Innovative Practices for Improving Student Performance in College Level Mathematics

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MARKET EVALUATION SURVEYING DATA ANALYSIS BENCHMARKING ORGANIZATIONAL STRATEGY

Innovative Practices for Improving Student Performance in College Level Mathematics

This report explores innovative initiatives undertaken by colleges and universities to improve the success rates of students in foundational college math courses.

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HANOVER RESEARCH SEPTEMBER 2011

© 2011 Hanover Research – Academy Administration Practice

Introduction and Key Findings In this report, Hanover Research examines innovative ways in which colleges and universities have sought to improve the performance of their students in foundational mathematics courses (such as College Calculus I & II and College Algebra & Trigonometry). As witnessed throughout our discussion, such efforts are often embedded within – and play a fundamental role in – broader Science, Technology, Engineering, and Mathematics (STEM) support and retention initiatives. Underscoring the importance of this issue, a number of researchers and institutions have witnessed a connection between performance in college-level mathematics and retention and graduation.1 For example, in a large-scale study seeking to identify the determinants of freshmen retention, Herzog found that successful completion of a first-year math course (earning a C or better), among other factors, increased the probability of re-enrolling, and reduced the chances of student “transfer, stop out, or drop out.”2 Focusing on retention in STEM fields in particular, an evaluation of a STEM support initiative conducted by faculty at Bowling Green State University found that students who “performed marginally in math and science” during their first semester or first year of college were more likely to withdraw from the STEM curriculum than students who performed well.3 Providing some additional context regarding students’ choices to drop out of STEM fields, the Bowling Green faculty explain:

Indicators of plausible losses from the STEM disciplines are shown as early as the first set of exams in the first semester math/science courses. During semester one, students entertain a decision to shift away from STEM areas, or change academic interests, due to perceived or real failure in math and science. Some will persist in their chosen majors into semester two (spring semester) by retaking a course that they dropped or received an F or D grade in the preceding fall. If they do not succeed in semester two, they often will change majors, and are forever lost from these STEM fields.4

1 Moore, C. and N. Shulock. “Student Progress Toward Degree Completion: Lessons from the Research

Literature.” Institute for Higher Education Leadership & Policy. September 2009. p. 4. http://www.csus.edu/ihelp/PDFs/R_Student_Progress_Toward_Degree_Completion.pdf

2 Herzog, S. “Measuring Determinants of Student Return vs. Transfer vs. Stopout vs. Dropout: A First-to-Second Year Analysis of New Freshmen.” Paper presented to the California Association for Institutional Research. November 2003. http://www.cair.org/conferences/CAIR2003/SergeHerzogBPComp.pdf Note that a version of this study was also published in Research in Higher Education in 2005.

3 Gilmer, T.C. “An Understanding of the Improved Grades, Retention, and Graduation Rates of STEM Majors at the Academic Investment in Math and Science (AIMS) Program of Bowling Green State University.” Journal of STEM Education. 2007. http://www.bgsu.edu/downloads/provost/file49754.pdf

4 Ibid. p. 18.

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This report focuses on institutional efforts to combat the potential loss of students – those who are either dropping out of STEM majors or dropping out of college entirely – particularly through improving their performance in foundational mathematics courses. In the first section of the report, we provide an overview of innovative practices designed to support college math performance. This information is drawn both from research literature on the topic as well as institutional examples (particularly examples of institutions that have received National Science Foundation funding in support of their efforts). The second section of the report provides additional detailed profiles of specific college math support initiatives. Key Findings Below we provide a brief overview of the findings of our research. A general trend that emerged from our review of institutional practices to

improve student performance in math courses is a movement away from lecture-based teaching methods and toward student-centered learning. Such practices promote active, cooperative, and inductive learning among students, as opposed to the more passive learning that typically takes place in the context of a lecture.

Many institutions have found that the integration of technology and

mathematics instruction, particularly through the use of interactive math software, provides an effective means of engaging students with course material. Instructional software packages such as ALEKS, Hawkes Learning Systems, WileyPlus, and MyMathLab, allow students to work through problems, receive immediate feedback on their progress, and follow guided solutions if they are unable to find the right answer.

An innovative way of using interactive math software is through the

emporium model. Under this model, the bulk of instruction and learning takes place in a math computer lab, as lectures are exchanged for individual and small group work activities.

Another student-centered learning approach – peer-led team learning (PLTL)

typically involves the use of small group workshops associated with specific courses and guided by trained peer leaders. During the workshops, students work together to complete challenging problems developed by faculty. The workshops are often a required part of the course and offer a supportive environment, where students can ask questions and engage in discussion.

Supplemental instruction (SI) represents another form of student-centered,

collaborative instruction and learning through the provision of non-remedial

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tutoring by peer instructors. SI differs from PLTL in that it usually involves outside-of-class support activities, rather than the integration of peer learning into the course itself. Further, supplemental instruction sessions often incorporate general learning and study skills into the instruction, including note-taking, vocabulary acquisition, and test preparation.

New STEM students facing a multi-course calculus sequence often feel

overwhelmed by the difficulty of the courses and are deterred by a low grade in one course. The daunting series of courses typically covers material that does not appear directly applicable to their intended major. In order to alleviate this situation and better engage students in the material, some institutions have emphasized real-world applications of math concepts, as well as have made connections between foundational material and more advanced topics.

Finally, summer bridge programs with a heavy math component represent

another important tool to supporting student success in foundational math courses. These programs are often targeted toward incoming students interested in STEM fields and are typically two to five weeks in duration. Program participants have the opportunity to earn math credit while strengthening math skills that will be critical in their anticipated program. The camps often move beyond math skills, applying math concepts to science and engineering, as well as providing training in general study skills for college success.

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Overview of Innovative Practices in Improving Mathematics Performance

In this section, we provide an overview of innovative practices institutions of higher education have implemented in order to improve their students’ performance in foundational mathematics courses. As noted previously, these practices were identified through a review of literature on the topic and an examination of what individual institutions are currently doing in this area, with particular attention paid to NSF-funded initiatives. Institutional examples are provided throughout this section to briefly illustrate each practice. More detailed profiles of university and college programs and practices are offered in the final section of this report. Practices discussed in this section include the use of:

Interactive mathematics software Peer-led team learning (PLTL) Supplemental instruction (SI) Applications of math concepts Summer bridge programs

Note that the first three practices are strong examples of student-centered learning approaches, a concept we discuss briefly below. Student-Centered Learning Approaches One broad trend that emerged from our review of practices to improve student performance in math courses is a movement away from lecture-based teaching methods and toward student-centered learning. Richard Felder, a professor emeritus of chemical engineering at North Carolina State University who has written extensively on teaching effectiveness, describes student-centered learning as including:

Active learning – in which students solve problems, answer questions, formulate questions of their own, discuss, explain, debate, or brainstorm during class

Cooperative learning – in which students work in teams on problems and projects under conditions that ensure both positive interdependence and individual accountability

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Inductive teaching and learning – in which students are first presented with challenges (questions or problems) and learn the course material in the context of addressing the challenges5

Providing a general example of an introductory mathematics course that utilizes a student-centered learning approach, Schumacher and Kennedy describe a class that has been divided into groups of four or five students. At the start of each class, students are provided a series of exercises “that would gently lead the groups through material of different degrees of difficulty.”6 It is the responsibility of the entire group to ensure that each member completes and understands each problem. Throughout the course meeting, the professor assists each group, clarifying any misunderstandings of the material. The course further features weekly quizzes that are designed to reduce students’ anxiety about the material and help them to continuously monitor their progress before taking a larger, more significant exam. While specific student-centered learning practices vary, Schumacher and Kennedy explain that a hallmark of this approach is that it is largely experiential, involving hands-on activities where students work through problems rather than listening to a lecture on the material.7 The National Center for Academic Transformation (NCAT), an organization that has been involved in 49 large-scale mathematics course redesign projects, a number of which have been funded by the Pew Charitable Trusts and the Fund for the Improvement of Postsecondary Education (FIPSE), echoes the importance of experiential, hands-on learning in mathematics. The organization states that the underlying principle to improved mathematics instruction is: “Students learn math by doing math, not by listening to someone talk about doing math.”8 Below we discuss three specific practices implemented by a number of universities and colleges that appear well aligned with a student-centered learning approach. Interactive Mathematics Software NCAT promotes active learning and instant feedback as part of a successful mathematics course design. In a 2011 article, Carol Twigg, the president of NCAT, explains that “the primary reason students do not succeed in the traditional math course is that they do not actually do the problems. As a population, they generally 5 Reproduced verbatim from source: “Student-Centered Teaching and Learning. Resources in Science and

Engineering Education. http://www4.ncsu.edu/unity/lockers/users/f/felder/public/Student-Centered.html

6 Schumacher, P. and K.T. Kennedy. “Lessons Learned Concerning a Student Centered Teaching Style by University Mathematics Professors from Secondary School Educators.” Education. Fall 2008. p. 102.

7 Ibid. 8 “Increasing Student Success in Developmental and College-Level Mathematics: A Summary of NCAT’s

Course Redesign Achievements.” The National Center for Academic Transformation. http://www.thencat.org/NCATPlans/Math%20Strategies.htm

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do not spend enough time with the material, and this is why they fail at a very high rate.”9 Many institutions have found that the integration of technology and mathematics instruction, particularly through the use of interactive math software, provides an effective means of combating this issue. Instructional software packages such as ALEKS,10 Hawkes Learning Systems,11 WileyPlus,12 and MyMathLab13 allow students to work through problems, receive immediate feedback on their progress, and follow guided solutions if they are unable to find the right answer. These programs typically feature a variety of learning components including “interactive tutorials, computational exercises, videos, practice exercises, and online quizzes,” appealing to students with a wide range of learning styles.14 Next, the self-paced nature of instructional math programs also helps alleviate potential student boredom with material they have already mastered. In a traditional lecture-based course, everyone moves at the same pace. Instructional software includes diagnostic assessments that allow for the development of personalized study plans. Students who have mastered material may move ahead, while students who are having difficulty with a topic may take more time to practice certain concepts. Further, when students encounter problems with the material, assistance is usually nearby. Universities using interactive math software will often encourage student collaboration through the arrangement of “pods” in computer labs (four to six computer stations in close proximity to each other) and often staff the labs with instructors, teaching assistants, and peer tutors.15 Most fundamentally, NCAT emphasizes that the use of interactive mathematics software requires students to work through math problems. Commenting on the success of Virginia Tech’s introduction of interactive mathematics software as a part of its Math Emporium model (discussed below), former math department chair John Rossi states, “I hate to use jargon but I think it’s active learning. We are forcing them to do the work. If they don’t do the work, they’ll flunk. It’s not like sitting in the back of a class of 500 and doing your email.”16

9 Twigg, C.A. “The Math Emporium: Higher Education’s Silver Bullet.” Change: The Magazine of Higher Learning.

May-June 2011. http://www.changemag.org/Archives/Back%20Issues/2011/May-June%202011/math-emporium-full.html

10 ALEKS. http://www.aleks.com/ 11 Hawkes Learning Systems. http://www.hawkeslearning.com/ 12 WileyPlus. https://www.wileyplus.com/WileyCDA/ 13 MyMathLab. http://www.mymathlab.com/ 14 Twigg, op. cit. 15 Ibid. 16 Mills, K. “Math Emporium – The Use of Technology has Changed the Way Virginia Tech’s Introductory

Math Courses are Taught.” National CrossTalk. Winter 2005. http://www.highereducation.org/crosstalk/ct0105/news0105-virginia.shtml

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In terms of integrating the software into introductory mathematics classes, universities will often follow one of two models – the replacement model or the emporium model. The replacement model involves replacing half of class time with computer lab meetings. Below are two examples of institutions that have adopted mathematics software using this model. In 2003, the University of North Carolina at Greensboro set out to

redesign three introductory mathematics courses, including College Algebra (Precalculus for Business and Social Science), Precalculus I, and Precalculus II. With the goal of promoting active learning among students, the university adopted MyMathLab course software to “provide interactive, guided, homework problems and practice tests; online tutorials and assessment tools; and student progress tracking.”17 The university also increased the availability of tutoring, both online and face-to-face, through its Math Help Center. Under the new model, while instructors still make presentations to their classes, they also devote a significant portion of class time to guiding students through their use of the software and addressing the questions of individual students. In a report on the success of its course redesign project, the university noted significantly improved final exam grades in two of the courses (Precalculus I and Precalculus II), as well as a reduced drop-fail-withdraw (DFW) rate in all three courses.18

In 2003 and 2004, the University of Mississippi also conducted a course redesign along the lines of the replacement model. The initiative involved two courses: College Algebra and Elementary Statistics. In its initial redesign, the university used both MyMathLab and Hawkes Learning Systems software. The structure of the courses was altered in order to require students to attend a math computer lab each week, as well as course lectures. In the lab, students use the software to work through math problems and receive help from instructors and graduate students as needed. In a report on the course redesign, the university noted improved final exam grades and course grades.19 A review of spring 2011 syllabi indicates that the University of Mississippi now uses another software package, WileyPlus, in its Elementary Statistics course20 and MyMathLab in its College Algebra course.21 Both courses

17 “The Roadmap to Redesign (R2R) – The University of North Carolina at Greensboro.” The National Center

for Academic Transformation. http://www.thencat.org/R2R/Abstracts/UNCG_Alg_Abstract.htm 18 Ibid. 19 “The University of Mississippi.” The National Center for Academic Transformation.

http://www.thencat.org/RedesignAlliance/C2R/Abstracts/UMS_Abstract.htm 20 “MATH 115 – Elementary Statistics – Syllabus Spring 2011.” University of Mississippi.

http://olemiss.edu/depts/mathematics/syllabi/Spring2011/115.doc 21 “MATH 121 – College Algebra Syllabus Spring 2011.” University of Mississippi.

http://olemiss.edu/depts/mathematics/syllabi/Spring2011/121-01.pdf

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require students to spend 50 minutes working in the university’s math computer lab each week, in addition to attending lectures.

The second common means of using mathematics software in introductory courses – the emporium model – also involves the use of a math computer lab. Unlike the replacement model, the bulk of instruction and learning takes place in the lab, as lectures are exchanged for individual and small group work activities.22 Students engage in the online tutorials and assessments, and instructors, teaching assistants, and tutors who staff the computer lab can assist as needed. Depending on the preferences of the institution/department, students may attend mandatory lab hours at their convenience or during scheduled hours. The emporium model was developed at Virginia Tech, and its success has led to its implementation at other institutions.23 In 1997, Virginia Tech pioneered the use of the emporium model through its

redesign of a Linear Algebra course. The traditional format of the course was based on two 50-minute lectures each week, with individual assistance available during office hours and/or review sessions. Under the redesigned format, all coursework was to be completed in the university’s 500-workstation Math Emporium and featured “interactive tutorials, computational exercises, an electronic hypertextbook, practice exercises with video solutions to frequently asked questions, applications, [and] online quizzes.”24 Coursework was organized into units of which students would cover one or two a week. Each unit featured a brief, automatically graded quiz. Students could work in the Math Emporium on their own schedule – the facility was to be open 24 hours a day, seven days a week. Also available to students were optional weekly lectures, faculty assistance through web and email communication, and on-site assistance from faculty, graduate teaching assistants, and peer tutors.25 The emporium model has been lauded as a success. Passage rates (grades of C or better) in the redesigned Linear Algebra course increased from 68 percent of students in fall 1997 to 90 percent by fall 2002.26 Today, the Math Emporium features 537 Apple computer workstations, as well as conference areas for student-faculty meetings, student study lounges, and a private classroom for tutoring sessions. The facility is still open every day, 24

22 “Redesigning Developmental and College-Level Math – Six Principles of Successful Course Redesign.” The

National Center for Academic Transformation. http://www.thencat.org/Mathematics/CTE/CTESix_Principles_DMCrsRed.htm

23 Twigg. Op. cit. 24 “Program in Course Redesign – Virginia Tech.” The National Center for Academic Transformation.

http://www.thencat.org/PCR/R1/VT/VT_Plan.htm 25 Ibid. 26 Mills, K. op. cit.

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hours a day.27 Seven courses are taught through the Math Emporium, including Elementary Calculus with Trigonometry, Elementary Calculus I, Linear Algebra, and Elementary Calculus with Matrices, among others.28 Instructor-led “Individual Course Help Sessions” for each of these courses are available throughout the week.29

Partly following the Virginia Tech example, the University of Alabama

redesigned its Intermediate Algebra course in 2000 to create a “student-centered, computer-assisted, self-paced tutorial course structure that allowed the individual student to focus precisely on his or her questions and difficulties.”30 Passive, lecture-based instruction in the traditional classroom was shifted to active student learning in the Mathematics Technology Learning Center (MTLC),31 the University of Alabama’s version of Virginia Tech’s Math Emporium. The new course featured 2.5 hours of work in the MTLC and 30 minutes of group work sessions. The course was coordinated by a faculty member and supported by instructors/graduate teaching assistants and undergraduate peer tutors.32 Following implementation, the university witnessed improved grades in the course, stronger student performances in subsequent courses (compared to students who did not take part in the redesigned course), and high student satisfaction ratings.33 Today, Intermediate Algebra, in addition to a number of other courses, is delivered through MyMathLab software and is conducted in the MTLC. While described as a “computer-based course” it appears that class meetings are held once a week. In terms of lab attendance, interestingly, students who score below a minimum of 75 percent on any assignment – including homework, quizzes, or tests – in a particular week are required to spend at least four hours working in the MTLC the following week. The hours may be completed at the students’ convenience, but must be accrued between Sunday and Friday of that week. If students achieve above 75 percent in all assignments that week, they are not required to spend this time in lab.34

27 “Welcome to the Virginia Tech Math Emporium.” Virginia Tech.

http://www.emporium.vt.edu/emporium/home.html 28 “Math Emporium – Course Info.” Virginia Tech. http://www.emporium.vt.edu/emporium/courseinfo.html 29 “Math Emporium – Individual Course Help Sessions.” Virginia Tech.

http://www.emporium.vt.edu/emporium/helpsessions.html 30 “Program in Course Redesign – The University of Alabama.” The National Center for Academic

Transformation. http://www.thencat.org/PCR/R2/UA/UA_Overview.htm 31 “Mathematics Technology Learning Center.” University of Alabama. http://mtlc.ua.edu/ 32 Ibid. 33 “Impact on Students – The University of Alabama.” The National Center for Academic Transformation.

http://www.thencat.org/PCR/R2/UA/UA_FR1.htm 34 “Welcome to the MTLC – MATH 100 – Fall 2011.” University of Alabama. http://mtlc.ua.edu/wp-

content/uploads/2011/08/Ma100_Fall_2011.ppt

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Peer-Led Team Learning Our review of institutional efforts to improve student math performance revealed that Peer-Led Team Learning (PLTL) is an innovative approach used in many NSF-funded STEM support programs. Originally developed for science education in the mid-1990s at the City University of New York, PLTL typically involves small group workshops associated with specific courses and guided by peer leaders. During the workshops, students work together to complete challenging problems provided by faculty. Peer leaders have received training to assist them in actively engaging students with the material and each other. Such a model yields a variety of benefits including: a supportive environment in which students may ask questions and engage in discussions that will help them understand important concepts; students engage in teamwork and become better communicators; and peer leaders gain important teaching and leadership skills.35 In his review of peer learning approaches, David Arendale lays out the following “guiding principles of PLTL”:

The program should be integral to the course through required attendance at two hours of workshop time weekly

Peer leaders are trained in group leadership and course content Activities and materials are challenging yet accessible Faculty are deeply involved in the program Physical space and environments are conducive to discussion and learning The program has strong support from the institution36

The PLTL approach to instruction has been adopted by hundreds of institutions, a handful of which are described below.

As part of its Gateways to Engagement, Mastery, and Success (GEMS) initiative, which has received NSF support,37 the University of Texas at Dallas offers PLTL study groups. Each group consists of roughly eight students who meet 80 minutes per week to collaboratively work through challenging problems. The sessions are facilitated by a Peer Leader who demonstrates various problem solving techniques, offers assistance when members of the group are having particular difficulties with a problem, and provides general encouragement to the group. The university notes that in addition to developing stronger communication and critical thinking skills,

35 Arendale, D.R. “Postsecondary Peer Cooperative Learning Programs: Annotated Bibliography.” College of

Education and Human Development, University of Minnesota. 2007. http://www.tc.umn.edu/~arend011/Peerbib03.pdf

36 Taken verbatim from Arendale, op cit. 37 Note that the initiative was formerly referred to as “Gateways to Excellence in Math and Science (GEMS).”

See: “NSF Grant Targets Shortage of Math-Science Grads.” University of Texas at Dallas. http://www.utdallas.edu/news/2009/11/19-002.php

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students who participate in the sessions typically earn better grades than students who do not participate. During fall 2011, the university is offering PLTL sessions for three math courses – Applied Calculus I, Differential Calculus, and Integral Calculus – as well as courses in chemistry, physics, and engineering.38

The Virginia Military Institute (VMI) also uses PLTL in some of its math and chemistry courses. Students in these courses attend one-hour workshops each week, led by student leaders trained in teaching techniques and course content. The workshops consist of six to eight students who work together through challenging, structured problems that have been developed by the course instructor. Student leaders and instructors meet weekly to discuss the previous workshop and prepare for the upcoming session. VMI notes that the workshops provide “an active learning experience for students, creates a leadership role for successful students, and engages faculty in a creative new dimension of instruction.”39 With assistance from a grant, the program was instituted in fall 2004. Due to its success, the PLTL program was extended beyond the life of the grant and “has been integrated into the routine tutoring options of the departments.”40

The University of Houston Downtown offers PLTL in math and science. Similar to the other programs discussed in this section, the program features study groups led by peer students who have received a B or higher in the associated course. An advertisement for peer leaders in support of a College Algebra PLTL workshop explains that weekly sessions last for 1.5 hours. In addition to facilitating the sessions, peer leaders are also asked to informally evaluate the progress of workshop participants using “leader logs” and engage in debriefing surveys and discussions regarding the workshops. In exchange for their work, leaders receive $500 for the semester.41 Notably, the program has received some funding through an NSF grant.42

38 “What is Peer Led Team Learning (PLTL)?” University of Texas at Dallas.

http://www.utdallas.edu/GEMS/assets/PLTL_for_students_final_Fall2011.pdf 39 “Learning Programs – Peer-Led Team Learning.” Virginia Military Institute.

http://www.vmi.edu/Content.aspx?id=12309 40 “Online SACS Review – Compliance Certification Report – Comprehensive Standards.” Virginia Military

Institute. http://www.vmi.edu/show_sacs.aspx?id=40945 41 “PLTL (Peer-Led Team Learning) – Conscientious and Enthusiastic PLTL Workshop Leaders Wanted for

College Algebra Classes.” University of Houston Downtown. http://cms.uhd.edu/Faculty/NakamuraM/PLTL/WSLApplication.PDF

42 “NSF – Broadening Participation in Computing – Computing Alliance for Hispanic-Serving Institutions.” University of Houston Downtown. http://www.uhd.edu/academic/colleges/sciences/ccsds/CAHSI/index.html

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Further, one professor of Computer and Mathematical Sciences at the university has archived a set of College Algebra PLTL workshop exercises that provide examples of specific problems assigned to student participants.43

Miami Dade College has incorporated PLTL sessions in fourteen of its STEM courses, including College Algebra, Calculus and Analytic Geometry I, Pre-Calculus Trigonometry, and Calculus and Analytical Geometry II. While the college does not provide a great deal of detail on the sessions, it indicates that, likethe other programs described above, trained peer leaders lead weekly course review sessions and faculty provide the peer leaders with advice on how to deliver instruction.44

Supplemental Instruction Supplemental instruction (SI) represents another form of student-centered, collaborative instruction and learning. The approach, developed by the University of Missouri-Kansas City in 1973, appears similar to PLTL in that it also utilizes peer instructors. In his discussion of peer learning approaches, Arendale makes the following distinction between SI and PLTL: SI typically involves “adjunct support through outside-of-class activities” with little change by the primary course instructor,” while PLTL involves the integration of peer learning into the course itself.45 Despite this distinction, the two approaches share many of the same characteristics. SI is described as a non-remedial tutoring method using collaborative learning strategies and is provided based on the assessment of high-risk courses rather than identification of high-risk students. This fundamental differentiation is important, as it removes much of the stigmatization associated with tutoring that may prevent many students from seeking assistance. Providing another point of distinction from PLTL, SI programs utilize integrated approaches that incorporate general learning and study skills into the instruction. These integrated skills may include note-taking, vocabulary acquisition, and test preparation.46 SI programs are typically offered on a voluntary basis to all students enrolled in the course. Below we provide some examples of SI programs focused on promoting student success in mathematics.

43 “PLTL Workshop Materials.” Department of Computer & Mathematical Sciences. University of Houston

Downtown. http://cms.uhd.edu/Faculty/NakamuraM/PLTL/WorkshopMaterials/CAWSMaterials.htm 44 “Peer-Led Team Learning (PLTL).” Miami Dade College.

http://www.mdc.edu/main/stemconnections/peerledteamlearning.asp 45 Arendale, D.R. “Postsecondary Peer Cooperative Learning Programs: Annotated Bibliography.” College of

Education and Human Development, University of Minnesota. 2007. http://www.tc.umn.edu/~arend011/Peerbib03.pdf

46 Lotkowski, Veronica, S. Robbina, and R. Noeth. 2004. “The Role of Academic and Non-Academic Factors in Improving College Retention,” p. 13. ACT Policy Report. http://www.act.org/research/policymakers/pdf/college_retention.pdf

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Oregon State University offers supplemental instruction to students taking high-risk courses such as Math 111: “College Algebra” and Math 112: “Elementary Functions.” The university explains that the SI sessions, also referred to as Study Tables, “integrate how-to-learn with what-to-learn” – in other words, the sessions integrate study skills into the review of course material.47 Students meet once per week with a Supplemental Instruction Leader for one hour. SI Leaders have already successfully completed the associated course and have received training in facilitating group learning and engaging fellow students.48 The university explains that students attending at least five SI sessions per term earn exam grades that range from one half to a full letter grade higher than students who do not attend sessions or attend less frequently.49

The University of the Virgin Islands received funding from the National Institutes of Health to provide supplemental instruction in mathematics, as well as biology, chemistry, and computer science courses. The sessions are non-remedial and held outside class on a regular schedule. Fitting with our earlier description of SI, the program supports “historically difficult” courses and involves regularly scheduled review sessions that are available to all students in the associated courses. The university notes that the sessions are “informal seminars in which students review notes, discuss readings, develop organizational tools, and prepare for examinations” and that students “learn how to integrate course content with reasoning and study skills.”50 Unlike some other SI programs, sessions may be led by an instructor or a peer leader. With regard to the effects of the program, the college indicates that students who participate regularly in the sessions typically earn higher grades in the associated course.

CUNY Lehman College maintains an Office of Supplemental Instruction and Technology. The office was created in spring 2007 through a Title V grant from the U.S. Department of Education in order “to improve student transition to the upper division of science disciplines, mathematics, and business studies.” SI sessions are guided by a peer leader or a recent graduate of the college and involve collaborative review of course material, practice of key concepts, development of study skills, and testing of course knowledge before exams.51 During spring 2011, the college offered SI

47 “What is Supplemental Instruction?” Oregon State University. http://success.oregonstate.edu/what-

supplemental-instruction 48 “What are Study Tables?” Oregon State University. http://success.oregonstate.edu/what-are-study-tables 49 “What is Supplemental Instruction?” op cit. 50 “STEM Supplemental Instruction.” University of the Virgin Islands.

http://www.uvi.edu/sites/uvi/Pages/ECS-Supplemental_Instruction.aspx?s=AC 51 “Title V Office of Supplemental Instruction and Technology.” Lehman College.

http://www.lehman.edu/supplemental-instruction/index.php

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sessions for College Algebra, Precalculus, and Calculus I, among other courses.52

Applications of Math Concepts In a paper addressing the retention of students in STEM fields, University of Michigan researchers at the Center for Research on Learning and Teaching noted that students who face a multiple-course calculus sequence in pursuit of their STEM degree often feel overwhelmed by the difficulty of the courses and are deterred by a low grade in one course. The long course sequence typically covers material that does not appear directly applicable to their intended major.53 The Michigan researchers discuss multiple studies demonstrating that “students’ perception of the usefulness of their learning affects their motivation to engage with course material and therefore their desire to persist in STEM majors.”54 Providing an example from mathematics, the researchers highlight a study examining the performance of students in pre-calculus course sections that used real-world, timely problems (such as differences in HIV infection rates across genders and races and the effects of climate change on agriculture) versus courses that involved more traditional material. The study found that students in the class using real-world problems had significantly higher completion rates and were more likely to finish the course with a grade of C- or better than their peers in the conventional course.55 In order to promote student engagement with the material and, more broadly, retention, the Michigan researchers suggest that instructors place concepts within the context of current events and technologies, such as asking “students to apply STEM concepts and skills to understand, evaluate or solve real-world problems (e.g., use polynomial functions to estimate how quickly a disease could be eradicated).”56 Faculty can also provide some discussion of their own research and/or how they became involved in the field. As discussed below, applications of course material may also take the form of demonstrating connections between concepts in introductory, gateway math courses and more advanced coursework, as well as their application across

52 “SI Review Sessions Spring 2011.” Lehman College. http://www.lehman.edu/supplemental-

instruction/review-sessions.php 53 Brown, K., C. Hershock, C. J. Finelli, and C. O’Neal. “Teaching for Retention in Science, Engineering, and

Math Disciplines: A Guide for Faculty.” CRLT Occasional Papers No. 25. 2009. p. 8. http://www.crlt.umich.edu/publinks/CRLT_no25.pdf

54 Ibid. 55 Winter, D. “Infusing Mathematics with Culture: Teaching Technical Subjects for Social Justice.” In M.

Kaplan and A.T. Miller (Eds.). The Scholarship of Multicultural Teaching and Learning. San Francisco: Jossey-Bass. 2007. Cited in Brown, et al., op. cit. p. 7-8.

56 Ibid.

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disciplines. Wright State University has developed an introductory math course based on this principle. The WSU Model Previously, Wright State University’s engineering program required a minimum of one full year of calculus before students could proceed to sophomore-year engineering courses. The university explained that this was a daunting challenge as students were required to take Calculus I, II, and III during the first three quarters of their enrollment. However, the university was witnessing high levels of attrition of engineering students following the freshman calculus sequence, with only 42 percent of students advancing past those courses. The institution described this issue as the “first-year mathematics bottleneck” and noted that similar situations are seen in engineering programs throughout the United States.57 In response to this issue, the university developed what it terms the WSU model for engineering mathematics education. The university created a new freshman engineering math course that is taught by engineering faculty and only addresses math topics that are directly applicable to introductory engineering courses. Under the previous curriculum, core engineering courses such as Physics I, Statics, Dynamics, Strength of Materials, Circuit Analysis I, C Programming, and Fortran Programming all required completion of Calculus I and some required completion of Calculus I-III and Differential Equations. The university recognized, however, that only some of the topics covered in these calculus courses directly applied to the core engineering courses.58 Therefore, the new course, EGR 101: “Introductory Mathematics for Engineering Applications,” replaces the traditional math sequence and allows students to progress into the engineering program without having first completed the calculus sequence.59 The EGR 101 course is comprised of lectures, labs, and discussion sections. Similar to our earlier discussion of student-centered learning approaches, the university explains that the lectures feature problem-based learning, while the lab and discussion sections encourage collaborative learning between students. Emphasis is placed on the use of physical experiments, as well as the engineering analysis software, Matlab. Topics addressed in the EGR 101 course include:

Linear and Quadratic Equations Trigonometry 2-D Vectors

57 “The Wright State Model for Engineering Mathematics Education: A Nationwide Adoption, Assessment and

Evaluation.” American Society for Engineering Education, 2009. p.2. http://www.engineering.wright.edu/cecs/engmath/AC_2009-1416.pdf

58 Ibid., p. 3. 59 Ibid.

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Complex Numbers Sinusoids and Harmonic Signals Systems of Equations and Matrices Basics of Differentiation Basics of Integration Linear Differential Equations with Constant Coefficients60

It should be noted that EGR 101 is not a replacement for the calculus sequence. Under the model, students take EGR 101 in the fall of their first year and proceed to Calculus I after completing the course. The remaining required calculus courses are taken during the sophomore and junior years. Further, as EGR 101 is the only required math course for entering sophomore-year engineering courses, students who do not pass Calculus I immediately may still proceed in their engineering courses while retaking the math course. For students entering the university unprepared for EGR 101 – those who have not completed trigonometry – the university developed EGR 100: “Preparatory Mathematics for Engineering and Computer Science.” The course covers high school math subjects through trigonometry and presents the topics in terms of their applications to engineering and computer sciences. Beyond this, the EGR 101 course is available each quarter, so students can get on track to proceed through the engineering curriculum directly after taking the trigonometry-based prerequisite.61 WSU witnessed impressive results following the introduction of the model. First-year retention in engineering increased from 68.0 percent in the four years prior to the model to 78.3 percent following model implementation. Additionally, students who participated in the EGR 101 course performed better in Calculus I – 89 percent of those who completed EGR 101 earned a grade of C or higher, compared to 60 percent of non-participants.62 Providing another indicator of the program’s success, funding under the NSF Course Curriculum and Laboratory Improvement (CCLI) Program was granted to support the expansion of the model to 15 institutions (including universities, as well as community colleges and one school district). Universities adopting the model included California Baptist University, University of Texas at El Paso, University of Toledo, Oklahoma State University, University of Cincinnati, and University of San Diego, among others.63 60 Ibid., p. 3-4. 61 Ibid., p. 7. 62 Ibid., p. 6-7. 63 Ibid., p. 9

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Summer Bridge Programs A final practice that we will address in this report is the use of summer bridge programs. Based on our review of NSF-funded STEM support programs, it appears that two- to five-week summer programs for incoming STEM freshmen are nearly ubiquitous. Many of the programs are math-focused and are sometimes characterized as math “bootcamps.” Students have the opportunity to earn math credit while solidifying math skills essential for their anticipated program. The camps sometimes move beyond math skills, making connections to science and engineering, or even more general study skills. Bowling Green State University provides a helpful example of a successful summer bridge program that focuses on math skills. As part of its Academic Investment in Math and Science (AIMS) initiative, a four-year program for students with high academic potential and an interest in STEM fields, the university devised a five-week summer program. The primary goals of the program are to help acclimate incoming freshmen to the campus and prepare them to succeed during their first semester at the university. The program consists of “mini-courses” in math and computer science, totaling 30 contact hours in the classroom over the five weeks. In addition, students participate in “science exposures” addressing topics in biology, chemistry, physics, geology, and astronomy, as well as work in labs. Aligning with our earlier discussion of applications of concepts, the program also features excursions to a variety of science-related organizations, including Pfizer Pharmaceutical, BASF Corporation, NASA, and Phoenix/Plastics Technology. For example, in a trip to Pfizer Pharmaceutical, students are presented with information regarding the development of a drug, including how “scientists, computer experts, engineers, statisticians/mathematicians, and health professionals” are all involved in the process.64 The math portion of the program is intended to give students a sense of how their college courses will be conducted, while bolstering their math skills. The course covers fundamental concepts of algebra, trigonometry, geometry, and calculus (including limits, derivatives, and integrals). In terms of the program’s success in the field of mathematics, the university reports that “a positive correlation between the achievements of AIMS Scholars in their summer math class and the ensuing first fall semester GPA’s was found.”65 Further, the university has compared AIMS student performances with those of Bowling Green students who did not participate in the program but are similar in terms of high school academics and demographics. The AIMS participants maintained higher average GPAs than non-participants beginning in the first semester and continuing throughout their time at the university.66 64 Gilbert, T.C. op. cit., p. 13-14. 65 Ibid., p. 17. 66 Ibid. 18.

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The University of Maryland offers a similar summer program, geared specifically toward minority students interested in STEM majors. The five-week Summer Bridge Program for Scientists and Engineers is offered to 20 students each year. The program consists of four main components, discussed in the table below.

Summer Bridge Program for Scientists and Engineers - Components Component Description

Morning Mathematics

Classes

Classes are offered in algebra, pre-calculus, and calculus – students take a placement test that determines which course they will take. Students successfully completing a course will receive three credits and may proceed to the next course in the sequence at the start of the fall semester.

Student Success Seminars

Held during the mid-morning hours, these workshops cover issues such as time-management, study and test-taking strategies, stress management, career development, diversity, and health awareness.

Summer Science Engineering Lab

(SSEL)

Students work on projects in a variety of disciplines including mathematics, physics, engineering, astronomy, meteorology, and geology. Students develop written reports and give presentations on their projects. As a secondary component of the SSEL, students visit science labs and research facilities, such as NASA, the National Institute of Standards and Technology, W.L. Gore & Associates, and a number of University of Maryland research centers.

Supplemental Instruction

University of Maryland students majoring in STEM fields provide peer-led tutoring to summer bridge participants, helping them work through problems related to their math courses.

Source: University of Maryland. In the fall semester following completion of the program, students enroll in a one-credit “Leadership and Scholarship, the Bridge to Effective Citizenship” seminar. The content of the seminar focuses on leadership philosophies and practices, while also acting as another support in helping STEM students transition into college by addressing “academic, career, and personal development strategies.”67 While an evaluation of the program was unavailable, a news item from the university indicates that 2011 was the 27th year of the program’s operation, suggesting that the program is well-established at the university.68

67 “LSAMP Bridge Program for Scientists and Engineers.” University of Maryland.

http://www.lsamp.umd.edu/bridge.html 68 “The Summer BRIDGE Program for Scientists and Engineers.” University of Maryland.

http://lsamp.umd.edu/news/news_story.php?id=1126

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Case Studies Below we provide four case studies of institutions that have adopted multiple approaches to improving the performance of students in foundational mathematics courses. As illustrated throughout the profiles, many of these institutions have implemented practices highlighted in the previous section of this report. As seen below, an additional innovative practice not directly discussed previously is featured – Washington State University’s restructuring of its precalculus course sequence. Note that while some of these practices are situated within broader STEM support initiatives, we primarily focus only on those practices most relevant to our current project – improving student performance in mathematics. University of South Florida The University of South Florida (USF) provides a strong example of an institution that has taken a multi-pronged approach to improving the performance of its students in foundational mathematics courses. Further, in support of its efforts, the university has received funding from the NSF.69 USF undertook this initiative after identifying low graduation rates among students studying in STEM fields as compared to students in other fields. In fact, the university found that six-year graduation rates among STEM majors were below 60 percent, while students majoring in business, nursing, and education exhibited graduation rates over 80 percent. USF identified foundational science and math courses as a source of this problem, noting that “students often change their major before even taking a class in it, due to loss of motivation in basic science and math courses and failure to see the relevance to their major.”70 Focusing on calculus in particular, the university found that, on average, only 55 percent of students were passing Engineering Calculus I, II, and III, and Life Sciences Calculus I and II. In order to remedy this situation, USF set out to redesign the curricula and sequencing of these foundational calculus courses through the implementation of three practices: project-based calculus instruction, peer leading, and introduction of a “STEM Mart.” All three are discussed below. Project-Based Calculus Instruction Providing an example of curriculum redesign, USF introduced “bridge” projects into Engineering Calculus II and III and Life Sciences Calculus II. This gave students the choice to complete a project rather than take a final exam. Students 69 “Award Abstract #0756847 – A STEP to Grow in Science-Engineering-Mathematics Undergraduate

Degrees.” National Science Foundation. http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0756847

70 “A STEP to Grow in Science-Engineering-Mathematics Undergraduate Degrees.” University of South Florida. 2010. http://www.math.usf.edu/data/nsf2010.ppt

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would pair up with a science faculty member or a workplace supervisor in order to “define a problem, write and analyze appropriate equations, and write a narrative report – in essence, they write a story problem, and then answer it and write it up as a scientific report.”71 In addition to promoting student-centered learning, this appears to align well with our earlier discussion of making connections between foundational math concepts and more advanced coursework or career applications. Based on fall 2008 through fall 2009 data, the university found that students engaging in projects were passing calculus courses at higher rates than students who did not engage in such a project. Peer Leading The second approach used by USF is peer leading. The university implemented a program in which undergraduate peer leaders guide 50-minute “cooperative learning inquiry sessions” each week for students in Engineering and Life Science Calculus I. These sessions are based on curricula designed by faculty and graduate students to guide students to discover calculus concepts before encountering them in lecture. The sessions also incorporate “warm-up” instruction in algebra and trigonometry. We provide a picture of the structure of peer-led activities below, reproduced from material provided by USF.

Structure of Peer-Led Activities Step Description

Pre-Assignment

Completed before class. Includes practice with algebra, often a missing skill. At the beginning of every peer-led session, there is a short quiz based on this pre-assignment and the previous week’s activity.

Student Group Structure Students work in groups of four. Each student has a different ‘role’ (manager, recorder, spokesperson, and strategy analyst), and these roles rotate each week.

Heart of the Activity

Groups work on discovery activities, structured to include discovery of a concept, concept formulation, and then concept application. The peer leader facilitates classroom discussions and provides support where difficulties occur.

End of Session Students summarize what they have learned and reflect on learning strategies that were or were not effective.

Source: University of South Florida.72 Similar to its use of project-based instruction, the university reports that students engaging in peer-led activities exhibited higher calculus pass rates (Life Sciences Calculus I and Engineering Calculus I) than students that did not participate in the activities.

71 Ibid. 72 Ibid. Reproduced with slight modification from source.

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STEM Mart Finally, the university offers a STEM Mart, where undergraduate tutors provide peer support in a “one-stop” tutoring lab. Assistance is provided in calculus, as well as basic courses in chemistry, physics, and biology. The STEM Mart offers evening and weekend hours for students’ convenience.73 Students interested in tutoring are required to submit an application detailing their performance in specific calculus courses, as well as any other relevant math, science, or engineering courses and names of professors who can attest to the students’ proficiency in calculus and the other relevant subjects. Prospective tutors may also be asked to interview for the position. Selections are made based on the needs of the tutoring program.74 Washington State University In 2009, Washington State University issued a memorandum to academic advisors regarding changes in its mathematics curricula, sequencing, and placement. Among other initiatives the document describes an “Alternate Precalculus Pathway.” The description begins with the following:

Precalculus is a gateway course into science, technology, engineering, and mathematics (STEM) majors, yet many students are unsuccessful in their first (or second or even third) attempt to pass it. This shatters the goals and ambitions of students and has serious implications in terms of retention.75

The document proceeds to explain that mathematics faculty members and graduate students, as well as members of the Department of Teaching and Learning sought to understand students’ difficulties in succeeding in these courses. One of the key findings of this work was that “even when students placed into precalculus using the current placement system, the background of many of the students was too fragile to support the pace and rigor expected in the course.”76 In addition to adjusting the university’s placement system, WSU developed an innovative new sequence for its foundational math courses. The new sequence is presented in the table below. 73 Ibid. 74 “Application for Undergraduate STEM Mart Success Center Tutors.” University of South Florida.

http://math.usf.edu/download/STEP-Undergraduate_Application.pdf 75 “Mathematics Update for Advisors and Counselors.” Washington State University. 2009.

http://vpue.wsu.edu/specialsections/AdvUpdMathematicsUpdateforAdvisorssu09.pdf 76 Ibid.

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Math Course Sequencing Course Sequence

Elements Description

Alternate Precalculus Sequence

Students with weaker math backgrounds will be encouraged to take a two semester sequence Math 106: “College Algebra” (3 credits), and Math 108: “Trigonometry” (2 credits), rather than the one semester Math 107: “Precalculus.” Math 106 will be a prerequisite for Math 108. Another advantage of this two course sequence is that transfer students often have taken the equivalent of Math 106 and this will allow them to take trigonometry by itself.

Precalculus “Safety Net”

A safety net is built in for Math 107 students by offering a late start Math 106 that will start the sixth week of the semester and will meet five days a week. With this in place a student who is failing Math 107 after the first exam will be able to transfer into a late start Math 106 and have a second chance to succeed in a mathematics class. Most sections of Math 106 will run the entire semester, but one or two late sections will be reserved for students at-risk of failing 107.

Calculus “Safety Net”

A Math 108 section will start the fifth week of the semester, will meet three days a week, and will be a safety net for some Math 171: “Calculus I” students. Math 107 students will only be able to transfer into Math 106, not both Math 106 and Math 108 late start sections.

Source: Washington State University. In addition to the changes to course sequencing, the memorandum highlighted “support courses” and study halls that are available to students taking entry-level math courses. Math 110: “Mathematics Tutorial for Math 107” and Math 111: “Mathematics Tutorial for Math 201” are offered as support courses (note that Math 201 is “Mathematics for Business and Economics”).77 These courses offer “individualized instruction focusing on what each student needs help with.”78 Students who qualify to enter Math 107 or Math 201 but are concerned about their math abilities are encouraged to enroll in the appropriate support course. Additional support is provided through “tutor-assisted” study halls, available at a number of locations during the week and on weekends, with daytime and evening hours. Students may seek assistance on a drop-in basis.79 University of Memphis A five-year program funded by the NSF and designed to increase retention and graduation rates among STEM students, the MemphiSTEP program incorporates a variety of STEM support initiatives at the University of Memphis. Of particular

77 “Department of Mathematics – Course Information.” Washington State University.

http://www.math.wsu.edu/Office/Courseinfo/cdescrip_schedule.php 78 “Mathematics Update for Advisors and Counselors.” Op cit. 79 “Department of Mathematics – Free Tutor-Assisted Study Halls.” Washington State University.

http://www.math.wsu.edu/studyhalls/welcome.php

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relevance to our current report, the university provides the following description of the program:

It has been well-established that the lack of a solid preparation in mathematics often can be a deterrent to a student’s success in a STEM major. Although we concentrate on all STEM areas across the campus and each year of a student’s undergraduate career, mathematics, especially as used in science and engineering will be a focal point in many of our strategies and activities, especially for the early undergraduate years.80

In line with this description, here we examine two elements of the initiative: a bootcamp and the use of interactive math software. Bootcamp Beginning with the bootcamp, students considering study in a STEM discipline are invited to participate in a “two-week refresher seminar designed to boost pre-calculus skills, demonstrate links between math, science, and engineering, and broaden knowledge of career opportunities in STEM fields.”81 According to an evaluation report of the bootcamp by University of Memphis faculty, the primary goals of the activity are to:

Improve math skills needed to succeed in Calculus I and other STEM courses Help students prepare for college by offering degree-related information and

social networking opportunities Increase awareness and interest in STEM careers, including computer science

and computer engineering Demonstrate connections among mathematics, science, and engineering82

The aforementioned evaluation report provides details of the August 2009 bootcamp. The authors explain that the program was offered over the course of ten days and comprised 20 morning and afternoon sessions. The sessions were led by faculty members from various STEM departments (including Mathematical Sciences, Computer Science, Electrical and Computer Engineering, among others). Each session included a 75-minute lecture by the faculty member, followed by another 75-minute practice session featuring collaborative work among students on problems related to the lecture. University of Memphis STEM majors served as assistants, working with students during the practice sessions.83

80 “MemphiSTEP: A STEM Talent Expansion Program at the University of Memphis.” University of

Memphis. http://www.memphis.edu/memphistem/pdfs/Final_Year_3_MemphiSTEM_Poster.pdf 81 Ibid. 82 Best, R.M., et al., “Math Bridge Bootcamp: A Strategy for Facilitating Undergraduate Success in STEM

Courses.” University of Memphis. http://stepcentral.net/media/uploads/forums/2011/06/20/Math_Bridge_Bootcamp_2010.pdf

83 Ibid., p. 2.

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The morning sessions focused on mathematics (primarily precalculus), while the afternoons featured science and engineering. However, the afternoon sections were connected to the morning sessions in that the mathematics topics covered earlier in the day were applied during the afternoon science and engineering sessions. Daily lunch sessions were used to promote both social networking among students, as well as to host guests including University of Memphis faculty, STEM graduates, and student mentors. These guests presented information regarding their experience working and/or studying in a STEM field and then fielded questions from bootcamp participants. The evaluation of the bootcamp yielded a variety of positive results. First, pre- and post-test data of participants indicated significant improvements in math skills. Focus groups and survey data also revealed that students believed that the bootcamp activities improved their math skills, boosted their confidence, and demonstrated how math is applied in the fields of science and engineering. Both the pre- and post-test data and the focus group results indicated an increased interest in STEM careers among participants. While at the time of the evaluation, comparison group data were unavailable, the authors report that participants in the program achieved an average GPA of 3.03 in their first semester, a high GPA given the difficulty of STEM courses the students were taking. Additionally, all students who had declared a STEM major (84 students) remained in their major for the fall and spring semesters.84 Interactive Math Software In the second year of the MemphiSTEP program, the university incorporated a web-based tool – WebAssign – into its Calculus I, II, and III courses. The program enables students to complete classroom and homework activities, as well as take tests. Similar to other institutions described in this report who have adopted interactive math software, the university explains that “WebAssign is designed to scaffold students’ understanding of math concepts by offering immediate feedback to responses and allowing students multiple opportunities to solve math problems.”85 While not covered in the MemphiSTEP materials reviewed for this report, it appears that the university has used MyMathLab software in its courses. For example, a Calculus III course redesign proposal describes the use of the software in Foundations of Mathematics and Elementary Calculus courses, as well as the use of WebAssign in Calculus I and II in fall 2008 and 2009. The author of the redesign plan explains that these courses met in a computer lab and featured a mix of

84 Ibid., p. 5. 85 “MemphiSTEP: A STEM Talent Expansion Program at the University of Memphis.” op. cit.

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lectures and web-based homework and assessments. Describing the interactive nature of the courses, the author notes that students work through practice problems each class period, and receive instant feedback through MyMathLab or WebAssign. He credits this interactive nature with the improved success and retention rates among students in the courses. For example, student success rates in the redesigned courses improved from 51 percent to 59 percent (while the author does not define “success rate” it appears that this is equivalent to pass rate).86 University of Maine A 2006 article published by mathematics faculty at the University of Maine discusses how peer-led team learning (PLTL) was integrated into math courses. Based on success of this approach in physics and chemistry classes at the university, three faculty members sought to apply it to their own classes, with the following three goals:

To improve student comprehension of mathematics so students can successfully solve both routine and non-routine problems.

To improve student attitudes about math. To provide an alternative way of learning.87

Using NSF funding, the mathematics department restructured two sections of Calculus I beginning in fall 2003. The sections included three 50-minute classes with the instructor and one 75-minute PLTL session every week, except in exam weeks, where the PLTL session was used to administer the exam. The PLTL sessions followed three different formats, including:

Discovery workshops – Before a concept is introduced in class, students engage in activities designed to facilitate collaborative discovery of an idea.

Exploratory workshops – After a concept has been addressed in class, students explore the topic in greater detail in order to generate a deeper understanding.

Review workshops – These workshops provide students time to practice the material learned in class.

The faculty members conducted a presentation of their use of PLTL in Calculus I at a workshop held at the City University of New York. As part of the workshop, the faculty provided copies of eight PLTL modules used in their Calculus I courses that

86 “Proposed Redesign of Math 2110 (Calculus 3).” University of Memphis. https://umdrive.memphis.edu/g-

alc/public/crf-2010/proposals-funded/Jamison%20%28MATH-2110%29.pdf 87 Drewniany, P., S. McGarry, and J. Tyne. Progressions. Summer 2006.

http://www.sci.ccny.cuny.edu/~chemwksp/Intro_Calculus_SU_06/PLTL-Calc-Introduction-Su-06.pdf

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are now available online and offer examples of exercises that could be used during a PLTL session.88 The faculty members also discuss the selection and training of peer leaders. In order to initially identify students who might be well-suited to leading PLTL sessions, mathematics instructors were asked to submit the names of students who had been successful in Calculus I courses and who they thought would have good leadership abilities. These students were then asked to attend an information session and submit an application to become a leader. The chosen peer leaders were required to attend weekly training sessions. Each session began with a discussion of the previous PLTL session, allowing leaders an opportunity to share successful approaches, gather suggestions for ways to deal with problems, and provide any feedback that could be used to improve the next section. Next, leaders were asked to discuss chapters from the book, Peer-Led Team Leading: A Handbook for Team Leaders,89 which provide guidance on leadership. Finally, training sessions provided time to work through the upcoming PLTL session. One of the instructors would take on the role of a peer leader, while the actual peer leaders would act as calculus students. In addition to providing a preview of how the session would be conducted, this exercise provided a basis for peer leaders to ask additional questions regarding how best to approach a topic. Beyond the trainings, peer leaders would submit journal entries discussing how students received each PLTL session, the level of difficulty of the material, and questions about how to address any situations that arose during the session.90 Reflecting on the implementation of the PLTL approach, the faculty members expressed positive impressions of its value. They noted improved student attitudes toward math, as well as increased opportunities for active learning among students. In terms of the experience of peer leaders, they found that these students were able to solidify their knowledge of calculus, found new approaches to student learning, and gained some experience with teaching. Faculty members indicated that they enjoyed working with the peer leaders during weekly leader training meetings, allowing for contact with a highly motivated group of students interested in math. The only drawback highlighted by the faculty members was the loss of a class meeting with students – the Calculus I course previously met four times a week but one meeting was replaced by the PLTL session.91

88 See: “Calculus I Modules.” The PLTL Project Newsletter.

http://www.sci.ccny.cuny.edu/~chemwksp/newsletter.html#calc 89 Roth, V., E. Goldstein, and G. Mancus. Peer-Led Team Learning: A Handbook for Team Leaders. Prentice Hall.

2001. http://www.pearsonhighered.com/product?ISBN=0130408115 90 Drewniany, P., S. McGarry, and J. Tyne. op. cit., p. 2. 91 Ibid., p. 3.

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Innovative Practices for Improving Student Performance in College Level Mathematics

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