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?
