In recent articles, I've been pointing out that parents and teachers - but especially parents - undermine the learning process by telling the child how to do things and what the answer is. This results in a child who knows a lot of stuff but can't think and will have a hard time on a GAT process.
When the parent breaks this habit, the long hard process of learning how to think begins for the child.
If you are in the middle of test prep, or if your older child has to get through a math homework assignment, you'll have to accommodate this process with "Scaffolding" so that you don't waste the entire half an hour having your child sit there dumbfounded.
The goal of Scaffolding is to let the child think through things - to a point - and jump in with lots of questions and guidance. If your child needs 12 skills to get though the work, but only has the first 3 (these 3 are reading the questions skills which I already outlined and I hope you already taught them), their current work will be painful process without more help.
What I like to do with the homework process is ask the child to look for things - anticipating the next few steps - and satisfied that the child started exercising skills 4 and 5, and maybe 6, I'll just guide them through the rest of the assignment and hopefully they'll pick up more skills the next time. For example, the child is never going to derive the Pythagorean theorem on his own no matter how gifted he is, or even know it exists, so just tell it to him and let him apply it. My 10 year old is not going to get through some of the questions in the SAT book unless I jump in there and help out, and some of these questions, frankly, I don't remember how to do. As we do these super hard problems together, he is picking up bits and pieces of problem solving techniques. I've noticed in subsequent sessions, on some problem types, he now just jumps in there and solves the whole thing whereas before, he couldn't get past the question.
With test prep, on the other hand, I usually don't guide the child in the same way. First of all, it's easy material (aka squares and circles) but tricky, and if you guide the child over the trick you ruined the lesson. In this case, I keep an easier workbook handy (eg Building Thinking Skills, whatever page they can actually do) and see how far the child can get in the harder work book (eg a COGAT test prep book) before we just stop and switch back to the easier work book.
Sometimes with test prep, I keep some paper, scissors and crayons handy. If we get stuck on a question like the folding questions, we'll either do a lesson on multiplication with blocks, or pick up a hole puncher and start punching holes. I'll ask a lot of questions and they'll do the work. Something easy. Then they can take another shot at the harder material. In the past, I've given hard material to a child that took 4 to 6 months before they could actually do it. Oops! My bad. As the World's Most Awesome Academic Coach, I know that I can just wait and try again. As a first time parent, I did not know this and I spent many frustrating hours trying to teach this material to my child.
To illustrate this, I'm going to give an example from my recent research with a 3rd grader doing a simple division math worksheet. He's a bright little kid with a bright future, but he stinks at problem solving. You'll see why.
After a few minutes of doing his work quietly, he came in to the room where I was talking to his mom about my research and asked "What's 121 divided by 11?" By this point, his mom knew not to say anything, but I asked her anyway what she would normally do. What would you as a parent do? So here's how the conversation went.
Kid: "What is 121 divided by 11?"
Me: "You tell me."
Kid: "I don't know. That's why I'm asking."
Me: "It's your homework. You tell me."
Kid: "If I knew the answer, I wouldn't ask you."
Me: "Go back to your desk, take a blank piece of paper, and write down the multiplication table for 11, starting with 11 x 1 and ending with 11 x 12"
Kid (Comes back in 5 minutes): "Is the answer 11?"
Me: "You tell me."
Kid: "I don't know."
Me: "Look at your multiplication table. What is 11 x 11?"
Kid: "It's 121".
Me: "OK, what is 121 divided by 11."
Kid: "Is it 11?"
Me: "You tell me."
I've had this same discussion with both of my sons at various points and with other kids I've coached. They won't give up asking until they are 110% certain that no help will be forthcoming from the adult. I would only do 2 things with my kids. The first thing is that I'll gladly point out their errors as many times as they would like.
The second thing is that I will gladly point out the parts of their assignment which they didn't know were there. In this case, we looked at the multiplication table of 11 for a pattern and found one. Then we googled patterns for multiplication and found out that all numbers have them. I asked him to write the multiplication tables for 3 and 9 and tell me the pattern. It was hard to do so I helped. Then we discussed how he could use these patterns to determine if he got an answer wrong, but this wouldn't help him know for sure that he got it wrong.
Finally, I told him that every single arithmetic problem he encounters requires cheating, and if he cheats good enough, he can do them all in his brain without having to memorizing anything. For example, 6 x7 is hard, but 5 x 7 + 7 is easy. 9 x7 is hard, but 10 x 7 - 7 is easy. And so on.
When your 3rd grade child asks you what 121 divided by 11 is, you now have 2 options. You can say "11", and the child can finish their homework. Or you can give them full responsibility for their work and dig deep into all of the things they are not learning, and you can unleash the Gifted and Talentedness of your child.
If you are currently doing test prep for some test, you are probably also doing some academic work, even with 4 year olds, who are learning to read and do simple counting and arithmetic. I generally did about 60% academic work and 40% or less test prep. Then I realized that the skills that the test wanted were the exact same skills used by top students in academic work. From that point on, everything is test prep, even division.
Thursday, April 30, 2015
Saturday, April 25, 2015
Teach to the Test
I love tests. I've always considered tests to be the Big Game of academics. A challenge of memorizing things, guessing, figuring out. I remember studying for tests in High School and College in courses I didn't really pay attention to, shooting for an A in 3 days or less. This was really good practice for Consulting, where a potential client drops out of the sky and I have 3 days to become an expert on their business. It's also good practice for certification exams that are prevalent in many fields, including Law, Medicine, and IT.
Recently, parents in my sons' program have been opting out of the new Illinois mandatory bi-annual standardize test, which was crammed in the annual academic schedule with 3 other multi-day tests. My first reaction was good - my son needs a break from all the work he has to do. Why would anyone complain about tests?
Then I started my recent research project on learning which has been discussed in my last 3 articles. That got me thinking. Tests are the worst possible thing you could do to a child's education (which I will explain below). Especially in Illinois, the annual testing cycle is destroying education of thousands of children, which will give my 2 children a distinct competitive advantage in high school and college.
It's time to take a closer look at tests.
If the test was a series of challenging content that exercises a child's learned cognitive skills, tests would become a valuable teaching tool. But tests are designed to determine whether or not the child has "learned" a bunch of facts and formulas and can apply them.
In Illinois, teachers and schools are evaluated on the results of the test. The rankings are published, and parents choose schools based on test scores.
If the test requires a child to know how to diagram a sentence or the dates of the Revolutionary War, the teacher has to make sure that the child knows the process and the facts. The Common Core standard has a long list of facts and processes. Too much to fit in a single year. Therefore the only option a teacher has is to present all of this information to the child for memorization and testing. That's what teachers do.
Unfortunately, this skips the learning process and goes directly to the desired outcome. In my At Home School program, we love the Revolutionary War, and follow interesting and complicated stories that spark our imaginations. It never occurred to me to find out when it began and when it ended. I hope some day my kids stumble across these dates in the process of some learning activity, but for now, it was sometime around 1776. We know a lot about the Revolutionary War, but mainly we know how to learn stuff on our own and in depth.
In a learning program, kids maintain high interest levels following things that are interesting and challenging, and pick up the skills they need to be successful in college and life. In our schools, children pick up a bunch of useless processes and facts and don't actually learn. The learning process is skipped to make sure children are prepared for the test.
The worst subject of all is math. The teacher presents a concept, shows some examples, and gives the children a worksheet where they regurgitate the calculation over and over until they memorized it. They know nothing of math, problem solving, exploration, or learning. At some point between middle school and college, their lack of skills will upend their progress and likely terminate their study of math and science.
Think about that next time you have to do Test Prep for a cognitive abilities test. You should prep "learning" and let the kid flounder on their own until they teach themselves the content.
Last night my 10 year old and I tried to solve this completely oddball problem that will never show up on a test: What is the remainder when the number composed of the digits "2013" repeated 2013 times (this a number with 8,052 digits) is divided by 333,333. We learned the following things:
1. Big problems have lots of steps
2. To solve a big problem, you probably have to solve a few smaller ones.
3. That question requires rereading about 2013 times.
4. The big number is divisible by 3, and the answer is 0671 repeated 2013 times. This was a dead end at first but helped us later.
5. The person who came up with this problem is insane.
6. Guessing is a really great tool for solving math problems in some circumstances
7. If you guess, you have to prove that you are correct
8. When you do a big problem, you might need multiple math books handy for reference.
9. And more.
I learned a lot too. It took us 25 minutes just to come up with a few viable strategies to solve this problem. I think my son got lost after step 7, but he learned so much I don't care. He's got time to learn the rest.
In the UK, there are some special schools that give no tests in between 1st grade and senior year of high school, and then the kids have to take the college entrance exam. With 12 straight years of learning, unencumbered by tests, the children do statistically way better than their peers in traditional test-focused schools. Finland has a similar experience.
I think the lack of tests is the reason why home schoolers do better in college than in-school kids. Again, it's because time is spent learning and not memorizing.
In Illinois, a big problem is when kids get to college they end up with B's or worse their freshman year. These kids have a high school transcript packed with A's in AP courses, and some of them worked and studied at a college level for more than a year in these courses. They bomb in college. Why is that? Because in college a student is expected to learn and these kids were never taught to learn. Who has time to explore a subject with 4 AP courses in their schedule each semester?
I have talked to college professors about these kids (because I have to deal with them professionally and they need a lot of remedial problem solving skills). It's pretty shocking to hear how the majority of these kids approach their course work. "Just tell me what is on the test" is the prevailing attitude. Of course this is the attitude, because that is all the kids learned for 12 years before college.
This summer's At Home Schooling program is going to focus on learning. I have some damage to undo.
Recently, parents in my sons' program have been opting out of the new Illinois mandatory bi-annual standardize test, which was crammed in the annual academic schedule with 3 other multi-day tests. My first reaction was good - my son needs a break from all the work he has to do. Why would anyone complain about tests?
Then I started my recent research project on learning which has been discussed in my last 3 articles. That got me thinking. Tests are the worst possible thing you could do to a child's education (which I will explain below). Especially in Illinois, the annual testing cycle is destroying education of thousands of children, which will give my 2 children a distinct competitive advantage in high school and college.
It's time to take a closer look at tests.
If the test was a series of challenging content that exercises a child's learned cognitive skills, tests would become a valuable teaching tool. But tests are designed to determine whether or not the child has "learned" a bunch of facts and formulas and can apply them.
In Illinois, teachers and schools are evaluated on the results of the test. The rankings are published, and parents choose schools based on test scores.
If the test requires a child to know how to diagram a sentence or the dates of the Revolutionary War, the teacher has to make sure that the child knows the process and the facts. The Common Core standard has a long list of facts and processes. Too much to fit in a single year. Therefore the only option a teacher has is to present all of this information to the child for memorization and testing. That's what teachers do.
Unfortunately, this skips the learning process and goes directly to the desired outcome. In my At Home School program, we love the Revolutionary War, and follow interesting and complicated stories that spark our imaginations. It never occurred to me to find out when it began and when it ended. I hope some day my kids stumble across these dates in the process of some learning activity, but for now, it was sometime around 1776. We know a lot about the Revolutionary War, but mainly we know how to learn stuff on our own and in depth.
In a learning program, kids maintain high interest levels following things that are interesting and challenging, and pick up the skills they need to be successful in college and life. In our schools, children pick up a bunch of useless processes and facts and don't actually learn. The learning process is skipped to make sure children are prepared for the test.
The worst subject of all is math. The teacher presents a concept, shows some examples, and gives the children a worksheet where they regurgitate the calculation over and over until they memorized it. They know nothing of math, problem solving, exploration, or learning. At some point between middle school and college, their lack of skills will upend their progress and likely terminate their study of math and science.
Think about that next time you have to do Test Prep for a cognitive abilities test. You should prep "learning" and let the kid flounder on their own until they teach themselves the content.
Last night my 10 year old and I tried to solve this completely oddball problem that will never show up on a test: What is the remainder when the number composed of the digits "2013" repeated 2013 times (this a number with 8,052 digits) is divided by 333,333. We learned the following things:
1. Big problems have lots of steps
2. To solve a big problem, you probably have to solve a few smaller ones.
3. That question requires rereading about 2013 times.
4. The big number is divisible by 3, and the answer is 0671 repeated 2013 times. This was a dead end at first but helped us later.
5. The person who came up with this problem is insane.
6. Guessing is a really great tool for solving math problems in some circumstances
7. If you guess, you have to prove that you are correct
8. When you do a big problem, you might need multiple math books handy for reference.
9. And more.
I learned a lot too. It took us 25 minutes just to come up with a few viable strategies to solve this problem. I think my son got lost after step 7, but he learned so much I don't care. He's got time to learn the rest.
In the UK, there are some special schools that give no tests in between 1st grade and senior year of high school, and then the kids have to take the college entrance exam. With 12 straight years of learning, unencumbered by tests, the children do statistically way better than their peers in traditional test-focused schools. Finland has a similar experience.
I think the lack of tests is the reason why home schoolers do better in college than in-school kids. Again, it's because time is spent learning and not memorizing.
In Illinois, a big problem is when kids get to college they end up with B's or worse their freshman year. These kids have a high school transcript packed with A's in AP courses, and some of them worked and studied at a college level for more than a year in these courses. They bomb in college. Why is that? Because in college a student is expected to learn and these kids were never taught to learn. Who has time to explore a subject with 4 AP courses in their schedule each semester?
I have talked to college professors about these kids (because I have to deal with them professionally and they need a lot of remedial problem solving skills). It's pretty shocking to hear how the majority of these kids approach their course work. "Just tell me what is on the test" is the prevailing attitude. Of course this is the attitude, because that is all the kids learned for 12 years before college.
This summer's At Home Schooling program is going to focus on learning. I have some damage to undo.
Thursday, April 23, 2015
Lack of Motivation 3 - Hard Problems
If you are taking advantage of my recommendations for either math or test prep, you and you child will encounter a really hard problem that you don't know what to do with. Your child may sit there and become frustrated.
When your child is in school, he may become frustrated with material that is new and hard, and he may be stuck.
This is a huge demotivater, and top 2 on the list of things that demotivate children. The other 1 is the opposite - the material is really easy. I'll come back to the easy material later.
The thing I like the most about test prep is that it teaches skills to tackle hard problems. This is what makes gifted kids gifted, provided that they have an interest in academic work and a home life that puts academic work 1st as the number one value. What I'm worried about is that I'm recommending super hard material - at least one year advanced, and readers and their children will run into a brick wall trying to do it. Therefore, this article provides the ladder to get over the brick wall.
First of all, as a parent, the child has to do all of the work. (Look at my prior article about public speaking.) Your job is to hand the work to the child. If the child says that the work is hard, and you do any of it, any at all, then you have failed the child. The learning process is taking hard material and figuring it out. The main failing of our school system and parents is that we teach this material to the children. They know it, but they don't know how to learn because we do that work for them. (The school system will be covered in a future article).
So what do you do? Here's what I do.
#1 Read the Question
I ask the child to read the question to me and explain it to me. I am looking for them to acknowledge parts of the question that they did not see before. The question may include a diagram. They have to read, describe, explain every part of the diagram to me. Kids tend to not think this is part of the question, but it is the main part of the question.
#2 What Do You Recognize
What parts of the question do you recognize? What words or definitions do you know. Have you ever seen any problems that are similar to parts of this problem?
#3 What Do You Not Recognize
Kids tend to skip right over words, phrases, or syntax that they are not familiar with. Saturday, my son saw 10√2. He had no idea what 10√2 was and worked on the problem for 5 minutes before I asked this question and he point it out.
When asking these 3 questions, you are giving the child the first few tools to do something with the problem other than just sit there and give up. Think about this approach. You aren't really helping by teaching the child the material. Don't ever explain the material. What you are doing is teaching the child how to learn for themselves, which should be the goal of every parent and teacher.
In school, especially in math, the kids are supposed to know everything and be able to do it quickly. Think of times tables. The children develop this expectation that academic work is about knowing things. This expectation puts them at a distinct disadvantage, because academic work is about learning things and figuring things out. When they get challenging material, they think they should know it - and they don't, or else why would I be giving it to them - and then they come to the conclusion that they are big dummies.
You as the parent have to undo this bad habit, first with yourselves as academic coaches, and secondly within your children as learners and figure-outers. There are other questions I ask after questions involving the problem, but the 3 questions above are the most important for Step One because they get the parent out of the explaining business and make the child think for himself.
When I encounter a child who is a genius at math tables for arithmetic, I assign a book of word problems or brain teasers. I have got crying and frustration from the kids for this assignment, but down the road the parents are very appreciative.
Spending a lot of time reading the question is a good first step. What you have to do next varies a bit with whether you are doing math or whether you are doing test prep with a set of answer choices.
Math
Here's an example that my 10 year old and I worked on. In the diagram below, side a and side b are both 10√2, and the line running through the middle of the triangle is parallel to the bottom of the triangle. (The actual question was convoluted and I'm not going to type it here because it's hard to present in HTML.) What is the area of the rectangle made up of the 2 squares?
After struggling with this problem to the point of tears, my son asked for help. I had no clue what the answer was or how to solve it. We started with him reading the problem to me for about 5 minutes until I was sure he knew what all the pieces were. The we discussed what square roots are and why the square root of 2 is just left there as notation and not a number. That took 10 more minutes.
I asked him to tell me what he knew about area, and he knew the formula for the area of a triangle, which was good. He also told me the area of the rectangle was half of the area of the triangle which was pretty astute. (Apparently I taught him something. We didn't prove it formally, but good enough.) Then we had to figure out the area of any of the triangles. It took about 45 minutes, and in the process, we learned a lot of math. We learned not to give up. It was not easy for me either.
I am not sure I could figure out this problem on my own without the problem solving steps we went through. I know for certain that without these problem solving steps, I wouldn't be able to help my son with math.
This question came out of the SAT practice test book we are going through. It's getting harder. We're down to about 1 to 3 questions per session. A lot more learning takes place with one question than a whole workbook of easy calculation questions. Like public speaking, the parent or academic coach just has to go really slowly and wait a lot. Sometimes, like in the case of this problem, the kid can get through one or 2 important steps in problem solving, but needs help with the other 9. That's OK. He can learn some by doing and some by watching, and eventually, maybe in a classroom setting, he'll be able to put all of the pieces together himself on something easier.
Test Prep
Test prep has a lot of the same elements but I usually go about it differently because the problems are much different. The goal of a cognitive abilities test is to present the child with a completely unfamiliar problem with it's own set of brand new rules and let the child figure these out. The goal of the parent is to teach the child these skills so that they do better in school and in life and on the SAT test prep math book they'll get later.
Here is a sample problem. The directions state that there is a relationship between the squares in the top row. Which shape would you pick for the blank box so that the same relationship holds true for the bottom row?
This one is pretty confusing, and would be preceded by some examples where the shape at top shrinks or grows along one or more dimensions, or turns or flips. The test intentionally sets the kid up for failure on this question. I don't think I got it the first time I saw it. I would have failed a 1st grade cognitive abilities test.
The first step in the test prep process is to understand what it means that there is a relationship between the two top shapes. We spent 3 months on that. What are all of the things that a square can do? Draw them. Cut out a square or find one in the toy box, and have your son demonstrate the basic operations, especially rotate and flip. What does the square look like when it is turning or flipping? Ideally, you would work with other shapes and a list of math vocabulary before attacking a question like this.
The children must look carefully and patiently at this question for a long time and start thinking about all of the things that may happen. Children who do well will linger on the question. Children who will bomb the test completely will look at the problem, immediately realize that they don't know the answer, and guess or move on without trying. Or they may ask the parent for help, the parent will explain the problem, and no learning will take place.
When really great teachers present problems in class at this level of challenge, they'll just change the subject and move on without telling the kid whether or not they got it right. They'll move on to working with things that can happen to shapes, and how each shape looks when it grows, rotates, widens, gets shorter, etc. (They of course don't do with COGAT questions but academic material.) At some point, either the lightbulb goes off for the child or they can come back to a problem like this and succeed where once they failed.
This problem could be out there unsolved for months. When we did test prep (aka Cognitive Skills building), I would skip lots of material or leave it ungraded and we would eventually come back to it.
The child learns by learning. If a parent explains this problem to the child, learning has failed. Also, test prep books are expensive and don't have a lot of problems in them, so don't waste even a single problem. If your child is stuck or doesn't know the answer, save it for later. If they say "I can't do this", say "You can't do this yet."
Parents often wonder why their child does so well on standardized tests but not cognitive abilities tests. In Chicago, kids can take the Classical test to get into an Academic Center, or a cognitive skills test to get into a Regional Gifted Center. The Classical test is a standardized test (eg what kids are learning in school) and the Academic center is an accelerated program. The gifted test is a cognitive abilities test and the gifted programs are accelerated, but the kids are expected to learn the material even though they spend most of their time on projects and field trips.
Back to the question. Why the disparity in scores? In short, the parent can teach the child academic material without teaching them how to think. It works for a while, and then by middle school the kid is failing.
I say don't teach your child anything. When they get stuck on hard material, do something else for a while. Let them make up their own test questions (we did this and it was fun) and see if they can make a test question with only one correct answer. Make up your own test question and let the child find the mistakes, like a question that has multiple answers or a question that doesn't have any answers. We did a lot of this. I noticed that much more learning was taking place when the test prep book wasn't open.
I better summarize because this article is so long. Here are the rules for a parent:
#1. Don't tell your children anything. Let them learn it on their own. Be prepared to wait a long time for them at first until they pick up these skills.
#2. If you have to explain something, don't. You can ask lots of questions, and don't forget the questions I presented in the math section. Make these questions opened ended, not prompts for the answer you want. Ask them over and over again until your child gives up expecting any useful help from you and starts doing the thinking on his own.
#3. Be prepared to spend an hour on a single question or save if for another time.
#4. Fill in the gaps with do-it-yourself projects that make it more fun.
#5. Have an easy workbook standing by as a crutch so that regardless of your child's skill level, they can do something productive and not wallow in their frustration for ever. As they grow, they can handle longer periods of frustration, or better yet, learn the skills to overcome the brick wall.
This list is a lot better than the advice you'd find in a parent magazine (e.g., get a good night's sleep before the test). I have a much more detailed list of problem solving steps to review later . This is just the part of the list to break the parent of the bad habit of undermining learning.
When your child is in school, he may become frustrated with material that is new and hard, and he may be stuck.
This is a huge demotivater, and top 2 on the list of things that demotivate children. The other 1 is the opposite - the material is really easy. I'll come back to the easy material later.
The thing I like the most about test prep is that it teaches skills to tackle hard problems. This is what makes gifted kids gifted, provided that they have an interest in academic work and a home life that puts academic work 1st as the number one value. What I'm worried about is that I'm recommending super hard material - at least one year advanced, and readers and their children will run into a brick wall trying to do it. Therefore, this article provides the ladder to get over the brick wall.
First of all, as a parent, the child has to do all of the work. (Look at my prior article about public speaking.) Your job is to hand the work to the child. If the child says that the work is hard, and you do any of it, any at all, then you have failed the child. The learning process is taking hard material and figuring it out. The main failing of our school system and parents is that we teach this material to the children. They know it, but they don't know how to learn because we do that work for them. (The school system will be covered in a future article).
So what do you do? Here's what I do.
#1 Read the Question
I ask the child to read the question to me and explain it to me. I am looking for them to acknowledge parts of the question that they did not see before. The question may include a diagram. They have to read, describe, explain every part of the diagram to me. Kids tend to not think this is part of the question, but it is the main part of the question.
#2 What Do You Recognize
What parts of the question do you recognize? What words or definitions do you know. Have you ever seen any problems that are similar to parts of this problem?
#3 What Do You Not Recognize
Kids tend to skip right over words, phrases, or syntax that they are not familiar with. Saturday, my son saw 10√2. He had no idea what 10√2 was and worked on the problem for 5 minutes before I asked this question and he point it out.
When asking these 3 questions, you are giving the child the first few tools to do something with the problem other than just sit there and give up. Think about this approach. You aren't really helping by teaching the child the material. Don't ever explain the material. What you are doing is teaching the child how to learn for themselves, which should be the goal of every parent and teacher.
In school, especially in math, the kids are supposed to know everything and be able to do it quickly. Think of times tables. The children develop this expectation that academic work is about knowing things. This expectation puts them at a distinct disadvantage, because academic work is about learning things and figuring things out. When they get challenging material, they think they should know it - and they don't, or else why would I be giving it to them - and then they come to the conclusion that they are big dummies.
You as the parent have to undo this bad habit, first with yourselves as academic coaches, and secondly within your children as learners and figure-outers. There are other questions I ask after questions involving the problem, but the 3 questions above are the most important for Step One because they get the parent out of the explaining business and make the child think for himself.
When I encounter a child who is a genius at math tables for arithmetic, I assign a book of word problems or brain teasers. I have got crying and frustration from the kids for this assignment, but down the road the parents are very appreciative.
Spending a lot of time reading the question is a good first step. What you have to do next varies a bit with whether you are doing math or whether you are doing test prep with a set of answer choices.
Math
Here's an example that my 10 year old and I worked on. In the diagram below, side a and side b are both 10√2, and the line running through the middle of the triangle is parallel to the bottom of the triangle. (The actual question was convoluted and I'm not going to type it here because it's hard to present in HTML.) What is the area of the rectangle made up of the 2 squares?
After struggling with this problem to the point of tears, my son asked for help. I had no clue what the answer was or how to solve it. We started with him reading the problem to me for about 5 minutes until I was sure he knew what all the pieces were. The we discussed what square roots are and why the square root of 2 is just left there as notation and not a number. That took 10 more minutes.
I asked him to tell me what he knew about area, and he knew the formula for the area of a triangle, which was good. He also told me the area of the rectangle was half of the area of the triangle which was pretty astute. (Apparently I taught him something. We didn't prove it formally, but good enough.) Then we had to figure out the area of any of the triangles. It took about 45 minutes, and in the process, we learned a lot of math. We learned not to give up. It was not easy for me either.
I am not sure I could figure out this problem on my own without the problem solving steps we went through. I know for certain that without these problem solving steps, I wouldn't be able to help my son with math.
This question came out of the SAT practice test book we are going through. It's getting harder. We're down to about 1 to 3 questions per session. A lot more learning takes place with one question than a whole workbook of easy calculation questions. Like public speaking, the parent or academic coach just has to go really slowly and wait a lot. Sometimes, like in the case of this problem, the kid can get through one or 2 important steps in problem solving, but needs help with the other 9. That's OK. He can learn some by doing and some by watching, and eventually, maybe in a classroom setting, he'll be able to put all of the pieces together himself on something easier.
Test Prep
Test prep has a lot of the same elements but I usually go about it differently because the problems are much different. The goal of a cognitive abilities test is to present the child with a completely unfamiliar problem with it's own set of brand new rules and let the child figure these out. The goal of the parent is to teach the child these skills so that they do better in school and in life and on the SAT test prep math book they'll get later.
Here is a sample problem. The directions state that there is a relationship between the squares in the top row. Which shape would you pick for the blank box so that the same relationship holds true for the bottom row?
This one is pretty confusing, and would be preceded by some examples where the shape at top shrinks or grows along one or more dimensions, or turns or flips. The test intentionally sets the kid up for failure on this question. I don't think I got it the first time I saw it. I would have failed a 1st grade cognitive abilities test.
The first step in the test prep process is to understand what it means that there is a relationship between the two top shapes. We spent 3 months on that. What are all of the things that a square can do? Draw them. Cut out a square or find one in the toy box, and have your son demonstrate the basic operations, especially rotate and flip. What does the square look like when it is turning or flipping? Ideally, you would work with other shapes and a list of math vocabulary before attacking a question like this.
The children must look carefully and patiently at this question for a long time and start thinking about all of the things that may happen. Children who do well will linger on the question. Children who will bomb the test completely will look at the problem, immediately realize that they don't know the answer, and guess or move on without trying. Or they may ask the parent for help, the parent will explain the problem, and no learning will take place.
When really great teachers present problems in class at this level of challenge, they'll just change the subject and move on without telling the kid whether or not they got it right. They'll move on to working with things that can happen to shapes, and how each shape looks when it grows, rotates, widens, gets shorter, etc. (They of course don't do with COGAT questions but academic material.) At some point, either the lightbulb goes off for the child or they can come back to a problem like this and succeed where once they failed.
This problem could be out there unsolved for months. When we did test prep (aka Cognitive Skills building), I would skip lots of material or leave it ungraded and we would eventually come back to it.
The child learns by learning. If a parent explains this problem to the child, learning has failed. Also, test prep books are expensive and don't have a lot of problems in them, so don't waste even a single problem. If your child is stuck or doesn't know the answer, save it for later. If they say "I can't do this", say "You can't do this yet."
Parents often wonder why their child does so well on standardized tests but not cognitive abilities tests. In Chicago, kids can take the Classical test to get into an Academic Center, or a cognitive skills test to get into a Regional Gifted Center. The Classical test is a standardized test (eg what kids are learning in school) and the Academic center is an accelerated program. The gifted test is a cognitive abilities test and the gifted programs are accelerated, but the kids are expected to learn the material even though they spend most of their time on projects and field trips.
Back to the question. Why the disparity in scores? In short, the parent can teach the child academic material without teaching them how to think. It works for a while, and then by middle school the kid is failing.
I say don't teach your child anything. When they get stuck on hard material, do something else for a while. Let them make up their own test questions (we did this and it was fun) and see if they can make a test question with only one correct answer. Make up your own test question and let the child find the mistakes, like a question that has multiple answers or a question that doesn't have any answers. We did a lot of this. I noticed that much more learning was taking place when the test prep book wasn't open.
I better summarize because this article is so long. Here are the rules for a parent:
#1. Don't tell your children anything. Let them learn it on their own. Be prepared to wait a long time for them at first until they pick up these skills.
#2. If you have to explain something, don't. You can ask lots of questions, and don't forget the questions I presented in the math section. Make these questions opened ended, not prompts for the answer you want. Ask them over and over again until your child gives up expecting any useful help from you and starts doing the thinking on his own.
#3. Be prepared to spend an hour on a single question or save if for another time.
#4. Fill in the gaps with do-it-yourself projects that make it more fun.
#5. Have an easy workbook standing by as a crutch so that regardless of your child's skill level, they can do something productive and not wallow in their frustration for ever. As they grow, they can handle longer periods of frustration, or better yet, learn the skills to overcome the brick wall.
This list is a lot better than the advice you'd find in a parent magazine (e.g., get a good night's sleep before the test). I have a much more detailed list of problem solving steps to review later . This is just the part of the list to break the parent of the bad habit of undermining learning.
Monday, April 20, 2015
Lack of Motivation 2 - Getting Started
Lately, I've been facilitating Leadership Training for 6 and 7 year olds. This has been a lot of fun.
One of the starter qualities is public speaking, and for little kids, I start with things that I know they have an opinion on - like "What is your favorite video game?" It's easy to get kids to talk about things they know, and the most obvious thing they know is themselves.
With some kids, I get a blank look. From experience, I know that kids will respond at their own pace. A few years ago, when we were eating dinner, I would ask my kids how their day went. The little one would just sit there. Sometimes for 20 minutes. I don't know what he was doing, perhaps going through every event minute by minute in his mind deciding what to share. This would of course frustrate the other people at the table, who would refine the question like "Did you have recess today?" or they would just move on or answer on his behalf.
This is a BIG mistake for parents
It used to frustrate me to wait for a response, and I thought additional prompts were necessary. One day, when everyone was in a particularly bad mood, the question was asked, and then there was 20 minutes of silent eating. Suddenly, he answered. The light bulb went off for me.
At other times, the question would be asked, conversation would move on, and then 20 minutes later in the midst of some discussion, the little one would begin to describe his day. The light bulb went on again.
At one of our leadership training exercises, I asked a kid a question that I expected an answer to. He just stared at me silently, and I stared at him. I'm more than happy to wait 20 minutes for a response. From experience, I know that I'll get one, and maybe the next time I ask a question, I'll only have to wait 19 minutes. With my little one, after me patiently waiting to give him an opportunity to formulate a response and then respond, over a period of 6 months or so, he became very good at responding, so good, in fact, that now he talks nonstop from morning to evening. When we do our leadership training, if I don't tell everyone to be quiet and wait their turn, my son answers all questions immediately and ruins the whole exercise.
Anyway, back to this kid. I asked the question and waited. His parent was sitting nearby and was very anxious about this, and then reasked the question, gave him prompts, and finally answered on his behalf. The kid said nothing the whole time.
That is why he doesn't talk. He doesn't have to. He has never learned to.
Some kids want to talk but are afraid because of the team setting. If they say they don't want to answer the question, I will respond, OK, then, just tell me one thing that you did today (or one video game you like, etc.). That is usually enough to clear the hurdle. But I never give them any other prompt or move on. I just wait. Parents, on the other hand, are extremely anxious during this discussion and want to do everything they can to help the kid. But they can only help by doing nothing.
I was an anxious parent before I dove into this 5000 hour research program I call my blog. The implications of this event and the parent response should be clear to all of my readers. What I am going to do in part 3 and 4 of my series on Lack of Motivation is take this same parent-child interaction and show how it plays out in test prep, math, and general learning to the detriment of the child. Or the benefit of the child.
One of the starter qualities is public speaking, and for little kids, I start with things that I know they have an opinion on - like "What is your favorite video game?" It's easy to get kids to talk about things they know, and the most obvious thing they know is themselves.
With some kids, I get a blank look. From experience, I know that kids will respond at their own pace. A few years ago, when we were eating dinner, I would ask my kids how their day went. The little one would just sit there. Sometimes for 20 minutes. I don't know what he was doing, perhaps going through every event minute by minute in his mind deciding what to share. This would of course frustrate the other people at the table, who would refine the question like "Did you have recess today?" or they would just move on or answer on his behalf.
This is a BIG mistake for parents
It used to frustrate me to wait for a response, and I thought additional prompts were necessary. One day, when everyone was in a particularly bad mood, the question was asked, and then there was 20 minutes of silent eating. Suddenly, he answered. The light bulb went off for me.
At other times, the question would be asked, conversation would move on, and then 20 minutes later in the midst of some discussion, the little one would begin to describe his day. The light bulb went on again.
At one of our leadership training exercises, I asked a kid a question that I expected an answer to. He just stared at me silently, and I stared at him. I'm more than happy to wait 20 minutes for a response. From experience, I know that I'll get one, and maybe the next time I ask a question, I'll only have to wait 19 minutes. With my little one, after me patiently waiting to give him an opportunity to formulate a response and then respond, over a period of 6 months or so, he became very good at responding, so good, in fact, that now he talks nonstop from morning to evening. When we do our leadership training, if I don't tell everyone to be quiet and wait their turn, my son answers all questions immediately and ruins the whole exercise.
Anyway, back to this kid. I asked the question and waited. His parent was sitting nearby and was very anxious about this, and then reasked the question, gave him prompts, and finally answered on his behalf. The kid said nothing the whole time.
That is why he doesn't talk. He doesn't have to. He has never learned to.
Some kids want to talk but are afraid because of the team setting. If they say they don't want to answer the question, I will respond, OK, then, just tell me one thing that you did today (or one video game you like, etc.). That is usually enough to clear the hurdle. But I never give them any other prompt or move on. I just wait. Parents, on the other hand, are extremely anxious during this discussion and want to do everything they can to help the kid. But they can only help by doing nothing.
I was an anxious parent before I dove into this 5000 hour research program I call my blog. The implications of this event and the parent response should be clear to all of my readers. What I am going to do in part 3 and 4 of my series on Lack of Motivation is take this same parent-child interaction and show how it plays out in test prep, math, and general learning to the detriment of the child. Or the benefit of the child.
Sunday, April 19, 2015
Complete Lack of Motivation
4th grade can be a tough year. 4th grade has a high probability that learning styles will clash with teaching styles and the demands for the curriculum and this can lead to a train wreck. Which is exactly what is happening.
We are lucky to have an awesome teacher. The class is full of bright, motivated students who share lots of books with each other, and share lots of really hard strategic thinking video games. What more could I ask for?
The downside is a big list:
Showing kids examples or "teaching" them a subject destroys the fun. Furthermore, kids have different learning styles, and I suspect this is a reflection of their cognitive skills. Some kids, and adults, learn well by paying attention and listening. Some kids learn by doing. Some kids are so Learn By Doing oriented that they really can't learn by listening. I'm one of the latter.
Has a teacher ever commented on your child's grades by pointing out that your child could do much better if he would just pay attention, keep careful notes, and try harder?
The teacher already has a hard enough job, so I don't say much. What I would like to say is "Stop teaching. Just give him the book. And not the current one. Give him a harder book. Even better, just give them problems with no book." The kids can read, they can figure things out, they can pick up new skills if they are only given a chance. It's more fun and more motivating. Sitting their passively taking notes is torture. Even better than a book would just be a bunch of problems; here's the book if you need to look things up. This is how kids are taught in the UK and China, and researchers think that this is the reason they are 2 years ahead of the US in school.
When I was in 4th grade, I routinely got D's and F's on tests on reading tests. At home, I was reading a 850 page book from my parent's book shelf in one hand (Herman Wouk's Africa) and in the other hand, I had a dictionary. There were lots of parent teacher conferences about how bad I was doing and finally the teacher put me in the advanced reading group and gave me more advanced material. It didn't help my math grade which stayed at a C before I got to high school. Algebra peaked my interest, and 4 years later I got a ribbon at regional Calculus competition against a roomful of geeks. I was 5th, and the 4 kids ahead of me all completed calculus the year before. A C in 4th grade didn't preclude me from studying 4 years of math in graduate school and finding a love of math. I'm not really bitter about my grades at age 10 because I didn't care and my parents didn't know what to do. I'm really bitter about my son's having to go through it.
I'm hearing similar stories from many parents of 4th grade boys in Chicago, mainly with boys who are unmotivated.
Is there a better way? Stay tuned for part 2.
We are lucky to have an awesome teacher. The class is full of bright, motivated students who share lots of books with each other, and share lots of really hard strategic thinking video games. What more could I ask for?
The downside is a big list:
- Common core standards require the teacher to teach and the kids to know a lot of rote material.
- The 4th grade teaching method, especially for math, is this: a) here is the material which I will explain, b) here are some examples, c) here is a math worksheet of 30 problems where you have to regurgitate like a robot the same thing I just showed you over and over and over.
- The kids are expected to know a bunch of useless concepts, e.g., the names of parts of the sentences, which are on the common core test, because the teacher is evaluated based on the outcome, and so is the school.
Showing kids examples or "teaching" them a subject destroys the fun. Furthermore, kids have different learning styles, and I suspect this is a reflection of their cognitive skills. Some kids, and adults, learn well by paying attention and listening. Some kids learn by doing. Some kids are so Learn By Doing oriented that they really can't learn by listening. I'm one of the latter.
Has a teacher ever commented on your child's grades by pointing out that your child could do much better if he would just pay attention, keep careful notes, and try harder?
The teacher already has a hard enough job, so I don't say much. What I would like to say is "Stop teaching. Just give him the book. And not the current one. Give him a harder book. Even better, just give them problems with no book." The kids can read, they can figure things out, they can pick up new skills if they are only given a chance. It's more fun and more motivating. Sitting their passively taking notes is torture. Even better than a book would just be a bunch of problems; here's the book if you need to look things up. This is how kids are taught in the UK and China, and researchers think that this is the reason they are 2 years ahead of the US in school.
When I was in 4th grade, I routinely got D's and F's on tests on reading tests. At home, I was reading a 850 page book from my parent's book shelf in one hand (Herman Wouk's Africa) and in the other hand, I had a dictionary. There were lots of parent teacher conferences about how bad I was doing and finally the teacher put me in the advanced reading group and gave me more advanced material. It didn't help my math grade which stayed at a C before I got to high school. Algebra peaked my interest, and 4 years later I got a ribbon at regional Calculus competition against a roomful of geeks. I was 5th, and the 4 kids ahead of me all completed calculus the year before. A C in 4th grade didn't preclude me from studying 4 years of math in graduate school and finding a love of math. I'm not really bitter about my grades at age 10 because I didn't care and my parents didn't know what to do. I'm really bitter about my son's having to go through it.
I'm hearing similar stories from many parents of 4th grade boys in Chicago, mainly with boys who are unmotivated.
Is there a better way? Stay tuned for part 2.
Saturday, April 18, 2015
More on Homework Concentration
I think I'm approaching my finest moment ever as the Worlds Most Awesome Academic coach. It's Saturday morning and my kids are focused on their math (2 pages), vocab (2 pages) followed by music practice, which I just added today. I was considering adding reading, but I don't want anyone hurrying through reading.
I can remember back a year when all I got was crying and whining for an hour - and the assignment was just a single page of math. Sometimes it took all day before a child would reluctantly do his math in order to have 15 minutes of computer usage before bed time.
In the year between crying and whining and Lean Mean Saturday Morning Homework machine I didn't do anything special or clever. Here's what I did:
1. I got the work together every Saturday morning and put it on the table where breakfast is eaten. With pencils. I think this is the key to success. Every morning, no matter how depressed I was.
2. I offered to sit with anyone and help as needed. When I would nag or get mad, it wouldn't help much. After a few weeks of helping, my kids think I'm more trouble than I'm worth, but the little one will still take help because his vocab is way beyond his level.
3. When they wake up, I am typing on my blog so that they would see the computer and say "Can I use the computer" and I would respond "Can you do your math?" No math, no computer.
4. I never let them use the computer during the week. Lately if they do their math, vocab and music practice and reading and all their school homework - which is impossible - and they ask me to use the computer I think I would let them, even on a Monday night. But it's impossible. Friday night and Sunday are not impossible. We get some work on Friday and Sunday too.
5. When 1 page of math was too easy, I increased it to 2 pages. I used to alternate vocab and math, now they have to do both. When they could get through the whole thing in 30 minutes or so, I added music practice.
Here's why things are going so well. The 6 year old ran out of material at his level and now does exclusively material that is way beyond him. I'm not sure what to do about that. Is this a good thing or a waste of time? But he still tries really really hard.
The 10 year old is doing Mathletes (way hard) and the SAT practice tests I got him (just right). I sent a thank you note to the customer service address for Mathletes and the author's wife responded. Apparently the author was invited to put together a gifted math curriculum for the Plano TX school district. I wish Chicago would do the same thing. In the mean time, the type of material in the curriculum is in this book.
The SAT problems are exactly the perfect way to practice math (assuming that you have Mathletes to learn math). The SAT practice book has every theorem, formula, or conceptual explanation a child would need. The technical math content of the SAT is accessible to anyone who has had 5th grade math. The problems are super convoluted and multistep and require lots of thinking. Algebra is not anywhere to be found unless needed for a solution to a problem. I think this is he way I would teach math. I see a high degree of motivation that I didn't see before. Yea! This could solve my problem. Not to mention we're doing hard core test prep at a level that makes insane look normal.
I may be up for the Competitive Parent Magazine Parent of the Year Award again.
I can remember back a year when all I got was crying and whining for an hour - and the assignment was just a single page of math. Sometimes it took all day before a child would reluctantly do his math in order to have 15 minutes of computer usage before bed time.
In the year between crying and whining and Lean Mean Saturday Morning Homework machine I didn't do anything special or clever. Here's what I did:
1. I got the work together every Saturday morning and put it on the table where breakfast is eaten. With pencils. I think this is the key to success. Every morning, no matter how depressed I was.
2. I offered to sit with anyone and help as needed. When I would nag or get mad, it wouldn't help much. After a few weeks of helping, my kids think I'm more trouble than I'm worth, but the little one will still take help because his vocab is way beyond his level.
3. When they wake up, I am typing on my blog so that they would see the computer and say "Can I use the computer" and I would respond "Can you do your math?" No math, no computer.
4. I never let them use the computer during the week. Lately if they do their math, vocab and music practice and reading and all their school homework - which is impossible - and they ask me to use the computer I think I would let them, even on a Monday night. But it's impossible. Friday night and Sunday are not impossible. We get some work on Friday and Sunday too.
5. When 1 page of math was too easy, I increased it to 2 pages. I used to alternate vocab and math, now they have to do both. When they could get through the whole thing in 30 minutes or so, I added music practice.
Here's why things are going so well. The 6 year old ran out of material at his level and now does exclusively material that is way beyond him. I'm not sure what to do about that. Is this a good thing or a waste of time? But he still tries really really hard.
The 10 year old is doing Mathletes (way hard) and the SAT practice tests I got him (just right). I sent a thank you note to the customer service address for Mathletes and the author's wife responded. Apparently the author was invited to put together a gifted math curriculum for the Plano TX school district. I wish Chicago would do the same thing. In the mean time, the type of material in the curriculum is in this book.
The SAT problems are exactly the perfect way to practice math (assuming that you have Mathletes to learn math). The SAT practice book has every theorem, formula, or conceptual explanation a child would need. The technical math content of the SAT is accessible to anyone who has had 5th grade math. The problems are super convoluted and multistep and require lots of thinking. Algebra is not anywhere to be found unless needed for a solution to a problem. I think this is he way I would teach math. I see a high degree of motivation that I didn't see before. Yea! This could solve my problem. Not to mention we're doing hard core test prep at a level that makes insane look normal.
I may be up for the Competitive Parent Magazine Parent of the Year Award again.
Wednesday, April 15, 2015
Summer Math Program of Awesomeness
I've got both parts of my Summer Math program - the SAT test prep book and the "Math Leads for Mathletes" book. I'm replicating my age 4-5 test prep regimen, only this time for ages 10-12. As I have been suggesting all year, my goals include an exciting At Home Schooling math program full of problem solving, and reluctantly, the beginning of test prep for the 7th grade testing hell in Chicago.
The Mathletes book is exactly what I want - real math. It says in the introduction that the book targets advanced 4th and 5th graders, or even really bright 3rd graders. It looks more like graduate level work to me. I am not kidding.
You may recall that we tried Patterns in Mathematics by Paul Swan the summer before third grade. It is similar material with a similar approach to Mathletes, only easier and more accessible, but like early Algebra, we had limited success. For material of this nature, learning takes place either when it's a tool to the end, or the child has the maturity and math experience to see its value in applications or appreciate it's beauty.
The SAT test prep is much easier, at least the official test questions from the College Board which are available online. I noticed right away that the test questions require the same basic cognitive skills that the K and 1st grade cognitive skills tests (aka OLSAT and COGAT). The questions present regular concepts in a novel way and require at least 2 steps to solve. I feel like there are no new tricks once you get pass testing 5 year olds.
This curriculum will probably last through the summer after sixth grade, unless we go faster than I expect (which usually happens 9-12 months into it as the kids pick up skills and mature) or unless I come up with the next fad of my choosing.
Like the 4-5 year old program, the new program requires an different approach on the part of the parent. With normal homework and workbooks, the child might be given 30 routine problems of the same topic, and be expected to complete them in 30 to 60 minutes. When using SAT or Mathletes material, a single problem might require 30 minutes, or a week. The book might have to be shelved while background or introductory material is found on the net and then given a second or third chance. Some of the material may have to be skipped and then revisited 6 months later. This is all about patience.
Here are some examples.
SAT Example
This is question #2 on the College Board's free online test.
The table above shows the temperatures, in degrees Fahrenheit, in a city in Hawaii over a one-week period. If m represents the median temperature, f represents the temperature that occurs most often, and a represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f, and a? (Answer choices not show, but it's variants of the answer below.)
The answer is a < m < f
This material is covered in Every Day Math at least for 4th and 5th grade. Notice that it's not about solving the for mean, mode and median, but ordering the results to derive the answer. Most of the work is in figuring out what the problem is asking and analyzing the data. It requires a whole bunch of skills from my Math Problem Solving Skills list, starting with "OK, I have no idea what I'm doing here. What do I recognize? Median...Mode...Average...I need to reread the question a few times...". I am confident that this will break 4th grade habits ingrained in children by boring arithmetic sheets.
It's not enough to solve this problem an get it right. If it takes the child a long time to calculate the average, challenge them to do better. Instead of adding all of these big numbers, how about adding 70 minus the number and adding back 70, ie -4 + 8 + 5 + -1 + 8 +7 + 0 to calculate the average.
Also, unlike homework, it's not at all about getting it correct the first time. It took me 3 tries, and I was more than happy plodding patiently along to find my mistake. That is the approach to math the kids need to get to higher levels - spending time figure out what to do with a math problem (instead of memorizing math facts) and overcoming incorrect answers.
Mathletes Example
In graduate school, I took a two semester course that had a single 60 page book. 30 pages the first semester, and 30 pages the second. At times we spent 6 classes on a single line from the book. It was a math book, but had no numbers. Mathletes is a little like that.
As I scroll through the book, there are things like this:
Even more generally, we find that the formula for m-gonal numbers is
Nn(m) = n + (m -2)n(n-1)/2
Even though the content leads up to this line, and explains things as it goes, this line might take a few weeks for the child to sort through. On the other hand, this material is great for young children - lots of new concepts and vocabulary and ideas and history that a child can handle, and lots of very slow thinking week by week to figure out what the math is. If you did articles from a few years ago, this was how I taught math to a 4 year old. The difference is that with younger kids, there is more vocab and concepts than thinking, and with younger kids lots more thinking. (This is the Classical Education at work.)
In high school, I remember working through trigonometry proofs on at a time, probably 20 minutes each, with more memorization than actual understanding. The material in this book will assist greatly with the sign function, and I've never seen this material covered in depth in a context where the student actually gets as much time to think through it and digest it as the original mathematician took to come up with it. Is it fair that a high school student gets 20 minutes on a proof that took a mathematician 2 years to derive? This book is great early prep work for trig. There is some algebra and geometry needed, but very little, and only used as a tool for other material. (This is how Jo Boaler once described how math should be taught.) I'm going back to the SAT prep for algebra and geometry.
I'm probably not going to get a mathematician despite my efforts, but I am going to get a thinker and a problem solver.
The Mathletes book is exactly what I want - real math. It says in the introduction that the book targets advanced 4th and 5th graders, or even really bright 3rd graders. It looks more like graduate level work to me. I am not kidding.
You may recall that we tried Patterns in Mathematics by Paul Swan the summer before third grade. It is similar material with a similar approach to Mathletes, only easier and more accessible, but like early Algebra, we had limited success. For material of this nature, learning takes place either when it's a tool to the end, or the child has the maturity and math experience to see its value in applications or appreciate it's beauty.
The SAT test prep is much easier, at least the official test questions from the College Board which are available online. I noticed right away that the test questions require the same basic cognitive skills that the K and 1st grade cognitive skills tests (aka OLSAT and COGAT). The questions present regular concepts in a novel way and require at least 2 steps to solve. I feel like there are no new tricks once you get pass testing 5 year olds.
This curriculum will probably last through the summer after sixth grade, unless we go faster than I expect (which usually happens 9-12 months into it as the kids pick up skills and mature) or unless I come up with the next fad of my choosing.
Like the 4-5 year old program, the new program requires an different approach on the part of the parent. With normal homework and workbooks, the child might be given 30 routine problems of the same topic, and be expected to complete them in 30 to 60 minutes. When using SAT or Mathletes material, a single problem might require 30 minutes, or a week. The book might have to be shelved while background or introductory material is found on the net and then given a second or third chance. Some of the material may have to be skipped and then revisited 6 months later. This is all about patience.
Here are some examples.
SAT Example
This is question #2 on the College Board's free online test.
| Mon | Tue | Wed | Thurs | Fri | Sat | Sun |
| 66 | 78 | 75 | 69 | 78 | 77 | 70 |
The table above shows the temperatures, in degrees Fahrenheit, in a city in Hawaii over a one-week period. If m represents the median temperature, f represents the temperature that occurs most often, and a represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f, and a? (Answer choices not show, but it's variants of the answer below.)
The answer is a < m < f
This material is covered in Every Day Math at least for 4th and 5th grade. Notice that it's not about solving the for mean, mode and median, but ordering the results to derive the answer. Most of the work is in figuring out what the problem is asking and analyzing the data. It requires a whole bunch of skills from my Math Problem Solving Skills list, starting with "OK, I have no idea what I'm doing here. What do I recognize? Median...Mode...Average...I need to reread the question a few times...". I am confident that this will break 4th grade habits ingrained in children by boring arithmetic sheets.
It's not enough to solve this problem an get it right. If it takes the child a long time to calculate the average, challenge them to do better. Instead of adding all of these big numbers, how about adding 70 minus the number and adding back 70, ie -4 + 8 + 5 + -1 + 8 +7 + 0 to calculate the average.
Also, unlike homework, it's not at all about getting it correct the first time. It took me 3 tries, and I was more than happy plodding patiently along to find my mistake. That is the approach to math the kids need to get to higher levels - spending time figure out what to do with a math problem (instead of memorizing math facts) and overcoming incorrect answers.
Mathletes Example
In graduate school, I took a two semester course that had a single 60 page book. 30 pages the first semester, and 30 pages the second. At times we spent 6 classes on a single line from the book. It was a math book, but had no numbers. Mathletes is a little like that.
As I scroll through the book, there are things like this:
Even more generally, we find that the formula for m-gonal numbers is
Nn(m) = n + (m -2)n(n-1)/2
Even though the content leads up to this line, and explains things as it goes, this line might take a few weeks for the child to sort through. On the other hand, this material is great for young children - lots of new concepts and vocabulary and ideas and history that a child can handle, and lots of very slow thinking week by week to figure out what the math is. If you did articles from a few years ago, this was how I taught math to a 4 year old. The difference is that with younger kids, there is more vocab and concepts than thinking, and with younger kids lots more thinking. (This is the Classical Education at work.)
In high school, I remember working through trigonometry proofs on at a time, probably 20 minutes each, with more memorization than actual understanding. The material in this book will assist greatly with the sign function, and I've never seen this material covered in depth in a context where the student actually gets as much time to think through it and digest it as the original mathematician took to come up with it. Is it fair that a high school student gets 20 minutes on a proof that took a mathematician 2 years to derive? This book is great early prep work for trig. There is some algebra and geometry needed, but very little, and only used as a tool for other material. (This is how Jo Boaler once described how math should be taught.) I'm going back to the SAT prep for algebra and geometry.
I'm probably not going to get a mathematician despite my efforts, but I am going to get a thinker and a problem solver.
Friday, April 10, 2015
Really Early SAT Prep
In my last article, I outlined my At Home Schooling strategy, which focuses on a few things that we can do effectively, mainly math and vocabulary. We try to maintain a home environment that fosters learning and exploration, but I don't push anything else in a concerted way because it will just backfire. Music is mandatory, and I "assist" with practicing.
I didn't mention this last time, but at least once a year I go through Reading Comprehension phases and we switch either vocab or math with a reading comprehension book or practice test.
It occurred to me today that the strategy of math and vocab is 2/3rd of the SAT test prep regimen. The other 1/3 is reading comprehension practice and making sure the test taker is conversant with the types of questions on the test. The SAT has undergone a few big changes since I took it in 1893. Therefore I just ordered an SAT test prep book to see what is in there. My wife will surely think that I've gone insane when it arrives.
It is well known in the Test Making industry that vocabulary is the single best predictor of "intelligence", and "intelligence" is the single biggest predictor of success in school. I'm using quotes around "intelligence" because, while no one has actually defined it, let alone measured it, the Test Making industry uses the working definition of "Things that we put in the test, mainly vocabulary and arcane math problems." These tests, like the SAT, are good predictors of how a person will do in college. The 2nd best predictor of how well a person will do in the future is how they are doing now, since people tend not to change their habits. During adolescences, about 15% of kids do change their habits and raise their scores by 15% or more, but mainly people don't change.
How can I use this for test prep?
After the elementary school entrance exam, the next major milestone is the high school entrance process, which consists of 7th grade grades, the 7th grade standardized test, and another entrance exam. Right now I have a 1st grader who I'm going to ignore for 2 years, and a 4th grader who needs about 3 years of test prep. But how to do test prep?
I've considered doing all of the 7th grade curriculum on the side, but this will backfire because he'll do poorly with material he's seen before out of boredom. Instead, I'm thinking of preparing him for the SAT. If he can pass the SAT, he should be able to pass the entrance exam, provided that these are similar tests. They should be. If vocabulary and arcane math problems are great predictors of school success, then the super secret entrance exam must have heavy doses of these. I'm not sure what else. I'm going to guess reading comprehension.
Time for another wall chart. There are 20 full length practice tests in the book I just ordered.
I didn't mention this last time, but at least once a year I go through Reading Comprehension phases and we switch either vocab or math with a reading comprehension book or practice test.
It occurred to me today that the strategy of math and vocab is 2/3rd of the SAT test prep regimen. The other 1/3 is reading comprehension practice and making sure the test taker is conversant with the types of questions on the test. The SAT has undergone a few big changes since I took it in 1893. Therefore I just ordered an SAT test prep book to see what is in there. My wife will surely think that I've gone insane when it arrives.
It is well known in the Test Making industry that vocabulary is the single best predictor of "intelligence", and "intelligence" is the single biggest predictor of success in school. I'm using quotes around "intelligence" because, while no one has actually defined it, let alone measured it, the Test Making industry uses the working definition of "Things that we put in the test, mainly vocabulary and arcane math problems." These tests, like the SAT, are good predictors of how a person will do in college. The 2nd best predictor of how well a person will do in the future is how they are doing now, since people tend not to change their habits. During adolescences, about 15% of kids do change their habits and raise their scores by 15% or more, but mainly people don't change.
How can I use this for test prep?
After the elementary school entrance exam, the next major milestone is the high school entrance process, which consists of 7th grade grades, the 7th grade standardized test, and another entrance exam. Right now I have a 1st grader who I'm going to ignore for 2 years, and a 4th grader who needs about 3 years of test prep. But how to do test prep?
I've considered doing all of the 7th grade curriculum on the side, but this will backfire because he'll do poorly with material he's seen before out of boredom. Instead, I'm thinking of preparing him for the SAT. If he can pass the SAT, he should be able to pass the entrance exam, provided that these are similar tests. They should be. If vocabulary and arcane math problems are great predictors of school success, then the super secret entrance exam must have heavy doses of these. I'm not sure what else. I'm going to guess reading comprehension.
Time for another wall chart. There are 20 full length practice tests in the book I just ordered.
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