Here at Cape High School "Physics First" is taught to all our 9th graders.
The CP Physics course is a typical high school course with a traditional textbook.
The Honors Physics course is a marvel. Dr Michael Efron has designed it as a Modeling Instruction type of class rather than a traditional textbook class. You can find a wealth of info describing Modeling Instruction at: http://modeling.asu.edu/modeling-HS.html
Dr Efron's Honors Physics class is remarkable:
There is no textbook for the class. Instead each unit begins with an experiment the students must perform in order to discover some important principle in Physics. (e.g. Newton's 2nd Law). The rest of each unit consists of worksheet (homework) problems, based on the unit's Physics principle, that students must attempt to solve at home and then present to the entire class.
The content of the course is equivalent to the first semester of a college physics course at a top engineering school. Of course al the problems have been drastically simplified and modified so that they can be solved with just simple algebra equations, but the actual Physics theory content is mostly the same as the first half of a college Physics course. As proof of this, the seniors who are taking the AP Physics with Calculus course will not reach a point where they are learning any new Physics theory beyond what was covered in 9th grade Honors Physics until mid January.
During the course of the year Dr Efron teaches the 9th grade students basic trigonometry (they need it to solve "ramp" problems. He also teaches them the relationship between the 3 graphs in his "stack of graphs".
graph 1 Position vs Time
graph 2 Velosity vs Time
graph 3 Acceleration vs Time
When Dr Efron teaches them how to transform one graph into another, he's actually teaching them the basic idea of Calculus - though he never tells them that they are learning Calculus!!
Here is a letter I sent to Tom Mikulka answering his question about the Physics Labs in 9th grade Honors Physics
Physics Lab Report
The Physics lab report that you asked me about was the “Newton’s Second Law” lab. The intent of the lab is for the student to investigate the relationships between Acceleration, Mass, and Force. This is one of the most important labs the students will perform during their 9th grade Physics course.
The basic setup is a small cart that can roll horizontally on a track with a pulley attached to one end of the track. A string is tied to the cart on one end, run over the pulley, and tied to a container that is hanging vertically from the pulley. Small masses can be added to the cart on the horizontal track and to the hanging container which can move vertically. The horizontal track is equipped with a motion sensor which, combined with software running on the Physics lab laptop computers, measures the horizontal Acceleration of the cart (along with the masses that have been added to the cart).
Dr Efron instructs the students to perform the lab in two parts.
• Part 1: How does Acceleration of the system change as Force on the system is changed?
• Part 2 How does Acceleration of the system change as the mass of the system is changed
There are many extremely important concepts that the student should understand when performing this experiment and many “common sense” misconceptions that the student must overcome. Some of them are:
• Since there are three quantities to investigate, Acceleration, Mass, and Force, the students must understand that acceleration is always the dependent variable and when they choose either mass or force as the independent variable they must hold the other (third) quantity constant so that all changes in the dependent variable (acceleration) can be solely attributed to changes in the independent variable.
• When the student adds mass to the cart, the mass of the system is being increased. When mass is being added to the hanging container the force on the system is being increased. This is counter intuitive to the students’ common sense and most find this very confusing. Dr Efron always tries to instigate student question/debate on this subject so that he can hint at the more subtle concept of inertial mass vs gravitational mass. He will return to this concept in a later unit when the students learn about the force of gravity.
• The students must understand exactly what “the system” means. If the mass being added to the hanging container is transferred from the masses in the cart, the mass of the system remains constant.
• The force diagram for the whole system is more complex than most they have seen to this point. They must realize that the gravity force and normal forces on the cart are perpendicular to the motion of the cart and do not contribute to the “net force on the system”. The students cannot draw a force diagram with a single point (the system) and show all the forces emanating from this single point as they have done in the past. Positive and negative values to motion and forces must be assigned according to the direction that the pulley rotates, not whether they point Up or Down.
After the students collect the data from each part of the experiment they enter it into their physics lab laptops and the software plots a line/curve. This plot will give them a general qualitative idea about the relationship between acceleration and the independent variable (either mass or force) for each part of the lab. But this is not enough to satisfy the lab. The lab requires them to make a math model for the relationship between acceleration and the two independent variables. They must be able to inspect each plot and determine if the relationship is linear or non-linear.
If the relationship is linear the math model will be of the form y = mx + b
If the relationship is non-linear, the students must use the graphical analysis techniques that Dr Efron showed them in the previous unit to determine the correct math model between the acceleration and the independent variable. For example, in this lab the students’ data plot of acceleration vs mass is not linear. They must recognize the shape of the data plot is an inverse relationship and confirm this by adjusting the data plot to acceleration vs 1/m. When the software shows this adjusted plot to be linear, the student knows that the inverse math model is correct.
The lab data should show that:
• A is proportional to F
• A is proportional to 1/M
• Therefore A = F/M and F = MA
Attachments from Dr Efron’s class:
• Format for Formal Lab Reports
• Experimental Design and Graphical Analysis of Data
• Scientific Methods Worksheet #4: Graphical Analysis
• Instructions for Formal Lab Report – Newton’s Second Law
Here's the type of thing that concerns me about our math program at Cape.
I tutor 9th grade Honors Physics students 3 or 4 days a week. Last week, I was working with one of the 9th graders and the problem we were working on (a block sliding down a ramp) eventually got to the point where we had a simple equation that required the student to solve for the force "F".
The student hesitated. He was unsure how to solve this because the unknown "F" was in the denominator of the right side of the equation. His first inclination was to divide both sides of the equation by "F". We worked on it for a minute or two and, with some prompting by me, he finally realized/remembered that he had to first multiply both sides of the equation by "F"; then divide both sides of the equation by "0.355" in order to isolate "F" on one side of the equation.
Now this student had taken Algebra in the 7th grade and Geometry in the 8th grade and was taking Algebra II currently. The solution to this simple equation should have been as automatic as tying his shoelaces. And his situation is not unique. Typically about a third of the 9th grade Honors Physics need help/reminders in order to solve this type of an equation - and almost 100% of them have already completed a year of Algebra in middle school.
Here's a sample problem on from the math section of the new SAT exam as described in a Jan 20, 2015 piece, "New SAT, New Problems", on The Atlantic web site at:
The new SAT math test will correspond with the Common Core Math Standards - it will focus on fewer types of math than the current version does, sacrificing breadth for depth and testing students on the material the College Board believes to be most essential to "college and career success."
This question, ranked by the College Board as "easy," is very much a product of the Common Core Standards, which ask students to both link abstractions (like the graph of a line) with real-world phenomena (such as the link between a person’s height and the length of his or her metacarpal bone) and express such connections verbally. (The answer, by the way, is A.)
The author worries that these are skills that students unfortunately haven’t yet mastered. and that few math teachers are ready and able to teach students these new skills.
The skills needed to answer this question are precisely what is being taught in our 9th grade Honors Physics classes.
Here's a good example of using calculus in the AP Physics course. It's an example of how to calculate the moment of inertia for a particular object.
The key is to get rid of the mass variable "dm" so there will only one remaining variable "R" in the expression we wish to integrate. The mass of the thin ring "dR" is equal to the density of the material times the volume of the thin ring. To get the volume, imagine that we cut the thin ring and spread it out so it's a 3D rectangle. Multiply the area of the top of the rectangle (R * dR) by the height h to get the volume.
Once you do this, the calculus part (integration) is simple. As is usually the case, most of the work is doing the high school algebra to rearrange terms.