The Massachusetts Board of Elementary and Secondary Education has adopted revised science standards. They are based on the Next Generation Science Standards, which itself is based on A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012), from the National Research Council of the National Academies.
High school students are expected to have learned certain math skills by the end of grade 8; they will use these math skills in this course. Additional math skills are introduced throughout the year.
Also see Benchmarks: American Association for the Advancement of Science. The American Association for the Advancement of Science (AAAS) is an American, non-profit organization promoting cooperation among scientists, defending scientific freedom, and supporting education and outreach for the betterment of all humanity. Their pioneering studies – Science for All Americans, and Benchmarks – have been used to reform science education, including the National Research Council’s A Framework for K-12 Science Education (2012) and the Next Generation Science Standards.
We are preparing students for college and real world careers, where assignments must be completed in a set amount of time. Timed standardized tests include:
Some MCAS exams, e.g. English Language Arts Session 2B
PARCC Math test: Algebra, Geometry, and Integrated Mathematics.
Unit 1 – 90 min, Unit 2 – 90 min, Unit 3 – 90 min
SAT subject area test in physics: 75 questions in 60 minutes
AP Physics: 50 multiple choice in 90 minutes, and 5 free-response in 90 minutes.
MCAS test sessions are designed to be completed within 60 minutes. The MA Department of Ed suggests that schools schedule a two-hour block for each test session. Most MCAS exams are currently untimed. Nonetheless, during the school year ALA has students take timed exams, for the above-stated reasons.
There are 45 questions per physics exam, with about 5 of them being full-page, open-response questions, which may involve writing, reasoning, mathematics, drawing, etc.
For the MCAS day itself, no test session may extend beyond the end of the regular school day, and any individual test session must be completed on the same day on which it begins.
1. No horseplay.
2. No using cell phones or other digital electronics (unless otherwise instructed)
3. Everyone participates – yet just one person at a time.
3. Always bring: pencils, colored pencil set, eraser, calculator, and both lined and blank paper to take notes on.
4. If you miss class it is your responsibility to find out what you missed. The first step is to get a copy of the notes/handouts.
Why Study Physics?
from University of Saskatchewan, Physics and Engineering Physics
Whether you spend a lifetime studying physics, or just take one class, at least a few of the reasons listed below will make the effort well worthwhile.
Physics is the most fundamental of the sciences. It is concerned with the most basic building blocks of all things – from ants to antennas, from quarks to quasars.
The study of physics means trying to find out what the universe is made of, and how these things move and interact with each other. So in one sense, all the other sciences are built on the knowledge gained through the study of physics.
Physics is beautiful. Physicists love simplicity. They are constantly striving to find the most fundamental ideas that can be used to describe even the most complex of phenomena. For example Newton found that only a very small number of concepts could be used to describe just about all of the mechanical world – from steam engines to the motion of the planets. Not only is this beautiful, it’s downright amazing!
Physics teaches you to think. This might seem like a strange statement. The study of all subjects teach you to think. But because physics deals with the most basic concepts, the application of such techniques as “Separation of Variables” and “The Scientific Method” are never more clear than they are in the study of physics. Once mastered you will find that these methods can be applied to all subjects, including the business world and just coping with everyday life.
Physics is a creative subject. The concepts of physics don’t come easily. Someone has to come up with a theory to begin with. This is just as much a creative process as composing music. But where physics, and science in general, differ from the Arts is that no one will accept your theory unless you have some way of testing its validity. Experimental physicists sometimes have to be enormously creative in coming up with methods of testing theories and measuring things in the world around them. For example, how do you tell that there is a planet orbiting a star that is so far away that it appears as nothing more than a spec of light in even the most powerful telescopes?
Physics gives you a new appreciation of the world around you. You can look a rainbow and say “Wow, pretty colours!”, or you can marvel at the amazing interactions between photons and electrons that come together in that particular way when light from the sun strikes spherical water droplets in the sky, and that you perceive as a multicolored arc suspended in the air. Now that’s awe!
Physics is fun. Lastly, studying physics gives you the opportunity of playing with a lot of really cool toys!
What math skills do you need?
Students are expected to know the content of the Massachusetts Mathematics Curriculum Framework, through grade 8. Below are some specific skills from the Mathematics Framework that students in this course should have the opportunity to apply:
Construct and use tables and graphs to interpret data sets.
Solve simple algebraic expressions.
Perform basic statistical procedures to analyze the center and spread of data.
Measure with accuracy and precision (e.g., length, volume, mass, temperature, time)
Convert within a unit (e.g., centimeters to meters).
Use common prefixes such as milli-, centi-, and kilo-.
Use scientific notation, where appropriate.
Use ratio and proportion to solve problems.
The following skills are not detailed in the Mathematics Framework, but are necessary for a solid understanding in this course:
Determine the correct number of significant figures.
Determine percent error from experimental and accepted values.
Use appropriate metric/standard international (SI) units of measurement for :
mass (kg); length (m); time (s); force (N); speed (m/s); acceleration (m/s2 ); frequency (Hz); work and energy (J); power (W); momentum (kg•m/s); electric current (A); electric potential difference/voltage (V); and electric resistance (Ω).
Use the Celsius and Kelvin scales
Mathematics is the language of physics
Natural philosophy [i.e., physics] is written in this grand book – I mean the universe – which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. [The universe] cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.
Galileo, Opere Il Saggiatore p. 171.
Mathematics is the language of physics. Physical principles and laws, which would take two or even three pages to write in words, can be expressed in a single line using mathematical equations. Such equations, in turn, make physical laws more transparent, interpretation of physical laws easier, and further predictions based on the laws straightforward.
Mesfin Woldeyohannes, Assistant Professor, Western Carolina University
ἀεὶ ὁ θεὸς γεωμετρεῖ – Aei ho theos geōmetreî. God always geometrizes.
Plato, 400 BCE, classical Greece, as quoted by Plutarch in his The Moralia, Quaestiones convivales. (circa 100 CE)
Wigner begins his paper with the belief, common among those familiar with mathematics, that mathematical concepts have applicability far beyond the context in which they were originally developed. Based on his experience, he says “it is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena.” He then invokes the fundamental law of gravitation as an example. Originally used to model freely falling bodies on the surface of the earth, this law was extended on the basis of what Wigner terms “very scanty observations” to describe the motion of the planets, where it “has proved accurate beyond all reasonable expectations”.
Another oft-cited example is Maxwell’s equations, derived to model the elementary electrical and magnetic phenomena known as of the mid 19th century. These equations also describe radio waves, discovered by David Edward Hughes in 1879, around the time of James Clerk Maxwell’s death. Wigner sums up his argument by saying that “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it”. He concludes his paper with the same question with which he began:
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
My teaching philosophy
Adapted from “Reclaiming Education”, Lisa VanDamme, March /April 1999, The Intellectual Activist.
It seems that science is not taught in the public middle schools today….At the high school level, most students are exposed to some science, and most are required to take a physics class. But these physics classes generally suffer from a serious [methodological] problem. Let me give you an example of this problem, and then I will explain it. The following scenario will probably be familiar to many of you. It is halfway through the semester, and your physics teacher is going to discuss Newton’s Laws. You come into class, sit down, and the teacher begins to write on the board:
“These are Newton’s three laws of motion. #1: Every body continues in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by forces impressed on it. #2:…,” and so on. No explanation is given as to what observations, integrations, or discoveries Newton made in order to arrive at these laws of motion. No account is given of the long history behind Newton’s laws of motion–of the earlier theories that were refuted or were accepted and refined.
Here, scientific knowledge is presented as a series of commandments rather than as conclusions that have been reached by a laborious process of observation, experiment, and induction. If taught physics this way, a student’s grasp of the principles is necessarily detached from reality.
This approach to teaching physics also fails to provide students with a real understanding of the scientific method. If they are not exposed to the way in which a great scientist makes observations and then integrates them to arrive at an innovative conclusion, then they will not understand how science is done. Like the writing process, it will seem like an innate gift of born scientists, and they will never understand that they too can learn the process by which new discoveries are made.
Because students are not learning the scientific method through real, historical examples of scientific discoveries, they usually have a few classes within the physics course devoted just to the scientific method. But the way this method is taught reflects the same rationalism. Students are told that the first step in the scientific process is to, “Choose a hypothesis.”
Not a word is said about the process of observation that should lead you to a hypothesis, so the implication is that the hypothesis must be chosen on a whim or divinely inspired. Again, what they leave out is observation, integration, and induction.
We need to use a way of teaching physics that gives students a real, grounded, and complete understanding of the principles of physics. The best way is to teach it chronologically. By chronologically, I do not mean that we try to chronicle every development in the history of physics. That would be practically impossible and pedagogically disastrous. Rather, we teach the essential discoveries of physics in their historical order of development.
By teaching physics chronologically you teach it inductively. Induction is the process of reasoning from concretes and lower-level abstractions to higher-level abstractions. The earliest discoveries in physics are necessarily the closest to the perceptual level. They are the simplest discoveries, and lay the groundwork for all later developments.
So, if you study physics historically, you begin with these simple discoveries, close to the perceptual level. After these discoveries are grasped, you can proceed to the next stage in history, integrating the most basic discoveries with the observations made by the next scientist, and grasping a conclusion at a step more removed from the perceptual level. As you proceed through history, you are able to grasp principles on increasingly wider levels of abstraction.
In our historical approach to physics, students gain their knowledge inductively, starting with knowledge close to the perceptual level and building to greater and greater levels of abstraction.
There is an added advantage to teaching physics historically. It is fascinating to learn physics as a story–to learn how and why one development led to the next, and to learn it in the context of the lives of actual scientists. We give some biographical detail when possible. Children love to be inspired by heroes–so knowing that Newton did most of his work in two years on a sheep farm, and hearing that Galileo did much of his work while under house arrest gives them more interest in each man’s scientific discoveries.
Previously released Physics MCAS exams
animations and GIFs
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