The majority of students entering community colleges are unprepared for college. A large number of the incoming students are placed into basic-skills math courses. At LaGuardia, more than half the students need basic-skills math courses, and more than 60 percent aspire to obtain a baccalaureate or higher degree. More than 60 percent of the students specified their major to be in science or applied sciences. More than half of LaGuardia graduates transfer to a four-year institution to pursue higher degree (CUNY, 2009: 15–34). Many of these students start at the basic skills level. Succeeding in basic math skills is important for students to stay in college and successfully complete their degree. Yet at community colleges, now the major gateway to higher education in this country, remedial classes accounted for approximately 57 percent (Lutzer, et al., 2005: 138) of mathematics program enrollments. Nationally, however, pass rates in remedial math remain lower than those for remedial writing and reading. Lack of math skills proficiency has a major effect on student retention (Parker, 2005).

Students in basic math courses have often had repeatedly unsuccessful experiences, viewing the subject as uninteresting and irrelevant. More than 35 percent of the students in basic-skills math courses retake the course at least once. We need to convince these students that mathematics makes sense and provide them with the tools and opportunities to think and reason. They are perhaps most in need of an approach such as SENCER — an interdisciplinary approach to teaching math and science that can deepen the settings and contexts and engage them. Some of the other approaches — such as the discovery method and inquiry-based learning — may seem unfocused without establishing an overall "compelling context." Most textbooks that use a problem-solving approach discuss applications that are disconnected and none of which can be explored deeply enough to become compelling. Instead, in adapting the SENCER approach, we can create a single, engaging context to be explored throughout the entire semester. The Project Quantum Leap (PQL) program at LaGuardia Community College, New York, was established to explore the SENCER approach to improve the basic-skills math education.

Method

To support the plan of adopting the SENCER approach to improve students' success in math basic skills, several mathematics faculty (Drs. Frank Wang, Gordon Crandall and I) and Dr. Kamal Hajallie (chair, Department of Mathematics, Engineering, and Computer Science) collaborated with Dr. Paul Arcario (Dean of Academic Affairs), and Dr. Bret Eynon (Director, LaGuardia Center for Teaching and Learning [CTL]) and applied for a U.S. Department of Education grant FIPSE (Fund for Improvement of Secondary Education) for $500,000 over three years (2007–2009). The project was funded.

The goal of the PQL project is to adopt the SENCER approach of teaching to a new setting and population: high-risk, urban community college students in basic-skills mathematics classes. The funding provided support for developing the required teaching material, training core faculty, and implementing the SENCER approach in classrooms. The project recently received support for an additional two years through a U.S. Department of Education Title V CCRA/STEM grant. The three courses targeted for the SENCER approach are Introduction to Algebra (MAT095), Elementary Algebra (MAT096), and College Algebra and Trigonometry (MAT115). MAT095 is the first basic-skills course and includes topics mostly in arithmetic; MAT096 is the second basic skills course and includes basic algebra topics; and MAT115 is a bridge course between math basic skills and pre-calculus. To contextualize the math topics, different themes were selected for each of the courses — environmental issues for MAT095, public health issues for MAT096, and financial issues for MAT115. The participating faculty attended professional-development seminars conducted by the PQL leaders with support from the LaGuardia CTL in order to develop the teaching materials and to discuss ways to implement them in the classes.

First Year

In the first year of the project, eight faculty from mathematics joined one faculty each from English, critical thinking, economics, and accounting and managerial studies for a year-long professional development seminar. Participants were divided into three teams corresponding to the three courses: MAT095 led by myself; MAT096 lead by Dr. Frank Wang; and MAT115 lead by Dr. Gordon Crandall. All participants from mathematics were also required to teach at least one section of the math course corresponding to their team. The four faculty not from math departments were involved in course pairs and learning-community settings with the targeted math courses. During the first semester, the math and non-math faculty pairs worked together to plan and develop joint class activities and projects. The paired courses were taught in the second and subsequent semesters.

Dr. David Ferguson (Distinguished Service Professor of Technology and Society and Applied Mathematics and Statistics at Stony Brook University and Chair of the National SENCER Leadership Fellows Board) joined us as a consultant during the first year. He provided insight into the SENCER philosophy and discussed ways to engage students in the classroom by providing examples of his own teaching lessons. Seminar activities were designed by the faculty leaders to engage the participants in studying several existing SENCER course models (SENCER, 2009) and discussing the issues related to adaptation to the LaGuardia setting.

We drafted and shared curriculum units and activities that link the chosen contexts to sequential development of mathematical skills and understandings. Many activities were shorter and more suitable for half-hour in-class activity, while other activities were lengthier and more involved, which are ideal for homework assignments following up to classroom discussions. Other activities included multiple math topics designed to be used as a synthesis of several math concepts contained in the course. Some activities were developed to review a specific math topic. A few were intended for introducing specific concepts to motivate students to learn math. Most of the activities required some writing by students to encourage them to use numerical facts in making decisions or to articulate their understanding of the non-math context. The more involved activities also asked students to write their reflections about learning math through such activities. Three websites were created as resources to collect research, articles, and links that faculty could use to contextualize the themes of their course.

In the second semester, all participating faculty were required to implement at least two larger and three smaller PQL-SENCER–type activities in their classrooms. These PQL classes were similar to the regular math basic-skills sections, with thirty students in each class. No special selection method or criteria was used to assign students into the PQL classes. Although all basic-skills math courses have a common departmental syllabus and textbook with online component for tutorial, homework, and quizzes, the participating faculty were asked to prepare a one-page syllabus cover sheet describing the purpose of SENCER approach and listing the various projects they were going to work on in the course. Attention was paid to ensure that the PQL-SENCER type activities were spread throughout the course and was integrated in our teaching. Students' math work and written responses to the activities were graded by the instructor and were part of the overall grade in the course. Two assessment instruments, Community College Survey of Student Engagement (CCSSE) and ACT, a national college admission and placement examination, were used for the assessment purpose. Pre- and post-student surveys were administered to measure the increase in student engagement with math and satisfaction with math courses that were taught using the PQL-SENCER approach. The pre- and post-student surveys were also administered to comparable (matching the time of the class, day or evening, and instructor type, more experienced or less experienced) non-PQL math section to compare the gains.

Second Year

To support faculty with content and resources in the areas of the environment, public health, and finance, we invited three consultants to present relevant information in the seminar and to lead discussions. This helped us find reliable resources and build knowledge for the activities, which allowed us to conduct insightful class discussions and to make the activities more powerful and relevant to the students.

Eight additional mathematics faculty joined the returning seven faculty members. In addition, one faculty each from critical thinking, English, and oral communication joined for the second-year PQL seminars. The four non-math faculty taught paired courses in learning community set-up. Over the course of the second year we refined and implemented the activities in our teaching. As in the first year, the pre/post student surveys and the assessment instruments were administered to track effectiveness. Seminar activities included discussions about writing lessons, shared lesson write-ups, and feedback. The lesson write-ups incorporated faculty reflection about conducting the activity and students' responses to the activity. A collection of twenty-four lessons were internally published as a sampler, available through the LaGuardia CTL website. This collection served as a teaching resource for current and future faculty. Environment-oriented math lessons in the sampler included diaper debates, asthma and air pollution, and the height and thickness of dust cloud. The public-health math lessons included topics ranging from the HIV and AIDS epidemic to the analysis of cheddar cheese cubes. Math lessons involving business and finance covered topics such as car buyers in Asia, investment rates, rising gas prices, and price per square foot.

Third year

A third cohort of seven full-time math faculty, six adjunct math faculty, and one faculty from the adult and continuing education department joined sixteen returning faculty in the Fall 2009 PQL program. To engage experienced PQL participants in advanced/leadership work, we divided participants into an advanced PQL group (ALEC [Advanced Leadership and Curriculum]) and a new participants group (intro PQL). The ALEC team — lead by Drs. Yasser Hassebo, Judit Torok, and myself — was responsible for leadership initiatives to advance PQL goals both within and outside the college via workshops, conference presentations, collaborations with other institutions, writing journal articles, mentoring junior and adjunct faculty, strengthening pedagogy, reshaping curriculum, and deepening teaching practices. In addition to sharing and revising PQL-SENCER activities and projects, the seminar activities also consisted of researching and discussing relevant articles in the areas of student-centered teaching approaches, curriculum development, assessment issues, and the scholarship of teaching and learning. The intro-PQL team — lead by Drs. Gordon Crandall, Frank Wang, and Roslyn Orgel — continued to explore the SENCER approach, develop additional new activities, and adopt existing activities from the sampler into their teaching.

Result

Over the three years, thirty-three math faculty and seven non-math faculty have participated in PQL seminars who taught twenty-six PQL-math courses and thirteen PQL-math learning communities and approximately one-thousand students were served. Together, faculty have created twenty-four class projects and activities that are part of the PQL sampler. A preliminary analysis of the students' responses to the CCSSE survey data from 2008–2009 shows that students in PQL classes demonstrated more confidence, comfort, and engagement with mathematics, when compared with students in non-PQL comparison classes (Table 1).

Table 2 compares the pass rates for PQL classes with non-PQL classes. Overall, the course pass rates in PQL classes is 54.7 percent compared with 47.6 percent in non-PQL comparison classes. However, these gains were concentrated in MAT095 and MAT115 courses. We continue to collect data and plan to conduct further analysis using appropriate statistical procedures. We hope to share a more-detailed and complete version of the results in the near future.

Discussion

Many issues in our civic life depend on quantitative information and our ability to synthesize that information to make decisions. The preliminary results suggest that the PQL-SENCER approach has a positive impact on students' quantitative literacy skills (Madison and Steen, 2008) as well as on the course pass rate. The benefits of adopting the SENCER approach, however, has not affected all courses equally, especially the Elementary Algebra course.

The outcomes in the college-level course College Algebra and Trigonometry matched our expectations: the increased confidence in science skills, interest in science, and civic behavior have been noted with SENCER approach applied to college level courses in other institutions (SENCER, 2006).

The Introduction to Algebra course showed only slight improvement in pass rate. Though not consistent, students' comfort level in using math improved. This is a course in arithmetic, designed to develop number sense, percentages, proportions, and basic geometry — everyday math. It provides ample scope for engaging students using current issues such as the environment, with many reports, articles, and data directly related to the math. Due to an overabundance of topics to be covered in a short period of time, however, both students and instructors found themselves unable to pursue a topic of particular interest in greater detail.

MAT096, Elementary Algebra, did not show similar gains. The reason for this could be multifold. Much of the content is based on algebraic manipulation skills, with little or no applications. There is a very limited scope in the curriculum to interpret the solutions. The topics discussed include concepts related to linear equations, solving liner and quadratic equations, and equations with rational expressions and radicals. In a technique-based course as this, many students find the discussion related to the interpretation of numbers out of context. Real-life problems often involve more complex models than those covered in the course. An overloaded curriculum also limited the use of SENCER approach in this course.

The math basic-skills students at LaGuardia College have to pass the course as well as the COMPASS standardized test — a computer-adaptive college placement test — in order to exit math basic skills. The course syllabi include all topics covered in the COMPASS exam. While we want students to develop the basic math skills and pass the COMPASS exam, we also want to prepare them for college-level math courses and the non-math courses for which basic math is a prerequisite. The PQL-SENCER approach appropriately addresses these objectives.

Each of these issues and objectives were discussed in the seminar at length. To incorporate the SENCER approach throughout the course we proposed using smaller activities. To tackle the overloaded curriculum, we are revising the curriculum by combining some topics and reducing the emphasis on others. In addition, we are exploring and piloting active-learning pedagogy in the classroom to improve student engagement in class.

Faculty training and the availability of resources are important components of any project intended to have impact on the outcome of an entire course. We have already trained thirty-three faculty (including adjuncts) in the math department and continue to train more. Resources and activities with complete lesson plans are being collected and are available online. We also are in the process of revising the common syllabi for the basic-skills courses to include PQL-SENCER-type activities and elements of student-centered pedagogy. With the available resources and support, we believe that we will be able to use the PQL-SENCER approach to teaching in most sections of basic-skills courses, as mentioned in the PQL project proposal.

Certainly much work remains to be done. It is possible that, while this approach is effective in certain types of courses, it may not be as effective in other courses. This requires further inquiry. The impact on follow-up courses taken by these students will also need to be studied. With strategies in place to follow up on these details, we hope to discover a methodology to improve basic-skills education and design a curriculum that is rich enough to engage students so their interest in math and science continues to grow.

Acknowledgements

This project was funded by grants from the U.S. Department of Education and is supported by the LaGuardia Center for Teaching and Learning. I thank Dr. Paul Arcario (Dean of Academic Affairs and principal investigator on the grant), Dr. Bret Eynon (Director of the LaGuardia Center for Teaching and Learning and co–principal investigator), and Dr. Kamal Hajallie (Chair of the Department of Mathematics, Engineering, and Computer Science) for their support and guidance in leading this project. I thank the faculty leaders of the leadership team Drs. Gordon Crandall, Frank Wang, Judit Torok, Marina Dedlovskaya, Yasser Hassebo, and Roslyn Orgel for their involvement, thoughtfulness, and teamwork in thinking through the details of the curriculum material and guiding the research. The support of the experienced personnel from the LaGuardia Center for Teaching and Learning and dedicated work by the participating faculty has lead to the success of the PQL project.

About the Author

Prabha Betne (Ph.D., 1994, University of Missouri-Columbia) is an associate professor in the Department of Mathematics, Engineering, and Computer Sciences at LaGuardia Community College, New York. Previously, she was a research statistician at the Columbia University and credit risk manager at Citigroup. Her research interest is to develop strategies to improve teaching basic mathematics and statistics.

References

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Lutzer, D.J., S.B. Rodi, E.E. Kirkman, and J.W. Maxwell. 2005. Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States Fall 2005 CBMS Survey, Chapter 6, "Enrollment, Course Offerings, and Instructional Practices in Mathematics Programs at Two-Year Colleges." http://www.ams.org/profession/data/cbms-survey/cbms2005 (accessed on July 25, 2010).

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