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This site is still under construction. MPPRI stands for Mathematics Preparation, Placement and Review Initiative. Background Students come to UCSC with different preparation levels in mathematics. We know that more needs to be done than placing students in classes based on one standardized test. We know that students need more opportunities for review than a textbook. Our realization that we need to offer content specific modules was influenced and supported from involvements and collaborations such as these: 1) UCSC utilizes the Calculus Readiness Placement and Diagnostic test only to place students in a mathematics class. This falls far short of the potential of the diagnostic test. (See the report “Feasibility Study and Implementation Strategies for Mathematics and Diagnostic and Placement Testing at UCSC” by Frank Bäuerle at http://count.ucsc.edu/~bauerle/Placement.htm. This is a study that was funded by the Division of Physical and Biological Sciences a few years ago to study and make recommendations on how to improve placement of students in mathematics classes.) In addition, this places many students in Math 3 that really only require a careful review of some aspect of the Precalculus curriculum rather than a whole course. This is a waste of students’ time and also not fair to those students that really struggle with the material. 2) As TA-trainer in math, Frank often hears that math TA’s face the dilemma of being asked in section to review a basic concept but do not have the time to do so. 3) Nandini has collaborated with Professor Pascale Garaud (Applied Mathematics and Statistics) in devising methods to help her Calculus students review algebra. 4) Nandini and Frank have discussed the issue of math preparation in Physical Chemistry (Chem 163A) with Professor Glenn Millhauser (Chemistry), and as a consequence he decided to offer a workshop reviewing the mathematical concepts required in the class. According to Professor Millhauser, this experiment was a huge success and encourages us greatly that our approach is the right one. The underlying idea that ties all these various aspects together is that we can offer targeted concept modules that present the material in a new way that builds on students’ knowledge rather than repeat a chapter in a textbook. These modules can be offered in collaborative learning-style workshops or the material can be reviewed in self-paced on-line modules before and during the quarter. Over the last few months we have made significant progress in working out some of the organizational details in selecting suitable students, realistic timelines and dates for workshops as well as identified some sources for freely available on-line resources. Initiatives need to be undertaken to help our students realize what they need to review and then empower and enable them to do just that. Impact on Teaching and Learning Learning excitement is generated when we enrich and excite students thinking with new material beyond the existing knowledge base. Reviewing old concepts to bring the whole class to the same level of background knowledge creates apathetic learners. Leaving the reviewing to the students’ with specific guided assistance will help make them responsible for their own education and eliminate boredom in the classroom. This in turn will make students more often motivated learners. When students just graduate from High School, they are ready for a new beginning. The approach in this pilot will encourage more responsible and effective learners. Students will be helped with specific content areas and the help will be learning-specific The use of technology makes it possible. We plan to use the Felder/Solomon learning styles diagnostic tool (see http://www.ncsu.edu/felder-public/RMF.html for more information) to determine whether students will be able to accomplish the required mastery through self-study with the aid of on-line resources or through workshops taught by qualified mathematics instructors or a combination of the two. One advantage of on-line resources is that the materials are available to students from home over the summer before they come to UCSC. Successful participants in this pilot will not need to take a full quarter of Precalculus when all they need is help with parts of its curriculum. This will save them time which in some cases can be significant, particularly if successful completion of Calculus is a prerequisite to other courses that might only be offered once a year (e.g. Physics 6A, 6B require Calculus 19A, 19B at least be taken concurrently, so a frosh intending to be a Physics major who needs to take Math 3 cannot take the Physics 6 series until a year later, likely extending their graduation time by one year.) Reviewing those concepts that are needed in a new light will further enhance students understanding of the underlying mathematical concepts, thereby better preparing them for subsequent courses. Similarly, review of calculus concepts in the context of a specific science will give students a better understanding of the calculus and the science class, and will increase the pass-rate in these classes (see note by Professor Millhauser with the additional materials.)
In this phase of the project we are implementing a pilot project to provide students with tools to supplement their mathematics background. The approach is personalized and focused on a particular students' needs. We consider this pilot as a crucial, but early phase of a comprehensive plan to address issues involving mathematics placement, preparation and review.
More specifically, in this pilot we focus on students expected to take Math 11A (Calculus with Applications) or Math 19A (Calculus for Engineering, Physics and Mathematics) for Fall 2007. Using the (usually unutilized) diagnostic feature of the math placement test we plan to diagnose weaknesses in students’ preparation and offer learning style specific opportunities to address these weaknesses in the form of workshops and self-paced on-line resources. The goal is to prepare students better and more efficiently for their Calculus classes as well as provide continued access to review materials for subsequent courses that utilize Calculus.
Nature of the Request This proposal is about addressing the very real problem of mathematics preparation of students in mathematics and other science courses in post-secondary education. This pilot will target students who will take Calculus at UCSC in all class levels who might need additional preparation. The core of the current proposal is to carefully diagnose weaknesses of a student's mathematics readiness and to offer an innovative teaching approach to overcome them. The advent of technology coupled with a better understanding in how students learn gives us new tools to do this. This pilot attempts to combine technology with proven successful teaching strategies, and as such it is innovative. According to Sally Johnstone (Executive Director of WCET, the Cooperative advancing the effective use of technology in higher education), this is not done anywhere else in the country. We have the opportunity to break some new ground. Project Assessment Direct assessment will occur in two ways. Firstly, student learning will be assessed for those students wishing to enter Math 11A or Math 19A instead of Math 3 by having them retake the placement exam. While they will be placed in the appropriate class, their new score will give us a raw measure of their learning in specific areas. This is particularly possible by comparing a students placement exam score in those areas where they had initial weaknesses. This assessment will take place after students take the placement exam a second time, near the beginning of each quarter when workshops are offered. Secondly, overall effectiveness of the project will be assessed by keeping track of participating students’ performance in Calculus and subsequent science courses as compared to a randomly selected group of students that did not participate. If funded, we will consult with Psychology faculty to do this effectively. We have received a commitment from Kathleen Dettman (Director, Academic Planning, Resources and Analysis, Budget Office) to help us with collecting data from SIS, and we have been assured that this can be done in full compliance of applicable privacy rules. This part of the assessment is on-going. Overall, assessment of this project is one of its exciting aspects, and we can see publishing a paper on our findings. Plan for Continued Funding Upon successful completion of the pilot, we will ask for continued funding for the workshops through the PbSci division which will be mostly salary for the teaching staff. The on-line resources will continue to be available without incurring additional cost both for incoming students for preparation and for continuing students for review. Since we consider this pilot as a beginning of a comprehensive approach to the problem of mathematics preparation, placement and review, our plan is to apply for an NSF grant that would allow us to considerably expand the scope of the project. Clearly the project can be expanded to other service courses such as Math 2 (College Algebra), Math 21 (Linear Algebra), etc.. Workshops could be developed for other science courses similar to what was done for Physical Chemistry. We see a great need to address this issue and foresee many opportunities in the future. Acknowledgement: We want to thank Henry Burnett for countless meetings on this project. His tireless enthusiasm for concrete, positive action on students’ behalf and his great insights into the effective use of on-line resources has been very valuable. Even though he does not appear as a principal applicant on the grant, his contributions to this proposal have been very significant. We are thrilled to have his commitment to pursue this project further.
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Bäuerle, Ph.D., UC Santa Cruz.
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