Environmental Geology and Natural Hazards (GEOL005)
at Hofstra University
Instructor: E. Christa Farmer
Challenges to using math in introductory geoscience
Hofstra University's Geology Department has several learning goals and objectives (as stated in the 12 July 2007 Outcomes Assessment report) that include enhancing students' quantitative skills; of these I intend for GEOL005 to fulfill the following:
1. Students will develop the basic observational skills they need to function as geoscientists.
1a. Students will make measurements and use various quantitative units to describe phenomena and will practice converting quantities from one unit to another.
2. Students will perform tests and collect data to analyze geological materials, features, and processes both qualitatively and quantitatively.
2b. Using a topographic map, students will measure elevation, construct accurate vertical profiles and calculate vertical exaggeration.
3. Students will apply critical thinking skills such as inductive, deductive, and mathematical reasoning to solve geological problems using the scientific method.
3f. Students will apply mathematical models and analysis to quantitatively describe or predict the behavior of geological phenomena.
Most of the students in this course are taking the course for science distribution credit. Many say things like "I hate math!" or "I can't do math!" and are extremely anxious about working with numbers and equations and graphs. Most have not worked with quantitative approaches to material since high school, which may be several years in the past.
More about your geoscience course
This course is an introductory Geology course that is offered every two years to fulfill students' Natural Science distribution requirements. There are traditional separate weekly "lecture" and "laboratory" sessions, taught in different rooms with different facilities. There are no regular Teaching Assistants, although occasionally an excellent student who has taken the course already is able to act as a "Peer Teacher" for the course. This position allows the student to play a limited role as assisting the new students with the course.
Inclusion of quantitative content pre-TMYN
Currently, the students complete four quantitative laboratory reports. I have spent up to one complete lecture period after each lab session making sure that the students can accomplish the problem-solving inherent in each report.
With TMYN, I hope to give the students more practice with the quantitative skills that I am trying to teach them. Giving the students repeated opportunities to solve problems, with the accompanying explanations of the necessary skills, should improve their ability to complete the laboratory reports and allow us to spend more time exploring the implications of the problems for Geology.
Which Math You Need Modules will/do you use in your course?I have used the following modules:
- Unit Conversions
- Rearranging Equations
Strategies for successfully implementing The Math You Need
I administered a pre-test at the beginning of the semester, which asked the same questions (with limited changes in variable values) as a post-test at the end of the semester for comparison. I designed this test to include questions from the three TMYN modules I plan to use: unit conversions, slopes, and manipulating equations. The first two of these modules was introduced in the two weeks before the laboratory exercise on calculating the specific heat of water, in which those skills were utilized. The third module was introduced in the week before the second laboratory report, which is on calculating the location of earthquakes from differences in S- and P-wave arrival times. I administered the post-test in the tenth week of the semester, allowing the students to complete all the "extra" work early in the semester before the end-of-semester crunch sets in.
Reflections and Results
Here's an update as I finish my first semester (Fall 2010) of using "The Math You Need" modules. My GEOL005 class this semester had 18 students enrolled in it, and overall I was quite pleased with how "The Math You Need" improved outcomes in my course. 17 out of 18 students took the pre-test, and the average score was 6.9 out of 10. 11 students took the post-test in the tenth week of the course, after completing three TMYN modules (unit conversions, slopes and rates, and rearranging equations) and writing two laboratory reports utilizing those skills. The average score on the post-test was 7.7 out of 10. You might think that this 8% improvement is only due to the non-completion of the post-test by low-performing students. And indeed, the average score on the first two module quizzes was about 10% higher for the group of students who did go on to complete the post-test. Of the 11 students who completed both the pre- and post-test, the average improvement on the post-test was 0.09 points.
I would say that the best evidence of the efficacy of TMYN is the improvement that I saw on the first two lab reports. When I last taught this course in 2008, the average on the first (specific heat of water) lab report was 73% and the average on the second (location of earthquakes) lab report was 80%. This year, with the utilization of TMYN modules and quizzes, the average on both lab reports was 86%. This average includes reports from all students in the class. I credit this improvement not only to the students' ability to work on their own in a guided manner to improve their skills, but also to the fact that I was able to take more class time to discuss the meaning of the laboratory exercises rather than spend so much time in class working on the quantitative skills needed to make the calculations in the reports. I also really appreciated not having to spend a lot of time in class on skills development because doing so tends to bore the students who are already proficient.I definitely plan to use TMYN in future courses. The only drawback I see to the program is the difficulty of getting students to complete the work outside of class. It seems to me that the students who need them most tend to be the ones who do not complete the units. As it turned out, only one student didn't complete the pre-test. But four students did not complete the first module quiz, five didn't complete the second one, six didn't complete the third one, and seven didn't complete the post-test. In most cases, it was the same students not finishing each next step (plus one more). This despite my near-daily announcements in class while the quizzes and tests were open, and my sending emails to remind the students to finish. Perhaps I need to attach higher stakes to each exercise? This semester, I made each of the five TMYN quizzes and tests worth 1% of their final grade (with the possibility of earning 2% extra credit for doing well on the pre- and post-tests). Maybe I will try making each quiz or test worth more like 5% in my "Introduction to Field Methods" course in the Spring 2011 semester.
I am a member of Hofstra's Center for Teaching and Scholarly Excellence, and as part of my role in that group I recently gave a brief presentation on The Math You Need during a lunch seminar. Professors from other disciplines were impressed with the improvements in the students' lab reports. We wondered if there are any similar programs focused on other disciplines, or plans to develop them, because everyone agreed that this approach seems promising for helping students develop and maintain their quantitative skills.
Inspired by Tom Hickson's presentation No more lecture, way more engagement: developing a 100% project-based course from the ground up, I reorganized this course to take a much more project-oriented approach with less traditional lecturing. This was tough to do, and I fell back on lecturing way more than I wanted to. But overall I think my efforts increased the student engagement in the course.
Update: Fall 2012
I taught Geology 5 Environmental Geology and Natural Hazards again this Fall, and again incorporated The Math You Need based on my positive experience with the program last time. This semester I had an additional challenge in that my course has been listed as a requirement of a new degree program in Urban Ecology. This attracted some much more advanced students to the course than the general population of introductory science students it usually draws. So I found TMYN to be more useful than ever in establishing a common denominator skillset for this diverse group of students.
The outcomes from TMYN scores were even better this year than the first time I used it: out of 16 students who finished the course, 9 students completed both the pre- and post-tests. The average change in the score from the pre- to the post-test was 0.83 points: compared to the gain of 0.09 points in Fall 2010, that's an impressive improvement. The students' grades on other assignments continued to be higher than before I utilized TMYN: this semester students averaged 89% and 93% on the first two lab reports.
I continue to be challenged by motivating students to finish all TMYN assignments: despite giving course credit for completion of all modules and the pre- and post-test, students only completed 2.25 modules on average, and only 9 out of 16 finished both the pre- and post-test. I found that students who did poorly on the pre-test were actually less likely to complete the modules and the post-test. This suggests that the students who need this help the most were actually scared off rather than inspired to improve their skills. Since the students already have the option to re-take the module quizzes until they are happy with their score, I'm not sure how else to motivate these students to try.