This blog post describes what got me interested in mastery learning in the first place: a new learning technology designed to educate everyone.
I propose a wiki-style website where the public can input prerequisite links and chains needed to learn topics, such as learning addition before multiplication. There would be a visual dependency graph of prerequisites, so you can determine what to learn in order to understand X, and the site could also record what you have previously learned.
Each topic would have to be clearly defined as to what needs to be learned. This may be more difficult for certain abstract topics. For instance, learning division may be more definable than learning to draw. However, I believe even these kinds of topics can be divided into a list of things to be learned. How the list of things to be learned are taught, or how they are tested, I cannot fully answer. But when tested, the prerequisite topics should also be included in the test, to ensure that the test taker remembers previously learned topics.
It is probably best to be tested via an oral exam. This allows the exam audience to analyze the student's thought process (which may be different from other students) and decide if the student understands the material required for the topic. The student will only pass if he knows everything required for the chosen topic.
Tuesday, August 10, 2010
On apathetic students
After telling our education reform ideas to colleagues, many of them reply with, "some students just do not care, and only strive for a passing grade to graduate." Since our proposed mastery learning would completely remove grades (you must master the topic to move on), then the worry is that apathetic students would be held back longer and this could cause a strain on the institutions. In this blog post, I discuss how our mastery learning system will have less apathetic students than the current education system.
Apathy plays an important factor when building an education system. Students with passion achieve much more than students without. I remember fellow students in elementary school claiming, "I will NEVER need to know how to do this!" Perhaps a student knowing that he will never apply a particular knowledge in the real world causes apathy. Our mastery learning fixes this problem by allowing students to choose what higher level topics they want to learn, and then the sub-topic prerequisites are chosen automatically. This way the student will always be learning precisely what he wants to learn! I think this will motivate students more than the current system.
But shouldn't ALL students learn X? I personally believe what-to-learn is a choice. It is recommended to learn basic things in order to comfortably live, such as basic math for managing finances.
Certain students will accelerate in topics faster than others. It's reality. One shouldn't feel ashamed to learn a particular topic at a slower rate. People are different. But does this time-to-learn difference cause overpopulations in institutions?
Well, this brings us to another topic which can be better described in a separate post: current institutions need to be revised to provide better education. By "institutions", I am referring to elementary, middle, and high schools and universities. One revision is to remove the notion of "grade levels" and use "topic levels" instead. Not everyone needs to go to "class", but you must take a test (at anytime you wish) to advance the topic. Some students may just wish to study themselves in a library, and only visit the institution for guidance.
Another revision is that teachers should only teach, and should stay away from designing tests, grading, and deciding who passes the class. Teachers should guide students based on the standardized requirements for a particular topic, which is made publicly clear in our proposed system.
There is a need for a more standardized learning system, so that when Joe from Louisiana learns topic X and Mary from New York learns topic X we can safely assume they learned the exact same thing. When learning a new topic that requires understanding X, it is safe to say that Mary and Joe both have sufficient knowledge to understand this new topic, regardless where and how they learned X.
With our proposed system, I believe academic learning will happen at a much greater speed. Students will only struggle with topics at hand, since their previous topics are already mastered. This makes less problems for the student to deal with, and allows the student to focus precisely on the topic area which is most confusing.
More about how to implement such a standardized mastery learning system will be outlined in my next post.
Apathy plays an important factor when building an education system. Students with passion achieve much more than students without. I remember fellow students in elementary school claiming, "I will NEVER need to know how to do this!" Perhaps a student knowing that he will never apply a particular knowledge in the real world causes apathy. Our mastery learning fixes this problem by allowing students to choose what higher level topics they want to learn, and then the sub-topic prerequisites are chosen automatically. This way the student will always be learning precisely what he wants to learn! I think this will motivate students more than the current system.
But shouldn't ALL students learn X? I personally believe what-to-learn is a choice. It is recommended to learn basic things in order to comfortably live, such as basic math for managing finances.
Certain students will accelerate in topics faster than others. It's reality. One shouldn't feel ashamed to learn a particular topic at a slower rate. People are different. But does this time-to-learn difference cause overpopulations in institutions?
Well, this brings us to another topic which can be better described in a separate post: current institutions need to be revised to provide better education. By "institutions", I am referring to elementary, middle, and high schools and universities. One revision is to remove the notion of "grade levels" and use "topic levels" instead. Not everyone needs to go to "class", but you must take a test (at anytime you wish) to advance the topic. Some students may just wish to study themselves in a library, and only visit the institution for guidance.
Another revision is that teachers should only teach, and should stay away from designing tests, grading, and deciding who passes the class. Teachers should guide students based on the standardized requirements for a particular topic, which is made publicly clear in our proposed system.
There is a need for a more standardized learning system, so that when Joe from Louisiana learns topic X and Mary from New York learns topic X we can safely assume they learned the exact same thing. When learning a new topic that requires understanding X, it is safe to say that Mary and Joe both have sufficient knowledge to understand this new topic, regardless where and how they learned X.
With our proposed system, I believe academic learning will happen at a much greater speed. Students will only struggle with topics at hand, since their previous topics are already mastered. This makes less problems for the student to deal with, and allows the student to focus precisely on the topic area which is most confusing.
More about how to implement such a standardized mastery learning system will be outlined in my next post.
On the importance of mastering
“Science is organized knowledge. Wisdom is organized life.” - Kant
Hello, my name is Daniel and I am a coworker of Daryl (the other contributer). We have similar opinions on changes that are needed in the current education system.
The biggest change needed, which this blog is about, is that students must master topics rather than barely learn them. There are many aspects to this: the benefits vs drawbacks, how to change the education system to make this happen, etc. In this blog post, I will discuss my viewpoint on the importance of mastering topics.
You may have heard the phrase, "Jack of all trades, master of none." This phrase of course refers to a generalist: a person with a wide array of knowledge, the opposite of which is a specialist. Are we saying that it is better to live as a specialist rather than a generalist? Not really. It's okay to know a little about everything, but it is more important to be able to make the connections between ideas.
The above diagram is an example of what we mean. When Joe wants to learn about basket weaving, Joe needs to learn about X, Y and Z. To learn X, he also needs to learn A, B and C, and so on. There is a hierarchical tree of subtopics to learn, and if Joe doesn't know B, it is obvious that Joe cannot fully understand X or basket weaving. Mastering a topic requires mastering a dependency chain of subtopics.
But isn't it okay for Joe to just learn B enough to get by (e.g., a school test grade of B)? No, because Joe's problems may increase exponentially over time! As Joe moves on to bigger and better things in life, he may want to learn about topics that require understanding basket weaving, but he cannot move forward! The point is that mastering the fundamentals is essential to an education that will last a lifetime.
It is the fundamentals that "stick in our head" as we move on to learn new topics. Mastering these fundamentals and connecting them is an important brain exercise that will allow us to solve problems more easily in the future.
As you have probably already guessed, I am not focused on child students, but rather everyone as a student, no matter the age. This is one small difference Daryl and I have. Daryl is more focused on child education (elementary/middle school) since he has kids in this age group.
Hello, my name is Daniel and I am a coworker of Daryl (the other contributer). We have similar opinions on changes that are needed in the current education system.
The biggest change needed, which this blog is about, is that students must master topics rather than barely learn them. There are many aspects to this: the benefits vs drawbacks, how to change the education system to make this happen, etc. In this blog post, I will discuss my viewpoint on the importance of mastering topics.
You may have heard the phrase, "Jack of all trades, master of none." This phrase of course refers to a generalist: a person with a wide array of knowledge, the opposite of which is a specialist. Are we saying that it is better to live as a specialist rather than a generalist? Not really. It's okay to know a little about everything, but it is more important to be able to make the connections between ideas.
The above diagram is an example of what we mean. When Joe wants to learn about basket weaving, Joe needs to learn about X, Y and Z. To learn X, he also needs to learn A, B and C, and so on. There is a hierarchical tree of subtopics to learn, and if Joe doesn't know B, it is obvious that Joe cannot fully understand X or basket weaving. Mastering a topic requires mastering a dependency chain of subtopics.
But isn't it okay for Joe to just learn B enough to get by (e.g., a school test grade of B)? No, because Joe's problems may increase exponentially over time! As Joe moves on to bigger and better things in life, he may want to learn about topics that require understanding basket weaving, but he cannot move forward! The point is that mastering the fundamentals is essential to an education that will last a lifetime.
It is the fundamentals that "stick in our head" as we move on to learn new topics. Mastering these fundamentals and connecting them is an important brain exercise that will allow us to solve problems more easily in the future.
As you have probably already guessed, I am not focused on child students, but rather everyone as a student, no matter the age. This is one small difference Daryl and I have. Daryl is more focused on child education (elementary/middle school) since he has kids in this age group.
Tuesday, June 15, 2010
Topic Based Learning
Until someone else shows up here, I'm just going to blab away about my pet theory of education.
The topic of today's post is topics. The way that education is structured today in most (all?) schools in the US is by grade level and by course (in middle school and high school). This is too coarse-grained to give an accurate picture of what a child has learned. There are two different unfortunate outcomes that can result from the course-based system. First, a child may pass the course even though there are essential skills and knowledge that he missed. This makes the followup courses that much more difficult, because he must not only learn the new material, but also catch up on the material that he should have learned, but didn't. The second unfortunate outcome is that the child may fail the course and must repeat the whole thing, even if he was successful in learning some of the material.
The more precise approach to assessing a child's achievements is to break material down into much smaller topics, where a topic covers a small enough range of subject matter that it is feasible to completely master it. (There also can be synthesis topics that involve several smaller topics. More about this later.) For example, in mathematics, topics might include: addition of 1-digit numbers, addition of multi-digit numbers, multiplication of 1-digit numbers, multiplication of multi-digit numbers, etc. The goal should always be mastery of topics.
To take the example of multiplication of multi-digit numbers, if a child can only correctly do 80% (say) of such problems, then that means that there is some aspect of multiplication that he does not understand. It is a mistake, in my opinion, for teachers to say: well 80% is not too bad, so let's move onto more advanced topics (division, or fractions, or whatever). It's a mistake because the more advanced topics depend on thoroughly understanding the more basic topics. It is so important to catch and correct gaps in understanding as soon as possible, because otherwise the flaws in understanding can go on to "infect" many followup topics.
In addition to base topics that are about a single thing such as multiplication, there will be synthesis topics that require applying several base topics. In mathematics, being able to solve "word problems" is an example of such a synthesis topic. The base and synthesis topics naturally form a hierarchy in which the mastery of one topic requires the mastery of lower-level topics. It is very important to have an accurate map of such a topic hierarchy, because that allows an effective approach to dealing with a child's lack of success in a topic: Find out what dependent topics the child has failed to master, and work on mastering those, first.
The advantage of such a topic based approach, with a hierarchy that is understood by all, is that both teachers and students know precisely what it is that they need to work on. This is much more effective than the information kids currently have about their skills, which is along the lines of "I'm bad at math".
In science and math, the topics and their dependencies are pretty straightforward. I believe, though, the topic-based approach is potentially useful in
"softer" subjects such as language, art, music. There is a difference between the hard and soft subjects, in that it might possible to become perfect at, say, adding multi-digit numbers, but there is no clear notion of being perfect at writing sentences or paragraphs or essays. So there will be a certain element of subjectivity to the assessment of such subjects. However, I think that the notion of mastery is still useful there, by interpreting topics as projects. Writing a story, writing an essay, learning to play a piece of music---each such activity can be considered a project in which the goal is excellence. The child should work on a project to the point that both the child and teacher agree that he has done an excellent job. A child learns most from doing things well, and learns very little from doing things in a mediocre way.
The topic of today's post is topics. The way that education is structured today in most (all?) schools in the US is by grade level and by course (in middle school and high school). This is too coarse-grained to give an accurate picture of what a child has learned. There are two different unfortunate outcomes that can result from the course-based system. First, a child may pass the course even though there are essential skills and knowledge that he missed. This makes the followup courses that much more difficult, because he must not only learn the new material, but also catch up on the material that he should have learned, but didn't. The second unfortunate outcome is that the child may fail the course and must repeat the whole thing, even if he was successful in learning some of the material.
The more precise approach to assessing a child's achievements is to break material down into much smaller topics, where a topic covers a small enough range of subject matter that it is feasible to completely master it. (There also can be synthesis topics that involve several smaller topics. More about this later.) For example, in mathematics, topics might include: addition of 1-digit numbers, addition of multi-digit numbers, multiplication of 1-digit numbers, multiplication of multi-digit numbers, etc. The goal should always be mastery of topics.
To take the example of multiplication of multi-digit numbers, if a child can only correctly do 80% (say) of such problems, then that means that there is some aspect of multiplication that he does not understand. It is a mistake, in my opinion, for teachers to say: well 80% is not too bad, so let's move onto more advanced topics (division, or fractions, or whatever). It's a mistake because the more advanced topics depend on thoroughly understanding the more basic topics. It is so important to catch and correct gaps in understanding as soon as possible, because otherwise the flaws in understanding can go on to "infect" many followup topics.
In addition to base topics that are about a single thing such as multiplication, there will be synthesis topics that require applying several base topics. In mathematics, being able to solve "word problems" is an example of such a synthesis topic. The base and synthesis topics naturally form a hierarchy in which the mastery of one topic requires the mastery of lower-level topics. It is very important to have an accurate map of such a topic hierarchy, because that allows an effective approach to dealing with a child's lack of success in a topic: Find out what dependent topics the child has failed to master, and work on mastering those, first.
The advantage of such a topic based approach, with a hierarchy that is understood by all, is that both teachers and students know precisely what it is that they need to work on. This is much more effective than the information kids currently have about their skills, which is along the lines of "I'm bad at math".
In science and math, the topics and their dependencies are pretty straightforward. I believe, though, the topic-based approach is potentially useful in
"softer" subjects such as language, art, music. There is a difference between the hard and soft subjects, in that it might possible to become perfect at, say, adding multi-digit numbers, but there is no clear notion of being perfect at writing sentences or paragraphs or essays. So there will be a certain element of subjectivity to the assessment of such subjects. However, I think that the notion of mastery is still useful there, by interpreting topics as projects. Writing a story, writing an essay, learning to play a piece of music---each such activity can be considered a project in which the goal is excellence. The child should work on a project to the point that both the child and teacher agree that he has done an excellent job. A child learns most from doing things well, and learns very little from doing things in a mediocre way.
Wednesday, June 9, 2010
Mastery for all students
This is a guest editorial on the topic that was published in The Ithaca Journal on June 9, 2010.
In Ithaca, a child who is eager to learn and who takes advantage of all the available educational opportunities can receive a first-rate education that will prepare him or her to go to the very best colleges. But many children do not benefit from these opportunities. At best, they drift through school, hoping not to bring attention to themselves, learning just enough to pass to the next course.
I believe that we are doing a tremendous disservice to these children. Superficial knowledge that gets a passing grade on a test and is quickly forgotten thereafter has no power to inspire anyone to greater things. It cannot provide a firm foundation for learning more difficult material. Whatever a child learns, he or she should learn well.
The letter grades that are given to children based on their performance contribute to the superficiality, rather than address it. They are inadequate to assess a child's strengths and weaknesses, or the child's readiness for more advanced material. Grades also fail as motivation. Giving a child a "C" simply tells the child that he is a "C" student and that he should accept mediocrity as his lot in life.
A child gets a poor grade in a subject because there is some topic, or skill, that he should have mastered but did not.
But if he hasn't actually failed, he will be sent along to the next more advanced subject, where it's hoped that he will learn the new material, in addition to whatever material he should have learned earlier.
Keeping up gets more difficult with each new semester. At some point, the child who is having academic trouble gives up on himself, and the school system gives up on him, as well. I consider that a tragedy, and a preventable one.
How can we do better?
An antidote to superficiality is to insist on the mastery of smaller topics, instead of mere exposure to larger topics. If a child fails to master a subject such as algebra, then it means the subject is too big a chunk for that child.
It should be broken down into smaller topics and skills that he or she can realistically be expected to master, and we should give children the time it takes to master them.
It makes no sense to put a child into more advanced classes, say trigonometry or calculus, if he hasn't really understood the topics in algebra. A child's confidence in himself and his commitment to doing well is boosted tremendously by having high standards set for him and making sure that he achieves those high standards.
Not every child will master every topic, but what the child does learn, he or she can learn well.
In Ithaca, a child who is eager to learn and who takes advantage of all the available educational opportunities can receive a first-rate education that will prepare him or her to go to the very best colleges. But many children do not benefit from these opportunities. At best, they drift through school, hoping not to bring attention to themselves, learning just enough to pass to the next course.
I believe that we are doing a tremendous disservice to these children. Superficial knowledge that gets a passing grade on a test and is quickly forgotten thereafter has no power to inspire anyone to greater things. It cannot provide a firm foundation for learning more difficult material. Whatever a child learns, he or she should learn well.
The letter grades that are given to children based on their performance contribute to the superficiality, rather than address it. They are inadequate to assess a child's strengths and weaknesses, or the child's readiness for more advanced material. Grades also fail as motivation. Giving a child a "C" simply tells the child that he is a "C" student and that he should accept mediocrity as his lot in life.
A child gets a poor grade in a subject because there is some topic, or skill, that he should have mastered but did not.
But if he hasn't actually failed, he will be sent along to the next more advanced subject, where it's hoped that he will learn the new material, in addition to whatever material he should have learned earlier.
Keeping up gets more difficult with each new semester. At some point, the child who is having academic trouble gives up on himself, and the school system gives up on him, as well. I consider that a tragedy, and a preventable one.
How can we do better?
An antidote to superficiality is to insist on the mastery of smaller topics, instead of mere exposure to larger topics. If a child fails to master a subject such as algebra, then it means the subject is too big a chunk for that child.
It should be broken down into smaller topics and skills that he or she can realistically be expected to master, and we should give children the time it takes to master them.
It makes no sense to put a child into more advanced classes, say trigonometry or calculus, if he hasn't really understood the topics in algebra. A child's confidence in himself and his commitment to doing well is boosted tremendously by having high standards set for him and making sure that he achieves those high standards.
Not every child will master every topic, but what the child does learn, he or she can learn well.
Welcome to Ithaca Mastery Learning
I'm an Ithaca parent with no particular training in education, but I have been frustrated by some aspects of public education in Ithaca. I believe that many Ithaca children receive excellent educations that prepare them to go on to successful college careers. But many children just coast through school, learning the bare minimum and never becoming engaged in what they learn.
This blog is an attempt to make a difference in how our public schools meet the needs of our students. I believe that all children can learn, and learn well, but for me kids, it's not going to happen by accident. We have to be vigilant in understanding the gaps in their skills and understanding that make future learning more difficult. We need much more feedback about the impediments to successful learning that each student encounters, and we must constantly work to overcome those obstacles. We cannot give up on students.
This blog is for parents whose children are drifting through school, unengaged and unmotivated, as well as for parents who feel that their kids who are not being sufficiently challenged in school. Our mission is to make sure that every child is living up to his or her potential, and can have confidence in their ability to achieve.
Followup posts will go into more detail about what I believe is needed to help students reach their potential. I also strongly encourage people to send me your ideas, and I will post them.
This blog is an attempt to make a difference in how our public schools meet the needs of our students. I believe that all children can learn, and learn well, but for me kids, it's not going to happen by accident. We have to be vigilant in understanding the gaps in their skills and understanding that make future learning more difficult. We need much more feedback about the impediments to successful learning that each student encounters, and we must constantly work to overcome those obstacles. We cannot give up on students.
This blog is for parents whose children are drifting through school, unengaged and unmotivated, as well as for parents who feel that their kids who are not being sufficiently challenged in school. Our mission is to make sure that every child is living up to his or her potential, and can have confidence in their ability to achieve.
Followup posts will go into more detail about what I believe is needed to help students reach their potential. I also strongly encourage people to send me your ideas, and I will post them.
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