I have been very lucky. I have been working in 2 very good schools in the last 22 years. First school, The Program for Pregnant and Parenting Teens, was closed because of the tightening budget in 2007. The other school was closed in June 2009 by Bloomberg-Klein administration.
Why am I saying that the schools were good? It’s because we really served the kids well. The teachers, guidance counselors, social workers, community services, nurseries for the babies, clinic – all of us helped the kids find the way out of difficult situations and become independent and self-reliant human being. In both schools we had great stories to tell. In both schools we had kids who needed help in breaking the cycle and being the first generation in their families to graduate from a High school, move on to a college and achieve a new level of success.
In both cases the schools were closed because the city was trying to save some money. They say they use a “business model” of accountability. They say our numbers were not good: either attendance was low or Regents Tests scores didn’t measure up.
My question is: why would you use the failing “business model” that brought the entire country into an economic recession to schools and replace some more humane model that worked for those kids?
I really don’t understand, why somebody would proudly say that they use this “business model” when everybody knows that the model makes rich richer and poor poorer. Would you use this model if you were poor? Bloomberg became richer when he closed our schools, the city became poorer.
Because of this “business model” the greedy executives, who would make profits even if their clients lose money, got so much that banks do not have any money to lend any longer. Would you use this model if you were not this executive? Bloomberg and Klein are those executives who make those decisions.
I have been lucky, in the last 22 years I made a difference in so many lives for the better future. I hope the kids in the new schools get as much help and understanding from young and new teachers and principals as we were giving to our students in our “bad” schools.
Saturday, March 20, 2010
Friday, March 19, 2010
Piaget and Standards
My daughter wrote this paper, when she was in college. I think she makes a good point: Is there any sense in our NYS “standards”?
It has been found that the American school system is not as strong as the rest of the worlds in math and science. There have been articles written on this subject across the country for the last few years. In June of 2005, in Ohio at a national PTA meeting, Margaret Spellings, the education secretary said that “poor attitudes and low test scores nationwide continue to plague the system and limit progress.”(p.08.A) Shortly before this meeting Spellings had made a trip to Japan, where “the Japanese are investing in math and science courses while Americans are worrying about the ink color teachers use to grade papers—preferring purple rather than the ‘angry red.’(p.08.A) American children score lower on average on performance assessment exams. An article from a newspaper in Colorado reported in December of 2004 that a comparison held by the Trends in International Mathematics and Science Study found that of 29 countries, America came in 24th. “The usual pattern with international comparisons is that American students do worse the longer they’ve been in school.”(p.7.E)
Everyone is pointing fingers, and trying to figure out why are American students failing in math and science? Some argue that teachers are not proficient enough in their fields. Some say that courses are too hard. Some even say that children just aren’t able to learn.
How has this happened? How have we come so far and now see that children are just not able to learn? Isn’t it in their nature to be curious, to explore, and isn’t it this characteristic that drives children to learn, to walk, and to talk?
I remember when I was young (4-7yrs.) and my parents would take me to camp on the weekends and through summers. My sister and I would make friends with other children our age while we chased small animals through the woods, or caught frogs by the water. We brought back any specimen we could find and interview our parents to get every bit of information we could about these animals. We would compare them to other animals we caught, big frogs versus little frogs, fish, which we couldn’t catch by hand but could catch using bait, and lizards that ran away while we still held their tails. These things are all parts of science, and at that age when I was still learning through physical contact, these are easy concepts to understand. I could categorize big, small, green, furry, fast, etc. These are elements we use in studying science, and they’re fun and easy for kids to understand. It is impossible that children are unable to learn.
It may be that teachers and supervisors aren’t proficient in math and science. It may be that standards and teaching methods are not corresponding, complementary or unified. It may be that courses are hard, but are they too hard or are they mismatched according to the stages of cognitive development?
Piaget is a star in the childhood developmental field because of his discoveries in how children understand and explain their worlds as they learn. Jean Piaget is a Swiss theoretician who discovered that children make similar mistakes on IQ tests according to their age. Using this information Piaget designed four distinct stages of cognitive development starting at birth going on through adulthood.
The first stage, birth until two years of age, is the Sensorimotor stage during which an infant and toddler learns to “organize activities in relation to the environment through sensory and motor activity.”(p. 30) It is during this stage that children learn that just because they can’t see something or someone doesn’t mean it has ceased to exist. Children learn that their actions have reactions and practice and repeat actions to test results.
At age two children move on to the Preoperational stage. This stage lasts until about seven years old. At this stage children are fascinated by everything around them and use play and language to correspond to the things they see and experience, but do not think logically yet. This is the age when language acquisition is extremely rapid. During this period children imitate everything they see and here. They start to ask questions about what is happening around them, although these questions are usually absurd or unscientific, but they are still reaching to understand. Children ask questions like “how do dogs get married,” and “why is the moon following me.”
The third stage starts at age seven and is called the Concrete Operations stage. It is during this stage that children start to think logically. They can apply all the things they learned earlier in more areas because now they can recognize a logical pattern. During the Preoperational stage a child will say a pound of bricks is heavier than a pound of feathers, because bricks are heavier than feathers. It is during the Concrete Operations stage that a child given the same example will realize that a pound of anything is equal to a pound of anything else.
Another example was my mother’s experience in first grade; she grew up in Russia and the system is different, she was seven years old and practicing cursive lettering. My mother remembers that they had been in first grade for a while now and she knew how to write the entire alphabet, and when her teacher asked to right a row of ten little “u’s” my mother was ready for the challenge. She looked down at her paper and started to imagine how she could write the smallest “u” in the class. She wondered for a minute and realized that this request is not possible only one of the students can write The smallest “u” and this is the second that it dawns on her the teacher wants a lower case “u” not a little “u.” She realized her misunderstanding and was about to start her lettering when the student next to her excited by his achievements nudged her to look and see he had managed to write a row of ten of the smallest “u’s.” This story illustrates that transition, how normal it is for children to think this way up until around 7 years of age, and how their thought processes evolve into logical assessments. Although children are able to think rationally they cannot yet think abstractly, which is the ability they gain after the age of eleven when they move from the Concrete Operations stage to the Formal Operations stage.
The Formal Operations stage is the last stage in Piaget’s model of cognitive development. During this stage, children, adolescents and adults learn to think abstractly and philosophically. They no longer need to experience learning “hands on.” Students can now discuss possibilities, create and plan hypothesis and experiments. Earlier children were experiencing and testing their surroundings based on what they could see touch and hear, now based on that information they can understand things they have not yet seen, touched or heard.
Many have argued that Piaget’s model is defective because he underestimates children’s abilities. Some theorists say that cognitive development is continuous opposed to Piaget’s rigid stage theory. These criticisms may be true but do not affect the validity of what he says. In Piaget’s theory of cognitive development children start without any knowledge except that which they can experience, they repeat actions to see if they get the same reactions, they observe their surroundings and ask questions based on these findings, eventually they learn logic and can delve into solving more complex problems eventually solving problems using abstract theories. This model needs to be introduced into the American learning system to make standards that match Piaget’s stages of cognitive development. If children are practicing and learning material appropriate to their age group they would not have problems acquiring and demonstrating their achievements, and especially will not lose their eagerness to learn.
The nation does not have set standards that must be met for children at various stages. Each state develops their requirements for each grade or school level. Very often it is only the teacher that plans what the students will learn. There are, although, nationwide tests given to assess children’s overall academic development. I have the standards from New York State printed and given to teachers in 1999. These books are now seven years old but the system standards have not changed; these are the current standards.
These Performance Standards list what is required of students at Elementary, Middle and High school levels. There are many sets of standards in different areas of the subjects, so I have chosen two sets that have the most general approach to Math and Science teaching and learning. Mathematical Skills and Tools, and Scientific Connections and Applications are the categories I have chosen you can find in the appendix below.
I have labeled each standard with a p, c, or f; these labels are according to the Piagetian Cognitive Development model and so p stands for Preoperational stage, c stands for Concrete Operations stage, and f stands for Formal Operations stage. I categorized the standards as Physical contact/tactile learning (p), Physical contact/ tactile with logical/critical thinking (c), and abstract/theoretical thinking (f). Now my goal is to create an academic system that learns the same material that is required above but in an order that matches Piagetian theory, hoping to maximize the students ability as they learn meanwhile encouraging cognitive development.
Since in the first, Preoperational, stage children do not think but are able and even enjoy collecting data I would start their mathematical and scientific educations using these inclinations. We would not discuss topics too complex to understand without being able to see and touch the matter being studied. Anything labeled p would be studied and mastered before finishing second grade (at which time most students turn seven).
Math could be practiced counting sides and naming shapes, (i.e. Octagon has eight sides) since language acquisition is very rapid at this stage of development this is the perfect age to practice math vocabulary of observable materials. Measuring can be used to learn to add, and multiply as students learn about length, area, volume, weight, etc. Measurements do not require logical or critical thinking, and would be easy for preoperational children to stay on task with. Children can practice reading clocks (i.e. what time is it now? What time will it be in 20 minutes? In one hour?)
In science children can learn the physical aspects of science. They can practice reading thermometers, and show what is cold and warm. The can watch the weather. Leaves turn colors in the fall; snow always falls in the winter, and during the spring flowers bloom, and leaves grow back on to branches. They can go to zoos and botanical gardens with identifying books to label animal and plant varieties. Students can find their way to a prize using a compass. Science that children can physically experience is best during this stage because their appetites are already whetted and their thirst will grow through their discoveries.
After second grade, more complex problems can be introduced. The teacher can go on to the next step in all subjects introduced earlier. Our weather corresponds to our seasons which define our climate, but in Arizona, in the desert, their climate is different and so is their weather. The animals that live in New York are also different from those that live in Arizona, or Africa, Russia, etc. Students can study Biomes, Food Chains for each Biome, Life Cycles for many plants and animals. Human Anatomy can also be studied, this is when we can introduce the organs, and eventually nutrition and drug effects on the body.
Math can also become more complicated. Before students were measuring to find length, width, height and weight, now the teacher can explain how to learn volume, area, and circumference, through measurement meanwhile also explaining the formulas that find these answers faster. The point is to learn that the formulas are logical and easier than measuring the entire block over and over again. At this age children understand logical and spatial realities and these new abilities should be put to use right away so students can further the development of these skills. Higher levels of previous problems can continuously be introduced. If a student has problems understanding a problem, go over an earlier version of the problem to show how similar the work is and that only the numbers vary in each of the problems.
By the time students are in high school, when they are entering the Formal Operations Stage, they will understand that the numbers are a small part of the subject of math, and will be able to discuss it in abstract ways in which there could be days that no numbers are mentioned. Students wouldn’t have to discuss shapes or areas anymore since they will be committed to memory as well as formulas with which to describe them with.
Science in High school can also go further to explain the theoretical. Students can study cells, atoms, DNA, complex abstract problems and speculations in fields from Biology to Chemistry to Physics and Astronomy.
According to Piaget’s Cognitive Development Theory students need to learn in order or observations, logic, and then lastly theory. In the New York System now children are expected to learn “big ideas and unifying concepts” from an elementary school level, before they even know of the possibilities in their own classrooms. In math children are given problems that are easy at first, but math does not evolve from the calculations they had to go through in first and second grade. They are ready to learn the reasoning of math but are denied and forced to study shapes and computations over and over again.
In America people blame teachers, supervisors, parents, and even children for not learning math and science as well as the rest of the world. The explanation to why in America students don’t learn these subjects as well is buried beneath layers or politics, funding and red tape. Anyone can explain how teachers aren’t able to teach their subjects; supervisors can set rules against any creativity; parents might not be available to answer all their children’s questions. There are many issues at hand here. I am only posing a question: Why do we study Piaget in Childhood Development if we don’t apply his theory to our children?
It has been found that the American school system is not as strong as the rest of the worlds in math and science. There have been articles written on this subject across the country for the last few years. In June of 2005, in Ohio at a national PTA meeting, Margaret Spellings, the education secretary said that “poor attitudes and low test scores nationwide continue to plague the system and limit progress.”(p.08.A) Shortly before this meeting Spellings had made a trip to Japan, where “the Japanese are investing in math and science courses while Americans are worrying about the ink color teachers use to grade papers—preferring purple rather than the ‘angry red.’(p.08.A) American children score lower on average on performance assessment exams. An article from a newspaper in Colorado reported in December of 2004 that a comparison held by the Trends in International Mathematics and Science Study found that of 29 countries, America came in 24th. “The usual pattern with international comparisons is that American students do worse the longer they’ve been in school.”(p.7.E)
Everyone is pointing fingers, and trying to figure out why are American students failing in math and science? Some argue that teachers are not proficient enough in their fields. Some say that courses are too hard. Some even say that children just aren’t able to learn.
How has this happened? How have we come so far and now see that children are just not able to learn? Isn’t it in their nature to be curious, to explore, and isn’t it this characteristic that drives children to learn, to walk, and to talk?
I remember when I was young (4-7yrs.) and my parents would take me to camp on the weekends and through summers. My sister and I would make friends with other children our age while we chased small animals through the woods, or caught frogs by the water. We brought back any specimen we could find and interview our parents to get every bit of information we could about these animals. We would compare them to other animals we caught, big frogs versus little frogs, fish, which we couldn’t catch by hand but could catch using bait, and lizards that ran away while we still held their tails. These things are all parts of science, and at that age when I was still learning through physical contact, these are easy concepts to understand. I could categorize big, small, green, furry, fast, etc. These are elements we use in studying science, and they’re fun and easy for kids to understand. It is impossible that children are unable to learn.
It may be that teachers and supervisors aren’t proficient in math and science. It may be that standards and teaching methods are not corresponding, complementary or unified. It may be that courses are hard, but are they too hard or are they mismatched according to the stages of cognitive development?
Piaget is a star in the childhood developmental field because of his discoveries in how children understand and explain their worlds as they learn. Jean Piaget is a Swiss theoretician who discovered that children make similar mistakes on IQ tests according to their age. Using this information Piaget designed four distinct stages of cognitive development starting at birth going on through adulthood.
The first stage, birth until two years of age, is the Sensorimotor stage during which an infant and toddler learns to “organize activities in relation to the environment through sensory and motor activity.”(p. 30) It is during this stage that children learn that just because they can’t see something or someone doesn’t mean it has ceased to exist. Children learn that their actions have reactions and practice and repeat actions to test results.
At age two children move on to the Preoperational stage. This stage lasts until about seven years old. At this stage children are fascinated by everything around them and use play and language to correspond to the things they see and experience, but do not think logically yet. This is the age when language acquisition is extremely rapid. During this period children imitate everything they see and here. They start to ask questions about what is happening around them, although these questions are usually absurd or unscientific, but they are still reaching to understand. Children ask questions like “how do dogs get married,” and “why is the moon following me.”
The third stage starts at age seven and is called the Concrete Operations stage. It is during this stage that children start to think logically. They can apply all the things they learned earlier in more areas because now they can recognize a logical pattern. During the Preoperational stage a child will say a pound of bricks is heavier than a pound of feathers, because bricks are heavier than feathers. It is during the Concrete Operations stage that a child given the same example will realize that a pound of anything is equal to a pound of anything else.
Another example was my mother’s experience in first grade; she grew up in Russia and the system is different, she was seven years old and practicing cursive lettering. My mother remembers that they had been in first grade for a while now and she knew how to write the entire alphabet, and when her teacher asked to right a row of ten little “u’s” my mother was ready for the challenge. She looked down at her paper and started to imagine how she could write the smallest “u” in the class. She wondered for a minute and realized that this request is not possible only one of the students can write The smallest “u” and this is the second that it dawns on her the teacher wants a lower case “u” not a little “u.” She realized her misunderstanding and was about to start her lettering when the student next to her excited by his achievements nudged her to look and see he had managed to write a row of ten of the smallest “u’s.” This story illustrates that transition, how normal it is for children to think this way up until around 7 years of age, and how their thought processes evolve into logical assessments. Although children are able to think rationally they cannot yet think abstractly, which is the ability they gain after the age of eleven when they move from the Concrete Operations stage to the Formal Operations stage.
The Formal Operations stage is the last stage in Piaget’s model of cognitive development. During this stage, children, adolescents and adults learn to think abstractly and philosophically. They no longer need to experience learning “hands on.” Students can now discuss possibilities, create and plan hypothesis and experiments. Earlier children were experiencing and testing their surroundings based on what they could see touch and hear, now based on that information they can understand things they have not yet seen, touched or heard.
Many have argued that Piaget’s model is defective because he underestimates children’s abilities. Some theorists say that cognitive development is continuous opposed to Piaget’s rigid stage theory. These criticisms may be true but do not affect the validity of what he says. In Piaget’s theory of cognitive development children start without any knowledge except that which they can experience, they repeat actions to see if they get the same reactions, they observe their surroundings and ask questions based on these findings, eventually they learn logic and can delve into solving more complex problems eventually solving problems using abstract theories. This model needs to be introduced into the American learning system to make standards that match Piaget’s stages of cognitive development. If children are practicing and learning material appropriate to their age group they would not have problems acquiring and demonstrating their achievements, and especially will not lose their eagerness to learn.
The nation does not have set standards that must be met for children at various stages. Each state develops their requirements for each grade or school level. Very often it is only the teacher that plans what the students will learn. There are, although, nationwide tests given to assess children’s overall academic development. I have the standards from New York State printed and given to teachers in 1999. These books are now seven years old but the system standards have not changed; these are the current standards.
These Performance Standards list what is required of students at Elementary, Middle and High school levels. There are many sets of standards in different areas of the subjects, so I have chosen two sets that have the most general approach to Math and Science teaching and learning. Mathematical Skills and Tools, and Scientific Connections and Applications are the categories I have chosen you can find in the appendix below.
I have labeled each standard with a p, c, or f; these labels are according to the Piagetian Cognitive Development model and so p stands for Preoperational stage, c stands for Concrete Operations stage, and f stands for Formal Operations stage. I categorized the standards as Physical contact/tactile learning (p), Physical contact/ tactile with logical/critical thinking (c), and abstract/theoretical thinking (f). Now my goal is to create an academic system that learns the same material that is required above but in an order that matches Piagetian theory, hoping to maximize the students ability as they learn meanwhile encouraging cognitive development.
Since in the first, Preoperational, stage children do not think but are able and even enjoy collecting data I would start their mathematical and scientific educations using these inclinations. We would not discuss topics too complex to understand without being able to see and touch the matter being studied. Anything labeled p would be studied and mastered before finishing second grade (at which time most students turn seven).
Math could be practiced counting sides and naming shapes, (i.e. Octagon has eight sides) since language acquisition is very rapid at this stage of development this is the perfect age to practice math vocabulary of observable materials. Measuring can be used to learn to add, and multiply as students learn about length, area, volume, weight, etc. Measurements do not require logical or critical thinking, and would be easy for preoperational children to stay on task with. Children can practice reading clocks (i.e. what time is it now? What time will it be in 20 minutes? In one hour?)
In science children can learn the physical aspects of science. They can practice reading thermometers, and show what is cold and warm. The can watch the weather. Leaves turn colors in the fall; snow always falls in the winter, and during the spring flowers bloom, and leaves grow back on to branches. They can go to zoos and botanical gardens with identifying books to label animal and plant varieties. Students can find their way to a prize using a compass. Science that children can physically experience is best during this stage because their appetites are already whetted and their thirst will grow through their discoveries.
After second grade, more complex problems can be introduced. The teacher can go on to the next step in all subjects introduced earlier. Our weather corresponds to our seasons which define our climate, but in Arizona, in the desert, their climate is different and so is their weather. The animals that live in New York are also different from those that live in Arizona, or Africa, Russia, etc. Students can study Biomes, Food Chains for each Biome, Life Cycles for many plants and animals. Human Anatomy can also be studied, this is when we can introduce the organs, and eventually nutrition and drug effects on the body.
Math can also become more complicated. Before students were measuring to find length, width, height and weight, now the teacher can explain how to learn volume, area, and circumference, through measurement meanwhile also explaining the formulas that find these answers faster. The point is to learn that the formulas are logical and easier than measuring the entire block over and over again. At this age children understand logical and spatial realities and these new abilities should be put to use right away so students can further the development of these skills. Higher levels of previous problems can continuously be introduced. If a student has problems understanding a problem, go over an earlier version of the problem to show how similar the work is and that only the numbers vary in each of the problems.
By the time students are in high school, when they are entering the Formal Operations Stage, they will understand that the numbers are a small part of the subject of math, and will be able to discuss it in abstract ways in which there could be days that no numbers are mentioned. Students wouldn’t have to discuss shapes or areas anymore since they will be committed to memory as well as formulas with which to describe them with.
Science in High school can also go further to explain the theoretical. Students can study cells, atoms, DNA, complex abstract problems and speculations in fields from Biology to Chemistry to Physics and Astronomy.
According to Piaget’s Cognitive Development Theory students need to learn in order or observations, logic, and then lastly theory. In the New York System now children are expected to learn “big ideas and unifying concepts” from an elementary school level, before they even know of the possibilities in their own classrooms. In math children are given problems that are easy at first, but math does not evolve from the calculations they had to go through in first and second grade. They are ready to learn the reasoning of math but are denied and forced to study shapes and computations over and over again.
In America people blame teachers, supervisors, parents, and even children for not learning math and science as well as the rest of the world. The explanation to why in America students don’t learn these subjects as well is buried beneath layers or politics, funding and red tape. Anyone can explain how teachers aren’t able to teach their subjects; supervisors can set rules against any creativity; parents might not be available to answer all their children’s questions. There are many issues at hand here. I am only posing a question: Why do we study Piaget in Childhood Development if we don’t apply his theory to our children?
Appendix: NYS Standards:
The state requires that at the Elementary school level a student should be able to “demonstrate fluency” in basic math concepts and use appropriate methods of solving problems as follows:
* Adds, subtracts, multiplies, and divides whole numbers correctly; that is; (c)
i. knows single digit addition, subtraction, multiplication, and division facts;
ii. adds and subtracts numbers with several digits;
iii. multiplies and divides numbers with one or two digits;
iv. multiplies and divides three digit numbers by one digit number
* Estimates numerically and spatially (f)
* Measures length, area, perimeter, circumference, diameter, height, weight, and volume accurately in both the customary and metric systems (c & p)
* Computes time (in hours and minutes) and money (in dollars and cents) (c)
* Refers to geometric shapes and terms correctly with concrete objects or drawings, including triangle, square, rectangle, side, edge, face, cube, point, line, perimeter, area, and circle; and refers with assistance to rhombus, parallelogram, quadrilateral, polygon, polyhedron, angle, vertex, volume, diameter, circumference, sphere, prism, and pyramid (p & c)
* Uses +, -, x, /,$,%, and decimal point, correctly in number sentences and expressions (c)
* Reads, creates, and represents data on a line plots, charts, tables, diagrams, bar graphs, simple circle graphs, and coordinate graphs (c)
* Uses recall, mental computations, pencil and paper, measuring devices, mathematic texts, manipulatives, calculators, computers, and advice from peers as appropriate, to achieve solutions; that is, uses measuring devices, graded appropriately for given situations, such as rulers (customary to the inch; metric to the centimeter), measuring cups (customary to the ounce; metric to the milliliter), and scales (customary to the pound; metric to the gram) (c & p) (p.168)
The state requires that at the Middle school level a student should be able to “demonstrate fluency” in basic math concepts and use appropriate methods of solving problems as follows:
* Computes accurately with arithmetic operations on rational numbers (c)
* Knows and uses the correct order of operations for arithmetic computations (c)
* Estimates numerically and spatially (f)
* Measures length, area, volume, weight, time, and temperature accurately (c)
* Refers to geometric shapes and terms correctly (p)
* Uses equations, formulas, and simple algebraic notation appropriately (f)
* Reads and organizes data on charts and graphs, including scatter plots, bar line, and circle graphs, and Venn diagrams; calculates mean and median (f)
* Uses recall, mental computations, pencil and paper, measuring devices, mathematic texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions (c) (p.168)
The state also has requirements for High school level students to be able to “demonstrate fluency” in math as follows:
* Carries out numerical calculations and symbol manipulations effectively, using mental computations, pencil and paper, or other technological aids, as appropriate (c)
* Uses a variety of methods to estimate the values, in appropriate units, of quantities met in applications, and rounds numbers used in applications to an appropriate degree of accuracy (c)
* Evaluates and analyzes formulas and functions of many kinds, using both pencil and paper and more advanced technology (f)
* Uses basic geometric terminology accurately, and deduces information about basic geometric figures in solving problems (p)
* Makes and uses rough sketches, schematic diagrams, or precise scale diagrams to enhance a solution (p)
* Uses the number line and Cartesian coordinates in the pane and in space (c & p)
* Creates and interprets graphs of many kinds, such as function graphs, circle graphs, scatter plots, regression lines, and histograms (c)
* Sets up and solves equations symbolically (when possible) and graphically (c)
* Knows how to use algorithms in mathematics, such as the Euclidean Algorithm (f)
* Uses technology to create graphs or spreadsheets that contribute to the understanding of a problem (c)
* Writes a simple computer program to carry out a computation or simulation to be repeated many times (f)
* Uses tools such as rulers, tapes, compasses, and protractors in solving problems (p)
* Knows standard methods to solve basic problems and uses these methods in approaching more complex problems (c) (p.168)
A New York state has separate standards for “Scientific Connections and Applications.” These standards require a student to produce demonstrations in understanding as follows in Elementary school:
* Big ideas and unifying concepts, such as order and organization; models, form and function; change and constancy; and cause and effect (f)
* The designed world, such as development of agricultural techniques; and the variability of technological designs (f)
* Personal health, such as nutrition, substance abuse, and exercise; germs and toxic substances; personal and environmental safety (f)
* Science as a human endeavor, such as communication, cooperation, and diverse input in scientific research; and the importance of reason, intellectual honesty, and skepticism (f) (p.202)
In Middle school the standards for the same category are:
* Big ideas and unifying concepts, such as order and organization; models, form, and function; change and constancy; and cause and effect (f)
* The designed world, such as the reciprocal nature of science and technology; the development of agricultural techniques; and the viability of technological designs (f)
* Health, such as nutrition, exercise, and disease; effects of drugs and toxic substances; personal and environmental safety; and resources and environmental stress (f)
* Impact of technology, such as constraints and trade offs; feedback; benefits and risks; and problems and solutions (f)
* Impact of science, such as historical and contemporary contributions; and interactions between science and society (f) (p.202)
Finally, the High school standards of scientific connections and applications are as follows:
* Big ideas and unifying concepts, such as order and organization; models, form and function; change and constancy; and cause and effect (f)
* The designed world, such as the reciprocal relationship between science and technology; the development of agricultural techniques; and the reasonableness of technological designs (f)
* Health, such as nutrition and exercise; disease and epidemiology; personal and environmental safety; and resources, environmental stress, and population growth (f)
* Impact of technology, such as constraints and trade-offs; feedback; benefits and risks; and problems and solutions (f)
* Impact of science, such as historical and contemporary contributions; and interactions between science and society (f) (p.202)
* Adds, subtracts, multiplies, and divides whole numbers correctly; that is; (c)
i. knows single digit addition, subtraction, multiplication, and division facts;
ii. adds and subtracts numbers with several digits;
iii. multiplies and divides numbers with one or two digits;
iv. multiplies and divides three digit numbers by one digit number
* Estimates numerically and spatially (f)
* Measures length, area, perimeter, circumference, diameter, height, weight, and volume accurately in both the customary and metric systems (c & p)
* Computes time (in hours and minutes) and money (in dollars and cents) (c)
* Refers to geometric shapes and terms correctly with concrete objects or drawings, including triangle, square, rectangle, side, edge, face, cube, point, line, perimeter, area, and circle; and refers with assistance to rhombus, parallelogram, quadrilateral, polygon, polyhedron, angle, vertex, volume, diameter, circumference, sphere, prism, and pyramid (p & c)
* Uses +, -, x, /,$,%, and decimal point, correctly in number sentences and expressions (c)
* Reads, creates, and represents data on a line plots, charts, tables, diagrams, bar graphs, simple circle graphs, and coordinate graphs (c)
* Uses recall, mental computations, pencil and paper, measuring devices, mathematic texts, manipulatives, calculators, computers, and advice from peers as appropriate, to achieve solutions; that is, uses measuring devices, graded appropriately for given situations, such as rulers (customary to the inch; metric to the centimeter), measuring cups (customary to the ounce; metric to the milliliter), and scales (customary to the pound; metric to the gram) (c & p) (p.168)
The state requires that at the Middle school level a student should be able to “demonstrate fluency” in basic math concepts and use appropriate methods of solving problems as follows:
* Computes accurately with arithmetic operations on rational numbers (c)
* Knows and uses the correct order of operations for arithmetic computations (c)
* Estimates numerically and spatially (f)
* Measures length, area, volume, weight, time, and temperature accurately (c)
* Refers to geometric shapes and terms correctly (p)
* Uses equations, formulas, and simple algebraic notation appropriately (f)
* Reads and organizes data on charts and graphs, including scatter plots, bar line, and circle graphs, and Venn diagrams; calculates mean and median (f)
* Uses recall, mental computations, pencil and paper, measuring devices, mathematic texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions (c) (p.168)
The state also has requirements for High school level students to be able to “demonstrate fluency” in math as follows:
* Carries out numerical calculations and symbol manipulations effectively, using mental computations, pencil and paper, or other technological aids, as appropriate (c)
* Uses a variety of methods to estimate the values, in appropriate units, of quantities met in applications, and rounds numbers used in applications to an appropriate degree of accuracy (c)
* Evaluates and analyzes formulas and functions of many kinds, using both pencil and paper and more advanced technology (f)
* Uses basic geometric terminology accurately, and deduces information about basic geometric figures in solving problems (p)
* Makes and uses rough sketches, schematic diagrams, or precise scale diagrams to enhance a solution (p)
* Uses the number line and Cartesian coordinates in the pane and in space (c & p)
* Creates and interprets graphs of many kinds, such as function graphs, circle graphs, scatter plots, regression lines, and histograms (c)
* Sets up and solves equations symbolically (when possible) and graphically (c)
* Knows how to use algorithms in mathematics, such as the Euclidean Algorithm (f)
* Uses technology to create graphs or spreadsheets that contribute to the understanding of a problem (c)
* Writes a simple computer program to carry out a computation or simulation to be repeated many times (f)
* Uses tools such as rulers, tapes, compasses, and protractors in solving problems (p)
* Knows standard methods to solve basic problems and uses these methods in approaching more complex problems (c) (p.168)
A New York state has separate standards for “Scientific Connections and Applications.” These standards require a student to produce demonstrations in understanding as follows in Elementary school:
* Big ideas and unifying concepts, such as order and organization; models, form and function; change and constancy; and cause and effect (f)
* The designed world, such as development of agricultural techniques; and the variability of technological designs (f)
* Personal health, such as nutrition, substance abuse, and exercise; germs and toxic substances; personal and environmental safety (f)
* Science as a human endeavor, such as communication, cooperation, and diverse input in scientific research; and the importance of reason, intellectual honesty, and skepticism (f) (p.202)
In Middle school the standards for the same category are:
* Big ideas and unifying concepts, such as order and organization; models, form, and function; change and constancy; and cause and effect (f)
* The designed world, such as the reciprocal nature of science and technology; the development of agricultural techniques; and the viability of technological designs (f)
* Health, such as nutrition, exercise, and disease; effects of drugs and toxic substances; personal and environmental safety; and resources and environmental stress (f)
* Impact of technology, such as constraints and trade offs; feedback; benefits and risks; and problems and solutions (f)
* Impact of science, such as historical and contemporary contributions; and interactions between science and society (f) (p.202)
Finally, the High school standards of scientific connections and applications are as follows:
* Big ideas and unifying concepts, such as order and organization; models, form and function; change and constancy; and cause and effect (f)
* The designed world, such as the reciprocal relationship between science and technology; the development of agricultural techniques; and the reasonableness of technological designs (f)
* Health, such as nutrition and exercise; disease and epidemiology; personal and environmental safety; and resources, environmental stress, and population growth (f)
* Impact of technology, such as constraints and trade-offs; feedback; benefits and risks; and problems and solutions (f)
* Impact of science, such as historical and contemporary contributions; and interactions between science and society (f) (p.202)
Old Things: trash or treasure?
Every spring and fall I go through my closets and decide what I keep and what I donate. Every time I find something to keep and every time there is something to pass on to others. There is a saying: one person’s trash is another person’s treasure. That saying made the new rules of Green Living possible: Reduce, Reuse, and Recycle. I can give away some of my old things so somebody else could reuse them and we together will reduce the content of landfills.
In spite of the saying the idea is new for America. More traditional view is that everything new and young is good, strong, energetic, enthusiastic, and brings money; and everything old is really a trash and a waste. Old things must be replaced by new ones; old surfaces must be resurfaced, old houses rebuilt, old furniture thrown out. Same is true about people: the old should just disappear, so they do not bother the gentle eye of an observer. I know, I know, written by an old person ;) But I am not as old as you think.
On the contrary, some old things never become trash, they become classic and antique. Unfortunately, this thought is not a happy one, because so many things do become garbage with age and overuse, and only a few become classic and chic if taken care properly. How many old people are thrown out of our lives? And how many of them become respected authority on a subject? Alas, even the most brilliant of us often become classic only after death. Often we take better care of the things than of the people.
Remember last year, when this old and experienced pilot landed on the Hudson River? I was thinking that he showed to the world that we are not dead yet. We are at the peak of our ability. At this age the experience is already there and the energy is still there. We are supposed to be the most valuable people at our jobs. 50 years old is not old even for Hollywood any longer. Some of us are living classics.
You, Mr. Bloomberg, just don’t know who. You are afraid to waste your money on what you think is old trash, so you are throwing out all experienced teachers when you close our schools. But remember this: you are one of us and in a couple of years you’ll become the same society trash, like you just made of me and others.
No, I am not depressed; I am at a fork on the road of my life. Which way to go?
In spite of the saying the idea is new for America. More traditional view is that everything new and young is good, strong, energetic, enthusiastic, and brings money; and everything old is really a trash and a waste. Old things must be replaced by new ones; old surfaces must be resurfaced, old houses rebuilt, old furniture thrown out. Same is true about people: the old should just disappear, so they do not bother the gentle eye of an observer. I know, I know, written by an old person ;) But I am not as old as you think.
On the contrary, some old things never become trash, they become classic and antique. Unfortunately, this thought is not a happy one, because so many things do become garbage with age and overuse, and only a few become classic and chic if taken care properly. How many old people are thrown out of our lives? And how many of them become respected authority on a subject? Alas, even the most brilliant of us often become classic only after death. Often we take better care of the things than of the people.
Remember last year, when this old and experienced pilot landed on the Hudson River? I was thinking that he showed to the world that we are not dead yet. We are at the peak of our ability. At this age the experience is already there and the energy is still there. We are supposed to be the most valuable people at our jobs. 50 years old is not old even for Hollywood any longer. Some of us are living classics.
You, Mr. Bloomberg, just don’t know who. You are afraid to waste your money on what you think is old trash, so you are throwing out all experienced teachers when you close our schools. But remember this: you are one of us and in a couple of years you’ll become the same society trash, like you just made of me and others.
No, I am not depressed; I am at a fork on the road of my life. Which way to go?
Monday, March 8, 2010
What is science?
Recently I received an email with the following questions. I decided to post my reply here and send this student a link:
1. How has science change throughout history??
To start we first must agree on the definition.
Science is an observation of the world around and an attempt to find explanations to the phenomena observed.
If we all agree on the definition then we can say that science changed through history thanks to the new tools for observation.
It was science that explained to the ancient people that the sun went around the earth. That was the only possible explanation to the observation of the sun going up and down every day. Technology allowed people to build high ceiling cathedrals that allowed Galileo to observe the daily change in the swinging of the pendulum which in turn allowed him to come up with an explanation that its the earth turning on its axis made the sun seemed to go around the earth. Our days we have planes and satellites flying up there and observe and record how the round earth going around the sun.
You can say the science changed through out the history, I would say that technology changed, but the science stayed true to its definition.
2. Is science based on facts or opinion??
Science is based on objective observations, measurements, and records available at the time.
3. Why are there so many different meanings of science??
I am not aware of any different definitions of science. If you do, recite them and put your references.
4. Is it possible to really prove anything with science??
If it is not proven it is not science.
5. How would you answer the question “What is Science” to a high school student??
I respect high school students enough to tell them the same thing I tell you here. Why should the definition be different for the high school kids?
6. What could be done to minimize the misunderstanding of science??
Nothing. If you don't want to understand you will never understand. The latter apples to everything in life not just to science or math. People "understand" whatever they want or choose to "understand".
7. Can you formulate a theory of how will science change in ten years??
Even more computers and robots will be in use for observations and recording.
8. What is the difference between Chemistry, Biology, and Physics??
You really can use a glossary of a textbook or a wikipedia? Chemistry is a study of matter, Biology is a study of life, and Physics is a study of forces in the world around us.
9. In order to understand science, how important is it to understand the past.?
Some people really need to see how the invention happened, but not all of us. Many people can learn science without memorizing the name of the person, who first explained the phenomenon and the circumstances around it.
10.Is science strictly based on theory?
Not at all. It never is based on any theory. Science is based on observations and measurements. Theory is an explanation for the observation, many theories changed as our observation abilities changed. I mostly admire those geniuses who could predict some of the explanations before the obvious observation was available for the general public. One example I already showed you above how Galileo explained the earth's rotation before any plane flue around.
Another example from biology: the word germ appeared in our vocabulary in 1644 almost 10 years before the word microscope was added. That means some genius while observing some phenomenon around predicted the existence of microorganisms before we could actually see them.
I'll post this now, but I will edit it later.
1. How has science change throughout history??
To start we first must agree on the definition.
Science is an observation of the world around and an attempt to find explanations to the phenomena observed.
If we all agree on the definition then we can say that science changed through history thanks to the new tools for observation.
It was science that explained to the ancient people that the sun went around the earth. That was the only possible explanation to the observation of the sun going up and down every day. Technology allowed people to build high ceiling cathedrals that allowed Galileo to observe the daily change in the swinging of the pendulum which in turn allowed him to come up with an explanation that its the earth turning on its axis made the sun seemed to go around the earth. Our days we have planes and satellites flying up there and observe and record how the round earth going around the sun.
You can say the science changed through out the history, I would say that technology changed, but the science stayed true to its definition.
2. Is science based on facts or opinion??
Science is based on objective observations, measurements, and records available at the time.
3. Why are there so many different meanings of science??
I am not aware of any different definitions of science. If you do, recite them and put your references.
4. Is it possible to really prove anything with science??
If it is not proven it is not science.
5. How would you answer the question “What is Science” to a high school student??
I respect high school students enough to tell them the same thing I tell you here. Why should the definition be different for the high school kids?
6. What could be done to minimize the misunderstanding of science??
Nothing. If you don't want to understand you will never understand. The latter apples to everything in life not just to science or math. People "understand" whatever they want or choose to "understand".
7. Can you formulate a theory of how will science change in ten years??
Even more computers and robots will be in use for observations and recording.
8. What is the difference between Chemistry, Biology, and Physics??
You really can use a glossary of a textbook or a wikipedia? Chemistry is a study of matter, Biology is a study of life, and Physics is a study of forces in the world around us.
9. In order to understand science, how important is it to understand the past.?
Some people really need to see how the invention happened, but not all of us. Many people can learn science without memorizing the name of the person, who first explained the phenomenon and the circumstances around it.
10.Is science strictly based on theory?
Not at all. It never is based on any theory. Science is based on observations and measurements. Theory is an explanation for the observation, many theories changed as our observation abilities changed. I mostly admire those geniuses who could predict some of the explanations before the obvious observation was available for the general public. One example I already showed you above how Galileo explained the earth's rotation before any plane flue around.
Another example from biology: the word germ appeared in our vocabulary in 1644 almost 10 years before the word microscope was added. That means some genius while observing some phenomenon around predicted the existence of microorganisms before we could actually see them.
I'll post this now, but I will edit it later.
Thursday, February 25, 2010
Just a few more words about Diabetes
I read this book last summer, my daughter sent it to me and it was the right time for me.
Now it's been almost a year since I stopped eating sugar completely. I didn't miss it and I am not going back to adding sugar into my coffee. Now I believe it's taster without sugar :)
I lost about 30 pounds during this year, by just taking sugar out. Not all sugar, I eat unlimited amount of fruits. Sometimes I think I'll go bankrupt because of apples, $10 of apples per day seems excessive. My apples are so expensive because they are either organic or from local farms. These apples cleans my liver from fructose and other toxins stored in a form of fat that had been deposited on my stomach for all the previous years. 30 pounds of fat is a lot of volume. I probably lost 2 dress sizes, all my cloths are hanging on me.
I reached a plateau in my weigh lose so I added some Pilates exercises recently, they build long slim muscles, so I hope to lose more fat, but I am not sure if I'll lose any weight. We'll see.
During this year I had 2 slices of cake, 8 portions of potatoes, and 4 portions of rice. I didn't suffer, I chose my protein diet and I liked it. For breakfast I eat ricotta cheese and coffee with half&half. Lunch always contains some meat and veggies. I drink combucha once or twice every day. My "desert" is made mostly of nuts. I love all kinds of nuts, so I practically do not limit myself in this area. Dinner is different every day, if I ate too many nuts, I just drink green tea and eat my apples. But if I am hungry I would eat soup, or eggs, or anything I have at home even some more meat or ricotta cheese. For those who would like to follow I also drink some water or lemon water (water with squeezed lemon juice) first thing in the morning. This is a good advice for regular bowl movements.
I understand that this kind of diet would be much harder to follow if I was a person who loved pasta, rice or bread, but I am not.
I am still a menopausal woman, I am still sweating every day, my hormones are still playing games with me. My vision is less blur and this summer I am going to train my eyes to work harder and I will wear glasses less and less.
I have some thoughts about some TV adds for people with Type 2 diabetes, vegans, and other people who want to change their diets. Just think about it: why do I need a chocolate cake? or why would a vegan want a burger? Why? The adds on TV make us believe that there are some kind of substitutes for what we suppose to be missing. Instead we have to tell ourselves that we are better off without all those products that made us sick in the first place. I do NOT want a chocolate cake. NEVER again I want to poison my body with any man-made product that will overload my poor liver with work it does not want to do. I am not a vegan, meat does not make me sick, but if it did, the first thing I would cut meat out of my diet for ever and wouldn't ask for a fake burger. Good luck to all of you people in creating your own diet that works for you :) and keeps you healthy.
Sunday, February 7, 2010
About Discipline
I do agree that kids need rules and discipline, they respect you more if you know the rules, follow them yourself, and enforce them, but they will be the first to curse you out and break all the rules if you apply negative reinforcement or if you do not apply the same rule to yourself. Even if they obey you and pretend that they follow the rules you are enforcing, they will break them the moment you turn away.
So before using positive reinforcement you must use your own example for every rule you want to set.
Too many people still think that to enforce the rules you have to be mean. The reality often is right opposite. The nicer you are the more kids will try to abide. Research shows again and again that positive reinforcement works much better than negative reinforcement, which only provokes and encourages resistance.
I want to share my personal experience on this topic :)
It happened in June 1982. We just started our Group for Establishing Trust between USA and USSR (peaceniks). The KGB and the soviet authority could not decide what to do with us. All we were saying was that we wanted peace, like everybody else in the country, but we wanted it independently. We never criticized the powers, but we made suggestions for building step by step atmosphere of trust between the people of these 2 countries. To decide what to do with us the KGB needed to talk to us, get the info of what it was all about. So they picked a few of us and brought to different militia precincts “for conversations”. I was one of those few people.
I found myself sitting in front of a nice intelligent man who tried to make a conversation. I, in turn, did not want the conversation, I wanted to stop talking. But he was so polite and nice; my tong could not turn and say something rude. I was sitting making short abrupt answers and thinking how can I tell him that I didn’t want to talk to him. Suddenly, he decided to change his tactics: he raised his voice and started to scream at me. We looked at each other, and we both knew, that whether he wanted or not I got what I wanted. I got the reason to stop talking to him. My entire posture changed: I set back, relaxed in my chair. I started to breathe deeply and freely. I think my eyes smiled. I did not need to talk to him any longer; he was not polite nice man any longer, so I didn’t have to do as he said either.
The rest of that hour was not important. He was saying some stupid things like: calling for peace during cold war could be punished by capital punishment and other stupid things like that. I didn’t listen. I was fine.
This story, just shows how hard it is to be rude to nice and positive powers.
Same happens with my students every day. Very often they do not want to follow my instructions, but I never give my instructions in a command-like manner. I just ask them politely to do something and they just follow. Very often they find the assignment interesting. Sometimes they try to rebel anyway. The best thing is that their rebellion is also quite polite and we usually can find some compromise when I do not make them complete the whole assignment, or I make a variation that best suits their taste and interests.
You see, with positive reinforcement everybody wins: you have your rules in place and the kids learn.
Sunday, January 31, 2010
Are we all the same?
Two days ago I switched from Cable company to Fios. I have to learn all about my new channels and services. So two days in a raw I am waking up to watch Pilates and Yoga. I love my new possibilities :) Today I am watching "What's the Alternative?" about treating different people with the same conditions using different methods. They discuss the natural ways to treat skin condition using household products. The doctor explained that different people develop similar health problem, but cannot be treated the same. They cannot even have the same diet or exercise routine.
This broadcast made me thinking about the other areas of our lives.
The same idea I heard from the financial consultant yesterday. She said: Trust your gut, do not listen to what other people tell you to do, only follow the advices if your gut tells you it's good advice or it is good for You.
There is an entire field of research. Their advisers, after testing, tell you what kind of a job will make you happy and complete person. Some really good guidance counselors in high schools test the students before helping them to apply for a college.
Most woman's magazines give you advices on how to listen to yourself and be different.
Now I am thinking of our education system :( and realize again and again that as always we are behind the rest of the areas of our life. Even worse. If the rest of the world is rushing forward with new individualized technology, new individualized testing and treatments, and exercises, and financial portfolios, and cars and houses. Everything in our lives is individualized except what you are doing at school.
The funniest thing is that they tell you that they prepare you for a job place and then make you do everything opposite to what you will be required at any job place. Ha-ha-ha-ha.
You will chose a job you want to do - at school you have to learn what the State requires you to learn.
You will be able to quit if you are not happy at work or ask for a raise at least - if you decide to quit school before a specific age the court will make you go there and police will escort you to your classes or threaten you parents with neglect charges.
You have rights at any work place: if you are sick you can take sick-day, you have meetings where you voice you concerns, there is a procedure to make complaints and grievances - school has such powers over the children that even parents are not able to fight for their kids rights. I do not want to go into details here, but those who experienced that know what I am talking about.
And at the end the students are required to take all the same tests at the same time and excel in all areas of their study. This one is the worst because it takes the individuality out of the question completely.
The politicians are preparing new regulations to strip any individuality off of our kids in the future. They call it higher standards. They don't even try to pretend that they will take individual needs of a student into consideration. Everybody has to fit the "Standard".
I want to ask you, where are standards in the chaos of life? How do we prepare the kids to their adult lives by making them to fit the "standard"? How can we bring up happy individuals by suppressing individuality from such a young age? How can they become independent individuals if they are only taught to be like the rest of the class?
You see, this new channels I have on my Fios really made me thinking :) and they say that TV is not good for you :) I'll never agree to that hahahahahaaaaaa
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