One fascinating thing about education is that everyone has an analysis or a miracle cure.
Even when correct, however, a lot of these theories seem to me superficial. They don’t deal with the deep-down pathologies.
If we’re seeing really bad results, can’t you usually be pretty sure there’s a really bad idea down there somewhere?
Rushing in where angels might fear to tread, I offer my checklist of bad ideas undermining many American schools:
Self-esteem is pushed
Constructivism is injected into every course
Arithmetic is badly taught
Reading instruction is flawed
Guessing is encouraged
Foundational knowledge is slighted
Group learning is favored
Memorization is dismissed
Handwriting is not taught
Fuzziness is praised
Put aside for the moment whether a school is rich or poor, the teachers good or bad, the students smart or not so smart; put aside all the explanations and alibis typically mentioned. Behind all of that, these bad ideas are humming away 24/7, diminishing educational effectiveness.
Presumably for ideological reasons, our Education Establishment is more focused on social engineering than on intellectual engineering. The result is that they tend to favor inferior pedagogical methods. That’s what I believe this list is: inferior pedagogical methods.
For a little more detail on each item, please see “46: Public Schools Seem To Be Designed To Fail,” the newest article on Improve-Education.org.
(NB: this article is very brief because it was originally written to make a YouTube graphic video (one of 40 at this point). For the 4-minute YouTube version, click here.)
.
About the Author
Bruce Price is the author of "THE EDUCATION ENIGMA--What Happened to American Education." He founded improve-Education.org in 2005. It now has 48 original articles. Reading is a focus. Please see "42: Reading Resources."
Friday, May 28, 2010
Thursday, May 20, 2010
Join the Educational Revolution!
I consider myself an Education Reformer. Through the years I have tried to reform education from the inside out. It has not worked. What makes me so smart, nothing really? I think every teacher wants to assist students with learning to the best of their ability. At least that is my deepest desire, to assist kids that struggled to overcome their challenges. Which in turn, produces more well-rounded, self-sufficient, educated people as citizens for our county. Does this seem far-fetched?
This is my general premise as per my paper, The Multi-Sensory Classroom (Aug. 2004):
“Each child develops sensory/motor preskills at a very young age (e.g., auditory processing, fine and gross motor skills, visual perception, reflexes, tactile processing, sensory modulation). These bottom levels of sensory/motor development are often taken for granted because they are basic and develop automatically in the typically developing child. When we teach a student at school, the child uses these sensory/motor preskills as a foundation for learning. Children in whom these preskills have not fully developed find learning difficult if not impossible; they become our struggling or special-needs children. Without the appropriate developmental foundation, they cannot build the abstract thinking skills we try to teach them in school. “
Therefore, students may struggle in an educational setting and it may not be obviously apparent why the struggle exists.
So here’s my beef. Many students receive the necessary tools to overcome struggles in public education by the support of parents, teachers and interventions. There are a great number of students who do not receive additional support for whatever reason. This fact needs to change very rapidly.
Case in point, let’s examines the test scores for the high school exit exam for California. According to the California Department of Education website’s data for July of 2008, 13, 237 students took the Math portion of the California Exit Exam and 13, 373 students took the English portion of the exam. 29% of the students passed the Math and 30% passed the English portions of the test for the state. That means that 9,423 students failed the Math and 9,420 failed the English! Holy Smoke!
I cannot be the only one screaming in the wildness. Where are you? Please don’t give me the spill about more qualified teachers and incentives. In today’s, New York Times, Week in Review section on page 5 there is an advertisement from the President of America Federation of Teachers. The name of the article which is really an advertisement is called, “ What Matters Most: Words into Action”. In the ad-like article the president, Randi Weingarten explains this problem in education, “ For too long and too often, teacher evaluation –in both design and implementation – has failed to achieve what must be our goal: continuously improving and informing teaching so as to better education all students”. She goes on to give an example from Colorado of the school board and teacher union working together. Then at the end she says that school board members, teachers, union leaders all feel the same way, they want what’s best for the kids. I felt the article was about working relationships in these difficult financial times. Maybe that needs to be the focus for the advertisement that educational higher ups and teacher unions do not need to eat each other alive so they can eventually help kids. Although our students are failing right now and I don’t want any kid to miss several years of learning because people who make a lot of money can’t get along. We are talking about kid’s futures here. Give me a break!
I’m tired of the Infomercial Education. The kind that keeps promising that magic ellixir yet, the product is just so-so. The real conversation needs to be around the individual differences of students or their learning styles and needs. Administrators, school boards, teachers and all school staff members need to be trained in how to recognize a struggling student’s needs: emotionally, developmentally and physically. They also need to know how to build or recognize curriculum for these needs and drive the curriculum based on assessment data, not a hunch or a feeling. I’m not saying that public education can fix it all and is a one-stop shop. But let’s be honest students come to school with all of these issues and as a whole we cannot ignore the numbers. Our students in this state are not making the cut. Our interventions are not making the cut. Identifying student’s needs are not based on each student’s individual differences or assessments yet blanket interventions are thrown on major problems.
So, we need an Educational Revolution…
About the Author
Lisa Y. Johnson-Collins, Director of Education Through Engagement, LLC and Learning Through Engagement bring complementary skills in education and child development. Lisa has thirteen years of experience in special education classrooms. Lisa also has worked in the field of social work, assisting children and families. She has a master’s degree in special education, a bachelor’s degree in psychology, and is a credentialed teacher in both special and general education, kindergarten through high school. She has taught children with, among other things, learning disabilities, physical disabilities, emotional disturbance, autism, and mental retardation, as well as children in general education classes. Lisa has also studied in the field of child development as it relates to children’s education, having completed the requirements for certification in DIR (Developmental Individual- differences Relationship Model/Floortime) in the area of Special Education from the Interdisciplinary of Council of Developmental and Learning Disorders (ICDL).
This is my general premise as per my paper, The Multi-Sensory Classroom (Aug. 2004):
“Each child develops sensory/motor preskills at a very young age (e.g., auditory processing, fine and gross motor skills, visual perception, reflexes, tactile processing, sensory modulation). These bottom levels of sensory/motor development are often taken for granted because they are basic and develop automatically in the typically developing child. When we teach a student at school, the child uses these sensory/motor preskills as a foundation for learning. Children in whom these preskills have not fully developed find learning difficult if not impossible; they become our struggling or special-needs children. Without the appropriate developmental foundation, they cannot build the abstract thinking skills we try to teach them in school. “
Therefore, students may struggle in an educational setting and it may not be obviously apparent why the struggle exists.
So here’s my beef. Many students receive the necessary tools to overcome struggles in public education by the support of parents, teachers and interventions. There are a great number of students who do not receive additional support for whatever reason. This fact needs to change very rapidly.
Case in point, let’s examines the test scores for the high school exit exam for California. According to the California Department of Education website’s data for July of 2008, 13, 237 students took the Math portion of the California Exit Exam and 13, 373 students took the English portion of the exam. 29% of the students passed the Math and 30% passed the English portions of the test for the state. That means that 9,423 students failed the Math and 9,420 failed the English! Holy Smoke!
I cannot be the only one screaming in the wildness. Where are you? Please don’t give me the spill about more qualified teachers and incentives. In today’s, New York Times, Week in Review section on page 5 there is an advertisement from the President of America Federation of Teachers. The name of the article which is really an advertisement is called, “ What Matters Most: Words into Action”. In the ad-like article the president, Randi Weingarten explains this problem in education, “ For too long and too often, teacher evaluation –in both design and implementation – has failed to achieve what must be our goal: continuously improving and informing teaching so as to better education all students”. She goes on to give an example from Colorado of the school board and teacher union working together. Then at the end she says that school board members, teachers, union leaders all feel the same way, they want what’s best for the kids. I felt the article was about working relationships in these difficult financial times. Maybe that needs to be the focus for the advertisement that educational higher ups and teacher unions do not need to eat each other alive so they can eventually help kids. Although our students are failing right now and I don’t want any kid to miss several years of learning because people who make a lot of money can’t get along. We are talking about kid’s futures here. Give me a break!
I’m tired of the Infomercial Education. The kind that keeps promising that magic ellixir yet, the product is just so-so. The real conversation needs to be around the individual differences of students or their learning styles and needs. Administrators, school boards, teachers and all school staff members need to be trained in how to recognize a struggling student’s needs: emotionally, developmentally and physically. They also need to know how to build or recognize curriculum for these needs and drive the curriculum based on assessment data, not a hunch or a feeling. I’m not saying that public education can fix it all and is a one-stop shop. But let’s be honest students come to school with all of these issues and as a whole we cannot ignore the numbers. Our students in this state are not making the cut. Our interventions are not making the cut. Identifying student’s needs are not based on each student’s individual differences or assessments yet blanket interventions are thrown on major problems.
So, we need an Educational Revolution…
About the Author
Lisa Y. Johnson-Collins, Director of Education Through Engagement, LLC and Learning Through Engagement bring complementary skills in education and child development. Lisa has thirteen years of experience in special education classrooms. Lisa also has worked in the field of social work, assisting children and families. She has a master’s degree in special education, a bachelor’s degree in psychology, and is a credentialed teacher in both special and general education, kindergarten through high school. She has taught children with, among other things, learning disabilities, physical disabilities, emotional disturbance, autism, and mental retardation, as well as children in general education classes. Lisa has also studied in the field of child development as it relates to children’s education, having completed the requirements for certification in DIR (Developmental Individual- differences Relationship Model/Floortime) in the area of Special Education from the Interdisciplinary of Council of Developmental and Learning Disorders (ICDL).
University Ranking - Top Online Universities in the World
Want to study for an online degree program? There are many online universities
and colleges offering high quality education online.
Online Degree Programs:
Online degree programs offer many advantages such as flexibility and cost savings. Learning can take place at anywhere in the world, individual student can choose where, when and how to study.
Online programs are offered at different levels ranging from Certificate program, Diploma program, Associate degree, Bachelor degree, Graduate Certificate
, Graduate Diploma, Master degree to Doctorate degree. Subject areas include business, psychology, nursing, education, sociology, information technology and so on.
Top 10 Online Universities:
According to “The Best and Worst Online Degree Programs” 2007, the top ten online universities in the world are as follows:
(1) The University of London (UoL)
(2) The University of South Africa
(3) The University of Phoenix
(4) The University of Texas
(5) University of South Australia (UniSA)
(6) University of Southern Queensland (USQ)
(7) The University of Maryland University College
(8) Golden Gate University
(9) Ellis College of NYIT
(10) Stanford University
The University of London is ranked number one in the world for its outstanding online degree programs. It offers more than 100 online and distance qualifications through the University of London External Programme. Students studying through the External Programme are examined to the same standard as full-time on-campus students.
The University of South Australia is the leading provider of distance education in Australia. With more than 32000 on campus and offshore students, it is now the largest university in South Australia.
Prospective students are advised to check the accreditation and reputation of online universities and colleges before enrolling into a program of study.
Please refer to the relevant guides for more information on the latest university ranking and world university ranking.
Loke Yuen Wong - About the Author:
The author, Loke Yuen Wong, holds an MBA from Heriot-Watt University (UK) and a BCom degree from The University of Adelaide (Australia). Other qualifications include the Postgraduate Diploma in Bus. Administration, Diploma in Instructor Skills, Diploma in Inferential Statistics, Group Diploma in Accounting, Group Diploma in Management Accounting, ACCA CertIFR, Pre-Cert (ES) TESOL, Certificate in Managing Performance, Certificate in Book-keeping & Accounts and English for Commerce.
Read more: http://www.articlesbase.com/online-education-articles/university-ranking-top-online-universities-in-the-world-571792.html#ixzz0oSYefPxu
Under Creative Commons License: Attribution
and colleges offering high quality education online.
Online Degree Programs:
Online degree programs offer many advantages such as flexibility and cost savings. Learning can take place at anywhere in the world, individual student can choose where, when and how to study.
Online programs are offered at different levels ranging from Certificate program, Diploma program, Associate degree, Bachelor degree, Graduate Certificate
, Graduate Diploma, Master degree to Doctorate degree. Subject areas include business, psychology, nursing, education, sociology, information technology and so on.
Top 10 Online Universities:
According to “The Best and Worst Online Degree Programs” 2007, the top ten online universities in the world are as follows:
(1) The University of London (UoL)
(2) The University of South Africa
(3) The University of Phoenix
(4) The University of Texas
(5) University of South Australia (UniSA)
(6) University of Southern Queensland (USQ)
(7) The University of Maryland University College
(8) Golden Gate University
(9) Ellis College of NYIT
(10) Stanford University
The University of London is ranked number one in the world for its outstanding online degree programs. It offers more than 100 online and distance qualifications through the University of London External Programme. Students studying through the External Programme are examined to the same standard as full-time on-campus students.
The University of South Australia is the leading provider of distance education in Australia. With more than 32000 on campus and offshore students, it is now the largest university in South Australia.
Prospective students are advised to check the accreditation and reputation of online universities and colleges before enrolling into a program of study.
Please refer to the relevant guides for more information on the latest university ranking and world university ranking.
Loke Yuen Wong - About the Author:
The author, Loke Yuen Wong, holds an MBA from Heriot-Watt University (UK) and a BCom degree from The University of Adelaide (Australia). Other qualifications include the Postgraduate Diploma in Bus. Administration, Diploma in Instructor Skills, Diploma in Inferential Statistics, Group Diploma in Accounting, Group Diploma in Management Accounting, ACCA CertIFR, Pre-Cert (ES) TESOL, Certificate in Managing Performance, Certificate in Book-keeping & Accounts and English for Commerce.
Read more: http://www.articlesbase.com/online-education-articles/university-ranking-top-online-universities-in-the-world-571792.html#ixzz0oSYefPxu
Under Creative Commons License: Attribution
Monday, May 10, 2010
Move to Learn – Unlock the Potential of the Brain
There are about as many nerve cells in the brain as there are stars in the Milky Way galaxy. The unique set of connections between neurons that each of us develops determines how we view the world, shapes our future experiences, and indeed, determines who we are. Successful students have developed rich, connected networks of neurons. Many factors encourage neurons to branch and communicate with each other. In this newsletter, our topic will be the vital role of movement in brain development.
In our quest to fathom intelligent behavior, we have failed to appreciate that learning does not occur strictly in the mind. Learning and creativity are a “whole body” phenomenon and cannot occur independently. We teach “to the head” only, asking students to sit in chairs for long periods of time, listening and looking almost exclusively at abstract symbols, even when they are very young. We don’t fully appreciate that the mind cannot excel without the support of the body. We don’t “get it” that we must move to learn.
What is the role of movement in learning?
Movement stimulates the growth of neural networks upon which learning depends. It affords us the opportunity to explore our world and gather the sensory data that fuels the development of intelligence, in other words, it provokes learning. Movement provides feedback that the brain requires in order to learn. Movement allows us to express knowledge and therefore advance to the next plateau in our understanding.
What can parents do to encourage stronger learning in their children?
Not very many years ago, children played in their yards for hours each day. They ran, climbed trees, built forts, made mud pies and pretended to fly. These experiences developed rich neural networks that supported brain development in these children. Young people today spend far less time moving. They watch considerably more television and play significantly more video games.
We can integrate movement into our children’s daily lives and augment their capacity to succeed. In particular, children who have learning issues benefit from the systematic inclusion of movement into their daily lives.
Each “body” learns in its own unique way. The following activities can be stimulating to the development of strong brain networks. Allow your child to experiment during homework time and find the particular combination of activities that are most effective.
Most students remember new information better when they talk, write or draw. Encourage your child to “teach” new information to others in the household. For those students who anchor information best by writing, provide them with a white board and erasable markers or encourage them to take notes on paper. It isn’t always necessary to keep notes or read them later in order to anchor information in memory. The act of writing down the information promotes the development of connections among concepts. Demonstrating the concepts of the learning is another powerful way to incorporate the new learning into existing neural networks. Allow your child to act out what has been read, build a model, draw a diagram or chart, sing or dance.
Many students attend, concentrate and learn better when engaged in a repetitive, low concentration task such as doodling, folding paper, rocking, or squeezing a ball. Your child can also try walking around the room while reading or studying. Suggest to your child that he or she do this every 15 minutes while completing homework.
Because the mouth is an important site of neural integration and is closely tied to brain development, some students find that chewing can be a highly integrating activity that promotes concentration and understanding. Chewing gum can actually be an effective way to focus! It’s best to keep it simple. Crunchy, spicy, salty or sour foods can be effective concentration boosters. Have your child try carrot sticks, sugar free gum, pretzels or a small sour candy.
Encourage your child to engage in cross lateral physical activity for five minutes every hour. Cross lateral movements engage hand and foot on opposite sides of the body. Most of these movements are more effective when done standing. The addition of rhythmic music provides a boost. Some cross lateral movements students enjoy are:
* Touch hand (or elbow) to opposite knee.
* Lazy 8. Use one hand to trace a large infinity sign in front of the body, following the hand with the eyes. Alternate hands and continue.
* Cross the arms in front of the face in the shape of an “X” tracing a lazy 8. Be sure to watch the path of the 8 while tracing it.
* Karate Cross Crawl: Kick while punching or chopping with alternate hand and foot (right hand chops while left foot kicks).
* Cross Crawl Sit-ups. While lying on the back with hands clasped behind the head for support, sit up and touch the right elbow to the left knee. Alternate touching elbow to opposite knee.
* Double Doodle. Draw a design with both hands simultaneously. Be sure the designs are mirror images of each other, rather than facing the same direction.
About the Author
Dr. Kari Miller is a Board Certified Educational Therapist and Director of Miller Educational Excellence in Los Angeles. She began her career almost twenty-five years ago as a special education resource teacher. She has worked with students in a vast array of capacities, including special education teacher and educational therapist. Dr. Miller has a PhD in Educational Psychology and Mathematical Statistics, a master’s degree in Learning Disabilities, Gifted Education and Educational Diagnosis, and a bachelor’s degree in Early Childhood Education and Behavior Disorders.
To contact Dr. Miller
Email: klmiller555@sbcglobal.net
Website: www.millereducationalexcellence.com
Phone: 310-280-9813
In our quest to fathom intelligent behavior, we have failed to appreciate that learning does not occur strictly in the mind. Learning and creativity are a “whole body” phenomenon and cannot occur independently. We teach “to the head” only, asking students to sit in chairs for long periods of time, listening and looking almost exclusively at abstract symbols, even when they are very young. We don’t fully appreciate that the mind cannot excel without the support of the body. We don’t “get it” that we must move to learn.
What is the role of movement in learning?
Movement stimulates the growth of neural networks upon which learning depends. It affords us the opportunity to explore our world and gather the sensory data that fuels the development of intelligence, in other words, it provokes learning. Movement provides feedback that the brain requires in order to learn. Movement allows us to express knowledge and therefore advance to the next plateau in our understanding.
What can parents do to encourage stronger learning in their children?
Not very many years ago, children played in their yards for hours each day. They ran, climbed trees, built forts, made mud pies and pretended to fly. These experiences developed rich neural networks that supported brain development in these children. Young people today spend far less time moving. They watch considerably more television and play significantly more video games.
We can integrate movement into our children’s daily lives and augment their capacity to succeed. In particular, children who have learning issues benefit from the systematic inclusion of movement into their daily lives.
Each “body” learns in its own unique way. The following activities can be stimulating to the development of strong brain networks. Allow your child to experiment during homework time and find the particular combination of activities that are most effective.
Most students remember new information better when they talk, write or draw. Encourage your child to “teach” new information to others in the household. For those students who anchor information best by writing, provide them with a white board and erasable markers or encourage them to take notes on paper. It isn’t always necessary to keep notes or read them later in order to anchor information in memory. The act of writing down the information promotes the development of connections among concepts. Demonstrating the concepts of the learning is another powerful way to incorporate the new learning into existing neural networks. Allow your child to act out what has been read, build a model, draw a diagram or chart, sing or dance.
Many students attend, concentrate and learn better when engaged in a repetitive, low concentration task such as doodling, folding paper, rocking, or squeezing a ball. Your child can also try walking around the room while reading or studying. Suggest to your child that he or she do this every 15 minutes while completing homework.
Because the mouth is an important site of neural integration and is closely tied to brain development, some students find that chewing can be a highly integrating activity that promotes concentration and understanding. Chewing gum can actually be an effective way to focus! It’s best to keep it simple. Crunchy, spicy, salty or sour foods can be effective concentration boosters. Have your child try carrot sticks, sugar free gum, pretzels or a small sour candy.
Encourage your child to engage in cross lateral physical activity for five minutes every hour. Cross lateral movements engage hand and foot on opposite sides of the body. Most of these movements are more effective when done standing. The addition of rhythmic music provides a boost. Some cross lateral movements students enjoy are:
* Touch hand (or elbow) to opposite knee.
* Lazy 8. Use one hand to trace a large infinity sign in front of the body, following the hand with the eyes. Alternate hands and continue.
* Cross the arms in front of the face in the shape of an “X” tracing a lazy 8. Be sure to watch the path of the 8 while tracing it.
* Karate Cross Crawl: Kick while punching or chopping with alternate hand and foot (right hand chops while left foot kicks).
* Cross Crawl Sit-ups. While lying on the back with hands clasped behind the head for support, sit up and touch the right elbow to the left knee. Alternate touching elbow to opposite knee.
* Double Doodle. Draw a design with both hands simultaneously. Be sure the designs are mirror images of each other, rather than facing the same direction.
About the Author
Dr. Kari Miller is a Board Certified Educational Therapist and Director of Miller Educational Excellence in Los Angeles. She began her career almost twenty-five years ago as a special education resource teacher. She has worked with students in a vast array of capacities, including special education teacher and educational therapist. Dr. Miller has a PhD in Educational Psychology and Mathematical Statistics, a master’s degree in Learning Disabilities, Gifted Education and Educational Diagnosis, and a bachelor’s degree in Early Childhood Education and Behavior Disorders.
To contact Dr. Miller
Email: klmiller555@sbcglobal.net
Website: www.millereducationalexcellence.com
Phone: 310-280-9813
Times Tables – Causes of Difficulties (1 – 3)
The brief enumeration of main causes of difficulties in mastering the multiplication tables described in my previous article needs to be detailed and motivated. Now I would like to dwell at some length upon the first three causes.
Cause #1. Pupils begin to learn the times tables while many of them have not mastered simple mental addition and subtraction totally.
Only the fact, that multiplication is repeated addition, defaults importance of the addition skills for understanding the multiplication idea. At the first stage of becoming accustomed to the times tables every pupil should obtain himself/herself each multiplication result from 2 x 2 = 2 + 2 = 4 to 9 x 9 = 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 +9 = 81. Undoubtedly, only the pupils, which have mastered the mental addition skills within the limits of 100 totally, can perform such a work successfully. Only in this case the times tables will cease to be a meaningless set of numbers, and, furthermore, the results obtained by a pupil without assistance will become more accessible to be retained in the memory.
If a kid meets significant difficulties in addition, if he/she can not perform mentally, for instance, 7 + 7 + 7 quickly and effortlessly, then the exhausting calculating procedure will hide the importance of the desired goal. Hereupon the final result will lose meaning for the kid, and, as is generally known, it is not easy to memorize any meaningless information.
After the times tables have been shaped by pupils, the work upon learning them by heart begins. The process of the memorizing will require certain quantity of time and some, maybe, considerable efforts. We know that our memory has bad habit to let us down at the very unsuitable moment. So pupils are needed to become acquainted with some tips which can help them to recall the forgotten result. The first of the tips is already mentioned. If a pupil remembers that multiplication is repeated addition, then, when, for instance, the result of 6 x 4 has been forgotten, he/she can get it by adding 6 + 6 + 6 + 6. But there are other tips also. If you remember that 6 x 3 = 18, you can perform the next procedure 6 x 4 = 6 x 3 + 6 = 18 + 6 = 24. Or if you remember that 6 x 5 = 30, you can act so 6 x 4 = 6 x 5 - 6 = 30 - 6 = 24. To use these tips effectively, pupils have to master totally both the addition skills and the subtraction skills within the limits of 100.
Cause #2. Pupils learn the times tables without simultaneous learning the corresponding to them division facts.
If you need to memorize new information quickly and firmly, the best way is to form many connections between the new facts and any other facts in your brain. As for the multiplication tables, the first connection is the close relation between multiplication and addition. The second one is symmetrical multiplication results, and then the connections between the multiplication facts and division facts must be mentioned. My experience show that the simultaneous learning interconnected results (3 x 6 = 18, 6 x 3 = 18, 18 : 3 = 6, 18 : 6 = 3, for example) helps to memorize each of them better. Some my pupils had memorized well the division facts first, and only then they achieved success in the memorizing the multiplication results. Evidently, remembering that 18 : 6 = 3 helps to recall that 3 x 6 = 18.
Cause #3. To memorize the multiplication facts, many pupils use the learning by rote only, and the knowledge which has been crammed is forgotten very soon.
If a pupil is weak in mental addition and subtraction, he/she has the only way to recall a forgotten result – looking at the multiplication charts, and the only way to memorize the times tables – learning them by rote. Sometimes even teachers encourage children to do so by asking them to recite the times tables over and over again. As a result, many of pupils do not understand what have been crammed in their heads, and if they are asked for the answer to 7 x 8 they can give it only by reciting from 1 x 8.
It is doubtful whether we can manage without learning some math facts by rote at all, but it is evident that the learning by rote can not be the single or main way of learning math. In all events children must at first understand well the information which then they will try to memorize by heart, and, secondly, they must constantly use this information. We know well, that the phone number used often is memorized easier than the phone number which we use once in a while.
About the Author
Victor Guskov, a teacher of mathematics, PhD, Pedagogical Sciences.
http://www.simplar.narod.ru/index1.html
Cause #1. Pupils begin to learn the times tables while many of them have not mastered simple mental addition and subtraction totally.
Only the fact, that multiplication is repeated addition, defaults importance of the addition skills for understanding the multiplication idea. At the first stage of becoming accustomed to the times tables every pupil should obtain himself/herself each multiplication result from 2 x 2 = 2 + 2 = 4 to 9 x 9 = 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 +9 = 81. Undoubtedly, only the pupils, which have mastered the mental addition skills within the limits of 100 totally, can perform such a work successfully. Only in this case the times tables will cease to be a meaningless set of numbers, and, furthermore, the results obtained by a pupil without assistance will become more accessible to be retained in the memory.
If a kid meets significant difficulties in addition, if he/she can not perform mentally, for instance, 7 + 7 + 7 quickly and effortlessly, then the exhausting calculating procedure will hide the importance of the desired goal. Hereupon the final result will lose meaning for the kid, and, as is generally known, it is not easy to memorize any meaningless information.
After the times tables have been shaped by pupils, the work upon learning them by heart begins. The process of the memorizing will require certain quantity of time and some, maybe, considerable efforts. We know that our memory has bad habit to let us down at the very unsuitable moment. So pupils are needed to become acquainted with some tips which can help them to recall the forgotten result. The first of the tips is already mentioned. If a pupil remembers that multiplication is repeated addition, then, when, for instance, the result of 6 x 4 has been forgotten, he/she can get it by adding 6 + 6 + 6 + 6. But there are other tips also. If you remember that 6 x 3 = 18, you can perform the next procedure 6 x 4 = 6 x 3 + 6 = 18 + 6 = 24. Or if you remember that 6 x 5 = 30, you can act so 6 x 4 = 6 x 5 - 6 = 30 - 6 = 24. To use these tips effectively, pupils have to master totally both the addition skills and the subtraction skills within the limits of 100.
Cause #2. Pupils learn the times tables without simultaneous learning the corresponding to them division facts.
If you need to memorize new information quickly and firmly, the best way is to form many connections between the new facts and any other facts in your brain. As for the multiplication tables, the first connection is the close relation between multiplication and addition. The second one is symmetrical multiplication results, and then the connections between the multiplication facts and division facts must be mentioned. My experience show that the simultaneous learning interconnected results (3 x 6 = 18, 6 x 3 = 18, 18 : 3 = 6, 18 : 6 = 3, for example) helps to memorize each of them better. Some my pupils had memorized well the division facts first, and only then they achieved success in the memorizing the multiplication results. Evidently, remembering that 18 : 6 = 3 helps to recall that 3 x 6 = 18.
Cause #3. To memorize the multiplication facts, many pupils use the learning by rote only, and the knowledge which has been crammed is forgotten very soon.
If a pupil is weak in mental addition and subtraction, he/she has the only way to recall a forgotten result – looking at the multiplication charts, and the only way to memorize the times tables – learning them by rote. Sometimes even teachers encourage children to do so by asking them to recite the times tables over and over again. As a result, many of pupils do not understand what have been crammed in their heads, and if they are asked for the answer to 7 x 8 they can give it only by reciting from 1 x 8.
It is doubtful whether we can manage without learning some math facts by rote at all, but it is evident that the learning by rote can not be the single or main way of learning math. In all events children must at first understand well the information which then they will try to memorize by heart, and, secondly, they must constantly use this information. We know well, that the phone number used often is memorized easier than the phone number which we use once in a while.
About the Author
Victor Guskov, a teacher of mathematics, PhD, Pedagogical Sciences.
http://www.simplar.narod.ru/index1.html
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