Much of becoming a 'math person' and pursuing a related STEM
(science, technology, engineering or math) career has to do with being
recognized and becoming interested - not just being able to do it," said
Hazari, who specializes in STEM Education at FIU's College of Education and STEM Transformation Institute, according to the NEA blog. "This is important for promoting math education for everyone since it is not just about confidence and performance."
Hazari, who worked with colleagues Jennifer D. Cribbs from
Western Kentucky University, and Philip M. Sadler and Gerhard Sonnert,
both from Harvard University suggests that interest and recognition are key factors that can help students develop math skills.
The team surveyed more than 9,000 college calculus students
from across the country. They found that students in the high-level
course wanted to pursue math mainly because they'd received recognition
for their abilities and also found it interesting.
In the survey, students were asked if they thought parents, friends, relatives, and math teachers saw them as a "math person."
Those who responded "yes" were classified as feeling recognized.
In other words, what motivates a student to pursue a career in STEM and encourages them to continue along this path is interest, recognition, and engagement.
"It is surprising that a student who becomes confident in his math
abilities will not necessarily develop a math identity," Hazari said.
"We really have to engage students in more meaningful ways through their
own interests and help them overcome challenges and recognize them for
doing so. If we want to empower students and provide access to STEM careers, it can't just be about confidence and performance. Attitudes and personal motivation matters immensely."
Source: http://www.ischoolguide.com/articles/15754/20150624/study-help-student-math-stem-career.htm Interested in learning to use effective study skills? For free tutoring by email fill out this form: Free Tutoring by Email . For paid tutoring and courses visit New Directions Education Services at www.ndes.wikidot.com
We know that success in study requires good study skills. Effective habits are necessary to develop effective study. Here are the 8 habits;
Take responsibility for yourself Recognize that in order to succeed you need to make decisions about your priorities, your time, and your resources
Center yourself around your values and principles Don't let friends and acquaintances dictate what you consider important
Put first things first Follow up on the priorities you have set for yourself, and don't let others, or other interests, distract you from your goals
Discover your key productivity periods and places Morning, afternoon, or evening? Find spaces where you can be the most focused and productive. Prioritize these for your most difficult study challenges
Consider yourself in a win-win situation When you contribute your best to a class, you, your fellow students, and even your teacher will benefit. Your grade can then be one additional check on your performance
First understand others, then attempt to be understood When you have an issue with an instructor (a questionable grade, an assignment deadline, etc.) put yourself in the instructor's place. Now ask yourself how you can best make your argument given his/her situation
Look for better solutions to problems For example, if you don't understand the course material, don't just re-read it. Try something else! Consult with the professor, a tutor, an academic advisor, a classmate, a study group, or your school's study skills center
Look to continually challenge yourself
Source: Effective habits for effective study at www.sudygs.net
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Learning to learn involves different techniques. These techniques apply in any subject whether it's math, science. languages, social study. etc. In this blog I am going to show a process of leaning that one can use before starting to learn a subject. To learn effectively you have to:
Know yourself
Know your capacity to learn
The process used successfully in the past
Your interest and knowledge in the subject you want to learn
The process involves four steps and there are questions in each one that someone can answer. The answers can be used to plan a study strategy in combination with some other study techniques.
Step One: Begin with the past. Answer questions about your past learning experiences. Learning experiences are of several types: reading, solving problems, memorizing, reciting, interpreting, speaking to groups, etc. Some people might get the information by reading it. Others might take time to memorize it by reading several times. Others learn by direct involvement in the subject at hand i.e either by doing, solving problems and teaching to others. Some learners like to summarize the information and ask questions about what they study. Some like to get the information from a variety of sources. Others like to study alone or in group. Other learners might like to get the information in short study sessions or in a longer one. Answer the following questions about your past study habits: Did you
like to read? solve problems? memorize? recite? interpret? speak to groups?
know how to summarize?
ask questions about what you studied?
review?
have access to information from a variety of sources?like quiet or study groups?need several brief study sessions, or one longer one?
What are your study habits?
How did they evolve? Which worked best? worst?
How did you communicate what you learned best? Through a written test, a term paper, an interview?
Step two: Proceed to the present
You have to evaluate your level of interest and the amount of time you need to spend to learn the subject you want to learn. Ask yourself what can prevent you from focusing on the subject. what circumstances you can control and others that are out of your control. Can you change these conditions for success? You need to have a plan that include your past study habits and your learning style. Here are the questions you need to ask yourself:
How interested am I in this?
How much time do I want to spend learning this?
What competes for my attention?
Are the circumstances right for success?
What can I control, and what is outside my control?
Can I change these conditions for success?
What affects my dedication to learning this?
Do I have a plan? Does my plan consider my past experience and learning style?
Step three: Consider the process, the subject matter
In learning a subject there are many strategies that one can use. First one has to get an idea of the title of the topic and learn the meaning of the key words. There might be other resources that can help to learn the subject or one might want to stay with one source. As you read the material it's necessary to ask yourself whether you understand or not, evaluate the reading speed to see if you can go quickly or more slowly. At some point it's worth to stop and summarize, ask if the concepts make sense. One can ask also whether one disagrees or not with the ideas in the material. Some times you might want to think the concepts over and come back later. You might also want to discuss the material with other learners or to consult a subject matter expert. Here are the questions to ask:
What is the heading or title?
What are key words that jump out?
Do I understand them?
What do I know about this already?
Do I know related subjects?
What kinds of resources and information will help me?
Will I only rely on one source (for example, a textbook) for information?
Will I need to look for additional sources?
As I study, do I ask myself whether I understand?
Should I go more quickly or more slowly?
If I don't understand, do I ask why?
Do I stop and summarize?
Do I stop and ask whether it's logical?
Do I stop and evaluate (agree/disagree)?
Do I just need time to think it over and return later?
Do I need to discuss it with other "learners" in order to process the information?
Do I need to find an authority, such as a teacher, a librarian, or a subject-matter expert?
Step four: Evaluate
In this process you evaluate your learning experiences. You ask yourself questions about what went right and how you can improve. You can ask yourself if your plan coincide with strengths and weaknesses. You can see whether you succeed or not and celebrate your success. Here are the questions you can ask yourself at this step:
What did I do right?
What could I do better?
Did my plan coincide with how I work with my strengths and weaknesses?
Did I choose the right conditions?
Did I follow through; was I disciplined with myself?
1. If you don't understand something, focus on mastering that topic before moving on to the next topic
Math topics are set in sequence. It is essential to master one topic before moving to the next one. Stick with the topic you don't understand until you understand it fully. Read the theories and examples a second time or use another book or other resources that can allow you to understand the topic better. Moving to the next topic without mastering the present one can lead to frustration and abandon.
2. Work example problems and check your answers to gain practice with every lesson
Start by reading the examples of problems done in class, a book or whatever materials you are using and masteri the procedures used to solve these problems. Then start solving the problems that have answers to them beginning with the easiest ones and moving to the hardest. Make sure to check the answers to the problems you are working on. Work a dozen or two problems before moving to the next section.
3. When beginning to work a Math problem, do not "map out a path from problem-to-answer" in your head before writing anything down
This srategy may lead to skipping the steps necessary to solve a problem and focusing on the answer. What is best to do is to start by writing down the problem. Then write each step leading to the solution of this problem.. Write down what you are going to do and do it in the next step. For example, if you are going to divide both sides of an equation by a number write that down and do it as another step which is the execution of what you just write down.
4.When you study and do homework, try to find a quiet place to do it
Try to find a quiet place at home or in the library to do school work. This will allow you to do your work more quickly because you are able to to focus and learn more.
5.If someone asks you for help, try to explain the topic to them as best as you can.
In studying in a group try to help someone who is behind. This has two benefits. First you help someone to succeed. Second, the fact that you are helping someone else helps you understand the subject matter better.
6.Never, ever work math problems in pen
When you use a pen you can erase some mistakes but your work will not be neat
7. Try to use a mechanical pencil with separate eraser, if you can
Mechanical pencils have cleaner lines. The separate eraser allows you to erase more cleanly.
8. Keep your solutions neat and line-by-line
Write vertically instead of horizontally. This allows you to present a more understandable work.
9. Don't work problems very late at night.
After doing different activities during the day it is not easy to concentrate at night because of tiredness. This may leads to make mistakes when working on problems. It's better to get a good night sleep and to wake up refreshed during the mornings. You'll find yourself in better shape to work on problems.
10. If the problem lends itself to it, draw a picture of the problem
Some math subjects such as Geometry and Trigonometry involve drawing shapes in order to solve problems. Other subjects such as Algebra are more abstract. However any mathematical concept or problem can lead to a visual representation. The visual representation allows to understand the problem more clearly. For free tutoring by email in math and other subjects fill out this form: Sign up form for free tutoring by email
It is essential to know the basic techniques of how to study in order to study better but there is also a lot of techniques that facilitate learning. These techniques are particularly helpful when someone learns something he is passionate about it either a subject, a field of knowledge for a profession or a hobby. Talent is the starting point to love learning at some thing. It can be natural or can come as a result of some circumstances. Natural talent means the ability to learn or do something comes without a lot of effort or external motivation. But sometimes one can develop some abilities for doing something from external influences. Natural or acquired talent, motivation, attitude and the application of some techniques are the elements that make people to become proficient learners. Below are the techniques:
1. Love it. Love is the fuel of motivation. If you love something you'll learn it better. 2. Read it. Reading about something helps you learn a lot about this thing. Learning the history of something can help you to know the evolution of the subject and master the key developments. Study the techniques of people who are famous at something can help to become good at it. Fischer, a famous american chess player, studied the history of chess and the techniques of famous Russian players and became the world champion. 3. Practice it. Do something many times makes you good at it. It becomes a routine. Writing a lot makes you a writer. Practice also helps you to see your mistakes and improves. 4.Get help from teachers, tutors and experts. Getting help from others who master the subject can help you to learn better. You can learn beyond the guidance of a particular teacher by forming a personal learning network made of people you can contact for questions or help in learning. 5. Study the history. Study the present. To become a master at something incorporate the study of the history and the present in the learning of that thing. An expert programmer would study all previous programs all the way to the modern ones. An entrepreneur would study the history of famous entrepreneurs. 6. Do easy projects first. Start by doing some basic projects and learn from it. Programmers start by doing the "Hello, World" program before becoming expert on more sophisticated programs. 7. Study what you did. If you fail at something you udertake look at it and see what was wrong. Find out what happened and what would have helped better. Ask good questions like: What did I do wrong and how can I improve?
8. Be part of a group. Findthe best group and spend the time to learn with them. 9. Find the right plan. Find a plan that is appropriate for you and come up with something new
Source: The Only Technique To Learn Something new.
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In the human being the brain performs actions on the body and makes mental representations of the environment. Learning occurs when the brain responds to certain stimuli from the environment or when a new mental representation is made. In animals learning occurs by habituation or associatively. If an animal is introduced in a cage where lives another animal the latter can have a certain reaction to its guest but over time can react differently. The new response from the animal that previously lives alone is considered as a modification of the behavior of the animal. This modification is considered as learning and this learning is non-associative and occurs over time. A dog salivates when they present it some kind of meat. The sound of a bell is associated to the presentation of the food and the association is repeated several times. Later the food isn't presented and the bell rings. The dog salivates when it hears the bell. The animal produces a response to a new stimulus in the environment which is the bell. This new response is a modification of its normal behavior and is considered as learning. This learning occurs from the association food-bell. For this reason it is called associative learning. This learning occurs as a result of the conditioning of the dog and this this type of conditioning is called classical conditioning. In operant conditioning learning occurs by rewarding or punishing a type of behavior. Now let's define learning.
Learning can be defined as:
1. The acquisition of knowledge or skills through experience, study or being taught
2. The cognitive process of acquiring skill or knowledge
3. The modification of behavior through practice, training or experience.
If learning is a process of acquiring knowledge there are some strategies that should be involved to acquire that knowledge, skills or behaviors. Here are the ten strategies based on experience and scientific study:
1. Test yourself before you study. According to Elizabeth Bjork, a psychologist, taking a test adjusts your thinking to what you need to know. This strategy may help to focus. 2. Space out your study session over time. Experiments done in mice showed that they remember better over multiple repeated sessions of training than in a single prolonged session according to Christine Gall and Gary Lynch from the University of California. 3. Change up your study environment. Changing your environment forces the brain to retrieve the information in different places and will therefore view that information more useful. The brain wants variations. It wants to move and periodic breaks Finding some new scenery will create new association in the brain and will make it easier to retrieve the information later. 4. Take regular naps. In 2013 sleep researchers at UMASS (University of Massachusetts), Amherst found that daytime naps support learning in preschool children by strengthening their memory. 5. Quiz yourself instead of re-reading. When you reinforce your memories by testing them, they get stronger than if you review the materials. 6. Check-in with yourself periodically. Make a list of everything you remember and go back and see what concepts you've missed. This strategy can be done for a chapter or an entire course. 7. Separate process from progress. Learning is a process that never ends. At different times you make progress on it. 8. Look forward to forgetting. Forgetting is part of the learning process. It strengthens the memory. 9. Imagine you'll be teaching someone else. When students expect to teach new materials to others, they remember more of the material and organize their recall more effectively, says John Nestojki, a postdoctoral researcher in psychology at Washington University in Saint Louis. 10. Study to learn not to know. Study to remember something for a lifetime is better than study for a test.
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Teaching is a guiding and temporary event while learning is more lasting and bears on the learner's responsibility. All learning isn't structured and doesn't imply the presence of a guide or teacher. Learning is formal and informal and happens during the whole lifetime. Teaching is worthless if the learner doesn't take the responsibility for his/her learning. If the teacher has to learn the best tools to teach, similarly the learner has to equip himself or herself with the appropriate tools for the most performant learning. It appears that more resources have been devoted to teaching than learning. More human, financial and physical resources have been allocated to teaching than learning. The proverb says: "it's better to learn someone how to fish instead of giving the fish". Teaching has long tried to impute the materials on the learner instead of teaching how to learn. Study requires a certain amount of effort from the learner, some skills and good habits. Here are the ten study habits of the most successful students.
1. Try not to do too much studying at one time. Doing too much study over one single period of time can make someone tired. Instead spread the study over shorter periods of time by taking breaks that restore the mental energy.
2. Plan specific times for studying. Study according to a schedule by assigning a specific time for the material studied or an assignment, a project, etc.
3. Try to study at the same times each day. Things that we do very often and at the same time create habits and become a routine. Studying at the same times becomes then a habit and requires less effort than if it was done at irregular times.
4. Set specific goals for the study times. Setting goals allow to stay focused. Learners establish goals for their study by stating the amount of material that they want to cover for example or what they want to accomplish at the end of their study time. 5. Start studying when planned. Not studying when planned leads to procrastination. It becomes hard to cover all the materials at once after putting time off to study. The best is to study at the time scheduled.
6. Start with the most difficult assignment. The most difficult assignment requires most energy. By tackling it first you you have the pool of energy not already used that serves to accomplish fully the difficult assignment.
7. Review notes before beginning an assignment. This can help to facilitate the execution of an assignment. Notes also can have instructions for doing the assignments.
8. Avoid talking over the phone during study times. Talking to friends during study times has two effects: loss of concentration and distraction. A loss of concentration makes it difficult to go back to study while distraction makes you lose focus. However talking over the phone can be beneficial if it is done as a break time.
9. Call someone or a friend for help. Sometimes it happens to have difficulties in learning some parts of the materials. Asking for help can overcome the learning difficulties.
10. Review schoolwork over the weekend. While weekends are generally spared for fun it may be worth to to take some time during this period to review the materials learned during the week. This will make it easier to learn the next week materials.
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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:
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.
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.
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.
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