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Thursday, January 20, 2011
Friday, January 14, 2011
Tuesday, January 11, 2011
Super Summary by Maria Carmen King
Why Don’t Students Like School?
When I chose this book, I thought it would be about strategies or tools for teachers to use when we know the reasons that students had for not liking school, so when I began reading it I felt disappointed. As I read the book’s chapters I discovered that I like it and that it contains very good and valuable information. The book is about the mind of the child and how it works.
Mr. Willingham gives a clear explanation and reasoning to every concept he presents. He focuses on the cognitive learning and difficulties some people experience concentrating and thinking. From the first chapter to the last, which it is dedicated to teachers, Mr. Willingham gives reasons for problem, ideas, and how to fix it. One of my favorite parts on this book is the “Implications for the Classroom” part that he includes in every chapter, which I found very useful.
I found myself relating to the concept of this book when I started with this class. I was so overwhelmed by my incomprehension of what I was doing and the quantity of work I had. That fear I had, could be the same fear many students have in school with certain subjects that are new to them.
Reading this book was good for me because it made me realize how difficult is for some students the whole concept of learning and how different every mind works. I like the concepts of this book and the ideas to solve different problems. I know that I will use this book as a reference in my classroom when problems approach or when I feel that the concept I am teaching is not going as I thought it would.
When I chose this book, I thought it would be about strategies or tools for teachers to use when we know the reasons that students had for not liking school, so when I began reading it I felt disappointed. As I read the book’s chapters I discovered that I like it and that it contains very good and valuable information. The book is about the mind of the child and how it works.
Mr. Willingham gives a clear explanation and reasoning to every concept he presents. He focuses on the cognitive learning and difficulties some people experience concentrating and thinking. From the first chapter to the last, which it is dedicated to teachers, Mr. Willingham gives reasons for problem, ideas, and how to fix it. One of my favorite parts on this book is the “Implications for the Classroom” part that he includes in every chapter, which I found very useful.
I found myself relating to the concept of this book when I started with this class. I was so overwhelmed by my incomprehension of what I was doing and the quantity of work I had. That fear I had, could be the same fear many students have in school with certain subjects that are new to them.
Reading this book was good for me because it made me realize how difficult is for some students the whole concept of learning and how different every mind works. I like the concepts of this book and the ideas to solve different problems. I know that I will use this book as a reference in my classroom when problems approach or when I feel that the concept I am teaching is not going as I thought it would.
Thursday, January 6, 2011
Final post
One of the key concepts in "Why Don't Students Like School" that I thought about long after putting down the book was how to free up space in working memory. Willingham's description of working memory as a box that "can only hold so much stuff" simplified what I've been wondering about for years: why do some students seem to get it while others struggle? My ah-ha moment came over Christmas break while I was trying to teach myself how to crochet. I struggled along for several nights alternately concentrating on my "So You Want to Crochet" book and pulling out my knotted stitches. After several more nights, I was able to complete a small project. After even more nights of practice, I was able to divide my attention between crocheting and watching "Will and Grace" at the same time. Hurrah! I cleared out some space in my working memory! (sidebar: now when I feel like vegging out in front of the TV, I can justify it by telling myself I'm improving my working memory)
The implications for my classroom: how can I reconcile my long-held belief that deep understanding and practicing basic skills are at odds? There must be a happy medium.
According to Willingham, deep knowledge is the goal, but proficiency requires practice. Now I'm constantly asking myself, "What do my students need to understand and what do they need to be able to do?" My confusion is which comes first. Do they need deep understanding of a concept before they are required to do/practice it, or will deep understanding come with practice? For example, do my students need number sense to practice their math facts or will number sense come because they practice their math facts? Maybe it doesn't matter; the bottom line according to Willingham is that my students have to do both.
I appreciate this book because it read like a novel, but once read, it can be used like a reference book. It has more information than my feeble working memory can hold, but I can see myself referring back to it in the next few weeks/months/years.
The implications for my classroom: how can I reconcile my long-held belief that deep understanding and practicing basic skills are at odds? There must be a happy medium.
According to Willingham, deep knowledge is the goal, but proficiency requires practice. Now I'm constantly asking myself, "What do my students need to understand and what do they need to be able to do?" My confusion is which comes first. Do they need deep understanding of a concept before they are required to do/practice it, or will deep understanding come with practice? For example, do my students need number sense to practice their math facts or will number sense come because they practice their math facts? Maybe it doesn't matter; the bottom line according to Willingham is that my students have to do both.
I appreciate this book because it read like a novel, but once read, it can be used like a reference book. It has more information than my feeble working memory can hold, but I can see myself referring back to it in the next few weeks/months/years.
Monday, December 27, 2010
Thursday, December 23, 2010
Sunday, December 19, 2010
Concept Review Of the Assigned Book
After reading this book, the key concepts seemed to be centered around memory wellness of both the student and teacher. Proficient understanding of cognitive learning helps both the students absorb and comprehend material more and allows teachers to improve their classroom knowledge. If a teacher seems bored or does not enjoy the content material that is required, imagine what/how the students feel trying to learn this material.
Since this book seemed aimed at the psychology of the mind and proficient learning, I intended to use some of the concepts I learned from this book, and introduce these concepts into my psychology class this spring. Since psychology is centered around the mind, brain and memory, it is important on my part to instruct this particular class with proficient "working" memory content. I hope to take the principles I learned in this book, to allow students to enjoy their short and long term cognitive skills.
Since this book seemed aimed at the psychology of the mind and proficient learning, I intended to use some of the concepts I learned from this book, and introduce these concepts into my psychology class this spring. Since psychology is centered around the mind, brain and memory, it is important on my part to instruct this particular class with proficient "working" memory content. I hope to take the principles I learned in this book, to allow students to enjoy their short and long term cognitive skills.
Chapter 9 Super Summary
Chapter 9 is about how we as teachers can improve or refresh our minds in the educational process. As the book states "teaching, like any complex skill, must be practiced to be improved." This section really preaches the importance of the effective mind of a teacher. To think in an effective manner, we as teachers need room in our memory and need the right factual and procedural knowledge for our long term memory. We need to obtain pedagogical knowledge to ease the burnout or drain on our minds.
The section suggests we use procedures to apply cognitive skills to teaching such as 1. space in our working memory 2. factual knowledge and 3. procedural knowledge. In addition, a teacher in their first five years are considered very good, after the 5 year period we become flat and as we progress up to the 20 yr mark we are no better than a 10 yr teacher in mindset.
To become stronger minded professionals we need to practice, practice, practice for improvement and obtain as much positive and constructive feedback as possible. The section suggests ways towards getting feedback
Step 1; Identify another teacher to work with
Step 2: tape yourself and watch tapes alone
Step 3: With your partner, watch tapes of other teachers (be supportive and concrete about what you have observed.
Step 4: With partner, watch and comment on each others topics
Step 5: Bring it back to the classroom and follow up.
To conclude the more we practice and rely on feedback we must in addition we must improve self-management.
1. Keep a teaching diary
2. Start a discussion group with fellow teachers
3. Observe other teachers
In turn we need to look at what aspects of our teaching work well for students, and what areas need improvement. Improvement requires more than just experience, it requires conscious effort and feedback.
The section suggests we use procedures to apply cognitive skills to teaching such as 1. space in our working memory 2. factual knowledge and 3. procedural knowledge. In addition, a teacher in their first five years are considered very good, after the 5 year period we become flat and as we progress up to the 20 yr mark we are no better than a 10 yr teacher in mindset.
To become stronger minded professionals we need to practice, practice, practice for improvement and obtain as much positive and constructive feedback as possible. The section suggests ways towards getting feedback
Step 1; Identify another teacher to work with
Step 2: tape yourself and watch tapes alone
Step 3: With your partner, watch tapes of other teachers (be supportive and concrete about what you have observed.
Step 4: With partner, watch and comment on each others topics
Step 5: Bring it back to the classroom and follow up.
To conclude the more we practice and rely on feedback we must in addition we must improve self-management.
1. Keep a teaching diary
2. Start a discussion group with fellow teachers
3. Observe other teachers
In turn we need to look at what aspects of our teaching work well for students, and what areas need improvement. Improvement requires more than just experience, it requires conscious effort and feedback.
Thursday, December 16, 2010
Key Concept and Review by Jeff Rieckman
The part or concept of the book "Why Don't Students Like School" that I related to and liked was when they talked about a students memory. They talked about the need for a student to make use of their working memory and then being able to transfer that knowledge to their long term memory for later recall.
Getting teachers to utilize different or various teaching methods is the best way to accomplish this, more teachers need to get away from the "drill it" methods.
My thoughts on this book were that I enjoyed it. Seems like I had to hurry through it at times but it was an easy read. I found parts of it a bit repetitive but all in all it contained some great information on that should help out our students in the classroom. I have already recommended the book to one member of our staff.
Getting teachers to utilize different or various teaching methods is the best way to accomplish this, more teachers need to get away from the "drill it" methods.
My thoughts on this book were that I enjoyed it. Seems like I had to hurry through it at times but it was an easy read. I found parts of it a bit repetitive but all in all it contained some great information on that should help out our students in the classroom. I have already recommended the book to one member of our staff.
Tuesday, December 14, 2010
Book Reflection by Pat Parks
Final Reflection for Why Don’t Students Like School?
I chose this book because after many years of teaching and many years of seeing many changes I thought I had a little idea of why students don’t like school. My ideas and the authors were miles apart – we are not surprised I know. My thought was students don’t like school because in the world around them. They are constantly surrounded by technology, video games, and a fast moving environment to keep their attention. Let’s see some of the ideas of Willingham.
I found the ideas of the author to be very interesting and they made a lot of sense. I have decided to summarize some of the parts of the book that I found to be of most interest to me. In chapter one, one of the facts that stood out to me was that the brain is not designed for thinking, it is designed to save you from having to think. Thinking is slow and unreliable, but it has been found that people enjoy mental work if they are successful. That reminds me of how we teach, to move a child forward we find where they are and challenge them appropriately with work that is not too hard and not to easy. It said that teachers should encourage students to think and to give them work that is not to difficult. If success is always just out of reach, school will not be a place they want to be. I also found the statement, “successful thinking relies on four factors: information from the environment, facts in long-term memory, procedures in long-term memory and the space in working memory. If any one of these factors is inadequate, thinking fails.”
As teachers, it seems that we are all about getting students to “think.”
I also was intrigued with the question, Is Drilling Worth It? Part of a comment made by Alfred North Whitehead is, “Civilization advances by extending the number of important operations which we can perform without thinking about them.” Through the use of practice we help make mental processes more automatic. To be smart about practice our author tells us the practice must be spread out over time and activities. We need to come up with many creative ways to practice skills and the basic skills will continue to be practiced while students work on more advanced skills.
Not only do students need to be considered in the question of practice, but also educators. According to Willingham, “Teaching, like any complex cognitive skill, must be practiced to be improved.” The program Willingham laid out is something I would be very interested in taking part in. His steps are: videotape teaching so it can be thought deeply about and so what happened can be remembered. Teachers need to see classroom dynamics because experts see the world differently than novices – they see deep structure not surface structure because they have deep experience in their field. To recognize dynamics of your classroom you must see others. Background knowledge is important for both students and teachers. For the teacher the background knowledge is not just subject matter knowledge, but knowledge of students and how they interact with you, each other, and with the material that is taught. We also learned that human intelligence can be changed through sustained hard work. Teachers need to show students through example that hard work does pay off.
“Thus, to ensure that your students follow you, you must keep them interested; to ensure their interest, you must anticipate their reactions, and to anticipate their reactions, you must know them.” “Know your students.”
I chose this book because after many years of teaching and many years of seeing many changes I thought I had a little idea of why students don’t like school. My ideas and the authors were miles apart – we are not surprised I know. My thought was students don’t like school because in the world around them. They are constantly surrounded by technology, video games, and a fast moving environment to keep their attention. Let’s see some of the ideas of Willingham.
I found the ideas of the author to be very interesting and they made a lot of sense. I have decided to summarize some of the parts of the book that I found to be of most interest to me. In chapter one, one of the facts that stood out to me was that the brain is not designed for thinking, it is designed to save you from having to think. Thinking is slow and unreliable, but it has been found that people enjoy mental work if they are successful. That reminds me of how we teach, to move a child forward we find where they are and challenge them appropriately with work that is not too hard and not to easy. It said that teachers should encourage students to think and to give them work that is not to difficult. If success is always just out of reach, school will not be a place they want to be. I also found the statement, “successful thinking relies on four factors: information from the environment, facts in long-term memory, procedures in long-term memory and the space in working memory. If any one of these factors is inadequate, thinking fails.”
As teachers, it seems that we are all about getting students to “think.”
I also was intrigued with the question, Is Drilling Worth It? Part of a comment made by Alfred North Whitehead is, “Civilization advances by extending the number of important operations which we can perform without thinking about them.” Through the use of practice we help make mental processes more automatic. To be smart about practice our author tells us the practice must be spread out over time and activities. We need to come up with many creative ways to practice skills and the basic skills will continue to be practiced while students work on more advanced skills.
Not only do students need to be considered in the question of practice, but also educators. According to Willingham, “Teaching, like any complex cognitive skill, must be practiced to be improved.” The program Willingham laid out is something I would be very interested in taking part in. His steps are: videotape teaching so it can be thought deeply about and so what happened can be remembered. Teachers need to see classroom dynamics because experts see the world differently than novices – they see deep structure not surface structure because they have deep experience in their field. To recognize dynamics of your classroom you must see others. Background knowledge is important for both students and teachers. For the teacher the background knowledge is not just subject matter knowledge, but knowledge of students and how they interact with you, each other, and with the material that is taught. We also learned that human intelligence can be changed through sustained hard work. Teachers need to show students through example that hard work does pay off.
“Thus, to ensure that your students follow you, you must keep them interested; to ensure their interest, you must anticipate their reactions, and to anticipate their reactions, you must know them.” “Know your students.”
Tuesday, November 30, 2010
Section 5 Summary by Jeff Rieckman
This section deals with people that are slow learners and how all students differ in intelligence but that ALL students can improve their intelligence and position through hard work.
Part of the chapter deals in what makes an intelligent person is it genetics vs. experience. One test that they completed said genetics had everything to with intelligence and that a persons environment made very little change in a persons standing.
The chapter went on to explain how as educators we could help slow learners in the classroom:
1. Praise a students effort not their ability.
2. Tell them how hard work pays off.
3. Treat failure as a natural part of learning.
4. Don't take study skills for granted.
5. Catching up is the long term goal.
6. Show students that you have confidence in them.
Part of the chapter deals in what makes an intelligent person is it genetics vs. experience. One test that they completed said genetics had everything to with intelligence and that a persons environment made very little change in a persons standing.
The chapter went on to explain how as educators we could help slow learners in the classroom:
1. Praise a students effort not their ability.
2. Tell them how hard work pays off.
3. Treat failure as a natural part of learning.
4. Don't take study skills for granted.
5. Catching up is the long term goal.
6. Show students that you have confidence in them.
Monday, November 29, 2010
Nancy's Voki
Click on this link to hear Nancy's Voki/quote:
(once the page loads, click on the play button to hear my Voki talk)
http://www.voki.com/php/viewmessage/?chsm=f67feca115fb8e7af117e0d22f17092c&mId=547916
(once the page loads, click on the play button to hear my Voki talk)
http://www.voki.com/php/viewmessage/?chsm=f67feca115fb8e7af117e0d22f17092c&mId=547916
Sunday, November 28, 2010
Sunday, November 21, 2010
Wednesday, November 17, 2010
Friday, November 12, 2010
Chapters 6 and 7
What's the Secret to Getting Students to Think Like Real Scientists, Mathematicians, and Historians?
Real Scientists, Mathematicians, and Historians are experts. None of these people thought like experts in the beginning, in truth, according to Willingham, no one thinks like a scientist, mathematician, or historian without a great deal of practice. Compared to novices, experts are much better suited to single out important details, produce solutions, and transfer their knowledge to similar domains. This includes the expert teacher who often seems to have eyes in the back of their head. Compared to the novice teacher the expert can quickly come up with
explanations of a concept and alternatives and they do it more quickly.
Experts do not have trouble seeing deeply into a situation, they see deeply and do not have to focus on the surface. Experts see the deep structure of a problem. That is why they can transfer from a former problem to a new problem and their judgements are sensible.
According to Willingham, experts save room in working memory through acquiring extensive, functional background knowledge, and by making mental procedures automatic. They do this by talking to themselves. Experts can draw implications from their self talk. Experts do not just narrate what they are doing, but they test their own understanding and talk through the implications of possible solutions.
Getting students to think like experts does take extensive practice. To be an expert one must put in the hours. Willingham thinks it is difficult to become an expert in any field in less then 10 years. Once you arrive a person must continue to practice to keep the status of an expert.
Implications for the Classroom
Experts are not just better thinkers in the field of their choice, but experts actually think in ways that are qualitatively different. After reading this, I know that as teachers we cannot realistically get our students to think like experts, but we can get them to understand what they are studying whether it is science, math, or history. We should try to draw a distinction between knowledge understanding and knowledge creation. Experts create and a realistic goal for our students. This would be knowledge comprehension according to Willingham. A student will not develop his own scientific theory, but he can develop an understanding of the existing theory.
The thing we must remember is as Ralph Waldo Emmerson put it, "Every artist was at first an amateur." That I believe would be true in all aspects of learning. We all have to be given an opportunity to start somewhere and to practice until an expert is born!
Chapter 7 How Should I Adjust My Teaching for Different Types of Learners?
The cognitive principle that guides this chapter is: "Children are more alike than different in terms of how they think or learn."
We know of course that students are different. One student's strength may help remedy a weakness and another idea is that teachers may take advantage of students' different way of learning and see it as how he learns best and how the material was taught. Making too many changes seems like a lot of work and is it really worth it? Cognitive abilities and styles are different in a few important ways. Abilities are how we deal with content and styles are how we prefer to think and learn. We think more ability is better than less ability, but one style is not considered better than the other.
The concept of visual, auditory, and kinesthetic learning is not new to us as educators. It is said that each person has a preferred way to learn - visually, auditorially or kinesthetically. Not only are learning styles different, but students differ from one to the other. It is the hope of Willingham that educators will use the differences in students to improve instruction. One method is based on differences in cognition style - that is all well and good, but no one has described a set of styles for which there is good evidence. The second way to take advantage of differences among students according to Willingham is rooted in the differences in ability.
Willingham states that he is not saying that teachers should not differentiate instruction. Is is something we should do, but scientists can offer no help.
Learning styles theories don't help us much when applied to students, but Willingham says, they are helpful when applied to content.
We need to remember that all students have value and every child is unique, whether they are intelligent in the way of mental ability or they bring pleasure to those around them.
In conclusion, I am looking forward to reading the next chapter to see why it is never smart to tell a student that she's smart. Willingham says that doing so makes her less smart.
Real Scientists, Mathematicians, and Historians are experts. None of these people thought like experts in the beginning, in truth, according to Willingham, no one thinks like a scientist, mathematician, or historian without a great deal of practice. Compared to novices, experts are much better suited to single out important details, produce solutions, and transfer their knowledge to similar domains. This includes the expert teacher who often seems to have eyes in the back of their head. Compared to the novice teacher the expert can quickly come up with
explanations of a concept and alternatives and they do it more quickly.
Experts do not have trouble seeing deeply into a situation, they see deeply and do not have to focus on the surface. Experts see the deep structure of a problem. That is why they can transfer from a former problem to a new problem and their judgements are sensible.
According to Willingham, experts save room in working memory through acquiring extensive, functional background knowledge, and by making mental procedures automatic. They do this by talking to themselves. Experts can draw implications from their self talk. Experts do not just narrate what they are doing, but they test their own understanding and talk through the implications of possible solutions.
Getting students to think like experts does take extensive practice. To be an expert one must put in the hours. Willingham thinks it is difficult to become an expert in any field in less then 10 years. Once you arrive a person must continue to practice to keep the status of an expert.
Implications for the Classroom
Experts are not just better thinkers in the field of their choice, but experts actually think in ways that are qualitatively different. After reading this, I know that as teachers we cannot realistically get our students to think like experts, but we can get them to understand what they are studying whether it is science, math, or history. We should try to draw a distinction between knowledge understanding and knowledge creation. Experts create and a realistic goal for our students. This would be knowledge comprehension according to Willingham. A student will not develop his own scientific theory, but he can develop an understanding of the existing theory.
The thing we must remember is as Ralph Waldo Emmerson put it, "Every artist was at first an amateur." That I believe would be true in all aspects of learning. We all have to be given an opportunity to start somewhere and to practice until an expert is born!
Chapter 7 How Should I Adjust My Teaching for Different Types of Learners?
The cognitive principle that guides this chapter is: "Children are more alike than different in terms of how they think or learn."
We know of course that students are different. One student's strength may help remedy a weakness and another idea is that teachers may take advantage of students' different way of learning and see it as how he learns best and how the material was taught. Making too many changes seems like a lot of work and is it really worth it? Cognitive abilities and styles are different in a few important ways. Abilities are how we deal with content and styles are how we prefer to think and learn. We think more ability is better than less ability, but one style is not considered better than the other.
The concept of visual, auditory, and kinesthetic learning is not new to us as educators. It is said that each person has a preferred way to learn - visually, auditorially or kinesthetically. Not only are learning styles different, but students differ from one to the other. It is the hope of Willingham that educators will use the differences in students to improve instruction. One method is based on differences in cognition style - that is all well and good, but no one has described a set of styles for which there is good evidence. The second way to take advantage of differences among students according to Willingham is rooted in the differences in ability.
Willingham states that he is not saying that teachers should not differentiate instruction. Is is something we should do, but scientists can offer no help.
Learning styles theories don't help us much when applied to students, but Willingham says, they are helpful when applied to content.
We need to remember that all students have value and every child is unique, whether they are intelligent in the way of mental ability or they bring pleasure to those around them.
In conclusion, I am looking forward to reading the next chapter to see why it is never smart to tell a student that she's smart. Willingham says that doing so makes her less smart.
Wednesday, November 10, 2010
Part Two Summary - Maria Carmen King
Part two emphasize the importance of knowledge for reading and comprehension and here are the points that are important to me.
First, one of the points in the book is how important background knowledge is to reading comprehension, and one thing that every teacher should consider in their classroom is that every student comes from a home with different economic, social, and intellectual background. Many students also come from other countries (like me) and they don’t have the same growing experiences as students born naturally here. How can we grade these students fairly that don’t have that knowledge?My second point is that sometimes students see some subjects or themes as a foreign item because they previously did not know anything about it and they cannot relate to their reading comprehension. Therefore, students will need more time to assimilate and think on what they are reading.
In my opinion, in order for us as teachers to come out with a theme that is meaningful and interesting to students we should find out more about their background and knowledge before we begin a new lesson.
Monday, November 8, 2010
Section Three Summary
Section Three (chapters four and five)
Chapters four and five explain why students struggle understanding abstract ideas and how practice can help.
According the Willingham, the goal of education is to teach students how to transfer knowledge to the world outside the classroom. To do this, students must understand abstract ideas. However, the mind prefers concrete ideas, so students need many concrete examples. Learners look at new information and compare it to old information, and since most of what students know is concrete, concrete examples help students make sense of the abstract.
One way to make comparisons is through analogies. Analogies help students relate the unknown to the known. However, it's not the quantity of the comparisons that help students understand abstractions, it's the quality. The comparisons have to be familiar to the student, and most of what students know is concrete -- hence the need for concrete examples to understand abstract ideas. As Willingham said on page 92, "Every new idea must build on ideas that the student already knows."
In chapter four Willingham contrasted shallow knowledge with deep knowledge and surface structure of problems with deep structure. With shallow knowledge students have some understanding of the material but their understanding is limited. They may see the parts but not the whole, and they may be focusing only on the simple surface structure of a problem. Students with deep knowledge can apply their knowledge in many different contexts and see the whole problem and how that problem changes when one part is altered. Students with deep knowledge understand abstractions and transfer that knowledge to new problems because they recognize that analogy between different problems.
Willingham stressed the importance of emphasizing deep structure in problems. Teachers can do this through the types of assignments and assessments they create and through daily questioning in the classroom. However, Willingham also assured his readers, "Shallow knowledge is much better than no knowledge at all, and shallow knowledge is a natural step on the way to deeper knowledge."
In chapter five Willingham explained how a store of factual knowledge and regular practice help students learn by clearing up space in their working memories. Practice that is spaced out over time help mental processes become automatic so the working memory can focus on more complex processes. Practice also helps with transfer and long-term memory.
Chapters four and five explain why students struggle understanding abstract ideas and how practice can help.
According the Willingham, the goal of education is to teach students how to transfer knowledge to the world outside the classroom. To do this, students must understand abstract ideas. However, the mind prefers concrete ideas, so students need many concrete examples. Learners look at new information and compare it to old information, and since most of what students know is concrete, concrete examples help students make sense of the abstract.
One way to make comparisons is through analogies. Analogies help students relate the unknown to the known. However, it's not the quantity of the comparisons that help students understand abstractions, it's the quality. The comparisons have to be familiar to the student, and most of what students know is concrete -- hence the need for concrete examples to understand abstract ideas. As Willingham said on page 92, "Every new idea must build on ideas that the student already knows."
In chapter four Willingham contrasted shallow knowledge with deep knowledge and surface structure of problems with deep structure. With shallow knowledge students have some understanding of the material but their understanding is limited. They may see the parts but not the whole, and they may be focusing only on the simple surface structure of a problem. Students with deep knowledge can apply their knowledge in many different contexts and see the whole problem and how that problem changes when one part is altered. Students with deep knowledge understand abstractions and transfer that knowledge to new problems because they recognize that analogy between different problems.
Willingham stressed the importance of emphasizing deep structure in problems. Teachers can do this through the types of assignments and assessments they create and through daily questioning in the classroom. However, Willingham also assured his readers, "Shallow knowledge is much better than no knowledge at all, and shallow knowledge is a natural step on the way to deeper knowledge."
In chapter five Willingham explained how a store of factual knowledge and regular practice help students learn by clearing up space in their working memories. Practice that is spaced out over time help mental processes become automatic so the working memory can focus on more complex processes. Practice also helps with transfer and long-term memory.
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