This article is necessary because my guidelines for coaching are very clear and I never follow them. They only work with the ideal child who is alert, well rested, just had a snack, and is ready to learn, as well as a parent who is cheery and patient. Since these two conditions never hold in this house, I have a second set of rules under the heading of Parent Survival Guide.
The goal of a coaching session is to get 15 good minutes of concentration and learning out of a 5 year old. With academic material, this might be 30 to 45 minutes. With older children, maybe 20 or 30 minutes on cognitive skills work. The reason for the 15 minute rule is that thinking is hard and I generally pick material so that after 15 minutes the child is mentally exhausted.
Rule #1 You will have bad days 40% of the time or more.
On a bad day, your child is sick, tired, or hungry. An inexperienced parent will not realize this until much later. An experience academic coach expects it. If you start yelling at your child (guilty) it will result in crying and frustration and the whole session is wasted. If you let them chose the material to do that day, they will pick something easy and at least they will exercise work habits if nothing else.
Rule #2 You don't know how it will go
I'm willing to bet that I have no readers who have experience teaching figure matrices to children where the trick in the question is that a square flipped but looks like nothing happened. The problem is that your kid is making no progress. Maybe it's way too hard for the kid at this juncture ("juncture" is an inappropriate word that coaches use in "pep" talks).
Plan B comes in many forms.
We take an unexpected detour to the shape box to start flipping shapes. We have this fantastic game from age 3 where you build patterns from shapes. We'll flip them and I'll let my child describe what happened. Flip the square. "I already did." No you didn't. "Yes I did..." This is the best way to learn anyway, but time constraints make it rare.
If I see that the child has exercised some of the skills and gotten the problem past the first step, I'll do the rest. For younger kids, this works fine sometimes because they don't care if they learn by doing or watching. With books, I used to read every other page. For older kids, I do this more often because many of the problems I give require a team and since there are only 2 of us, I'm the rest of the team.
Note that I never do any figuring out or solving on test prep questions. There isn't enough material out there. For test prep questions, I'll just circle it on the chart and we'll try again a few weeks later. In fact, with an early enough start, you might circle a whole section or book if the child isn't ready. But on really hard math problems and reading comprehension, I'll jump right in there and work away side-by-side with my child, although I've been known to randomly get things wrong sometimes until they don't trust my help.
I may set aside my goal of 6 problems and we will spend the rest of the time dissecting the hard problem.
Or we can just read. I don't know why, but strong reading families pick up these skills anyway, just not in time for the test. (Curse you, strong reading families.)
Speaking of Dissecting
There is so little good material (aka hard) out there that you want to squeeze every last drop of learning and behavior planning out of each and every problem. This is good, because it enforces the right skills. I think we once spent 3 months on a practice test doing this, probably a year earlier than it should have been covered. I never planned or expected to do a full length practice test just for the sake of doing a full length practice test.*
Step 1: Describe what is happening in the problem in excruciating detail. The kid, not you.
Step 2; Ask questions about what they are describing. What if? Show no interest in hurrying into the solution.
Step 3: Describe the solution set. Again, this is not you.
Step 4: Ask them to explain the rules of this problem because you are confused and until the child is about 10 they won't realize that you are the dumbest parent on the planet. (By age 10 they are convinced you don't know anything because you always just ask dumb questions and never help them do their homework in any meaningful way. The downside of this is that when they are struggling to finish their math homework at 9 pm they won't take your suggested answer.)
If they are really floundering, ask them to explain the example to you and then come back to this problem.
If they are totally clueless and you're getting desperate, ask them to memorize the mantra "Shape, Size, Color, Count'. I did this because one of these things was always changing, although now that I think about it, the test may have been in black and white and "Shape" doesn't really mean anything. I actually sent my child into the test asking him to use the mantra anyway. Maybe he was baffled by the test (100% certainty because it's designed for that and way harder than anything you will practice) and the mantra brought him back to the practice rounds when he was figuring things out. Maybe not.
Step 5: Let them try to solve it as many times as necessary to get the correct answer.
Step 6: When they finally get the correct answer because there are only 4 possible answers and their guesses on the last 3 were not correct, ask them to prove it to you, or at least explain why it's correct and the other 3 aren't. I always make my kids prove it to me because their work with Vocabulary Workshop have made them expert guessers, and guessing is not one of the skills I'm looking for on the figure matrix problem. When they guess correctly because they eliminated 2 impossible answers, I'm proud but we start over with Step 1.
Successfully problem solving a novel test problems rests heavily on your child's ability to do Step 1 and Step 4 as a matter of practice. This is not at all like school and I'm not sure where kids will learn this approach if it is not coached. Step 6 is a high level of Executive Functioning and reinforces the bookend skill of checking the problem. Making them live the problem elements during the discussion burns in working memory if it's not strong enough yet. (I'm 10% sure of that last statement. I'd like to think it is true because a project centered curriculum is a strong test prep method. This may just reinforce executive skills). Again, let me reiterate that they will be confused by the test and the practice material is not going to give them an edge because they recognize one of the easy questions. You are teaching thinking, and not 7 + 8 = 14, which it doesn't anyway.
Remember these steps, because you will go through something very similar from ages 6 through geometric proofs in AP Geometry and can help even though you don't remember who Pythagoras was.
Getting It Wrong
Take the reward for getting the right answer out of the culture. This is about learning, not getting right answers. The general rule is that if your child is getting more than 50% correct, then you have the wrong material. This rule of thumb is derived as follows: they get a problem incorrect, thereby proving that they just came across something (skill or otherwise) that they needed to learn, and they get a problem correct (at some point, maybe not the next one) to show that they actually learned something.
How are you going to coach the thinking skills above if your child doesn't need to learn them? I've had days where the error rate was closer to 100%. If my child ever hands me a page with a score of 0%, we cancel the rest of the night and go out for ice cream. I've had to adjust the policy a bit with bad report cards, because I'm not the one who feels bad, but not my general rule that failure is not against the law. Does a report card with bad marks across the board guarantee straight A's will show up some time next year? I think so. That's an article for down the road.
*The Full Length Practice Test
I not only did a full length practice test, I made a deal to have a teacher give my son the test one-on-one in her classroom, all the while assuming a stern and intimidating persona. Did this do any good? If it was worth a quarter of a percentage point, it was a quarter of a percentage point that we needed to get over the bar. Unfortunately, we needed another 1/4% but I was out of ideas.
The other one managed to get in with nothing but ridiculously super hard problems I randomly found or created like roman numerals and zenn diagrams and reading comprehension problems when he couldn't read. Did this do any good? Yes, I think it was more important than a practice test.
Readers often ask "What do I do?" This is easy to answer when you have to get a 99.9% on the test and there's plenty of time. The answer is all of it. I'm happy to give this answer because if they don't have enough time, they can start right in where they left off the day after the test. Like I did. Three times. Although it turns out it wan't always necessary but it was always helpful.
The prescription gets harder when there's less time or the bar is something like 95%. Then it's a matter of "what are my priorities with my limited time?"
Here is my answer, in reverse time order starting a week before the test:
1. A practice test to prepare for the format of the test. (3%-4%, $30)
2. Really hard reading comprehension questions 2 grades in advance, even if you have to read these to a non-reader (5%-10%, 10$)
3. Really hard problems of any type. (5%-10%, not much on the market except for me)
4. A practice test to coach like I describe above (5% - 15%, $30)
5. Vocabulary Workshop and Building Thinking Skills, Mind Benders, etc, but this would be over a period of months
6. Lots and lots of reading, which you should be doing anyway, test prep or not
7. A good math workbook a year ahead of your child's level. (Level, not grade. You can only pull this off once in grades 1-4 so use it wisely. After that, you need to stick to level or they will hate math.)
I may move #5 up above #4. It's odd that practicing the test is so low on my list. We did the practice test coaching a year in advance, which made it a learning exercise. By the time of the test, the material is much too easy if your child has the approach down. If not, it makes more sense. Rest assured that it doesn't matter if they are struggling with an easy practice test and the test is rapidly approaching. The cognitive skills are not that hard to learn if you have the proper approach to coaching.
I use my coaching steps above on everything, not just practice tests with an emphasis on #1 and #6.
Reading only comes in at #6 because test prep is for kids who didn't teach themselves to read at age two, which is most of us.
Good luck!
Saturday, October 31, 2015
Tuesday, October 20, 2015
The GAT Skill List
The purpose of a cognitive skills tests appear to be measuring cognitive skills. Or does it? This is the first of a 2 part series evaluating just what the heck a cognitive skills test is measuring and how to beat it.
For the last few years I've been happily working with a framework that seemed so obvious to me. I am double checking and it before I get to obvious we have to wade through a dark and murky swamp.
The Big Picture
#1 Cognitive Skills + Interest + Will To Do It = academic and life success.
The aspect of teaching cognitive skills without destroying interest or crushing will is called coaching. If you google my blog and the terms "crying" or "whining" I'm referring to coaching. The last post is half on an article on this concept, and a discussion of coaching will complete the picture that this article begins. (I'm going to be adding to the coaching article over time and will warn everyone when it is complete.)
#2 Cognitive Skills + Interpersonal Skills (e.g., empathy) + Intrapersonal Skills (e.g. self control) = The Full Skill Set
If you child is missing one of these skill sets there is work to be done. I think band and Cub Scouts/Girl Scouts are really good activities for little kids to address the last 2 skill sets. Executive Functioning programs are good for preK training if you have $30,000 to spend on pre school; if not, projects, crafts and art help. Music in general is great for the first and last skill set.
I don't think team sports at young ages are good at all for any of these skill sets.
#3 The Classical Education
For a really inspiring discussion of the classical education, read the first 30 pages of Susan Wise Bauer's The Well-Trained Mind.
Here is my butchered summary: Grades 1-4: Cram as much information into their brains as possible. Grades 4-8: Think analytically. Grades 8-12: Think logically, and grades 12-16 (yes, there is overlap in grades) I haven't gotten this far yet.
If you pair this with Piaget's Theory of Cognitive Development, then you can see that there are things expected of older children that would be impossible for younger children. This is obvious. What is not obvious is whether or not later skills like logic need new cognitive skills or just refinement of an underlying skills.
Since my focus is grades K-4 and I only dabbled in 5+ (because I found out the SAT is using problem solving skills and cognitive skills to improve their test), this theory will have to be explored later.
I'm interested more in training the brain at ages 5-9 to handle info and teaching higher order skills, but I can assure you that I've done as much information cramming as anyone into my kids' brains.
#4 Is 99% attainable for long periods of time with a normal kid?
Every 4 years the bar moves and the list deepens. Cognitive skills training at age 5 only buys so much for a 9 year old, especially if he hasn't practiced his skills for 5 years. So far, my plan is simple. Find out what the skills are and what the level is, and provide suitable learning material. Test prep is a great opportunity for this effort.
But at some point the only people who really need 99% in anything are those who really want it. When I get to the point where I'm helping with sign ups for AP Calculus, AP History, AP Literature, AP Civics, Orchestra, Play Practice, Cross Country and I don't know what else, we're going to have a goals planning session and make some choices. But that is many years away and I've changed my mind before. If I'm dropping $250,000 for college, we're back to 99% and this is not negotiable.
#5 Tests
There is a really great article here summarizing the NCBI's grouping of skills. What I find most interesting is the discussion of problem solving on the PISA, that international test on which US students deliver a spectacularly inept performance. The paper also evaluates graduate placement exams. Cognitive skills and tests go hand-in-hand. A cynical parent might be motivated by the need for their child to pass tests. A benevolent parent wants their child to have the same skills that test makers use to predict success.
Types of Research
Research comes in 2 flavors. The first half is totally made up intelligence crap that provides a lot of useful sounding words, and the second approach is watching kids work, succeed and fail and applying these words to what is really happening. I think you know what side I'm on.
There is a third branch of research and that is super secret GAT tests which are good at predicting academic outcomes, and to some extent, life outcomes. I spent quite a bit of time gleaning cognitive skills from this area and apply it to problem solving skills. Angela Duckworth's Grit research almost fits into this category but she made it publicly available from the get-go and is the fourth inductee in the Competitive Parent Hall of Fame behind Jo Boaler, Susan Wise Bauer, and George Poyla. (David Lohman is on the fence.) The difference between cognitive skills and GAT tests is that GAT tests use a much longer list called "cognitive abilities". I note these on the chart below.
Blooms Taxonomy
I was hoping to start here, but this is a depricated construct.
Poyla's Problem Solving Method (1945)
This is pretty close to my approach to cognitive skills. I have lined up cognitive skills to the problem solving steps and this is my focus for teaching. If a problem solving step requires a cognitive skill that isn't there, we work on it.
Some math workbooks start with a very detailed section on problem solving strategies. I was very excited about this section until my son applied a strategy to successfully solve a problem without knowing what he was doing, then I ripped the section out of his book. I've noticed these books work step-by-step with scaffolding. I've talked to parents who's kids used these books and struggle to get a high score on the COGAT. I'm not using them anymore or recommending them.
Critical Thinking
I think there is a big overlap between Critical Thinking skills, Cognitive Skills, and Problem Solving Skills. Any 2 should almost define the complete system with the addition of Working Memory. Working Memory is a necessary prerequisite to using these skills.
The critical thinking list strikes me as overly detailedThese appear to be things derived from lower order cognitive skills. For example, a critical thinking skill is "observing similarities and differences" which should follow from the higher order Problem Solving skill would be "stare at the problem until you understand it". I think the COGAT test agrees with me but I'm not sure what they would call that skill. Maybe "ability to compare things", maybe "see details in things".
The List
I'm going to take Poyla, a critical thinking list, and an Executive Functioning list and organize it into my biased construct with cognitive skills. Finding a list of cognitive skills is impossible so I created an unathoritative list from the lists available that I think appear on GAT tests. There is a great list on SharpBrains.com that looks like it is reading-comprehension-centric but I don't use it.
My interpretation of Poyla is over simplified so that it applies to 5-9 year old children. I would have a different presentation for different age groups.
I'm surprised that no one has done this before (curse you cognitive researchers) but if researchers had been on the ball for the last few decades I wouldn't have started this blog, my writing skills would stink even worse than they do, and my slightly above average children would never have had a shot at cheating their way into a GAT program nor succeeding in it.
There is a much looser connection with Grit than I would like. Duckworth's research is on a longer term connection between work and fortitude and outcome. I need a really short term connection, like the time it takes to sit for a test. The Grit column has weak associations so I didn't include Grit in the chart except as notes under Executive Functioning.
It wasn't until I sat down to do this comparison that I realized just how bad the list of cognitive and critical thinking skills are. They are either too narrow, incomplete, or more commonly too broad to base a curriculum on. I have found that problem solving skills are well defined and concrete, easy to diagnose and best of all, make a great approach to beating a GAT test or getting an A in a course. For this exercise, in the back of my mind I'm thinking about GAT tests and how different problems would use what skill, and this approach is tailoring my framework.
Note that the "Understand the Problem", "Solution Strategy", and "Execute Strategy" sections have such a high degree of overlap that many of the activities within either section could easily happen in the other. In fact, for most children the first 3 steps are a blur of activity. For example, on a pattern problem does pattern recognition happen when understanding the problem or solving it? Part of the problem is that cognitive skills tests have well defined rules and the solution strategy is almost a foregone conclusion. The example tells the child exactly what to do. The other problem is that children are not properly trained to spend most of their time analyzing the problem and usually just jump in to solve it - prematurely I might add.
The solution strategy section is the biggest gap for Critical Thinking and Cognitive Skills literature. The Poyla list has an important set of learned skills. Experiments with EF programs proved that kids with EF training do much better on GAT tests (by a ridiculous margin). Conversely, Problem Solving skills don't really define "Understand the Problem", yet cognitive skills break this section down. This difference is most pronounced on non-verbal tests. After 1st grade, all tests have a greater portion of verbal and quantitative questions.
I think the main difference is that Poyla's list as I represent it doesn't care what the problem is and is silent on the assumed skill set. In practice, it is usually geometry theorems. GAT tests have a well defined set of skills for problem solving, but don't care about problem strategies because the problem strategy is pre-defined. For GAT tests, the most important competitive advantage comes from the first and last sections - understanding the problem and checking the answer. I know that from coaching. Anyone can learn to rotate triangles. It's much harder to teach patience,carefulness, and diligence.
There is a list of critical thinking skills that can be found here that looks like it applies almost 100% to reading comprehension questions. My list primarily applies to all other question types but not reading comprehension. Ironically, I feel strongly that reading comprehension is a great practice for non-verbal and cognitive skills tests. The two reasons are working memory and understanding the problem, which combine to form about 65% of the magic. Reading comprehension is great practice for both skills.
This brings me back to my goal of Test Prep Math and why I'm spending my week off working on it. My working theory is that a child who is patient (understand the question) and careful (check the answer) and diligent (tries again) will have an advantage both in school and on any test over a child who does 1,000's of figure matrices or arithmetic problems. In fact, hurrying through a worksheet with lots of problems may teach speed over patience, carelessness, and boredom. Working memory is essential and working memory is not exercised with fast, easy problems. I'm closing the gap.
For first grade, this is what I have in mind. Take a figure matrix. Throw out the format, because it's copyrighted. Come up with something that has the same cognitive objectives but is so convoluted that when the child asks "Did I get the right answer?" the parent has to spend 15 minutes staring at it to see if the child was correct. I'll work on it this summer.
For the last few years I've been happily working with a framework that seemed so obvious to me. I am double checking and it before I get to obvious we have to wade through a dark and murky swamp.
The Big Picture
#1 Cognitive Skills + Interest + Will To Do It = academic and life success.
The aspect of teaching cognitive skills without destroying interest or crushing will is called coaching. If you google my blog and the terms "crying" or "whining" I'm referring to coaching. The last post is half on an article on this concept, and a discussion of coaching will complete the picture that this article begins. (I'm going to be adding to the coaching article over time and will warn everyone when it is complete.)
#2 Cognitive Skills + Interpersonal Skills (e.g., empathy) + Intrapersonal Skills (e.g. self control) = The Full Skill Set
If you child is missing one of these skill sets there is work to be done. I think band and Cub Scouts/Girl Scouts are really good activities for little kids to address the last 2 skill sets. Executive Functioning programs are good for preK training if you have $30,000 to spend on pre school; if not, projects, crafts and art help. Music in general is great for the first and last skill set.
I don't think team sports at young ages are good at all for any of these skill sets.
#3 The Classical Education
For a really inspiring discussion of the classical education, read the first 30 pages of Susan Wise Bauer's The Well-Trained Mind.
Here is my butchered summary: Grades 1-4: Cram as much information into their brains as possible. Grades 4-8: Think analytically. Grades 8-12: Think logically, and grades 12-16 (yes, there is overlap in grades) I haven't gotten this far yet.
If you pair this with Piaget's Theory of Cognitive Development, then you can see that there are things expected of older children that would be impossible for younger children. This is obvious. What is not obvious is whether or not later skills like logic need new cognitive skills or just refinement of an underlying skills.
Since my focus is grades K-4 and I only dabbled in 5+ (because I found out the SAT is using problem solving skills and cognitive skills to improve their test), this theory will have to be explored later.
I'm interested more in training the brain at ages 5-9 to handle info and teaching higher order skills, but I can assure you that I've done as much information cramming as anyone into my kids' brains.
#4 Is 99% attainable for long periods of time with a normal kid?
Every 4 years the bar moves and the list deepens. Cognitive skills training at age 5 only buys so much for a 9 year old, especially if he hasn't practiced his skills for 5 years. So far, my plan is simple. Find out what the skills are and what the level is, and provide suitable learning material. Test prep is a great opportunity for this effort.
But at some point the only people who really need 99% in anything are those who really want it. When I get to the point where I'm helping with sign ups for AP Calculus, AP History, AP Literature, AP Civics, Orchestra, Play Practice, Cross Country and I don't know what else, we're going to have a goals planning session and make some choices. But that is many years away and I've changed my mind before. If I'm dropping $250,000 for college, we're back to 99% and this is not negotiable.
#5 Tests
There is a really great article here summarizing the NCBI's grouping of skills. What I find most interesting is the discussion of problem solving on the PISA, that international test on which US students deliver a spectacularly inept performance. The paper also evaluates graduate placement exams. Cognitive skills and tests go hand-in-hand. A cynical parent might be motivated by the need for their child to pass tests. A benevolent parent wants their child to have the same skills that test makers use to predict success.
Types of Research
Research comes in 2 flavors. The first half is totally made up intelligence crap that provides a lot of useful sounding words, and the second approach is watching kids work, succeed and fail and applying these words to what is really happening. I think you know what side I'm on.
There is a third branch of research and that is super secret GAT tests which are good at predicting academic outcomes, and to some extent, life outcomes. I spent quite a bit of time gleaning cognitive skills from this area and apply it to problem solving skills. Angela Duckworth's Grit research almost fits into this category but she made it publicly available from the get-go and is the fourth inductee in the Competitive Parent Hall of Fame behind Jo Boaler, Susan Wise Bauer, and George Poyla. (David Lohman is on the fence.) The difference between cognitive skills and GAT tests is that GAT tests use a much longer list called "cognitive abilities". I note these on the chart below.
Blooms Taxonomy
I was hoping to start here, but this is a depricated construct.
Poyla's Problem Solving Method (1945)
This is pretty close to my approach to cognitive skills. I have lined up cognitive skills to the problem solving steps and this is my focus for teaching. If a problem solving step requires a cognitive skill that isn't there, we work on it.
Some math workbooks start with a very detailed section on problem solving strategies. I was very excited about this section until my son applied a strategy to successfully solve a problem without knowing what he was doing, then I ripped the section out of his book. I've noticed these books work step-by-step with scaffolding. I've talked to parents who's kids used these books and struggle to get a high score on the COGAT. I'm not using them anymore or recommending them.
Critical Thinking
I think there is a big overlap between Critical Thinking skills, Cognitive Skills, and Problem Solving Skills. Any 2 should almost define the complete system with the addition of Working Memory. Working Memory is a necessary prerequisite to using these skills.
The critical thinking list strikes me as overly detailedThese appear to be things derived from lower order cognitive skills. For example, a critical thinking skill is "observing similarities and differences" which should follow from the higher order Problem Solving skill would be "stare at the problem until you understand it". I think the COGAT test agrees with me but I'm not sure what they would call that skill. Maybe "ability to compare things", maybe "see details in things".
The List
I'm going to take Poyla, a critical thinking list, and an Executive Functioning list and organize it into my biased construct with cognitive skills. Finding a list of cognitive skills is impossible so I created an unathoritative list from the lists available that I think appear on GAT tests. There is a great list on SharpBrains.com that looks like it is reading-comprehension-centric but I don't use it.
My interpretation of Poyla is over simplified so that it applies to 5-9 year old children. I would have a different presentation for different age groups.
I'm surprised that no one has done this before (curse you cognitive researchers) but if researchers had been on the ball for the last few decades I wouldn't have started this blog, my writing skills would stink even worse than they do, and my slightly above average children would never have had a shot at cheating their way into a GAT program nor succeeding in it.
There is a much looser connection with Grit than I would like. Duckworth's research is on a longer term connection between work and fortitude and outcome. I need a really short term connection, like the time it takes to sit for a test. The Grit column has weak associations so I didn't include Grit in the chart except as notes under Executive Functioning.
It wasn't until I sat down to do this comparison that I realized just how bad the list of cognitive and critical thinking skills are. They are either too narrow, incomplete, or more commonly too broad to base a curriculum on. I have found that problem solving skills are well defined and concrete, easy to diagnose and best of all, make a great approach to beating a GAT test or getting an A in a course. For this exercise, in the back of my mind I'm thinking about GAT tests and how different problems would use what skill, and this approach is tailoring my framework.
Note that the "Understand the Problem", "Solution Strategy", and "Execute Strategy" sections have such a high degree of overlap that many of the activities within either section could easily happen in the other. In fact, for most children the first 3 steps are a blur of activity. For example, on a pattern problem does pattern recognition happen when understanding the problem or solving it? Part of the problem is that cognitive skills tests have well defined rules and the solution strategy is almost a foregone conclusion. The example tells the child exactly what to do. The other problem is that children are not properly trained to spend most of their time analyzing the problem and usually just jump in to solve it - prematurely I might add.
| Poyla Problem Solving | Critical Thinking | Cognitive Skills | Executive Functions |
|---|---|---|---|
Understand the Problem
|
Analyzing Information Seeking Context |
Visual Spacial Processing Working memory Attention to Detail Identify Patters Identify Similarities/ Differences Inductive and Deductive Reasoning Inference Resolve ambiguity (GAT) |
Ignore Distractions Perception Flexibility (thinking modes) Pattern Recognition |
Solution Strategy
|
Problem Solving Decomposition Algorithms |
Working Memory Problem Decomposition Apply examples (GAT) Eliminate answers (GAT) |
Problem Solving Decision Making Planning Apply rules Sequencing (Project Management) Set Goals (Grit and EF) |
Execute the Strategy
|
Classification Analogous reasoning Similarities/ Differences Applying rules Predicting Transforming Reasoning Generalize |
Working Memory Meta Cognition Spacial Reasoning Analogous reasoning Mentally fold (GAT) |
Self Control Overcome setbacks (Grit) Maintain Interest (Grit) Diligence (Grit) |
Check the Answer
|
Evaluation | Rethink assumptions when answer isn't ther (GAT) |
Finish the Job (Grit) |
The solution strategy section is the biggest gap for Critical Thinking and Cognitive Skills literature. The Poyla list has an important set of learned skills. Experiments with EF programs proved that kids with EF training do much better on GAT tests (by a ridiculous margin). Conversely, Problem Solving skills don't really define "Understand the Problem", yet cognitive skills break this section down. This difference is most pronounced on non-verbal tests. After 1st grade, all tests have a greater portion of verbal and quantitative questions.
I think the main difference is that Poyla's list as I represent it doesn't care what the problem is and is silent on the assumed skill set. In practice, it is usually geometry theorems. GAT tests have a well defined set of skills for problem solving, but don't care about problem strategies because the problem strategy is pre-defined. For GAT tests, the most important competitive advantage comes from the first and last sections - understanding the problem and checking the answer. I know that from coaching. Anyone can learn to rotate triangles. It's much harder to teach patience,carefulness, and diligence.
There is a list of critical thinking skills that can be found here that looks like it applies almost 100% to reading comprehension questions. My list primarily applies to all other question types but not reading comprehension. Ironically, I feel strongly that reading comprehension is a great practice for non-verbal and cognitive skills tests. The two reasons are working memory and understanding the problem, which combine to form about 65% of the magic. Reading comprehension is great practice for both skills.
This brings me back to my goal of Test Prep Math and why I'm spending my week off working on it. My working theory is that a child who is patient (understand the question) and careful (check the answer) and diligent (tries again) will have an advantage both in school and on any test over a child who does 1,000's of figure matrices or arithmetic problems. In fact, hurrying through a worksheet with lots of problems may teach speed over patience, carelessness, and boredom. Working memory is essential and working memory is not exercised with fast, easy problems. I'm closing the gap.
For first grade, this is what I have in mind. Take a figure matrix. Throw out the format, because it's copyrighted. Come up with something that has the same cognitive objectives but is so convoluted that when the child asks "Did I get the right answer?" the parent has to spend 15 minutes staring at it to see if the child was correct. I'll work on it this summer.
Saturday, October 17, 2015
Impact Coaching
My kids woke me up this morning at 6 am which would have been great if I didn't stay up late last night reading a book I couldn't put down. One of the TWO children's librarians at the library at the end of our block recommended it.
As you know from previous articles, reading for a boy between the ages of 8 and 10 is a big challenge. We managed to survive on reading junk food. As a competitive parent, however, I'm feeling nervous about middle school, especially the big testing year. One Saturday morning, recently, my 2nd grader and I were loudly searching the children's shelves when across the room came the response from the children's librarian. I thought she was a student. Instead, she has read every book published for kids and teens and we left with a stack of good books.
A week later, we went a bit earlier to the library and found a different children's librarian, again appearing to be just out of grade school, albeit with ear rings and tattoos. I described my older son in detail and he recommended some of his favorite books. He warned me that some of them were for teens. Therefore I am reading these ahead of time to ensure the content is appropriate (my values don't match most authors or screen writers). So far each book is better than the last.
My reading coaches are at the end of the block.
On to the GAT test. I like to leave my best advice at the end of my article to weed out impatient readers. Impatience is taught by parents and impatient kids are at a distinct disadvantage on the test. Perhaps these parents are too busy because of all the things they have to do, things which they really need to eliminate, starting with their cell phones and social media pages. Since this whole articles is important, I thought I'd start it after a boring preamble.
When I started my quest, all of the material I found specifically on the GAT test was prepared by people who believe that giftedness is some how hereditary or a gift. Like it magically happens. I can't take advice from people so stupid. I felt like a lone survivor on a raft in a sea of morons. I had only one person on this blog challenge the law that intelligence is 0% genetic, but just in case I developed overwhelming crushing logic to silence those who need a little help thinking more clearly.
A few years later, I know exactly which books do what and can lay out a program for 12, 6 and 3 months for anyone. Suppose this stack arrives in the mail. What do you do next? The problem for most parents is that they have no experience "teaching" or "coaching" a child through this type of material. Worse, you only get one shot per child and you can't blow it in some cases. In other cases, you can try every year.
I've been putting bits and pieces of coaching advice in my articles over the years. I want to highlight the starting elements in this article.
The Books
Unless it's crunch time, the books I use cover the full range of skills and skill levels. I always keep easy and hard, academic and skills based material for both language and math. For lack of time, vocabulary comes in one flavor - slightly hard. On 4 nights a week and during a double or triple session on Saturday morning, the material and my child's attention span and energy level determine what will get done.
In most cases, I encounter a problem with the material that there are only 2 types. The first type is too easy, and the second type is way too hard. The test prep material is too easy unless you start at age 4, but it has a different role. Since we have a definite time limit, and this test is all about thinking skills, we're going to use the material that is too hard. When I start this type of program with a kid for the first time, I usually just jump in with way toi hard material and 6 months of hell later use a balance. I call this Catch Up.
The Chart
The biggest problem with the test prep program is that it has a definitive time limit. The goal is to cram as much skill into your child's brain as possible before the test. You might only get about 20 good minutes a day. Your child might start out taking 20 minutes just to answer the first question. This can be unnerving for a parent.
My solution is to create a poster. Across the top, I draw a time line ending with the test date. Down the left side, I list all of the workbooks that I am going to use and other activities like reading/read-to and forced fun. In the row for each workbook, I'll just write all of the page numbers sequentially in the space allowed. For something like Building Thinking skills or a COGAT test prep book, where we jump around a lot, each section gets its own row, or I draw boxes around the page numbers and mark the section.
As we go, I cross out page numbers. I write check marks for things like forced fun (HAVE 20 MINUTES OF FUN, DARN IT!)
As the weeks go by, I can see how quickly my child is going and this calms my nerves. Sometimes we have to adjust the material, which I can do because I'm carefully gauging progress. Sometimes I notice that we are going to fast and will run out. Usually I just notice what started out as painfully slow becomes much faster over time.
The Process
This topic is going to be a series of articles on its own or you have to dig through the whole mess of my blog to find tips.
For starters, the process I assume is a parent sitting with the child coaching the whole time, checking the work. In my experience, it takes a long time, maybe 6 to 12 months, until the child can work independently. This is probably the biggest single benefit of my mission - redirecting parents from a myriad of distractions back to one-on-one work with their children (i.e., throw away your cell phone.).
The main benefit, over and above an increase in academic skills, is a social secure and socially effective child. I can watch a group of children and spot a child who spends a lot of time with his parents in a matter of seconds. Try it some time.
Next, a child working on one really hard question for 45 minutes is very powerful, doing 30 worksheet questions in 20 minutes is practically useless.
Finally, a coach is a coach. Watch a baseball manager (go Cubs!) or a football coach standing on the side lines. What do they actually do in terms of throwing balls or catching them? Nothing. In your case, this means not explaining things and not figuring things out for your child. Just keep score and ask lots of questions. Be like Yoda. Let the child fail. Don't make it painful. Don't pressure your child.
I reserve the right to add to this article, but the cryptic coaching proverbs will end up being future articles. For now, this summarizes my mission:
As you know from previous articles, reading for a boy between the ages of 8 and 10 is a big challenge. We managed to survive on reading junk food. As a competitive parent, however, I'm feeling nervous about middle school, especially the big testing year. One Saturday morning, recently, my 2nd grader and I were loudly searching the children's shelves when across the room came the response from the children's librarian. I thought she was a student. Instead, she has read every book published for kids and teens and we left with a stack of good books.
A week later, we went a bit earlier to the library and found a different children's librarian, again appearing to be just out of grade school, albeit with ear rings and tattoos. I described my older son in detail and he recommended some of his favorite books. He warned me that some of them were for teens. Therefore I am reading these ahead of time to ensure the content is appropriate (my values don't match most authors or screen writers). So far each book is better than the last.
My reading coaches are at the end of the block.
On to the GAT test. I like to leave my best advice at the end of my article to weed out impatient readers. Impatience is taught by parents and impatient kids are at a distinct disadvantage on the test. Perhaps these parents are too busy because of all the things they have to do, things which they really need to eliminate, starting with their cell phones and social media pages. Since this whole articles is important, I thought I'd start it after a boring preamble.
When I started my quest, all of the material I found specifically on the GAT test was prepared by people who believe that giftedness is some how hereditary or a gift. Like it magically happens. I can't take advice from people so stupid. I felt like a lone survivor on a raft in a sea of morons. I had only one person on this blog challenge the law that intelligence is 0% genetic, but just in case I developed overwhelming crushing logic to silence those who need a little help thinking more clearly.
A few years later, I know exactly which books do what and can lay out a program for 12, 6 and 3 months for anyone. Suppose this stack arrives in the mail. What do you do next? The problem for most parents is that they have no experience "teaching" or "coaching" a child through this type of material. Worse, you only get one shot per child and you can't blow it in some cases. In other cases, you can try every year.
I've been putting bits and pieces of coaching advice in my articles over the years. I want to highlight the starting elements in this article.
The Books
Unless it's crunch time, the books I use cover the full range of skills and skill levels. I always keep easy and hard, academic and skills based material for both language and math. For lack of time, vocabulary comes in one flavor - slightly hard. On 4 nights a week and during a double or triple session on Saturday morning, the material and my child's attention span and energy level determine what will get done.
In most cases, I encounter a problem with the material that there are only 2 types. The first type is too easy, and the second type is way too hard. The test prep material is too easy unless you start at age 4, but it has a different role. Since we have a definite time limit, and this test is all about thinking skills, we're going to use the material that is too hard. When I start this type of program with a kid for the first time, I usually just jump in with way toi hard material and 6 months of hell later use a balance. I call this Catch Up.
The Chart
The biggest problem with the test prep program is that it has a definitive time limit. The goal is to cram as much skill into your child's brain as possible before the test. You might only get about 20 good minutes a day. Your child might start out taking 20 minutes just to answer the first question. This can be unnerving for a parent.
My solution is to create a poster. Across the top, I draw a time line ending with the test date. Down the left side, I list all of the workbooks that I am going to use and other activities like reading/read-to and forced fun. In the row for each workbook, I'll just write all of the page numbers sequentially in the space allowed. For something like Building Thinking skills or a COGAT test prep book, where we jump around a lot, each section gets its own row, or I draw boxes around the page numbers and mark the section.
As we go, I cross out page numbers. I write check marks for things like forced fun (HAVE 20 MINUTES OF FUN, DARN IT!)
As the weeks go by, I can see how quickly my child is going and this calms my nerves. Sometimes we have to adjust the material, which I can do because I'm carefully gauging progress. Sometimes I notice that we are going to fast and will run out. Usually I just notice what started out as painfully slow becomes much faster over time.
The Process
This topic is going to be a series of articles on its own or you have to dig through the whole mess of my blog to find tips.
For starters, the process I assume is a parent sitting with the child coaching the whole time, checking the work. In my experience, it takes a long time, maybe 6 to 12 months, until the child can work independently. This is probably the biggest single benefit of my mission - redirecting parents from a myriad of distractions back to one-on-one work with their children (i.e., throw away your cell phone.).
The main benefit, over and above an increase in academic skills, is a social secure and socially effective child. I can watch a group of children and spot a child who spends a lot of time with his parents in a matter of seconds. Try it some time.
Next, a child working on one really hard question for 45 minutes is very powerful, doing 30 worksheet questions in 20 minutes is practically useless.
Finally, a coach is a coach. Watch a baseball manager (go Cubs!) or a football coach standing on the side lines. What do they actually do in terms of throwing balls or catching them? Nothing. In your case, this means not explaining things and not figuring things out for your child. Just keep score and ask lots of questions. Be like Yoda. Let the child fail. Don't make it painful. Don't pressure your child.
I reserve the right to add to this article, but the cryptic coaching proverbs will end up being future articles. For now, this summarizes my mission:
- You have a duty to build the cognitive skills of your child. It's not going to happen in school.
- There is material out there that you need.
- You have to pace yourself.
- You have to invest lots of one-on-one time with your child.
Once you subscribe to this approach, and many, many readers have already, you are on the way to a successful child through 4th grade. After that, you have to do it all over again at a different level with different goals.
Monday, October 12, 2015
Oragami Jazz Festival
Last Friday night, I had to baby sit at my arch rival's house. Conveniently, his name is Arch Rival. His wife Nem was busy and he had to speak to a preschool program about his children's gifted program. In Chicago, we call GAT "options".
I sat there for an hour in the family room while the kids slept. This room looks like a library only with more books than could fit in a library. Archie goes to 2nd hand stores and buys boxes of children's books. But that's not the worst part. There was a book on tape coming from the room of the 2 girls. It was audible when I arrived a few minutes before their official bed at 8 pm, and it didn't end until about 8:40 pm.. Are you kidding me? Books on tape during bed time? Curse you Arch.
Saturday morning, I went to the library with my youngest and we checked out stacks of books on tape. After a few hours of listening, my kids and I decided that this was not going to be our thing.
It's hard to compete with the Rivals. They don't follow my academic regimen. Instead they become super readers and eventually their kids get into gifted programs. Nem teaches high school math so I am going to have a hard time competing on that front. The kids are super nice and socially well adjusted. And we both do music.
Music is one of those activities like reading wherein if you do it well, everything else will follow, everything else being success academically and otherwise. My oldest and I practice together every day, so he gets a daily lesson if needed. The youngest is going to join this routine when he starts band, but for now he is expected to teach himself piano.
For my wife's birthday, we took the kids to the Jazz Showcase to hear a Tammy McCann with the Chicago Jazz Orchestra. On Sunday's at 4 pm, the Jazz Showcase has a 60 minute performance and kids get in for free. The performance was amazing and I'm glad I live in Chicago. We went so that our kids could see a big band. I didn't expect Tammy McCann to be so darn good. (Normally, I would have invited the 5th grade Rival because he's a friend of my son's, but this was a birthday outing with dinner to follow. There was a 3 piece jazz band playing at dinner, by the way.)
Here is a picture of the Test Prep Pioneer and his brother Test Prep Ninja with Tammy. We almost always talk to the performers after each show. In this case, it was hard not to. Tammy was extremely bright and her extremely bright children were there. I wanted to interview them at length, but since that would be totally inappropriate, I had to settle for confirming the fact that her kids are very friendly and articulate. Her husband was in attendance, and from the stage she announced that he is running for a judge position. If we lived in Beverley, they would make great rivals, but we don't, so I'll just admire the family from afar.
During the show, my kids replicated the stage with origami. The oldest is on the left, and always liked origami. The youngest is on the right, and looks a lot bigger than he really is because he is closer to the camera. He went to COGAT folding question school so can fold almost as well as his brother. If you look closely, you can see Origami Tammy next to the piano.
This doesn't fully address my problem with the Rivals, but it's a start.
I sat there for an hour in the family room while the kids slept. This room looks like a library only with more books than could fit in a library. Archie goes to 2nd hand stores and buys boxes of children's books. But that's not the worst part. There was a book on tape coming from the room of the 2 girls. It was audible when I arrived a few minutes before their official bed at 8 pm, and it didn't end until about 8:40 pm.. Are you kidding me? Books on tape during bed time? Curse you Arch.
Saturday morning, I went to the library with my youngest and we checked out stacks of books on tape. After a few hours of listening, my kids and I decided that this was not going to be our thing.
It's hard to compete with the Rivals. They don't follow my academic regimen. Instead they become super readers and eventually their kids get into gifted programs. Nem teaches high school math so I am going to have a hard time competing on that front. The kids are super nice and socially well adjusted. And we both do music.
Music is one of those activities like reading wherein if you do it well, everything else will follow, everything else being success academically and otherwise. My oldest and I practice together every day, so he gets a daily lesson if needed. The youngest is going to join this routine when he starts band, but for now he is expected to teach himself piano.
For my wife's birthday, we took the kids to the Jazz Showcase to hear a Tammy McCann with the Chicago Jazz Orchestra. On Sunday's at 4 pm, the Jazz Showcase has a 60 minute performance and kids get in for free. The performance was amazing and I'm glad I live in Chicago. We went so that our kids could see a big band. I didn't expect Tammy McCann to be so darn good. (Normally, I would have invited the 5th grade Rival because he's a friend of my son's, but this was a birthday outing with dinner to follow. There was a 3 piece jazz band playing at dinner, by the way.)
Here is a picture of the Test Prep Pioneer and his brother Test Prep Ninja with Tammy. We almost always talk to the performers after each show. In this case, it was hard not to. Tammy was extremely bright and her extremely bright children were there. I wanted to interview them at length, but since that would be totally inappropriate, I had to settle for confirming the fact that her kids are very friendly and articulate. Her husband was in attendance, and from the stage she announced that he is running for a judge position. If we lived in Beverley, they would make great rivals, but we don't, so I'll just admire the family from afar.
During the show, my kids replicated the stage with origami. The oldest is on the left, and always liked origami. The youngest is on the right, and looks a lot bigger than he really is because he is closer to the camera. He went to COGAT folding question school so can fold almost as well as his brother. If you look closely, you can see Origami Tammy next to the piano.
This doesn't fully address my problem with the Rivals, but it's a start.
Thursday, October 1, 2015
Test Prep Math Level 3
August 2017 Update - This article is now a bit dated, but I am reluctant to delete it. Test Prep Math Level 2 and Test Prep Math Level 3 are big hits. Both are now in their 3rd edition, and both have the addition of a quantitative section and a visual spatial section that followed the same successful formula as the word problems. I had all of this material but thought then and now that the word problems would pay off the most down the road, so this is where I started.
Test Prep Math Level 3 is making it's debut.
I created this book because after buying and trying dozens of workbooks from 1st through 5th grade, I've been really disappointed. There are 3 primary groups of math workbooks: one group is too easy, one group overdoes computation and calculations with no learning or thinking involved, and the third group goes into advanced math. My kids don't care about number theory at a young age. The GAT practice test books are great for their role - to review the format and find out before the test if your child is going to get confused and blow it - but these books aren't good at teaching skills and are really easy in my opinion. By age five, my second child completed all of the GAT test prep books through 6th grade and I don't think we learned anything. I didn't even use them with my first child and just stuck with more difficult material that I created.
I spent 5 years researching GAT tests, 2 of it trying to reverse engineer them. You'll see in my articles that I slowly built a list of skills and abilities that these tests were trying to measure, and then focused on teach them. The problems in Test Prep Math are designed to teach these skills.
I'm getting questions about whether or not younger kids could use Level 3. Since the "View Inside" isn't available yet for the book, I'm going to show you sample problems and describe how they unfold, and then comment about Level 2.
I expect the child to do the arithmetic in their brain, even though that might take a few tries to get it correct. There is a 5 page coaching guide about how to get through this book, and in the solutions I include commentary on harder or unusual questions.
Here is the first problem. I tried to make it as easy as possible simply to introduce the thinking that is going to be required and encourage the child to do the problem mentally. This seems easy enough, but I'm surprised how many bright kids get to the end of the question and forget what was asked.
Dragonflies and damselflies were sitting on a boat. There were 5 dragonflies and 4 damselflies. 4 more dragonflies landed on the boat. 8 more damselflies landed on the boat. How many more damselflies are on this boat than dragonflies?
Bonus Question: A flock of birds comes by and ate half of the damselflies. How does this change your answer?
Notice that the child has to solve 3 equations. The pattern of matrices problems is 1 and 1/2 equations (solve one equation and apply the delta to another number), so I doubled it to be on the safe side. There is a new word in the problem that you'll have to google. Then for this question, there is a bonus question that requires tapping the working memory once again.
Question 2 has the wrong answer! Arrgh. I'll have another edition out to fix it in 2 weeks. I undermined myself with a last minute edit to the question. Fortunately, all of the solutions show the equations so mistakes are easy to spot. Ironically, since I've been making my own material, my kids and I have had lots of questions and/or solutions that didn't work They have a whole different approach to math, but I wouldn't intentionally put this in a book.
During the next 40 or so questions, the characters are introduced and the plot slowly unfolds (as much of a plot as I could muster given that I'm working with as much space as a haiku). At about the middle of the book, the questions look like this:
In the center of Metroville, there is a super villain named Destructovil breaking into the Metroville bank. Rubberband girl got a distress call on her cell phone, but she is on the south end of the city in a train station. There is a train leaving at 3:00 pm that will take her to the Metroville bank. The train takes 12 minutes to go from the train station to the bank. She has to wait 4 minutes for the train. Speedy Man is in the next town over, but he can get to the bank in 8 minutes because he is Speedy Man. First, he needs to finish his cup of lemonade because he's too thirsty to be speedy. That will take 7 minutes. It is a very large cup of lemonade. Destructovil's getaway car is coming to pick him up at exactly 3:14 pm. Who will save the bank?
Bonus Question: Who is Rubberband girl?
My 10 year old told me "your problems aren't lame." I think that was a compliment.
If you had been doing all of the problems, you would be able to figure out who Rubberband girl is. If not, you have to refer back to a previous problem (officially an academic skill which I call for repeatedly) to figure out. Note that this is not a question a child can read once or twice and then solve. I also use time a lot because it requires an extra degree of thinking to do the arithmetic.
By the end of the book the questions fill the page and become even more convoluted and goofy (all with proper grammar except when the pirate character talks.) At this point, we're basically in math-reading-comprehension space, which I invented. I'll write a whole article on reading comprehension because I'm becoming more and more convinced that it is a pillar of success on a GAT test, and by way of the GAT objectives, to a strong academic career. As the book progresses, I start to move on to more advanced skills and because of that, some of the questions look like brain teasers, but they aren't, because everything can be derived logically after a few days of debate.
I'm working on Level 2 for younger kids which removes the need to read questions over and over again to understand what the problem is. I'm using a math abstraction that I invented to make things really taxing on the brain. I think some kids will find Level 2 harder than Level 3 and vica versa, but in both cases I'm seeing results and am pleased. Level 2 will take a few months to finish. By next year, I'm going to introduce Level 1 which I can only describe as diabolical. Level 1 was in the works since the beginning, but 3rd grade is the biggest gap for people right now so I started there. Then if I'm not completely exhausted, I'm going to work on Level 4 which teaches the Most Powerful Math Skill ever, which I can't find anywhere in any elementary aged book, but which we routinely use to solve anything.
So if this sounds like something that fills a need in your At Home Schooling or test prep, give it a try and let me know how it goes. Provided I don't sell more than 12 copies (which is going to be the case unless I find the time to do any marketing), I'll respond quickly.
Test Prep Math Level 3 is making it's debut.
I created this book because after buying and trying dozens of workbooks from 1st through 5th grade, I've been really disappointed. There are 3 primary groups of math workbooks: one group is too easy, one group overdoes computation and calculations with no learning or thinking involved, and the third group goes into advanced math. My kids don't care about number theory at a young age. The GAT practice test books are great for their role - to review the format and find out before the test if your child is going to get confused and blow it - but these books aren't good at teaching skills and are really easy in my opinion. By age five, my second child completed all of the GAT test prep books through 6th grade and I don't think we learned anything. I didn't even use them with my first child and just stuck with more difficult material that I created.
I spent 5 years researching GAT tests, 2 of it trying to reverse engineer them. You'll see in my articles that I slowly built a list of skills and abilities that these tests were trying to measure, and then focused on teach them. The problems in Test Prep Math are designed to teach these skills.
I'm getting questions about whether or not younger kids could use Level 3. Since the "View Inside" isn't available yet for the book, I'm going to show you sample problems and describe how they unfold, and then comment about Level 2.
I expect the child to do the arithmetic in their brain, even though that might take a few tries to get it correct. There is a 5 page coaching guide about how to get through this book, and in the solutions I include commentary on harder or unusual questions.
Here is the first problem. I tried to make it as easy as possible simply to introduce the thinking that is going to be required and encourage the child to do the problem mentally. This seems easy enough, but I'm surprised how many bright kids get to the end of the question and forget what was asked.
Dragonflies and damselflies were sitting on a boat. There were 5 dragonflies and 4 damselflies. 4 more dragonflies landed on the boat. 8 more damselflies landed on the boat. How many more damselflies are on this boat than dragonflies?
Bonus Question: A flock of birds comes by and ate half of the damselflies. How does this change your answer?
Notice that the child has to solve 3 equations. The pattern of matrices problems is 1 and 1/2 equations (solve one equation and apply the delta to another number), so I doubled it to be on the safe side. There is a new word in the problem that you'll have to google. Then for this question, there is a bonus question that requires tapping the working memory once again.
Question 2 has the wrong answer! Arrgh. I'll have another edition out to fix it in 2 weeks. I undermined myself with a last minute edit to the question. Fortunately, all of the solutions show the equations so mistakes are easy to spot. Ironically, since I've been making my own material, my kids and I have had lots of questions and/or solutions that didn't work They have a whole different approach to math, but I wouldn't intentionally put this in a book.
During the next 40 or so questions, the characters are introduced and the plot slowly unfolds (as much of a plot as I could muster given that I'm working with as much space as a haiku). At about the middle of the book, the questions look like this:
In the center of Metroville, there is a super villain named Destructovil breaking into the Metroville bank. Rubberband girl got a distress call on her cell phone, but she is on the south end of the city in a train station. There is a train leaving at 3:00 pm that will take her to the Metroville bank. The train takes 12 minutes to go from the train station to the bank. She has to wait 4 minutes for the train. Speedy Man is in the next town over, but he can get to the bank in 8 minutes because he is Speedy Man. First, he needs to finish his cup of lemonade because he's too thirsty to be speedy. That will take 7 minutes. It is a very large cup of lemonade. Destructovil's getaway car is coming to pick him up at exactly 3:14 pm. Who will save the bank?
Bonus Question: Who is Rubberband girl?
My 10 year old told me "your problems aren't lame." I think that was a compliment.
If you had been doing all of the problems, you would be able to figure out who Rubberband girl is. If not, you have to refer back to a previous problem (officially an academic skill which I call for repeatedly) to figure out. Note that this is not a question a child can read once or twice and then solve. I also use time a lot because it requires an extra degree of thinking to do the arithmetic.
By the end of the book the questions fill the page and become even more convoluted and goofy (all with proper grammar except when the pirate character talks.) At this point, we're basically in math-reading-comprehension space, which I invented. I'll write a whole article on reading comprehension because I'm becoming more and more convinced that it is a pillar of success on a GAT test, and by way of the GAT objectives, to a strong academic career. As the book progresses, I start to move on to more advanced skills and because of that, some of the questions look like brain teasers, but they aren't, because everything can be derived logically after a few days of debate.
I'm working on Level 2 for younger kids which removes the need to read questions over and over again to understand what the problem is. I'm using a math abstraction that I invented to make things really taxing on the brain. I think some kids will find Level 2 harder than Level 3 and vica versa, but in both cases I'm seeing results and am pleased. Level 2 will take a few months to finish. By next year, I'm going to introduce Level 1 which I can only describe as diabolical. Level 1 was in the works since the beginning, but 3rd grade is the biggest gap for people right now so I started there. Then if I'm not completely exhausted, I'm going to work on Level 4 which teaches the Most Powerful Math Skill ever, which I can't find anywhere in any elementary aged book, but which we routinely use to solve anything.
So if this sounds like something that fills a need in your At Home Schooling or test prep, give it a try and let me know how it goes. Provided I don't sell more than 12 copies (which is going to be the case unless I find the time to do any marketing), I'll respond quickly.
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