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Center for Digital Education
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The City University of New York and the Center for Digital Education are proud to host The CUNY 2012 Mathematics Conference: Effective Instructional Strategies on the changing shape of mathematics education.
This day-long conference will feature faculty panel discussions on new and best practices in mathematics instruction related to technology, curriculum, pedagogy and faculty development. Also featured will be faculty poster presentations on improving mathematics learning and innovative instructional practices.
The CUNY 2012 Mathematics Conference: Effective Instructional Strategies will provide CUNY mathematics faculty, department chairs and administrators an opportunity to network with and learn from each other.
Registration is complimentary for all higher education faculty and staff.
Caren Diefenderfer, Professor of Mathematics, Hollins University, Roanoke, VA
Caren Diefenderfer has been a member of the Hollins mathematics department for over 30 years and was instrumental in establishing the Hollins quantitative reasoning program in 1998. She received her AB from Dartmouth College and her MA and PhD degrees from the University of California at Santa Barbara. Diefenderfer is the president of the National Numeracy Network (NNN) and the director of the Tensor for Women and Mathematics Grant program of the Mathematical Association of America (MAA). Currently, she is a co-PI with Michael Pearson, Bernie Madison and Marilyn Carlson on NSF Grant #DUE-1122965, Using Research to Shape Instruction and Placement in Algebra and Precalculus (URSIP). She has published articles on quantitative reasoning in both Peer Review (the Journal of AAC&U) and in Numeracy (the online journal of the NNN).
8:00 to 9:00 a.m. – REGISTRATION / CONTINENTAL BREAKFAST / EXHIBIT AREA OPEN
9:00 to 9:15 a.m. – OPENING REMARKS
Chair: Joan Lucariello, University Dean of Education
Dr. Alexandra Logue, Executive Vice Chancellor
Warren Gordon, Chair, CUNY Math Discipline Council
9:15 to 10:25 a.m. – Paper and Panel Discussion #1: NEW PERSPECTIVES ON PEDAGOGY
Chair: G. Michael Guy, Queensborough Community College
Predictable and Systematic Mathematical Misconceptions
Thomas Johnstone, PhD, New York City College of Technology
In this talk/discussion, the presenter will address well-known mathematical misconceptions that weak to moderate math students often have. For instance, they lack a basic understanding of the intimate connection between algebra and arithmetic; they prefer to memorize rules rather than understand concepts; they are lost if minor mistakes make them fall into non-textbook situations; they ‘simplify’ algebraic expressions that simply don’t simplify; they struggle with real-life questions that can be solved using mathematical techniques that they have learned; etc.
What puzzles this presenter is that these misconceptions and errors are so predictable and systematic, yet he feels our standard math instruction – instructors, textbooks, syllabi, curricula, pedagogy alike – do not do enough to correct them. Dr. Johnstone believes small pedagogical and curriculum changes could go a long way, such as:
Adapting the Singapore Model Method of Problem Solving Framework to College Level
Umesh Nagarkatte, Kay Lashley, Herbert Odunukwe and Lavoizier St. Jean, Medgar Evers College
Singapore Mathematics and Science consistently rank first in the world in the Trends in International Mathematics and Science (TIMSS) studies. Starting with Basic Skills, we are revamping our math courses. We will involve the Singapore model and the Theory of Constraints (TOC) thinking tools. The Singapore Model is an implementation of TOC. The framework – logical and deeply rooted in underlying mathematics principles of effective problem-solving methods – is represented in a pentagon of five interrelated associated components: Concepts, Skills, Processes, Metacognition, and Attitudes.
Great emphasis is placed on the quantitative aspect of learning the concepts of numbers and the four basic arithmetic operations. The key feature of the model method is illustrated in rectangular bars which are pictorial representations of the models helping students learn the mechanics involved in solving word problems. This concrete-pictorial-abstract approach is depicted by the part-whole and comparison models in arithmetic and algebra. Students learn to set up equations from the beginning.
TOC is used to transcend the student from pictorial to logical thinking approach showing the logical connection between the assumptions and the unknown/s. Arithmetic problems need only sufficient conditional logic while some algebra problems require necessary condition logic.
Gaming Your Classroom
Dr. Kathleen Offenholley, Borough of Manhattan Community College
Games-based learning is an interactive, interdisciplinary pedagogy that uses best practices in collaborative learning and simulations. Mathematician Keith Devlin has written about the great potential for gaming in mathematics education. As a steering committee member of the CUNY Games Network, Dr. Kathleen Offenholley understands the potential that games-based learning offers, and has seen her classroom transformed by games-based learning into students who are engaged and who understand.
Dr. Offenholley will give a short introduction to the theory and evidence for games-based learning, followed by several examples of games that can be played in mathematics classes from pre-algebra through upper-level mathematics.
Neuroscience Approach to Teaching Mathematics in the Technology-intensive Environment
Alexander Vaninsky, PhD, Hostos Community College
Teaching and learning mathematics may be viewed as an interactive process of creation of specific domains in the human brain. The domains act later as mathematics knowledge centers. Learning mathematics may be regarded as a development of connections among these and other centers. Topology of mathematics-related brain structures is a promising area of research. We refer to this approach as Neuro Mathematics Education (NME) and focus on the role of technology. The NME approach allows for a new insight into mathematical abilities and paves the way for development of original teaching tools, strategies and techniques. In particular, it stresses the principal importance of elimination of mathematics anxiety – the main barrier to success in mathematics.
Among the new tools for teaching mathematics are active development of mathematical intuition; using sleep-learning and hypnosis; and instruction delivery in the multifaceted interactive Internet-based environment, to name a few. The goal of the NME is the creation of a positive mental environment for perception and storage of mathematical information: concepts, notions, rules, techniques, etc. Dr. Vaninsky will present evidence that using technology contributes to the implementation of the NME in practice and has a positive impact on perception of mathematics and its applications.
10:30 to 11:20 a.m. – ROUNDTABLE / POSTER PRESENTATIONS and BREAK, Cafeteria
Chair: Annie Han, Borough of Manhattan Community College
Roundtable and poster presentation descriptions are listed below the agenda.
11:20 to 11:30 a.m. – Return to Lecture Hall
11:30 a.m. to 12:30 p.m. – Paper and Panel Discussion #2: CURRICULAR INNOVATIONS
Chair: John Velling, Brooklyn College
Quantway CUNY Presentation Abstract
Michael George, Yevgeniy Milman, Annie Han, Borough of Manhattan Community College
One of the prevailing themes in developmental mathematics education reform is the sense among many students that they are not learning mathematics that will be useful to them in the future. Introductory Algebra, a mainstay of the developmental mathematics curriculum, is largely designed to prepare students for more advanced mathematics courses, leading up to and including Calculus. For those students who are not bound for STEM-related careers or majors, algebra constitutes an arguably dead-end educational trajectory.
“Quantitative Literacy” represents an alternative pathway for the mathematics education of these students. Loosely conceived around understanding quantitative ideas in everyday life, Quantitative Literacy has recently made a great leap forward in both content and implementation. Funded and directed by the Carnegie Foundation, the “Quantway” project has brought together faculty from eight two-year colleges to help produce the materials and design for an original course. This presentation will provide an overview of our involvement in developing the Quantway Curriculum, and relate our experiences implementing the innovative pedagogical methods that follow from the Quantway Curriculum. Student data will be shared.
Success and Opportunity: Curricular and Structural Implications from Scaling Arithmetic WARM UPS
Michael Guy, Queensborough Community College, Chancellor’s Award Winner
Over the last several years, Queensborough Community College's Department of Mathematics and Computer Science has experimented with strategies to improve student success in the developmental math sequence. As part of QCC’s Improving Math Learning Project, a new four-week modular version of arithmetic, Arithmetic WARM UPS, was created. In Fall 2011, the Arithmetic WARM UPS version of developmental arithmetic was scaled to include the vast majority of arithmetic students (N~950). In this talk, we will look at the outcomes of this scale. We will discuss the curricular and structural modifications that may further improve student progression as we attempt to scale our work to the entire developmental sequence rather than only a single course. This is joint work with Jonathan Cornick, Robert J. Holt and Andrew Russell, and has been possible thanks to departmental, college and university funding and support.
A Data-based Approach to Building an Introductory Course for a Data-Intense Subject
Bill Williams and Sandra Clarkson, Hunter College, Chancellor’s Award Winners
In 2006, we threw away our textbook and our twice-weekly lectures and embarked on a very new approach to teaching statistics. With the addition this year of online testing, we are continuing to use a data-driven approach to building a data-driven course for a data-driven subject. In this talk, we discuss the reasons that drove us to take our basic course in statistics from a traditional textbook-based course to a hybrid, with combined lectures and computer-labs and, finally, to a totally computer-based course.
This is the best of both worlds – the usefulness of having one's instructional material available at all times and places where a computer is available, as well as having an instructor to provide helpful computer-based exercises and both one-on-one and group help. Students in this course are successful in subsequent courses and data gathered during course assessment continues to move them forward.
This course is taught by adjuncts and coordinated by full-time faculty. Changes in the course are carefully monitored to determine their effectiveness. The talk will center on setting up, monitoring and improving a course using data and how technology made this possible.
12:30 to 1:30 p.m. – LUNCH, Cafeteria
1:30 to 1:40 p.m. – Return to Lecture Hall
1:30 to 2:40 p.m. – KEYNOTE ADDRESS
Introduction: Professor Warren Gordon, Baruch College / Chair, CUNY Math Discipline Council
Keynote: Quantitative Reasoning: The Good, The Bad and The Unknown
Professor Caren Diefenderfer, Hollins University
2:40 to 3:40 p.m. – Paper and Panel Discussion #3: RE-THINKING EDUCATIONAL EXPERIENCE WITH TECHNOLOGY
Chair: John Verzani, College of Staten Island
Toward a Unification of Purposes: eTexts, Assessment and Best-Practice Analysis
John Velling, Brooklyn College
The Holy Grail of mathematics pedagogy is no longer unimaginable. The trifecta of
1. interactive text with embedded, randomly generated examples, tutorials, walk-throughs and practice sessions;
2. algorithmically graded and instantly compiled evaluation tools along with the ability to create and manipulate learning materials, allowing for a virtual class-of-one interface with students; and
3. the cross-section, cross-session, cross-institution tracking of student success/failure on a per-topic basis, allowing for a best-practice analysis is within reach.
MathLynx is operative, and has already shown that the nature of the online student experience need not be restricted to clicking buttons and moving sliders. Sophisticated problems can be built and incorporated into an algorithmically-presented learning experience tailored to each student according to personal progress. The instructor's in-class time can now identify issues as they develop, and classroom face-to-face time evolves from lecture to more address student stumbling blocks.
By cross-section, cross-session tracking, we can more closely identify problematic topics, instructors who successfully negotiate specific problem points and allow for the communication to spread successful strategies.
The Instructional Network: Using Facebook to Enhance Undergraduate Mathematics Instruction
Peter Gregory, Baruch College, Chancellor’s Award Winner
Facebook has been used so much by so many as a way to stay in touch with old friends, advertise new business ventures, brag about children, etc., that it has become a part of users’ daily lives and a part of our global culture. The power of social networking, along with the socio-cultural learning theories of Vygotsky and Bruner, suggest that Facebook could also be used to affect change in education. In this presentation, the presenter will show how Facebook can be used successfully as an instructional tool; give a procedure for creating a group on Facebook that ensures both instructor and student privacy; show how to make this group have an instructional rather than a social focus; show what these Facebook groups look like and how they work by using examples of actual groups in action from current and past classes. Survey results and quantitative student achievement data will be presented that show how the use of Facebook in this way positively affects student participation and performance.
Precalculus as a Hybrid Course: A Model for Student Success
Sarah Harney, Baruch College
Given levels of student preparedness and high failure rates in basic college math courses, it would seem counter-intuitive to suggest that a hybrid course structure would be successful. We often feel students need more classroom time, not less.
Experience at Baruch College teaching Precalculus as a hybrid indicates otherwise. By presenting this course partially online, we change the way in which students learn and encourage them to take responsibility for their learning. We replace the often passive learning environment of a lecture with a dynamic, technology-infused, collaborative learning environment. Effective instructor intervention and interaction amongst students ensures students are engaged and actively learning. Moreover, such a course structure allows for a course that can be customized for the needs of individual students. Face-to-face lecture time is now used to scaffold the learning of the students rather than to provide central instruction. This requires students to formulate questions on what they do not understand.
We will discuss how the Precalculus course is presented as a hybrid at Baruch, with reference to the specific technology and resources used. We will also compare the results of the students in the hybrid sections with the students in traditional classes.
3:40 to 4:30 p.m. – RECEPTION, Cafeteria
4:30 p.m. – Adjourn
1. An Internet-based Homework System to Improve Student Performance in Precalculus *
* Improving Math Learning (IML) Grant Award
Edward Grossman and Stanley Ocken, City College
The principal research question addressed by this project was whether a well-designed system of Internet-based homework and content resources would improve overall student performance, compared to the pencil-and-paper approach currently used in CCNY's precalculus course. We developed a database of homework assignments using Maple TA, a web-based testing and assessment system. Students received feedback on all homework, which included Flash-based graphics questions not usually assessed through online homework. The database consisted of more than 500 questions, with randomized inputs, paralleling those selected from the Mathematics Department's current precalculus text.
In both fall 2010 and spring 2011, the entire day session cohort of the course was randomly assigned into experimental classes using Maple TA and control sections following traditional homework methodology. Both groups followed the same homework, with the problem parameters randomized for the Maple TA cohort. The principal measure of comparison was the final exam, which was the same for all students and was group-graded by all instructors. Outcomes were analyzed adjusting for baseline student math preparation, such as scores on the Compass math placement exams, Math SAT scores and New York State Math Regents. The hypothesis that online homework would improve performance was not supported. In both semesters there was no significant mean difference between the groups on final exam grades. Nor was there a significant mean difference between the groups in course grades. Because of its more objective nature, findings bearing on the final exam were deemed more important than the findings bearing on course grades. For the Maple TA cohort, we were able to show that the homework completion rate was significantly correlated to performance on the final exam, controlling for precourse mathematics knowledge. Because parallel data on homework performance in the control classes was not available, we could not compare the relation of homework performance to final exam performance in the two groups.
2. The Effects of Study Skills Training and Peer Coaching of ‘At-Risk Students' on Retention and Passing Rates in a Remedial Mathematics Course *
* Improving Math Learning (IML) Grant Award
Leonid Khazanov, Michael George and Chris McCarthy, Borough of Manhattan Community College
Remedial mathematics at the college level has evidenced strikingly low retention and passing rates. Many efforts to improve student success have involved refinements to pedagogical strategies. However, it has been shown that at least 25% of the variation in student performance is explained by students' affective variables such as attitudes, study habits and skills, dispositions and math and test anxiety. This study endeavored to address these affective variables by
1. incorporating the teaching of study skills, time management strategies, test-taking skills and anxiety reduction strategies into an Elementary Algebra course, and
2. identifying at-risk students and assigning these students "coaches," who function both as tutors and counselors, providing regular personalized assistance.
It was hypothesized that course sections in the experimental group (i.e., those sections in which study strategies were incorporated into the teaching of the course and in which at-risk students are provided with coaches) would evidence significantly higher outcomes than equivalent sections to which these interventions were not applied. The data show that (1) the attrition rate was significantly lower in the treatment groups (p = 0.01299); (2) the passing rate was higher for the treatment groups, but not significantly so (p = 0.3013); (3) our diagnostic test successfully identified at-risk students (p= 0.0021); (4) the overall passing rate for coached students was significantly higher than for those who were not assigned coaches when adjusted for risk scores (p = 0.03356).
3. Increasing Student Success and Retention in Mathematics through Student-centered Instruction and Collaborative Learning *
* Improving Math Learning (IML) Grant Award
Claire Wladis and Alla Morgulis, Borough of Manhattan Community College
This project tested the hypothesis that a change in instructional format from a traditional lecture-based class to a more student-centered and collaborative one would increase student success in Intermediate Algebra and Trigonometry at the Borough of Manhattan Community College at the City University of New York (BMCC/CUNY), and that it would improve student attitudes toward mathematics, thus also leading to better recruitment, retention and progress toward graduation in the mathematics major. The study was conducted by running pilot experimental sections each semester, each with a comparable control section. Experimental and control sections were matched: They were taught by the same instructors, offered at a similar day/time and contained similar exams and other assignments. Pilot instructors underwent training to ensure effective and consistent use of techniques. The intervention’s effectiveness was evaluated using data on student pass rates in the course, changes in student attitudes toward mathematics and scores on departmental exams. The statistical analysis suggested that specific collaborative learning projects used as a part of a comprehensive course structure can have a significant effect on student success. However, this success is contingent upon a suitable period of instructor practice, training and revision of course structures and assignments. Collaborative learning can potentially work very effectively, but there is a learning curve for both instructors and curriculum developers. However, collaborative group work in stable base groups can lead to increases in student performance on exams of approximately two-thirds of a letter grade and about a thirteen percentage point gain in successful course completion compared to standard courses using a lecture format as the primary course structure.
4. Using a Graphics Tablet and Graphics Editing Software to Present Live or Online Lessons
Andréa Marchese, City College
For classes requiring an interactive and dynamic presentation of material, standard presentation software is often too limiting. The use of an inexpensive graphics tablet and graphics editing software offers the ability to combine handwritten notes with graphic images. Scanned pages from textbooks, selections from PDF handouts and graphics developed in outside software packages can easily be pasted into the scroll of class notes, which can be later posted online. In addition, digitally presented lessons can be recorded with screen-capturing software for use with hybrid or online classes.
5. WebWork Online Homework System
Judy Broadwin and Jarrod Pickens, Baruch College
WebWork, a computer generated set of problems in calculus and other subjects from the MAA, is entirely free. The students do their homework online and the homework is graded online. There are 35 permutations of every problem and each student has different numbers from his or her classmates. The number of problems on each topic seems endless and the instructor can easily make up problem sets from the National Program Library. The instructor knows at a glance what students are doing homework at any specific time and a quick email to the student who has not prepared informs the student that the teacher is aware that the student is not working. Failure is reduced to a minimum.
6. Accelerated Workshop Approach to Remedial Mathematics Using Problem-Solving *
* Improving Math Learning (IML) Grant Award
Jonathan Cornick, G. Michael Guy, Robert J. Holt and Andrew Russell, Queensborough Community College
Anecdotal evidence suggests that many students who 'almost' pass COMPASS Arithmetic (S1) placement test fail or drop out of MA-005, a semester-long remedial arithmetic course, because they are discouraged by a course which attempts to re-teach them material they have already seen for several years in high school. These students often do not re-enroll in the following semester and fail to make progress towards a degree despite their initial desire to do so. To meet the needs of such students and prepare them for a credit bearing course, a new course, MA-005M (modular workshop), was developed in Summer 2009 and offered for the first time in the Fall 2009 semester. It is an accelerated four-week, twenty-hour workshop including four computer lab hours, in which the emphasis is on students engaging in problem solving to improve their arithmetic skills. Students were required to take the COMPASS Arithmetic test again following their coursework. If they score at least 30 on their second attempt, then their arithmetic remediation is complete and they may register for a remedial algebra course in the following semester. The main goal of this project was a four semester (Fall 2009 – Spring 2011) statistical analysis and comparison of S1 exit scores for students taking MA-005M and MA-005 in order to identify subpopulations of students who can benefit from the workshop format, and who can thus sufficiently improve their skills and exit mathematics remediation more quickly. The course pass rate was 44% for the control group versus 73% for the experimental group, which showed a statistically significant difference. The within-semester retention rates were also significantly different between 65% for the control group and 84% for the experimental group. In addition, there was a statistically significant difference between 58% from the experimental group and 44% from the control group enrolled in the following remedial course. However, there was no statistically significant difference between approximately 15% for the control group and 19% for the experimental group passing the following remedial course.
7. Teaching Pre-Algebra and Algebra Concepts to Community College Students Through the Use of Virtual Manipulatives *
* Improving Math Learning (IML) Grant Award
Violeta Menil and Eric Fuchs, Hostos Community College
The project tested the effectiveness of virtual manipulatives (http://nlvm.usu.edu) on the performance of students in the two gateway courses: pre-algebra and algebra. The project also investigated the impact of virtual manipulatives on the students’ attitudes toward mathematics and confidence in doing mathematics. Two faculty members from Hostos Community College and Bronx Community College (BCC) taught both the control and the experimental groups. The students were randomly assigned to their sections by their respective mathematics departments in their respective campuses. While the control group learned mathematics through traditional teacher-centered lectures, the experimental group learned the same topics by using virtual manipulatives, i.e., manipulating colored blocks and fraction pieces on computer screens. The research project obtained mixed results as far as the students’ performance in mathematics was concerned. For the Hostos pre-algebra classes, the experimental group outperformed significantly the control group in all five assessments (p < .05). By contrast, BCC pre-algebra control group performed significantly better than the experimental group in all the five assessments (p < .001). Contributing factors for the control group’s better performance over the experimental group were time effect (8:00 a.m. class vs. 10:00 a.m.); age effect (younger students vs. mature students); student preparation (inadequately prepared vs. better prepared students). For the Hostos algebra classes, the experimental group showed a statistically significant performance than the control group in one of the four assessments (p < .05). For the BCC algebra classes, the experimental group had a statistically significant performance than the control group also in one of the four assessments (p < .05). The qualitative data, however, confirmed our hypotheses that virtual manipulatives were useful for students learning basic mathematics concepts. Students expressed this usefulness clearly in their reflections, in face-to-face interviews and through their responses in the Fennema-Sherman questionnaires on attitudes toward mathematics and confidence in doing mathematics. The faculty researchers conclude that virtual manipulatives are more effective for students learning pre-algebra rather than algebra. Further research is needed to determine the longer-term benefits of using virtual manipulatives for learning basic mathematics concepts.
8. Improving Undergraduate Mathematics Learning: The Effect of Small-group Homework Tutoring on Remedial Mathematics Learning *
* Improving Math Learning (IML) Grant Award
Alice Welt Cunningham and Olen Dias, Hostos Community College
This project analyzed the findings from an 18-section experiment studying the effect of homework-completion tutoring on community college students’ remedial mathematics performance. The experiment involved 529 students registered for two remedial math courses: math skills and algebra. For each course, the experiment studied nine sections: three experimental with multiple tutors for online homework, three control with a single tutor for online homework and three control with a single tutor for pencil-and-paper exercises. While state budget constraints delayed the availability of tutors for the experimental group until midway through the semester, that group outperformed the pencil-and-paper group at a 0.05 significance level, while the performance of the online homework control group categories surpassed those of the corresponding pencil-and-paper categories at up to a 0.001 significance level. In addition, for each course, math lab attendance for both the experimental and control online homework cohorts surpassed that of the pencil-and-paper cohorts. These results corroborate and extend earlier research and show the importance of active problem-solving rather than passive absorption in increasing remedial mathematics performance.
9. Community College Study of Mathematical Concepts and Skills Retention in Elementary Algebra: The Role of Distributed Practice and Problem-Centered Learning *
* Improving Math Learning (IML) Grant Award
Madelaine Bates and Susan L. Forman, Bronx Community College
Community college students enrolled in remedial mathematics courses often struggle with retention of the course material. Distributed practice and problem-centered learning are two instructional approaches that may improve student performance. Distributed practice is a method in which homework exercises on one topic are spread across several assignments, rather than being assigned all at once. The problem-centered approach uses real-life problems to motivate a topic and leads to a rationale for learning the related skills and concepts. The project attempted to answer two questions:
1. Does distributed practice of homework assignments lead to higher passing rates in the course?
2. Does a problem-centered approach with distributed practice lead to higher passing rates in the course?
The experimental design was quasi-experimental in nature. In Spring 2010, the PI and Co-PI each taught one section of Elementary Algebra using the departmental syllabus as written, assigning the homework exercises as specified on the syllabus. This was the control group. In Fall 2010, the same instructors each taught a section using distributed practice. In Spring 2011, they each taught a section using a problem-centered approach with distributed practice. Data gathered were the results on each of the unit exams, the departmental final and attendance. It appears that both experimental treatments, distributed practice and problem-centered learning, had a significant impact on learning and retention of concepts and skills as evidenced in the final examination results. Distributed practice contributed to students’ retention of the material and problem-centered learning contributed to their increased ability to work with word problems.
There is no room block set up for this event. Below is a list of nearby hotels.
Sheraton New York Hotel and Towers
811 7th Avenue between 52nd and 53rd Streets
Sheraton Manhattan at Times Square
790 7th Avenue at 51st Street
Doubletree Metropolitan Hotel New York City
569 Lexington Avenue at 51st Street
Holiday Inn Midtown
440 West 57th Street between 9th and 10th Avenues
Hampton Inn Manhattan-Times Square
851 Eighth Avenue at 51st Street
There is no parking available on campus. There are several pay parking garages along 59th Street between 9th and 11th Avenues.
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