I was always a dutiful student. I did those things kids are supposed to do: pay attention in class, complete homework assignments, study for tests, read. For the most part I did pretty well: I got into a gifted and talented public middle school program and went on to be accepted to Stuyvesant High School. I also got into both of the private schools I applied to, with 95% scholarships. Obviously, I was doing pretty well in all of my core subjects.
But, despite this evidence, I never felt like I was good at math. I also disliked it, largely because I never felt like I really understood what was going on, no matter what my test scores may have said.
Because I had been in a G&T program in middle school, I entered high school one year ahead of schedule in math. I struggled with geometry freshman year and fought to retain consciousness throughout sophomore algebra II and trigonometry. The thought of pre-calculus made me ill, so in my junior year I escaped to “Dr.Kolb’s math class for kids who hate math”. (Not the official course title!) It wasn’t a prestigious class, and the tests were pretty easy, but we actually did some deep mathematical thinking, at a relatively relaxed pace. It wasn’t too bad- and I even learned something about logical thinking. Nevertheless, I was hugely relieved to escape from math my senior year. I made a promise to myself that I’d never put myself through that (i.e., math) again. That’s how I ended up applying only to colleges that allowed students to major in biology without taking calculus or statistics.
My mathematical epiphany happened in the summer of 1999, just before my senior year of college. I was doing a summer scientific research internship at Emory University, and my research had gone pretty well. My advisor told me that if I could do a good statistical analysis of the research, I could probably get the work published. Wow! Did I want that! With a little help from a professor of statistics and an old textbook he recommended, I taught myself the necessary math. I understood what I was doing and why I was doing it. For the first time in my life, math felt like an ally rather than an enemy.
Since then, I have continued to have a positive relationship with math, but I still vividly remember my days of math avoidance and anxiety. This combination has proved to be an ideal background for tutoring.
When I sit down with a student who becomes desperately anxious at the thought of doing math, I’m able to be compassionate (which is critical for gaining the student’s trust) and also to see a way out of the negative feedback loop. Each student is different, but there are some repeating themes that come up more often than not when I help students who don’t like math. First, I find that it is important to acknowledge that not everyone has to love math or excel at math- but that a fundamental competency is possible for nearly everyone and will open doors in a wide variety of fields. Next, I think that it is very important to retreat to the last relevant topic where a student achieved mastery, and proceed from there (i.e., if a student is having trouble with algebraic fractions, it may be necessary to backtrack all the way to the idea of what a fraction actually is, review simple arithmetic fractions, then more complex arithmetic fractions, before finally returning to the topic of algebraic fractions). Finally, it is absolutely critical to underscore that math is not effortless- students who appear to “just know everything” almost always study more than their peers and their classmates assume they do.
It is ironic that I once vowed to avoid math at all costs, but I now make my living largely by teaching math. Not only that, but I enjoy it. I think my story is a useful one because it demonstrates that early discomfort with a subject does not have to be the end of things- there is always an opportunity for a second chance.
Wednesday, December 23, 2009
Tuesday, December 22, 2009
Review of The Art of Problem Solving
I was recently introduced to The Art of Problem Solving, which is a series of math textbooks aimed at gifted middle and high school students, especially those who are interested in math competitions. I only looked through one of the books, Introduction to Algebra, by Richard Rusczyk , and this review will be about that text only. Other books in the series delve into topics such as geometry and probability.
The Art of Problem Solving bills itself as a book for 6th to 10th grades. This evaluation is quite ambitious! It is, however, in character with the rest of the book, as ambitious is the best word I can come up with to describe the overall tone. (According to the author’s biography, he was a high level math competition champion as a child, and I think it would be fair to suggest that he wrote this book with his younger self in mind.) I would warn parents and teachers to take the pre-test provided on the website very seriously. If your student(s) can not get a perfect score on the pre-test without your help, they are not ready for this book, regardless of their age.
As an adult who is comfortable with math, I loved this book. Both the text and the problems are thoughtfully written and very interesting. The explanations provided are lucid. If time was not a constraint, I would joyfully devote an hour or two a day to methodically working through this book- it would probably take me a year or so to finish, and I have no doubt that I would learn a great deal. However, while my endorsement of this book is strong, it is also very limited and specific. So that you can understand, let me tell you a little bit about myself.
As a child, I was an insanely conscientious student. Not surprisingly, I did well in school and was placed in an accelerated math program in middle school. Nevertheless, I found no joy in math (and always had the nagging feeling that my success on tests and report cards was due to some sort of cosmic mistake rather than real achievement on my part.) In high school, I stopped pursuing math as soon as I decently was able. I never took pre-calculus, never mind calculus. I chose my college partly based on where I would be able to major in biology without taking higher math classes. Fortunately, I experienced an epiphany at the age of 21.
My epiphany was the result of a research project that I was perusing- I was researching certain aspects of ancient salt marshes, and my advisor told me that if I could successfully do a statistical analysis of my data, it could most likely be published. With that enormous inducement, I began studying elementary statistics, and with almost no instruction except from a textbook, I soon understood statistics well enough to analyze my data. My paper was published and, much more importantly, my fear of math was conquered.
Years past, and I became a tutor. I teach test preparation and science as well as math, but I spend the largest portion of my time teaching math to 8-14 year olds. (I’ve hired other tutors to teach more advanced math.) I’m very good at what I do, and I think it is in large part because I have a very thorough understanding of math through high school algebra, a genuine affection for the subject and, simultaneously, a clear memory of a time when math was not my friend.
All of this history is a roundabout way of explaining why I feel like I have a lot to learn from this book- although it starts out with basic algebra, it ends up covering topics normally reserved for pre-calculus. Furthermore, when I look at The Art of Problem Solving, Introduction to Algebra through the lens of my remembered childhood feelings about math, I see a terrifying tome. It does not gently lead the student forward, first with easy problems and then with gradually more challenging ones. Instead, it dashes ahead and dives straight into hard problems. This approach is great for a motivated, interested person with a solid background in the pre-requisites, but it could easily prove miserable, frustrating, and ultimately counter productive for students who do not meet that description.
I intend to begin using The Art of Problem Solving, Introduction to Algebra, but only with a select group of students who are already robustly successful in math and who are coming to me for enrichment. For example, I will incorporate Art of Problem Solving problems into my work preparing students for the Hunter College High School and Anderson School entrance exams.
I wish to offer one further warning about The Art of Problem Solving, Introduction to Algebra, specifically to homeschool families. If your child is ready for this textbook and eager for the challenge it presents, then that is a wonderful thing. However, if you plan on integrating your child into a school environment, you should be aware that the book does not touch on topics that are important in both middle and high school curriculums (primarily geometry and probability) and you might therefore want to provide supplementation in these topics.
The Art of Problem Solving bills itself as a book for 6th to 10th grades. This evaluation is quite ambitious! It is, however, in character with the rest of the book, as ambitious is the best word I can come up with to describe the overall tone. (According to the author’s biography, he was a high level math competition champion as a child, and I think it would be fair to suggest that he wrote this book with his younger self in mind.) I would warn parents and teachers to take the pre-test provided on the website very seriously. If your student(s) can not get a perfect score on the pre-test without your help, they are not ready for this book, regardless of their age.
As an adult who is comfortable with math, I loved this book. Both the text and the problems are thoughtfully written and very interesting. The explanations provided are lucid. If time was not a constraint, I would joyfully devote an hour or two a day to methodically working through this book- it would probably take me a year or so to finish, and I have no doubt that I would learn a great deal. However, while my endorsement of this book is strong, it is also very limited and specific. So that you can understand, let me tell you a little bit about myself.
As a child, I was an insanely conscientious student. Not surprisingly, I did well in school and was placed in an accelerated math program in middle school. Nevertheless, I found no joy in math (and always had the nagging feeling that my success on tests and report cards was due to some sort of cosmic mistake rather than real achievement on my part.) In high school, I stopped pursuing math as soon as I decently was able. I never took pre-calculus, never mind calculus. I chose my college partly based on where I would be able to major in biology without taking higher math classes. Fortunately, I experienced an epiphany at the age of 21.
My epiphany was the result of a research project that I was perusing- I was researching certain aspects of ancient salt marshes, and my advisor told me that if I could successfully do a statistical analysis of my data, it could most likely be published. With that enormous inducement, I began studying elementary statistics, and with almost no instruction except from a textbook, I soon understood statistics well enough to analyze my data. My paper was published and, much more importantly, my fear of math was conquered.
Years past, and I became a tutor. I teach test preparation and science as well as math, but I spend the largest portion of my time teaching math to 8-14 year olds. (I’ve hired other tutors to teach more advanced math.) I’m very good at what I do, and I think it is in large part because I have a very thorough understanding of math through high school algebra, a genuine affection for the subject and, simultaneously, a clear memory of a time when math was not my friend.
All of this history is a roundabout way of explaining why I feel like I have a lot to learn from this book- although it starts out with basic algebra, it ends up covering topics normally reserved for pre-calculus. Furthermore, when I look at The Art of Problem Solving, Introduction to Algebra through the lens of my remembered childhood feelings about math, I see a terrifying tome. It does not gently lead the student forward, first with easy problems and then with gradually more challenging ones. Instead, it dashes ahead and dives straight into hard problems. This approach is great for a motivated, interested person with a solid background in the pre-requisites, but it could easily prove miserable, frustrating, and ultimately counter productive for students who do not meet that description.
I intend to begin using The Art of Problem Solving, Introduction to Algebra, but only with a select group of students who are already robustly successful in math and who are coming to me for enrichment. For example, I will incorporate Art of Problem Solving problems into my work preparing students for the Hunter College High School and Anderson School entrance exams.
I wish to offer one further warning about The Art of Problem Solving, Introduction to Algebra, specifically to homeschool families. If your child is ready for this textbook and eager for the challenge it presents, then that is a wonderful thing. However, if you plan on integrating your child into a school environment, you should be aware that the book does not touch on topics that are important in both middle and high school curriculums (primarily geometry and probability) and you might therefore want to provide supplementation in these topics.
Thursday, December 17, 2009
Suggested Non-Fiction Reading for Advanced Students
Last year, I worked with a particularly gifted student applying to Hunter College High School (she got in, by the way). She was only 11 years old, but she had a fully adult level of reading comprehension and a desire to tackle interesting, sophisticated, and challenging material. At the same time, she was still a child and books written about certain adult experiences and emotions simply held no interest for her. Working with this girl got me started thinking about books that might interest a child or teenager while being challenging for even the most advanced students.
It’s a crime to think of excellent literature in terms of test preparation. And yet, as a tutor, I sometimes find myself framing reading in those terms. Instead of doing that here, let me just say reading literature at this level makes the reading comprehension on a test such as the SHSAT or even the SAT seem like child’s play. It is also probably the only way for a child to have a real chance at a school like Hunter College High School or The Anderson School.
My basic criterion for choosing these books is that they had to be interesting to me, contain rich vocabulary and complex thoughts, and not be sexually explicit or wantonly violent. Furthermore, they had to have something in them that I think would be interesting to many young people- for example, many of these books feature young protagonists. To be part of this particular list, the book had to be non-fiction- at a later date, I will write a similar list of recommended fiction books for advanced readers. Obviously, this list is highly idiosyncratic and far from comprehensive. The books range from moderately to extremely challenging.
Non-Fiction
Wild Swans by Jung Chang
In Wild Swans, the author tells the history of modern China through the history of her own family, in particular her grandmother, her mother, and herself. This book is emotionally difficult as well as technically difficult: it is long and complex, and it deals with some of the darkest aspects of human nature. On the other hand, it is richly informative and gripping. It also shows some people being the best that humans can be.
It seems to me that many classic novels that are often read in middle and high school (1984, Lord of the Flies, Deliverance) are popular at least in part because they encourage an exploration of society gone wrong. In my personal opinion, a flaw of many of these books (and all of the ones I just listed) is that it is too easy to dismiss the mistakes of the characters because they are not real and, ultimately, not fully convincing. Wild Swans on the other hand, paints portraits of people who do deeply evil as well as exceptionally heroic things, that are much harder to dismiss because they are actually real and because the author is able make her characters’ motivations understandable.
Uncle Tungsten: Tales of a Chemical Boyhood by Oliver Sacks
In this book, the author tells of his childhood love affair with chemistry. It takes place in England, around the time of World War II, and perhaps the most immediately astonishing part of the story is how much freer children were at that time. His parents are clearly loving and responsible, but he nevertheless conducted a wide variety of hair-raising chemistry experiments that would never be allowed today. Indeed, many of the materials that he so casually bought as a boy are now almost impossible for a private individual of any age to purchase legally.
The writing style of this book is relatively challenging, but most of the content should be easy for young people to identify with. While Oliver Sacks was no doubt an unusual boy, his excitement when he discovers something new to him or when he causes a particularly good explosion is contagious. Likewise, his emotions surrounding negative events caused by World War II are easy to relate to.
The Cannon by Natalie Angier
When I think about science books, I don’t usually think about books filled with deft word play, cultural references, and delicious prose that reads almost like poetry. And yet, that is exactly what The Cannon delivers. This book is written by a New York Times science reporter, and it is about the biggest, most important ideas in science, as defined by a wide range of working scientists. The science is clearly intended for a non-scientific, yet sophisticated, audience. I think that many students would get a real kick out of reading about what they are learning in science class, but in a far more sophisticated and artful way than any textbook has ever been written.
There is nothing simple about the writing style of this book; indeed I would go so far as to say that a big part of the tragedy of low reading comprehension levels is that people who have them will never be able to enjoy a book like this. On the other hand, this book is truly a reward for those skilled enough to enjoy it.
The Interesting Narrative by Olaudah Equiano
The title of this book does not lie; it is an exceptionally interesting narrative! Olaudah Equiano was born around 1745 in what is now Nigeria, was kidnapped when he was about ten years old, and was sold into slavery. As a slave, he served as an officer in the British Navy and then as a clerk, laborer, sailor, and even ship captain for a private owner. Eventually, he purchased his freedom. As a free man, he had an astonishingly wide range of experiences, which included working as an overseer of slaves, attempting to sail to the North Pole, having an intense religious conversion, marrying an Englishwoman, and working hard to end slavery.
The Interesting Narrative was written as part of Olaudah Equiano’s anti-slavery efforts. It is a complex book that is difficult to summarize. It is not an easy read; it is from a very different time and both the language and the concepts are somewhat different from what we are used to. However, it is also an extremely vivid, rewarding read that opens a window into a world that no longer exists.
The Last Algonquin by Theodore L. Kazimiroff
In 1924, a 12 year old boy who was studying for a Boy Scout merit badge encountered Joe Two Trees, a man who believed that he was the last living member of the Algonquin tribe. Joe Two Trees, who was living a traditional hunter-gather life and who had not regularly spoken to another human being for decades, decided to tell his life story to that boy. This did not happen in a remote, wild area- it happened in New York City. Specifically, it happened in Pelham Bay Park, a very large park in the Bronx.
The story that Joe Two Trees told is exciting, moving, and sometimes very sad. It is also a reminder that astonishingly drastic change can take place during one person’s life time. The boy he told it to was Theodore Kazimiroff, Sr and The Last Algonquin was written by his son.
It’s a crime to think of excellent literature in terms of test preparation. And yet, as a tutor, I sometimes find myself framing reading in those terms. Instead of doing that here, let me just say reading literature at this level makes the reading comprehension on a test such as the SHSAT or even the SAT seem like child’s play. It is also probably the only way for a child to have a real chance at a school like Hunter College High School or The Anderson School.
My basic criterion for choosing these books is that they had to be interesting to me, contain rich vocabulary and complex thoughts, and not be sexually explicit or wantonly violent. Furthermore, they had to have something in them that I think would be interesting to many young people- for example, many of these books feature young protagonists. To be part of this particular list, the book had to be non-fiction- at a later date, I will write a similar list of recommended fiction books for advanced readers. Obviously, this list is highly idiosyncratic and far from comprehensive. The books range from moderately to extremely challenging.
Non-Fiction
Wild Swans by Jung Chang
In Wild Swans, the author tells the history of modern China through the history of her own family, in particular her grandmother, her mother, and herself. This book is emotionally difficult as well as technically difficult: it is long and complex, and it deals with some of the darkest aspects of human nature. On the other hand, it is richly informative and gripping. It also shows some people being the best that humans can be.
It seems to me that many classic novels that are often read in middle and high school (1984, Lord of the Flies, Deliverance) are popular at least in part because they encourage an exploration of society gone wrong. In my personal opinion, a flaw of many of these books (and all of the ones I just listed) is that it is too easy to dismiss the mistakes of the characters because they are not real and, ultimately, not fully convincing. Wild Swans on the other hand, paints portraits of people who do deeply evil as well as exceptionally heroic things, that are much harder to dismiss because they are actually real and because the author is able make her characters’ motivations understandable.
Uncle Tungsten: Tales of a Chemical Boyhood by Oliver Sacks
In this book, the author tells of his childhood love affair with chemistry. It takes place in England, around the time of World War II, and perhaps the most immediately astonishing part of the story is how much freer children were at that time. His parents are clearly loving and responsible, but he nevertheless conducted a wide variety of hair-raising chemistry experiments that would never be allowed today. Indeed, many of the materials that he so casually bought as a boy are now almost impossible for a private individual of any age to purchase legally.
The writing style of this book is relatively challenging, but most of the content should be easy for young people to identify with. While Oliver Sacks was no doubt an unusual boy, his excitement when he discovers something new to him or when he causes a particularly good explosion is contagious. Likewise, his emotions surrounding negative events caused by World War II are easy to relate to.
The Cannon by Natalie Angier
When I think about science books, I don’t usually think about books filled with deft word play, cultural references, and delicious prose that reads almost like poetry. And yet, that is exactly what The Cannon delivers. This book is written by a New York Times science reporter, and it is about the biggest, most important ideas in science, as defined by a wide range of working scientists. The science is clearly intended for a non-scientific, yet sophisticated, audience. I think that many students would get a real kick out of reading about what they are learning in science class, but in a far more sophisticated and artful way than any textbook has ever been written.
There is nothing simple about the writing style of this book; indeed I would go so far as to say that a big part of the tragedy of low reading comprehension levels is that people who have them will never be able to enjoy a book like this. On the other hand, this book is truly a reward for those skilled enough to enjoy it.
The Interesting Narrative by Olaudah Equiano
The title of this book does not lie; it is an exceptionally interesting narrative! Olaudah Equiano was born around 1745 in what is now Nigeria, was kidnapped when he was about ten years old, and was sold into slavery. As a slave, he served as an officer in the British Navy and then as a clerk, laborer, sailor, and even ship captain for a private owner. Eventually, he purchased his freedom. As a free man, he had an astonishingly wide range of experiences, which included working as an overseer of slaves, attempting to sail to the North Pole, having an intense religious conversion, marrying an Englishwoman, and working hard to end slavery.
The Interesting Narrative was written as part of Olaudah Equiano’s anti-slavery efforts. It is a complex book that is difficult to summarize. It is not an easy read; it is from a very different time and both the language and the concepts are somewhat different from what we are used to. However, it is also an extremely vivid, rewarding read that opens a window into a world that no longer exists.
The Last Algonquin by Theodore L. Kazimiroff
In 1924, a 12 year old boy who was studying for a Boy Scout merit badge encountered Joe Two Trees, a man who believed that he was the last living member of the Algonquin tribe. Joe Two Trees, who was living a traditional hunter-gather life and who had not regularly spoken to another human being for decades, decided to tell his life story to that boy. This did not happen in a remote, wild area- it happened in New York City. Specifically, it happened in Pelham Bay Park, a very large park in the Bronx.
The story that Joe Two Trees told is exciting, moving, and sometimes very sad. It is also a reminder that astonishingly drastic change can take place during one person’s life time. The boy he told it to was Theodore Kazimiroff, Sr and The Last Algonquin was written by his son.
Friday, December 11, 2009
Conceptual Physics
Traditionally, physics has been considered the most difficult science, which should only be attempted by mature students with a strong mathematical background. There is some truth to this- being comfortable with advanced math can certainly open up some areas of physics and there are topics in a solid, college-preparatory physics class that require some pretty serious number-crunching. However, there is another side to this story and a growing feeling among educators (myself included) that even elementary school students can and should study physics.
One of the strongest arguments for introducing physics at a young age is that it is the most “basic” of the sciences. In other words, it’s really not possible to have a good understanding of photosynthesis if you don’t know anything about light. Learning about light is, of course, a branch of physics.
There’s currently a “physics first” movement that is trying to upend the traditional order of high school science classes so that the sequence becomes physics in freshman year, then chemistry, and finally biology. In this model, physics is taught as a more conceptual and less calculation-based subject because younger students do not have the mathematical knowledge of older ones.
Physics first could be the best thing that ever happened to physics education, if it is done correctly. Beyond the obvious perk for physics-enthusiasts everywhere that physics would studied by far more people than ever before, it could potentially be taught much more effectively. One of the flaws in traditional physics education is that it assumes that students will learn the concepts that the mathematics illustrate by applying the math to problems. Unfortunately, this doesn’t work well most of the time. Most people need to approach physics from a conceptual point of view before they can understand the mathematics in a meaningful way. This is true even for smart, mathematically inclined people, and it is at least part of the reason that so many people learn so little in high school physics classes. In essence, the goal of physics first education is to help all students achieve a solid qualitative understanding of the physical world. Interested students can then refine that pre-existing qualitative knowledge into a quantitative understanding in a later, more advanced class.
The philosophy behind physics first doesn’t have to be restricted to educating high school freshmen. It can effectively be applied to much younger children as well. For example, I teach science to a group of nine and ten year old homeschoolers, and we have done quite a bit of physics, with very little math beyond basic arithmetic. For example, last year we explored levers and turning effect. This year we will be looking into pulleys and simple circuits. I don’t shy away from using age-appropriate math, including simple formulas, but neither do I emphasize formulas over a verbal understanding of events. These kids are hardly advanced physics students, but they have achieved significant understanding while retaining a strong interest in learning more.
Critics of a conceptual approach to physics education worry that it is merely a way to lower standards. I share their desire for the highest standards possible, and I acknowledge that a poorly executed conceptual physics program could lack rigor. As always, details matter. A good conceptual physics program should involve hands-on (and “brain-on”) experiments, extensive writing, and some math. It should not be easy. On the other hand, it shouldn’t leave conscientious, hard working students feeling like they are studying an impossible subject- and traditional physics education leaves far too many students with that feeling.
One of the strongest arguments for introducing physics at a young age is that it is the most “basic” of the sciences. In other words, it’s really not possible to have a good understanding of photosynthesis if you don’t know anything about light. Learning about light is, of course, a branch of physics.
There’s currently a “physics first” movement that is trying to upend the traditional order of high school science classes so that the sequence becomes physics in freshman year, then chemistry, and finally biology. In this model, physics is taught as a more conceptual and less calculation-based subject because younger students do not have the mathematical knowledge of older ones.
Physics first could be the best thing that ever happened to physics education, if it is done correctly. Beyond the obvious perk for physics-enthusiasts everywhere that physics would studied by far more people than ever before, it could potentially be taught much more effectively. One of the flaws in traditional physics education is that it assumes that students will learn the concepts that the mathematics illustrate by applying the math to problems. Unfortunately, this doesn’t work well most of the time. Most people need to approach physics from a conceptual point of view before they can understand the mathematics in a meaningful way. This is true even for smart, mathematically inclined people, and it is at least part of the reason that so many people learn so little in high school physics classes. In essence, the goal of physics first education is to help all students achieve a solid qualitative understanding of the physical world. Interested students can then refine that pre-existing qualitative knowledge into a quantitative understanding in a later, more advanced class.
The philosophy behind physics first doesn’t have to be restricted to educating high school freshmen. It can effectively be applied to much younger children as well. For example, I teach science to a group of nine and ten year old homeschoolers, and we have done quite a bit of physics, with very little math beyond basic arithmetic. For example, last year we explored levers and turning effect. This year we will be looking into pulleys and simple circuits. I don’t shy away from using age-appropriate math, including simple formulas, but neither do I emphasize formulas over a verbal understanding of events. These kids are hardly advanced physics students, but they have achieved significant understanding while retaining a strong interest in learning more.
Critics of a conceptual approach to physics education worry that it is merely a way to lower standards. I share their desire for the highest standards possible, and I acknowledge that a poorly executed conceptual physics program could lack rigor. As always, details matter. A good conceptual physics program should involve hands-on (and “brain-on”) experiments, extensive writing, and some math. It should not be easy. On the other hand, it shouldn’t leave conscientious, hard working students feeling like they are studying an impossible subject- and traditional physics education leaves far too many students with that feeling.
Friday, December 4, 2009
Review of Dragon Genetics
Piles and piles of research show that students learn better when they are fully and actively engaged in what they are learning, rather than attempting to passively absorb information. That is why good teachers in all subjects and at all levels find ways to get students fully involved. In science classes, one of the most important tools to achieve this goal is hands-on lab work.
Unfortunately, some topics don’t lend themselves very well to classroom experimentation. Genetics is a good example. Most studies of genetics require breeding large numbers of organisms through several generations. Some teachers manage to do fruit fly, bacteria, or Arabadopisis (a species of quick growing mustard plant) breeding experiments, but the logistics are daunting. Fortunately, there are alternatives. The very best alternative that I am aware of is Dragon Genetics.
Dragon Genetics is a free, downloadable program made by Pedogicica. As the name suggests, it allows users to explore the genetics of dragons in great depth. By happy coincidence, dragons have many genetic parallels with more familiar organisms, including humans.
Dragon Genetics is admirably clear and thorough. It starts out at the very beginning, and it goes all the way through the topics covered in AP Biology. From the beginning, it explicitly links the principles of genetics with the physical structure of chromosomes, rather than following the historical path of first discussing phenotypes and patterns of inheritance and only later connecting those facts to the physical structure of DNA.
Dragon Genetics teaches about monohybrids, dihybrids, mutations, and x-linked traits, among other topics. It does not discuss epigenetics, mitochondrial inheritance, or other similarly advanced subjects.
One of the characteristics that make Dragon Genetics effective is its sense of whimsy. The graphics are not cutting-edge, but the cartoon dragons are appealing and it is fun to figure out how to breed fire-breathing animals. At least as important is the structure of Dragon Genetics. The student must actively engage with the program, and do so successfully before being allowed to move on. In essence, the student learns about genetics by performing “experiments” and interpreting the results. Carefully structured questions guide the student through the process of interpreting “experimental” data. Of course the experiments are just computer models, with pre-determined results, but they are very good models and they allow for a genuine process of inquiry to take place.
As a tutor, I have used Dragon Genetics as an independent-study tool with considerable success. Because time is often quite limited when I’m helping students prepare for exams such as the Living Environment Regents, the SAT subject test in biology, and AP Biology, I will have students use Dragon Genetics to review genetics and related topics such as meiosis on their own, thereby buying more time to spend on everything else. In my experience, students who have completed Dragon Genetics almost always demonstrate a very good understanding of the material covered.
The program could also be used in a classroom context, as long as sufficient computers are available. Dragon Genetics is broken down into eight core lessons and four optional lessons. Each of the core lessons are designed to take about 45-50 minutes, so they will fit into most class periods. The optional lessons are shorter.
As a tutor who needs to get “results”, in the form of higher test scores, I appreciate the way that Dragon Genetics teaches content. As a teacher who genuinely loves science and cares about teaching logical thinking skills and the thought processes that underlie all science, I am enthusiastic about the way that Dragon Genetics teaches critical thinking and scientific method.
Unfortunately, some topics don’t lend themselves very well to classroom experimentation. Genetics is a good example. Most studies of genetics require breeding large numbers of organisms through several generations. Some teachers manage to do fruit fly, bacteria, or Arabadopisis (a species of quick growing mustard plant) breeding experiments, but the logistics are daunting. Fortunately, there are alternatives. The very best alternative that I am aware of is Dragon Genetics.
Dragon Genetics is a free, downloadable program made by Pedogicica. As the name suggests, it allows users to explore the genetics of dragons in great depth. By happy coincidence, dragons have many genetic parallels with more familiar organisms, including humans.
Dragon Genetics is admirably clear and thorough. It starts out at the very beginning, and it goes all the way through the topics covered in AP Biology. From the beginning, it explicitly links the principles of genetics with the physical structure of chromosomes, rather than following the historical path of first discussing phenotypes and patterns of inheritance and only later connecting those facts to the physical structure of DNA.
Dragon Genetics teaches about monohybrids, dihybrids, mutations, and x-linked traits, among other topics. It does not discuss epigenetics, mitochondrial inheritance, or other similarly advanced subjects.
One of the characteristics that make Dragon Genetics effective is its sense of whimsy. The graphics are not cutting-edge, but the cartoon dragons are appealing and it is fun to figure out how to breed fire-breathing animals. At least as important is the structure of Dragon Genetics. The student must actively engage with the program, and do so successfully before being allowed to move on. In essence, the student learns about genetics by performing “experiments” and interpreting the results. Carefully structured questions guide the student through the process of interpreting “experimental” data. Of course the experiments are just computer models, with pre-determined results, but they are very good models and they allow for a genuine process of inquiry to take place.
As a tutor, I have used Dragon Genetics as an independent-study tool with considerable success. Because time is often quite limited when I’m helping students prepare for exams such as the Living Environment Regents, the SAT subject test in biology, and AP Biology, I will have students use Dragon Genetics to review genetics and related topics such as meiosis on their own, thereby buying more time to spend on everything else. In my experience, students who have completed Dragon Genetics almost always demonstrate a very good understanding of the material covered.
The program could also be used in a classroom context, as long as sufficient computers are available. Dragon Genetics is broken down into eight core lessons and four optional lessons. Each of the core lessons are designed to take about 45-50 minutes, so they will fit into most class periods. The optional lessons are shorter.
As a tutor who needs to get “results”, in the form of higher test scores, I appreciate the way that Dragon Genetics teaches content. As a teacher who genuinely loves science and cares about teaching logical thinking skills and the thought processes that underlie all science, I am enthusiastic about the way that Dragon Genetics teaches critical thinking and scientific method.
Monday, September 7, 2009
Review of Brain Maths, Volume 1
Brain Maths, by Tan Thoo Liang, is a supplemental math book associated with Singapore Math. It is a two volume series, and this review is about Volume 1. It is aimed at students 8 years old and older.
On the back cover, it states that “Brain Maths is a series of two volumes which have been written to help you increase your IQ score and also develop your mental flexibility.” I admit, I’m quite dubious about this book actually making a person smarter, but the problems are genuinely challenging and varied and they require flexibility in mathematical thinking. In the credits, it lists a number of previously published books of puzzles and brainteasers- of the books listed; I am most familiar with several by Martin Gardener. If you are also familiar with Martin Gardener, you have some idea of the flavor of Brain Maths. However, Brain Maths is far easier than anything written by Martin Gardener, as befits a book written for grade school aged children.
As a math tutor, I use this book in several contexts. It is useful for students who are preparing for entrance exams to gifted and talented schools, such as Hunter College High School or The Anderson School. Those exams expect children to be able to solve non-routine math problems using a wide variety of techniques, and the problems in this book promote exactly those skills. For that type of advanced student, this book is relatively easy- they can do the problems quickly, and they make good warm-ups that I then string together with more complex problems of a similar nature.
I also use this book with homeschoolers. No matter how good a math curriculum is, it is almost always flawed because the problems in the curriculum have a particular “flavor”. Students who use a curriculum can get very good at solving the flavor of problems in that curriculum, but still become flummoxed when presented with problems from a different curriculum, and therefore with a different flavor. For that reason, I always use supplemental materials including Brain Maths, books by Edward Zaccaro, Math Olympiad problems, and so on.
For students who are not particularly advanced, many of the problems in Brain Maths are challenging. I often present them as puzzles, and sometimes have appropriate manipulatives ready for the student to use.
I rarely teach math to groups, but if I did, I think that many of the problems in this book would be ideal for elementary school students to work on in small groups. They are complex enough so that they can be fruitfully approached from multiple perspectives, giving opportunities for interesting group discussion.
Although I like this book a lot, there are a few minor caveats to my recommendation. First, the book is from Singapore, so a few conventions may be slightly confusing. For example, they refer to Order of Operations by the acronym BODMAS (instead of the American PEMDAS). I’m still not quite sure what the B and the O stand for. A bigger flaw is that all of the cartoon people are either white or Asian. Finally, I want to make clear that this is not in any way a text book- rather, it is a book of supplemental math problems.
On the back cover, it states that “Brain Maths is a series of two volumes which have been written to help you increase your IQ score and also develop your mental flexibility.” I admit, I’m quite dubious about this book actually making a person smarter, but the problems are genuinely challenging and varied and they require flexibility in mathematical thinking. In the credits, it lists a number of previously published books of puzzles and brainteasers- of the books listed; I am most familiar with several by Martin Gardener. If you are also familiar with Martin Gardener, you have some idea of the flavor of Brain Maths. However, Brain Maths is far easier than anything written by Martin Gardener, as befits a book written for grade school aged children.
As a math tutor, I use this book in several contexts. It is useful for students who are preparing for entrance exams to gifted and talented schools, such as Hunter College High School or The Anderson School. Those exams expect children to be able to solve non-routine math problems using a wide variety of techniques, and the problems in this book promote exactly those skills. For that type of advanced student, this book is relatively easy- they can do the problems quickly, and they make good warm-ups that I then string together with more complex problems of a similar nature.
I also use this book with homeschoolers. No matter how good a math curriculum is, it is almost always flawed because the problems in the curriculum have a particular “flavor”. Students who use a curriculum can get very good at solving the flavor of problems in that curriculum, but still become flummoxed when presented with problems from a different curriculum, and therefore with a different flavor. For that reason, I always use supplemental materials including Brain Maths, books by Edward Zaccaro, Math Olympiad problems, and so on.
For students who are not particularly advanced, many of the problems in Brain Maths are challenging. I often present them as puzzles, and sometimes have appropriate manipulatives ready for the student to use.
I rarely teach math to groups, but if I did, I think that many of the problems in this book would be ideal for elementary school students to work on in small groups. They are complex enough so that they can be fruitfully approached from multiple perspectives, giving opportunities for interesting group discussion.
Although I like this book a lot, there are a few minor caveats to my recommendation. First, the book is from Singapore, so a few conventions may be slightly confusing. For example, they refer to Order of Operations by the acronym BODMAS (instead of the American PEMDAS). I’m still not quite sure what the B and the O stand for. A bigger flaw is that all of the cartoon people are either white or Asian. Finally, I want to make clear that this is not in any way a text book- rather, it is a book of supplemental math problems.
Friday, September 4, 2009
Reflections on a Reluctant Reader
Of all of the work I have done as a tutor, I am perhaps most proud of the work I did with Cassandra (of course, not her real name). Cassandra was in the seventh grade when we first met, and she had always scored either a one or a two on her New York State language arts tests. (A one is the lowest possible score and a four is the highest possible score; both ones and twos indicate that a student is performing poorly.) Her parents were frustrated by the lack of progress she was making in school and decided that private English tutoring was the way to go.
This was near the beginning of my tutoring career, and at the time I had never worked with a student like Cassandra before. She was a lovely girl; behavior problems were clearly not at the root of her academic struggles. She had never been diagnosed with a learning disability, and while she may have had one, she lacked obvious symptoms such as atrocious spelling and reversed letters. Her family appeared to be warm and supportive, and they clearly valued education. I had no idea what was the root of her problem, so I didn’t have a clear idea of what to do to help her. The only think I could think of was to simply make sure she got a lot of practice reading and writing, so with some trepidation, I set about trying to make that happen. (Although we worked on both reading and writing, this essay is about the reading instruction that I gave Cassandra.)
When I asked Cassandra what she liked to read, she was unable to give me any answer. (Not surprising, since she didn’t like to read!) Therefore, I decided to just pick books for her. We started with easy books from my personal collection. I wanted to make sure that we started out with books that were actually a little bit below her reading level in hope that this would break the cycle of her having difficulty reading, feeling bad about that, and then trying to avoid reading in the future. The Fantastic Mr. Fox by Roald Dahl and The Toothpaste Millionaire by Jean Merrill are examples of early books that we read together.
I instituted a modified form of shared reading. When we were together, we would read the books aloud. I would start, read for a few pages, and then hand the book to Cassandra. Then she would read for as long as she felt comfortable, and when she was done, she would hand the book back to me. When I felt it was necessary, we would stop and discuss the book. For homework, I initially assigned her about 10 pages of reading per day.
As her reading became more proficient (and as I ran out of reasonably interesting, very simple books in my personal collection), I gradually introduced more challenging material and increased the number of pages that I expected her to read each day. I also began offering her limited choice. For example, after about three months, I would show up at a tutoring session with two books such as The Story of Madam Curie by Alice Thorne and Hatchet by Gary Paulsen that she could choose between. At this stage, I was assigning about 15 pages of reading per day.
After about six months of gradually increasing the volume and complexity of the reading that I required from Cassandra, she was up to about 30 pages a day and beginning to approach a grade-appropriate level of reading. Books that she selected from the choices I gave her included The Watsons Go to Birmingham- 1963 by Christopher Paul Curtis and several titles from “A Series of Unfortunate Events” by Lemony Snicket.
After about eight months, Cassandra really was reading proficiently and she was also becoming interested in choosing her own books, without guidance. This was when we found out how wildly our tastes diverged! She kind of liked the books I picked for her, but it turns out she loved books such as A Child Called “It”: One Child’s Courage to Survive by Dave Pelzer. I wasn’t familiar with this book, but started out eager to read it with her. That came to a swift end after I nearly threw up while reading a particularly gruesome passage. After that, we agreed to go back to reading books that she picked from a limited list that I gave her, but I searched for somewhat grittier tales. The Color of Water by James McBride is one of the books that we shared during this period. That was probably the most challenging book that we read together.
Ten months after we first met, Cassandra took her eighth grade New York State language arts test. She scored a fairly high three, and for the first time in her life was officially considered a proficient reader. Shortly after she got her test score back, her parents and I decided that my work was done, and Cassandra graduated from English tutoring. In ten months (about 40 hours of tutoring, plus many more hours of reading on her own) her reading level went up approximately 3 grade levels! I have rarely been so proud and impressed by a student’s improvement.
Since Cassandra, I have worked with a number of students with low reading levels. Although I have not always had such dramatic results, I have found that this method of gradually and consistently increasing the complexity and volume of reading while also increasing the amount of choice the student has works well. I recommend it highly.
This was near the beginning of my tutoring career, and at the time I had never worked with a student like Cassandra before. She was a lovely girl; behavior problems were clearly not at the root of her academic struggles. She had never been diagnosed with a learning disability, and while she may have had one, she lacked obvious symptoms such as atrocious spelling and reversed letters. Her family appeared to be warm and supportive, and they clearly valued education. I had no idea what was the root of her problem, so I didn’t have a clear idea of what to do to help her. The only think I could think of was to simply make sure she got a lot of practice reading and writing, so with some trepidation, I set about trying to make that happen. (Although we worked on both reading and writing, this essay is about the reading instruction that I gave Cassandra.)
When I asked Cassandra what she liked to read, she was unable to give me any answer. (Not surprising, since she didn’t like to read!) Therefore, I decided to just pick books for her. We started with easy books from my personal collection. I wanted to make sure that we started out with books that were actually a little bit below her reading level in hope that this would break the cycle of her having difficulty reading, feeling bad about that, and then trying to avoid reading in the future. The Fantastic Mr. Fox by Roald Dahl and The Toothpaste Millionaire by Jean Merrill are examples of early books that we read together.
I instituted a modified form of shared reading. When we were together, we would read the books aloud. I would start, read for a few pages, and then hand the book to Cassandra. Then she would read for as long as she felt comfortable, and when she was done, she would hand the book back to me. When I felt it was necessary, we would stop and discuss the book. For homework, I initially assigned her about 10 pages of reading per day.
As her reading became more proficient (and as I ran out of reasonably interesting, very simple books in my personal collection), I gradually introduced more challenging material and increased the number of pages that I expected her to read each day. I also began offering her limited choice. For example, after about three months, I would show up at a tutoring session with two books such as The Story of Madam Curie by Alice Thorne and Hatchet by Gary Paulsen that she could choose between. At this stage, I was assigning about 15 pages of reading per day.
After about six months of gradually increasing the volume and complexity of the reading that I required from Cassandra, she was up to about 30 pages a day and beginning to approach a grade-appropriate level of reading. Books that she selected from the choices I gave her included The Watsons Go to Birmingham- 1963 by Christopher Paul Curtis and several titles from “A Series of Unfortunate Events” by Lemony Snicket.
After about eight months, Cassandra really was reading proficiently and she was also becoming interested in choosing her own books, without guidance. This was when we found out how wildly our tastes diverged! She kind of liked the books I picked for her, but it turns out she loved books such as A Child Called “It”: One Child’s Courage to Survive by Dave Pelzer. I wasn’t familiar with this book, but started out eager to read it with her. That came to a swift end after I nearly threw up while reading a particularly gruesome passage. After that, we agreed to go back to reading books that she picked from a limited list that I gave her, but I searched for somewhat grittier tales. The Color of Water by James McBride is one of the books that we shared during this period. That was probably the most challenging book that we read together.
Ten months after we first met, Cassandra took her eighth grade New York State language arts test. She scored a fairly high three, and for the first time in her life was officially considered a proficient reader. Shortly after she got her test score back, her parents and I decided that my work was done, and Cassandra graduated from English tutoring. In ten months (about 40 hours of tutoring, plus many more hours of reading on her own) her reading level went up approximately 3 grade levels! I have rarely been so proud and impressed by a student’s improvement.
Since Cassandra, I have worked with a number of students with low reading levels. Although I have not always had such dramatic results, I have found that this method of gradually and consistently increasing the complexity and volume of reading while also increasing the amount of choice the student has works well. I recommend it highly.
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