at California University of Pennsylvania
Implementor(s): Kyle Fredrick
First Implementation: 09/01/2011 - Fall 2011 (Semester)
Challenges to using math in this course
California University of Pennsylvania is a comprehensive, 4-year public institution, in southwestern Pennsylvania. The university, located on the shores of the Monongahela River in eastern Washington County, is in the heart of a geological hotbed of activity related to shale gas exploration and environmental challenges. Graduates of the CalU Geology program generally work in the petroleum, natural gas, or coal industries, or regulatory and environmental agencies throughout the region. Quantitative skills are highly valued in a competitive employment marketplace.
The biggest challenge is overcoming students' fear and aversion to math. Most of my students come in unprepared from their high school or early college math and science courses for the introduction of physical principles based on quantitative analysis. Even though my Hydrology course is a 300-level course, it is usually the second or third Earth Science course the students take after Introduction to Geology. The administration could indirectly play a role in challenges to quantitative content simply because of enrollment pressure. In order to maintain high major and course enrollment numbers, there is pressure to make courses more "student-friendly." This makes quantitative-heavy courses, mostly by reputation, unattractive. TMYN provides several implementable ideas to get my students (Geology) and those major students I service (Meteorology, Env. Science) to open up to math much earlier.
Student demographics for the University include mostly local to regional students, within a radius of about 50 miles. There is a large proportion of commuters, which lends itself to a somewhat fragmented and individualistic student population. Socioeconomic status ranges from middle-class to below the poverty line, with a large number of our students coming from poor areas of southwestern PA, and many first-generation students. The region's public school systems are mostly economically challenged, and STEM doesn't seem to be generally encouraged as potential career-developing. The Geology program seems to attract few non-traditional students, being mostly composed of upper-level students that have changed their major from something else. It is not a culturally diverse group of students, so there is quite a bit of empathy between students and especially from upper-division students to younger ones. Specific to mathematics, the challenges based on background are just a general aversion or lack of exposure. However, a unique problem, especially as it relates to the Meteorology and to a lesser degree the Geology students, is their inability to work through problems in the context of science. Many of the Meteorology students enter the university knowing that they need at least 5-6 math classes, and many have successfully completed Calculus in high school. However, when faced with incorporating those skills into "story problems" and making sense of graphical representations and analysis of data, they are unprepared and even resistant. I attribute this to their relative success in math at lower levels, and overconfidence in their ability to apply what they've learned.
In terms of proportion of the course spent on Quantitative Skills, the following applies to years 2007 through 2010, prior to the first implementation of TMYN in Fall 2011. The amount of student time and effort can be divided up for in-class and outside of class. We would spend approximately 40 percent of our time in class on QS, including lecture, preparing for and reviewing problem sets, and in-class work on labs and homework. The students ended up spending about 70 percent of their time outside of class on QS. It was my goal to reduce the In-class portion of time to allow for more lab time and more varied experiences and topics. In terms of the assessment and grading, QS occupies about 65% of the students grade, though this is difficult to quantify. Much of the remaining 35% is still dependent upon reading graphs, understanding topography and slopes, etc. No Teaching Assistants are available for this course, or any within my program. Problem Set grading can be challenging and time consuming, especially when students don't organize their work well. This is something that is outside of the capacity for TMYN to help with, but I do spend class time teaching simple strategies to problem set up.
More about your geoscience course
Hydrology is an integral part of our departmental curriculum. It is required of all Geology, Environmental Earth Science, and Meteorology majors. It is also taken as a related elective by many of our Environmental Science (Biology) and Parks/Recreation majors. The Geology pre-requisite for Hydrology is EAS 150 - Introduction to Geology. Occasionally, one or two students will take it as a co-requisite. The math pre-requisite is College Algebra. Most students enter the course ONLY having had this course, though about 20-40% of the class may have had Pre-Calculus or higher.
There is no defined lab component to the course, but there is some integrated lab and field experience that I use to develop skills and demonstrate job-related equipment and principles for those students wishing to enter environmental fields. The course is two days per week for 1.5 hours each meeting. This does not leave much time for conventional lab work. However, hands-on activities are critical to student learning for this course, because for many students it is their first time dealing with water from a physics-based approach. Labs occur within the framework of the normal schedule, but may also include work outside of class, in small groups. They include visitation to a local stream to measure discharge and take water samples, flume experiments in the lab, mapping exercises, and simple pH and conductivity sampling. TMYN serves to augment the problem sets that are assigned throughout the course, as well as to develop the students ability to analyze data they collect during the lab exercises.
Hydrology, though it is a major course for Geology and Meteorology, lays the groundwork for many upper-division courses within the curricula. Geology, Environmental Earth Science, and Earth and Space Science Education students may follow Hydrology up with one or more of the following related courses for which it is a pre-requisite: Sedimentology/Stratigraphy, Groundwater Hydrology, Watershed Evaluation, Advanced Environmental Geology, Computer Applications in Earth Sciences. Meteorology students continue on to subsequent atmospheric courses, based on different scales and dynamics. Quantitative Skills learned and/or developed during Hydrology serves these students throughout their major curricula.
Inclusion of quantitative content pre-TMYN
I use problem sets and integrate quantitative content as a major part of the course. My desire is to do it more effectively and to overcome the math aversions earlier, to make students more receptive and independent. Historically, I began the course with a "Math Quiz" to gauge their incoming competence level. Then, we slowly ramp up from simple unit conversions and algebra into introductory level fluid mechanics with calculus and PDE's. A disproportionate amount of time is spent on getting students "up-to-speed" in BASIC math skills (Unit conversions, setting up and rearranging equations, scientific notation, reading graphs). Many of the students struggle with Problem Sets because of these fundamentals, even though they may understand the "big picture" concepts.
Problem Sets are assigned differently each time the course is offered, but within a general framework. The pace, number, and timing of these assignments is based on how well students are performing and how much in-class time is spent on QS. The general order of topics is:
- Unit Conversion
- Water Balance/Hydrologic Cycle
- Atmospheric Water
- Lapse Rate
- Surface Water
- Infiltration/Overland Flow
- Stream Geometries and adjustments
- Fluvial Geomorphology
- Ground Water
- Bernoulli's Equation
- Darcy's Law
- Human Impacts
Which Math You Need Modules will/do you use in your course?Unit Conversions: Changing units within and without Metric and SI,Dimensional Analysis, Conservation Equation
Rearranging Equations: Dimensional Analysis, Conservation of Mass, Conservation of Energy
Plotting Points AND Graphing: Rating Curves and Hydrographs, Vapor Pressure and Dew Point
Best Fit Line AND Reading Points from a Line: Rating Curves, Correlations (pH, temp, Conductivity, etc.)
Density: Saltwater/Freshwater Interface, Lake Inversion, DNAPL/LNAPL
Rates: Stream Discharge, Wind and Evaporation, Incipient Motion and Sediment Transport
Topographic Profile AND Slopes: Watershed Delineation, Stream Flow Direction, Headward Erosion, Cross-sectional Profiles
Strategies for successfully implementing The Math You Need
I integrated TMYN in several ways in my course. I began the course with a pre-test, to evaluate the students' initial abilities and attitudes. Over the next several weeks, about every week to week and a half, I assigned a short module/assessment. Each of these assessments was assigned before we got into the part of the course with which we addressed that topic. After each module and assessment, we opened up that qualitative topic/activity, and applied those to the hydrologic topic of the unit. At about the three-quarter point in the course, the students completed the post-test, a duplicate of the pre-test, to assess their overall change in competence. Only five modules were used, as I joined multiple topics into single assessments. In rough order, they were Unit Conversions, Scientific Notation and Logarithms, Scales and Density, Reading Graphs and Slopes, and Rates. A sixth "review" quiz was done to address particularly problematic questions from earlier assessments. We completed the modules by week 11, in the 15-week semester. Well over half the course content and assessment was dependent upon the students' abilities to successfully use and integrate quantitative skills in Hydrological sciences. TMYN components totaled 6 percent of the course grade. Each post-module assessment was worth 0.5% of the student grade. The pre-test was pass/fail based on completion, with one attempt allowed and worth 1%. The post-test was graded, with one attempt allowed and worth an additional 1%. The interim assessments allowed for two attempts, and were graded.
Reflections and Results (after implementing)
I consider the implementation of TMYN in my Hydrology course to have been a success. All of the students improved their scores from the Pre- to Post-tests, with an average improvement of 21%. Students struggled most with the Graphing module and assessment, which was not a surprise. However, it was clear that these students had significantly higher competency for reading and analyzing graphs in class, demonstrating that the modules were having an impact on their learning, and especially preparation.
My main goal for using TMYN was to spend less time in class on remedial math skills. This goal was met, allowing me much more time to work on higher-level quantitative principles and topics that I wasn't able to "get to" in previous years. The quantitative nature of the class was not minimized because the responsibility of remediation was put on the students, it was augmented!
Following the full implementation, I conducted a separate attitudinal survey to assess the students perspectives on TMYN and my implementation of it. Briefly, students found the Unit Conversions module to be their favorite as well as most useful. Scientific Notation was the least appealing. In evaluating why the STUDENTS thought they improved, 43% attributed their improvement to Increased Understanding, 25% to Familiarity with Questions, 21% to Familiarity with Format, and 11% for logistical, non-academic reasons. Finally, I asked my students to complete the following Likert survey:
How do you feel The Math You Need impacted you?
(out of 5)
I feel MORE CONFIDENT in my ability to address quantitative problems.
The questions/content were relevant to work I will likely do in my career.
My quantitative skills have improved.
The instructor used these tasks for busy-work, not to improve my skills.
The quizzes provided adequate repetition and breadth
In my opinion, TMYN was a benefit to me and my students. I will use it again without hesitation. The one thing I will change is to emphasize the use of the modules, to avoid having students jump right to the assessments. But overall, it was a successful implementation and seems to have served my purposes.
ResourcesCourse Syllabus, Fall 2010 (Acrobat (PDF) 151kB Jul28 11)
Hydrology Problem Set 1 (Microsoft Word 2007 (.docx) 16kB Jul28 11)
Hydrology Problem Set 5 (Acrobat (PDF) 205kB Jul28 11)