This is a message I sent to my department head that outlines some of my frustrations with teaching science in the current educational climate. For my out-of-state readers, MCAS is the Massachusetts Comprehensive Assessment System–a set of high-stakes tests that high school students in Massachusetts must pass in order to graduate.
My department head sent the following message around to all of the high school science teachers at my school:
In preparation for next Tuesday’s professional development day, would you please start thinking about how mathematics is applied in your courses? I will send you a grid tomorrow that lists typical skills that you can use. One of the goals of next Tuesday is to compile a list of mathematical skills which can be shared with math teachers, coaches, etc.
Thank you,
$DEPARTMENT_HEAD
For starters, the Mass. Frameworks for Chemistry say:
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 (g); length (cm); and time (s).
* Use the Celsius and Kelvin scales.
Of the items specifically listed above, I’ve found personally that C1 chemistry students are weak at using/remembering common prefixes, converting within a unit, and using scientific notation, all of which are in the math frameworks. Most of them also do not know how to properly enter a number in scientific notation into their calculator (using the EE or EXP function instead of entering the number as an algebraic expression).
Approximately 1/3 of my C1 students have trouble grasping the concept that holding the x-value constant and changing the y-value means moving vertically on a graph, whereas holding the y-value constant and changing the x-value means moving horizontally.
In addition to the above, probably at least 10% of my C1 students are weak on other basic math skills, such as correctly setting up & simplifying fractions in order to enter the numbers into a calculator.
When we get to pH, the students who have taken Algebra 2 have seen logarithms, but they don’t have a working knowledge of what a logarithm means, and they have never seen logarithmic or semi-logarithmic graph paper.
In terms of the bigger picture, the constant drilling and the focus on low-level techniques in math classes in the post-MCAS world has produced students who have never been taught to examine or contemplate the process they’re using to solve problems, and most of them are ill-equipped to consider the question of why a particular problem-solving method works, which is the basis of scientific thought. It is no longer a good assumption that the kind of thinking that students are taught in their math classes will apply directly to their science classes. (This is probably one of the reasons college professors have observed that post-MCAS college students are performing less well than their pre-MCAS counterparts, despite the year-to-year increase in test scores.)
Post-MCAS students are also much quicker to give up on a problem if they don’t immediately see or remember how to do it, probably because in their math classes, if they don’t remember the trick or technique they were made to memorize, they have no hope of figuring out what to do from first principles. The post-MCAS students who do remember how to solve problems are much quicker to jump in and start applying a technique without analyzing the problem to see whether the technique applies to the problem.
In short, yes there are some specific math skills that students are lacking, but the real problem is much more systemic, and can’t be solved by simply asking math teachers to apply the same teaching techniques to our pet topics.
Nevertheless, I’ll enter my request list into your grid when you send it.
