We have found, by visiting middle schools, talking to middle school teachers, and giving teacher workshops on conceptual difficulties encountered by students in physical science classes, that most middles school science teachers are not trained in physical science. The vast majority of middle school science teachers are trained in biology. We have even encountered teachers with backgrounds in subjects totally unrelated to science, such as English, art, and home economics (no lie). Indeed, some biology teachers do a decent job when assigned to physical science classes, but many have difficulty grasping the material since they were not specifically trained for the subject. As a result, they use the text book as a crutch with little more understanding than the students get. This leads to a memorization exercise in middle school physical science classes that leave the students feeling like one would if they one were asked to memorize nonsense syllables. Indeed memorization is important, but without a proper framework upon which to hang the items to be memorized, they are quickly forgotten once the test is over. Try memorizing trig identities without understanding the unit circle and its relation to the Pythagorean Theorem, for example.

The idea for this web site began in 2007 when Fred Meshna reluctantly agreed to teach a 6th grade math class at the International School of Boston. That assignment opened his eyes to a gap that exists between arithmetic and algebra. It became apparent to Fred that many students do not successfully bridge that gap, partly as a result of a weak grasp of proportional reasoning. After one eye-opening lesson in which he defined Π (pi), he drew a big circle on the board and asked about how many times a string held up across the circle going through the center would fit around the perimeter of the circle. The answers were submitted on paper. Virtually the entire class said that the line going through the middle would fit around the perimeter either twice or a bit more than twice. They all claimed to have understood his lecture on pi, and to some extent they did. But the big idea was not driven home. Since then, we have had the opportunity to ask scores of middle school students this question after giving them the definition of pi (circumference / diameter), and even though they could all find the circumference of a circle given a specific diameter, when asked the above question out of context, the overwhelming majority of them answered the same way…”about two times.”

In 2011 Fred came out of retirement to teach honors physics to seniors in an upper middle class school district in Massachusetts. When he posed the question asked of the 6th grade students to his senior physics students, only about half answered correctly (about 3.14 times). The vast majority of the class did not understand the concept of a constant of proportion. When explaining the variables in Newton’s Universal Law of Gravitation, the students were at a loss to explain what was meant when told that big G in the equation is a constant of proportion. When it was explained that G is a constant of proportion like the gas constant R in the ideal gas equation learned in their junior year, they said, almost in unison, that they never really understood where R came from. This is exactly the same as the 6th grade students being able to use pi to find a circumference of a circle with a given diameter, but still not understanding that pi that is a constant ratio. The idea is the same as reducing fractions, but for some reason we are not bridging that gap.

What we have concluded from this is that teachers are not taking the time to make sure our students really grasp the nature of ratios and proportions. This problem becomes compounded when in chemistry and physics, students are required to measure and use measured quantities in labs, tests and assignments. Measured quantities include units, and units are concepts. A chronic complaint among science teachers is that students either completely ignore units or wrongly apply them. We believes that the reason for this problem is that, firstly, students do not understand the concepts behind many of the units they are introduced to in science classes. And secondly, when units are combined in a ratio, the conceptual difficulty is multiplied. Most students, for example, do not understand the unit for power (Watt), thinking that it is an amount of electricity, when in fact a Watt is a rate or ratio of a certain amount of work per time. Specifically a Watt is a Joule/second. But as with pi, when this concept is introduced, students can chug and plug out answers, but they prove they are missing the big picture when they say claim that 50 Watts is less energy than 100 Watts. This is like saying that 50 meters/second is less distance than 100 meters/second. Or saying that my house is only 15 miles/hour from school. The problem with giving ratio units a name such as the Watt, or the Volt is that these names mask the fact that they represent rates, or ratios. Furthermore, the units that comprise a ratio such as Joules/second for Watts, and Joules/Coulomb for Volts are most often poorly understood. So the combination of a weak grasp of proportional reasoning, coupled with a poor understanding of the concept behind units that make up ratio measurements, results in confusion.

This website is designed specifically to address these two problems. By giving a complete and historical background behind some of the more difficult concepts, and by interweaving math lessons that clarify the use of ratios and proportions focusing on units, we hope that teachers not specifically trained in physical science will be able to help students connect ideas more efficiently. Furthermore, it is our hope that even seasoned science teachers with a strong background in chemistry and physics might find some of the ideas in this site helpful.

It is important that before using this web site, teachers familiarize themselves with all of its components and with the way the components work together to facilitate a deeper understanding of the fundamental principles behind the physical sciences.

We hope you find the site useful.