A few weeks ago a reporter from South Korea visited the period 7-8 class of juniors, and observed a class very different from what typically happens in South Korean high school science classes - we were doing a lab, where students were using measurements to develop an empirical mathematical relationship for the period of a pendulum. In addition, they were using and evaluating four different measuring techniques to get the timing data (stop watch, video, electronic force sensor, and a computer simulation to test the effect of gravity on the period). In South Korea, a huge percentage of students complain they do not enjoy science, nor will go into science, as their schools must focus on strict testing and science is largely reduced to memorizing facts for those tests. Check out the article here.
Also, check out more links related to our work with NU in STEM education, and our Korean connection.
Monday, December 23, 2013
A Computational Thinking Challenge - Developing a Programming Mentality a Graphical Way
Check out the site https://blockly-demo.appspot.com/static/apps/maze/index.html?lang=en. There is a set of 10 challenges, where you have to set up a set of instructions (i.e. an algorithm), to accomplish the task. You effectively are writing a program to solve the task, without actually using a programming language. It is graphics based, instead, but it helps develop a programming mentality and begins teaching how a real program is structured and setup. Enjoy! And let me know if you figure out the last challenge in articular - it is tough, and I have not yet figured out the correct algorithm! :-)
Thursday, December 12, 2013
Anthill Art (and complexity)
I've never seen anything quite like this. Thanks to Aly for sending the link. Check out the complexity and intricacy of an anthill.
Wednesday, December 11, 2013
How We Use Del (MV Calculus) in Physics
For students who are in multivariable (MV) calculus, one of the main topics you study has to do with the vector differential operator called del (the upside down triangle). Using this operator we can define gradient, divergence, and curl. Another useful operator for waves, E&M, quantum mechanics, and other physics topics, is the laplacian (del-squared).
In physics, gradients can be used to describe vectors that are directed from high values of a scalar quantity to low values. An example is the force of gravity, which is directed to move objects from high potential energy to low potential energy. We have electric fields flow from high electric potential (voltage) towards low electric potential. We see heat flow from high temperature towards low temperature, or air masses flow from high pressure towards low pressure. These can all be described by gradients.
Divergence is used for vector fields that radiate from a point source. This could be light, sound, radiation, gravitational fields, or electric fields, all radiating from point sources.
Curl is used for vector fields that circulate around some vector source. A prime example is the circulating magnetic fields that are found around electric currents, or circulating electric fields around a changing magnetic field.
Check out the video to see a few examples, and hopefully you will see how these strange mathematical operators are applied to real, physical phenomena.
In physics, gradients can be used to describe vectors that are directed from high values of a scalar quantity to low values. An example is the force of gravity, which is directed to move objects from high potential energy to low potential energy. We have electric fields flow from high electric potential (voltage) towards low electric potential. We see heat flow from high temperature towards low temperature, or air masses flow from high pressure towards low pressure. These can all be described by gradients.
Divergence is used for vector fields that radiate from a point source. This could be light, sound, radiation, gravitational fields, or electric fields, all radiating from point sources.
Curl is used for vector fields that circulate around some vector source. A prime example is the circulating magnetic fields that are found around electric currents, or circulating electric fields around a changing magnetic field.
Check out the video to see a few examples, and hopefully you will see how these strange mathematical operators are applied to real, physical phenomena.
Learn General Relativity!!
Here is a 2 hour lesson on general relativity, taught at a relatively 'basic' level. You need to know geometry, algebra, and some calculus. I have watched a bit of this, and what I saw is quite good and understandable. Give it a try if you are interested in more details about what Einstein's great theory says and predicts, and some of the mathematical concepts of general relativity.
Monday, December 9, 2013
How to Handle Dielectrics in Capacitors
Capacitors are circuit components that store charge and energy. There are two surfaces, which take the shapes of either two plates, two concentric spheres, or two concentric cylinders. One surface is positive, and the other equally charged negative. An electric field in between the two surfaces provides the mechanism for storing energy.
By definition, capacitance is the ratio of the charge on one of the surfaces, Q, divided by the voltage difference between the surfaces, V. We have C = Q/V. If you want to see how we do this for spheres and cylinders, check out this video.
A dielectric is an insulating material that fills the gap between the charged surfaces, and essentially all capacitors in your electronic gadgets have dielectrics. Dielectrics will partially polarize, produce a small opposing electric field due to the polarization, and weaken the net E-field of the capacitor. This reduces the voltage difference, which finally increases the capacitance. C_new = KC_o. K is a dielectric constant > 1.
Check out the video, which also shows how to calculate the new capacitance when the gaps are partially filled with dielectrics, at least for parallel plate capacitors.
By definition, capacitance is the ratio of the charge on one of the surfaces, Q, divided by the voltage difference between the surfaces, V. We have C = Q/V. If you want to see how we do this for spheres and cylinders, check out this video.
A dielectric is an insulating material that fills the gap between the charged surfaces, and essentially all capacitors in your electronic gadgets have dielectrics. Dielectrics will partially polarize, produce a small opposing electric field due to the polarization, and weaken the net E-field of the capacitor. This reduces the voltage difference, which finally increases the capacitance. C_new = KC_o. K is a dielectric constant > 1.
Check out the video, which also shows how to calculate the new capacitance when the gaps are partially filled with dielectrics, at least for parallel plate capacitors.
Sunday, December 8, 2013
How to do Multi-Loop Resistor Circuits
In E&M, one of the circuits we try to understand is a multi-loop resistor circuit. This is a circuit that has multiple batteries arranged in a way that takes away our ability to find the total resistance in the circuit. Basically, the multiple batteries ruin pure parallel combinations of resistors in our circuit. We cannot find the total resistance, and therefore cannot find a total current for the circuit. We need a new method since the traditional, usual method we learn to do does not work.
The technique of this video involves using Ohm's law and Kirchhoff's series rule (i.e. voltage of the batteries = sum of the voltage losses of the components of the loop) to set up loop equations, and then solve the loop equations for the loop currents. The math is algebra, specifically solving a system of equations for multiple unknown currents. Check it out, and I hope the example helps.
The technique of this video involves using Ohm's law and Kirchhoff's series rule (i.e. voltage of the batteries = sum of the voltage losses of the components of the loop) to set up loop equations, and then solve the loop equations for the loop currents. The math is algebra, specifically solving a system of equations for multiple unknown currents. Check it out, and I hope the example helps.
Project Excite Overview
As students have heard about in class, we are beginning work with our 14th cohort of Project Excite 3rd grade students. But what is Project Excite? What are these young students doing when they come over to ETHS ten times for science and math related activities? Does this effort pay off?
One of the primary goals for Project Excite is to prepare minority students for honors and AP level science and math classes by the time they are in the high school. The model for doing this revolves around the notion that we must start young. The academic achievement gap begins forming very early, and many years prior to high school. We start with the 3rd grade, where there is already a significant academic achievement gap, at least as represented by a variety of testing measures and teacher experience.
By working consistently with about two dozen students per cohort, the achievement gap is eliminated by the 7th grade on average, again as measured by some tests (ISAT and EXPLORE). On paper, these students tend to be as strong and as prepared for high school as white students. One issue that we may be seeing (this is a hypothesis) is related to stereotype threat, where on paper a group should be able to perform as well as other groups, but in reality they underperform. This can happen in many contexts when there is a social stereotype or expectation that a group is supposed to underperform. But if one can take away that stereotype threat, then the same group performs at the same level as the 'dominant' group.
Whatever the reason, we are now working on figuring out what supports are needed at the high school level to ensure the Excite students do well in those honors and AP classes, and get into top-tier colleges so they have multiple options available for majors and careers.
One of the primary goals for Project Excite is to prepare minority students for honors and AP level science and math classes by the time they are in the high school. The model for doing this revolves around the notion that we must start young. The academic achievement gap begins forming very early, and many years prior to high school. We start with the 3rd grade, where there is already a significant academic achievement gap, at least as represented by a variety of testing measures and teacher experience.
By working consistently with about two dozen students per cohort, the achievement gap is eliminated by the 7th grade on average, again as measured by some tests (ISAT and EXPLORE). On paper, these students tend to be as strong and as prepared for high school as white students. One issue that we may be seeing (this is a hypothesis) is related to stereotype threat, where on paper a group should be able to perform as well as other groups, but in reality they underperform. This can happen in many contexts when there is a social stereotype or expectation that a group is supposed to underperform. But if one can take away that stereotype threat, then the same group performs at the same level as the 'dominant' group.
Whatever the reason, we are now working on figuring out what supports are needed at the high school level to ensure the Excite students do well in those honors and AP classes, and get into top-tier colleges so they have multiple options available for majors and careers.
Saturday, December 7, 2013
Rotational Motion Introduction
Honestly, for many students rotational motion is the least familiar, and therefore challenging, topic in mechanics. To help make our studies of rotations as painless and as familiar as possible, we will compare basic quantities needed for rotations to old favorites from linear motion. Basically, just about everything we did in linear motion will have the same mathematical relationship in rotations. For example, constant acceleration, Newton's 2nd law, and kinetic energy will all have the same general concept and form in rotations, just with new rotational quantities.
It is these basic rotations quantities that are introduced in this video. They include angular displacement, angular velocity, angular acceleration, torque, angular momentum, and rotational KE.
It is these basic rotations quantities that are introduced in this video. They include angular displacement, angular velocity, angular acceleration, torque, angular momentum, and rotational KE.
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