An Independent Episcopal Day School for Ages 3 Through 12th Grade in Burlington, New Jersey

Is that mass? Or is that meters?

Michael Russell, Chair of Mathematics and Science Departments / May 1

“I get the concepts, but I don’t know where to start in this problem.” This is a common complaint I hear from students in my Physics classes. Though they feel confident in their ability to describe concepts and terms, students are stumped by the challenge of quantitatively applying those same concepts and terms through algebraic problem solving. I have struggled to understand why this mental barrier exists. After reading both “Neuroteach” and Daniel T. Willingham’s “The Reading Mind,” I think I have a firmer grasp of one of the primary contributors - cognitive overload while reading through word problems.

Consider the letter “m”. Within the first two weeks of class, students learn three very different uses for that letter. In equations, it represents an object’s mass. When measuring distances, it is the way we indicate it was measured in meters. Finally, a lowercase ‘m’ prefix on a unit stands for ‘milli-,’ meaning quantity preceding it should be multiplied by 10-3.

Keeping those three different uses in mind, it is very easy to see why a student might reach cognitive overload when reading the following word problem:

“A box with m = 2.5 kg is accelerated from rest at a constant rate over a distance of 1.5 m in 15.5 s. It is then decelerated by a -1250 mN force over a distance of 0.95m. Calculate the final speed of the box in m/s.”

All three of the different uses for the letter ‘m’ are utilized to build the problem to be solved above. According to Willingham, studies suggest that readers need to know the definition of no less than 98% of the words they encounter in order to demonstrate comfortable comprehension. In the 50-word problem above, that means more than one unfamiliar term or symbol is liable to push a reader beyond their comfort zone and into a mental territory where they give up on trying to understand what they’ve read.

Furthermore, Willingham notes that true mastery of what is read requires a reader to build a situation model wherein they not only understand each word, but also how the word fits contextually within its surrounding words. Thus, a student who perseveres might recognize what each ‘m’ means, but they may not be able to build a visual representation of the problem in order to solve it because they don’t see how ‘mass’, ‘milli-’, and ‘meters’ all allow us to solve for speed.

In reading “Neuroteach,” I started to realize that my instructional approach to decoding word problems could be improved if I more effectively deployed the interweaving strategy throughout the year. While I spent a significant portion of time at the beginning of Physics teaching students the units of measurement, unit prefixes, and how equations are to be interpreted, I did not spiral back to these topics quite as deliberately as I should in later units. As a result, those students who have a “one and done” attitude to learning struggled, as they had not yet built firm interlocking memories of these concepts and had lost the short term memory access that earlier allowed them to access the necessary information.

As I’ve built the rest of my activities and assessments for this year, I’ve tried to create meaningful review problems that help connect back to previously covered content in an effort to further build my students’ ability to read and comprehend Physic word problems. I’ve also pointed out to students when these problems occurred as a means of helping them know what to review if they’re struggling, thus helping them “mini-review” targeted concepts in preparation for class. My plan for next year is to change the structure of my lessons focused on solving word problems by including some of the situation-mapping activities Willingham demonstrates throughout “The Reading Mind” with the goal of helping more students feel they can comfortably comprehend the words on the pages of their Physics worksheets.