## Monday, October 24, 2011

### Science in Elementary School

 Kids are left behind in science.

What has happened to science in elementary school?
With an emphasis on math and reading, science has been pushed to the side in many elementary school classrooms [1]. There is no time and little equipment. Often, K-8 teachers do not know enough science to teach it well. Furthermore, the math needed to do science is seldom taught or introduced. Science is highly mathematical, yet K-8 science textbooks and teachers seem to limit the math. None of this is new. Science has been neglected for decades.

The thinking required in science, however, is different from the thinking done in school math. Mathematical statements are shown to be true or false by following a set of rules called number properties (axioms) of operations, equality, etc. [2]. One true statement forms the basis for another true statement and so on. This is the way math knowledge builds: one idea builds on another. In short, the rules (properties of numbers) in math do not change. The definitions in our number system do not change either. A fraction (rational number) will always be represented by the quotient of two integers (a/b, b ≠ 0). Equivalents like 3/4 = .75 = 75% will not change; 7 is always 6 + 1, etc. Equivalency and substitution are important ideas in mathematics.

In science, however, there is no "true or false" like in school math. Instead, there are observations and inferences. There are no absolutes in science. The rules in science can change based on "partitioning by scale." In short, Newton's laws of motion still work, but not at the atomic (very tiny) scale.

There are facts, such as the number of protons in the hydrogen atom, etc. Kids must know facts (background knowledge). In addition, they also must know how to measure (make observations), how to draw valid inferences (conclusions) based on observations (data), how to minimize confirmation bias and errors in experiments, how to do the required math, how to communicate results with charts and graphs, and how to distinguish between correlation and cause-effect. Above all, students must learn to distinguish between observation and inference. But, this is not the organizing principle of science textbooks. Too often, TV programs, documentaries, news programs, textbooks, and other materials blend the two. Often, students interpret an inference as fact.

Students should do science projects that have clearly defined independent and dependent variables and control.  Moreover, students should be taught what the late Richard Feynman calls intellectual honesty in science, something that is often lacking. In real science, we bend over backward to prove our conjectures wrong through experiments. We also present data that does not support our conjectures. We do not fudge data. And, we do not extrapolate beyond known data, i.e., make an inference based on an inference. An inference based on another inference is a misguided conclusion. Such extrapolation of data is more common than most people think. A common example would be a computer model of a complex system [stock market, weather, etc.] that attempts to forecast the future [based on the past] and makes unproven claims. This is not science; it is speculation

Feynman states, in a lecture, that physicists guess theory, then they test it. "If [we guess a theory that] disagrees with experiment, then it is wrong." Science is not based on, authority, opinion, consensus, or political agenda. It is based on an experiment. Furthermore, experiments must be repeatable and peer-reviewed. Lisa Randall, a particle physicist, writes, "People too often confuse evolving scientific knowledge with no knowledge at all and mistake a situation in which we are discovering new physical laws with a total absence of reliable rules."

Dr. Randall clarifies, "Science evolves as old ideas get incorporated into more fundamental theories. The old ideas still apply. The wisdom and methods we acquired in the past survive. Today's methodology began in the seventeenth century." Kids should study Newton's laws of motion because they still apply. Randall says that we can still measure pressure, temperature, and volume because they are real quantities. In short, fundamental scientific knowledge is important and should be stressed in school.

Regrettably, many of the elementary school science textbooks I have seen are incomplete and often perpetuate misconceptions. They are almost math-less, which misleads students. The real world is explained (modeled) through equations. The textbooks do not teach what science really is. One fundamental idea is that scientists try to prove ideas wrong, not right, by carefully crafted experiments; i.e., science does not prove anything right. Scientists seek out counterexamples and correct itself by getting rid of false ideas. According to Karl Popper, every theory must be falsifiable.

New Science Framework

The new science Framework from the National Research Council, oddly enough, was written by the Division of Behavioral and Social Sciences and Education and its committee, which is made up of mostly of educators, not real scientists. In fact, the "science content" experts (i.e., the design team) were not allowed in meetings in which the final decisions (consensus) regarding content were made (p. 17). Surely, You're Joking. No! Also, read the K-12 Science Framework.
I was disappointed after reading parts of the new K-12 science framework from the National Research Council (July 19, 2011).  The Framework committee merges science with engineering and technology, skimps over math needed to do science, stresses scientific processes (called "practices" in the document) over content, requires little content knowledge in elementary and middle school, and combines chemistry and physics, leaving important content out.
In my view, the new Science Framework from the National Research Council is flat. It does not challenge children, and it does not paint a true picture of what science is all about. The fundamental idea, that science does not prove anything right, is missing. The Framework also lacks a historical perspective. Missing are the great scientists and how they changed the focus of science, e.g., Galileo, Dalton, Maxwell, Bohr, Heisenberg, Plank, Dirac, Einstein, Feynman, Higgs, etc. Moreover, the Framework lumps technology and engineering together; however, they are applications or products of science, not science. The framework skimps on chemistry and physics and the math needed to do the science. Is this the best we can do? It is disappointing!
Note. I wrote an analysis of the Framework last summer (July 2011). It is very long. Here is a snippet: The Framework writers insist that a hypothesis (or theory) is not a guess. It is. This is what scientists do--they guess or make conjectures, then they test to see if the guess can be shown false. If an idea (guess) is not testable, then it is not science. We need to teach the testability principle by experiment to kids learning science. David Deutsch (The Beginning of Infinity, 2011) writes that conjecture (making a guess) is the real source of all our theories. Theories must be testable. He writes, “Knowledge must be first conjectured and then tested.” In science, we do not rely on authority or opinion. We have “a tradition of criticism,” says Deutsch. The bottom line, according to physicist Richard Feynman is, “If it does not agree with experiment, then it is wrong.” In other words, real science self-corrects itself over time. Ideology does not. Science does not prove ideas right; it eliminates wrong ideas.

Many old ideas (e.g., Newton's laws of motion) are correct but incomplete. The laws work well at one scale, but not at another scale (e.g., atomic). We should not toss out Newton because his "laws" are incomplete. Lisa Randall, a particle physicist, says that many of the old ideas apply and have practical applications at the right scale ("appropriate conditions"). This [the scales] is what we should teach kids. Scales are an organizing principle in science.

Elementary and middle school kids should learn Newton's laws of motion and the historical contributions of scientists like Galileo. The radical methods pioneered by Galileo in the 17th century are still used today: proof by experimentation (not authority, opinion, or consensus), thought experiments, and the use of technology to extend our senses to make better observations. For Galileo, the technology was the telescope. Technology plays an important role in science, but it is not science. by LT, ThinkAlgebra, July 2011

If we want students to understand the world, then we should teach them substantially more physics and mathematics early on. Furthermore, we should establish math and science standards that, at the least, match the benchmarks from nations that excel in these academic disciplines. In my view, the new K-12 Science Framework does not do this. The Science Framework is the latest version of science education written by a committee made up of mostly nonscientists. It is off-target because it requires very little knowledge of math needed to do science and very little science content knowledge. The committee's makeup and its frame of mind in composing the framework are troublesome. It is not the best we can do.  It is not even close. And, as ZE"ve Wurman, a critic of Common Core math standards, explains, the conceptual science Framework is "science appreciation" all over again.

Also, read  Most Kids Don't Understand Science by ThinkAlgebra

Endnotes
[1] A report supporting my observations was released at the end of October (Strengthening Science Education in California). The report states the obvious: little science is taught in elementary school. But, neglecting science in grade school is not new. In my experience, not much science has been taught in elementary school for decades. Middle school science has gone downhill, too. There is not enough stress on basic science content, reading science, and learning the math needed to do science. Furthermore, many teachers are ill-prepared to teach science. 10-28-11

[2] There are not that many properties. A few of the basic properties [axioms] of numbers that should be learned in first grade in the first month or two of school are: add zero [identity] property, add one property, commutative property of addition (2 + 3 = 3 + 2), equality [or equivalency] property (2 + 3 = 1 + 4), "add in any order" property (3 + 4 + 7 is 10 + 4 or 14), etc. The idea that teaching arithmetic to 1st graders should use a framework based on number properties, rather than counting, is absent in American programs. Morris Kline writes, "Axioms are suggested by experience and observation. Kline also writes, "Operations on numbers [must] give a result that fits our experience." He states that "axioms are useful when our experience fails us or leaves us in doubt." Indeed, axioms (number properties) come in handy as kids learn arithmetic. For example, 3 + 5 = 10 - 2 is a true statement because of the transitive property of equality. In "little kids" talk, both 3 + 5 and 10 - 2 name the same point on the number line and, therefore, are equal to each other (equivalent).

Mathematician Morris Kline (Mathematics for the Nonmathematician) states that operations (let's say, fractions) are designed to "fit experience." Arithmetic facts and operations are learned mostly by rote, but students should also be aware of the axioms or properties (e.g., commutative property of addition and multiplication) that govern operations to determine whether or not the mathematics is correct. For example, I can explain why 1/2 of 1/3 is 1/6 on the number line, but this type of understanding does not come into play when students are multiplying fractions (e.g., 2/3 x 3/4). In short, when applying the multiplication of fractions algorithm, students do not think in terms of marking off 3/4 of one whole on a number line, then dividing each fourth into thirds, which gives 12ths (but from 0 to 3/4, there are nine equal parts or ninths. Converting 2/3 to 9ths = 6/9). Counting over 6 tick marks, you end up at 6/12 or 1/2, etc. Sounds confusing? It is to many kids.

Furthermore, making a number line model for fractions with larger numerators or denominators becomes a total mess. The multiplication of fractions algorithm can be inferred from a number line demonstration. Students should be taught to depend on efficient methods (algorithms, step-by-step procedures, operations on numbers, or recipes) that produce correct answers fast

The multiplication of fractions algorithm can be "formulated" by the number line idea and other clues by the 3rd or 4th grade. For example, ½ of a number (e.g., 1/2 of 10) produces a smaller number, not a larger number (½ of 10 is 5; it means ½ x 10 = 5). We know this by experience and develop a multiplication of fractions algorithm so that the answer is always correct. (See Example 2 below)

In division, 5 oranges divided into halves is 10 (halves). In arithmetic, this is 5 ÷ ½ = 10. To divide by ½ gives the same result as multiplying by 2/1 (the reciprocal of the divisor. This is invert and multiply). The algorithm for the division of fractions is formulated to fit experience. In short, 5 ÷ 1/2 = 5 x 2/1. Thus, to divide by any number, multiply the number by the reciprocal of the divisor and then apply the multiplication of fractions algorithm. In short, students change division to multiplication.

In Example (1), adding the fractions should produce a larger fraction. Thus, the idea of adding the numerators and adding the denominators does not work because it does not fit our experience. Adding fractions can be represented by adding lengths on the number line. The answer is greater than one, not less than 1. The algorithm does not work.

In Example (2), multiplying the numerators and multiplying the denominators works
(fits our experience). It is the algorithm that kids are taught to use when multiplying fractions. A fractional part of any number (fractional part must be less than 1) produces a smaller number. (But, 3/2 x 7/5 will produce a larger number because 3/2 is 1 + 1/2 and 7/5 is 1 + 2/5. This is consistent with our experience when both factors are greater than 1.)

Algorithms (operations on numbers) must fit experience, be efficient, and produce the correct answer.
10-24-11, 10-28-11, 11-1-11, 12-223-11