Reforming Developmental Math, A Data Driven Approach:

Reforming Developmental Math, A Data Driven Approach: Perspectives from Dyscalculia, to curriculum, to pedagogy; using what works (a preliminary report) Elizabeth Chu, James Fulton, and Regina Keller

Developmental Math has been called the Bridge to Nowhere WHY? The national average for the passing rate of a developmental math course is about 50%. If a student has to take two developmental math courses. Then only 50% X 50% = 25% ever make it to a college level math course, and only a fraction of those 25% ever pass a college level math course! This is a national problem that colleges across the country have been trying to find a solution for. It is truly a multi-billion dollar problem, not to mention the costs to a student's self-esteem.

Numerous Colleges are Focusing on the Developmental Math Challenge Accelerating Remedial Math Education (Fast Start) Housatonic Community College, an Achieving the Dream college in Connecticut, is piloting a self-paced, modularized, competency-based, developmental math course. The course is offered in a lab setting, with open entry and exit so that students can start and finish their coursework at their own pace. State and institutional leaders are looking for ways to overcome obstacles that HCC has encountered in overcoming financial aid and other policy constraints, even as the college is trying to expand this program model more broadly across the institution. Community College of Denver has developed Fast Start, a developmental education design that enables students to take modules of two different courses in the same semester. This accelerates their progress through both a traditional class setting and a self-paced option. State system policies around managing enrollment data have made it easier for CCD to offer this option. Mountain Empire Community College, an Achieving the Dream College in Virginia, has developed short refresher courses for developmental math students. These courses take less time to complete and cost the student less than more traditional developmental courses. Students can move through more than one of the short courses in a single semester. As in Denver, Virginia s enrollment, financial aid, and student data system policies have not presented any obstacle to Mountain Empire s innovations.

Focus on the Dev. Math Challenge (cont.) Florida colleges to drop remedial classes for thousands By Denise-Marie Ordway, Orlando Sentinel For years, men and women wanting to take classes at their local community colleges have been discouraged to learn they must complete a remedial program before enrolling in college-level courses.... Now, amid an outcry for nationwide reforms in remedial education, Florida lawmakers have ordered a complete overhaul of the state's college remedial programs.... Starting in 2014, a large segment of students will be able to immediately enroll in college-level courses, regardless of their academic abilities. They will not have to take remedial courses or even a placement test, which is required by community colleges to detect gaps in learning.... Why Is Florida Ending Remedial Education for College Students? Starting this fall, academically underprepared students at Florida's public universities no longer have to take classes designed to help them catch up. By Janell Ross August 25, 2014 Back when remedial education was popular in policy circles, it was seen as a way to help those students most at risk of dropping out of college. Instead of immediately finding themselves overwhelmed after arriving at college academically underprepared, students could get up to speed through remedial courses offered side-by-side with traditional college classes. In the last few years, however, critics have begun to question whether remedial classes solved any problems or instead created more of their own, as the share of students required to spend valuable financial-aid funds and time on zero-credit courses that brought them no closer to a degree expanded....

Focus on the Dev. Math Challenge (Cont.) Statway/Quantway: The Carnegie Foundation has created an alternative (non-algebraic) approach for servicing developmental math students. For $25k per year your institution can join a consortium of other institutions, but you must use at least 80% of their material and follow their guidelines. Currently claims to have around 33 Institutions on board. Suffolk is considering paying $50k for a two year commitment, plus expenses associated with sending 5 potential instructors to California to be trained. Quantway boasts a 56% pass rate for first time developmental students. Currently Suffolk has first time pass rates of 56.1% for MAT001 and 62.9% for MAT007. Key factors driving their degree of success: Small classes (limited to 24 students, but typically only half that number enroll.) A student focused teaching pedagogy. They spend a lot of time on the non-cognitive aspects of engaging the students.

Focus on the Dev. Math Challenge (Cont.) California State Universities transforming course design for developmental mathematics. The wide variety of contexts amongst the various campuses in the CSU system prohibits a one size fits all approach to developmental mathematics course redesign. Because of this, the CSU Transforming Course Design teams have opted not to recommend a single redesign approach, but rather to construct a menu of course redesign components from which faculty at any given campus can select various components of redesign that are appropriate for their particular student needs and campus resources. 1. Diagnostic and Placement Tests 2. Early Start Programs 3. Alternative instructional strategies A. Mastery Learning B. Redesigning Instructional Strategies - Online Technology C. Supplemental Instruction D. Alternate Course Designs for Specific Cohorts 4. Integrating Technology in Teaching Techniques North Carolina Community Colleges began offering developmental math courses in the Fall of 2013 as four-week course modules with each module worth one credit hour in four weeks. The number of course modules a student will need will be determined by the college level math course required by the student's degree program or major.

Focus on the Dev. Math Challenge (cont.) Illinois Community Colleges improves their developmental math. Guiding principles for any developmental math program Institute high levels of organization for the program in terms of consistent content, pace, instruction, and expectations. Establish program assessment measures that are used and evaluated regularly to gauge program effectiveness and possible areas of improvement. Assess persistence, retention, and performance of students in subsequent courses. Use results to improve the program. Create structures and support for adjunct faculty such as materials, training, mentoring, and professional development. Goals for each facet of the developmental math program Placement: Refine testing, placement and administrative procedures to ensure that students enroll in the developmental courses [and/or programs] they need. Advising: Assist students to enter and succeed in the courses and programs that best meet their needs. Courses: Improve and diversify course offerings to support diverse ability levels, learning styles, and goals. Instruction: Provide quality instruction that fosters student engagement and learning. Support: Establish multiple and varied means to support students through the program. www.imacc.org/developmental/best_practices.pdf

Focus on the Dev. Math Challenge (cont.) Cleveland State Community College is redesigning its developmental math program, which consists of three courses: Basic Math, Elementary Algebra and Intermediate Algebra. These courses have historically been offered primarily in a traditional lecture format, enrolling over 1200 students annually with ~200 students in Basic Math, ~500 students in Elementary Algebra, and ~500 students in Intermediate Algebra. DropFailure-Withdrawal (DFW) rates have averaged 45% in these courses. Elementary Algebra has presented the biggest obstacle to student success, often having DFW rates of more than 50%. Cleveland State has redesigned these three math courses using the Emporium Model pioneered at Virginia Tech and replicated at many additional institutions. At CSCC, students meet one hour in class and two hours in a large computer lab. The one-hour class meetings are held in small labs (20 computers). Instructors do not lecture during class meetings. Instead, students work online and instructors help students individually. Instructors also review student progress and help students with their action plans for the coming week. Prior to the redesign, an average of 55% of students taking any developmental math course at Cleveland State earned a final grade of A. B or C. After the redesign during fall 2008, 72% earned an A, B or C, which represents a 31% increase in course completion rates. http://www.thencat.org/ncatplans/inc%20success%20in%20dev%20math%20article.htm

Focusing on What Works Some colleges focused on: the courses, how they were delivered, and what they taught student diagnostics and placement acceleration/fast track early start Removing it altogether A Common Thread: All the reforms that focused on the students, making the students understand that they mattered and that the teachers would check up on the student and their progress throughout the process, and explored ways to motivate the students, including peer-to-peer teaching, showed the greatest levels of success. The first, and most important, reason for success is Student Engagement. The primary reason many students do not succeed in developmental math courses is that they do not actually do the problems. As a population, they generally do not spend enough time with the material, and this is why they fail at a very high rate. The Non-Cognitive aspects were the most important piece for student success!

What Should be Considered When Reforming a Developmental Program Students Content What is Required? What should the course achieve? The end objective What is needed to obtain this? A clear and common curriculum Capabilities Expectations What can be Understood? Is the material at the proper cognitive level? Does the student have the needed background to grasp the concept? Pedagogy Cognitive Best method/ practices to teach a given topic Understand how a student learns Understand the cognitive ability of the student Assess and mitigate risks Non-Cognitive Motivate Coach Connect with Show they matter Be a cheerleader Require them to work Check their work One-on-one Peer-to-peer

Understanding Our Developmental Students What do we know about Suffolk's Developmental Students? Our analysis looked at developmental math students from the Fall of 2010 to the Spring of 2014. There were a total of 33,832 developmental students (actually 21,641 unique students) included in this study. We also looked at historical data from 1988-1992 (8,536 unique students) The overall persistence rate (the rate at which students move on to a college level math course) is quite low. Only 37% of developmental students move on to take a college level math course, with only 25% of the original number passing that course with a D, and 19% passing with a C or better. There is a significant difference between MAT001 and MAT007 with persistence, passing and success rates of 19%, 13%, 10% for MAT001 and 43%, 31%, 25% for MAT007. There is also a fairly significant difference between the lecture and the lab with the data favoring the lecture over the lab. This is a huge opportunity for the college. We lost 62% of the 21,641 or 13,405 students in this 4 ½ year study, as they never went on to take a college level math course. We need to find a better way to meet the needs of these students and provide them with a plan for their future. The fact that ONLY 10% of our MAT001 students will eventually succeed (C or above) in a college level math course is a major problem that needs addressing. Special thanks to the Office of Institutional Effectiveness for providing us with the data in an expeditious manner

Selective Data from Developmental Study

Understanding Our Developmental Students What do we know about Suffolk's Developmental Students? Students MAT001/L Rate All first timers 56.1% Overall Passing Rate All first timers 19.0% Persist to College Level Math All first timers 12.5% Receive D or higher in College Level Math All first timers 9.7% Receive C or higher in College Level Math Of those first timers that Pass 33.9% Persist to College Level Math Of those first timers that Pass 22.4% Receive D or higher in College Level Math Of those first timers that Pass 17.4% Receive C or higher in College Level Math Of those that Pass and Persist 66.0% Receive D or higher in College Level Math Of those that Pass and Persist 51.2% Receive C or higher in College Level Math Qualifier Special thanks to the Office of Institutional Effectiveness for providing us with the data in an expeditious manner

Understanding Our Developmental Students What do we know about Suffolk's Developmental Students? Students MAT007/L Rate All first timers 62.9% Overall Passing Rate All first timers 43.3% Persist to College Level Math All first timers 30.6% Receive D or higher in College Level Math All first timers 24.7% Receive C or higher in College Level Math Of those first timers that Pass 68.9% Persist to College Level Math Of those first timers that Pass 48.7% Receive D or higher in College Level Math Of those first timers that Pass 39.2% Receive C or higher in College Level Math Of those that Pass and Persist 70.8% Receive D or higher in College Level Math Of those that Pass and Persist 57.0% Receive C or higher in College Level Math Qualifier Special thanks to the Office of Institutional Effectiveness for providing us with the data in an expeditious manner

SC SB SA 882 708 473 Understanding Our Developmental Students Total 3501 0.08 0.20 0.13 0.25 0.20 0.14 Lecture versus Lab Success Rate 0.41 2010-2014 Success Rate = ALL (2010-2014) MAT001 MAT001L W 912 355 U 1845 1124 R 1061 396 S 4505 2141 Total 0.46 Success Rate = W U R SC SB SA Total 8323 0.11 0.22 0.13 0.541 MAT006 293 684 461 882 708 473 3501 4016 0.09 0.28 0.10 0.533 Success Rate = 0.59 MAT007 MAT007L 1340 284 2795 1270 1384 737 2914 859 2409 1658 1783 541 W U R SC SB SA Total 0.44 12625 0.11 0.22 0.11 0.23 0.19 0.14 5349 0.05 0.24 0.14 0.16 0.31 0.10 0.563 0.563 0.572

Understanding Our Developmental Students Persistence to another Math Course All: MAT001/L and MAT007/L Persistence Rate Pass rate C or above rate MAT001 Persisted 1799 Passed (D) 1169 Success (C) 897 Total 0.372 0.241 0.185 Rate MAT001L 0.216 696 0.140 396 0.108 315 8323 3960 MAT007 Persisted 5879 Passed (D) 3847 Success (C) 2965 Rate MAT007L 0.465 2351 0.304 1541 0.235 1191 Total 12639 5351 Rate Combined 0.176 0.203 0.100 0.127 0.080 0.099 Rate Combined 0.439 0.457 0.288 0.299 0.223 0.231

Criminal Justice Business Administration Non Matriculated Early Childhood Education Liberal Arts Psychology Culinary Education Child Studies Accounting Visual Arts Auto service Radio & TV Business Marketing Photo Imaging Graphic Design Human Services Info Tech CS Computer Art Chemical Dependency Paralegal Fire Protection Liberal ArtsBiology Music Infor Tech Network Dietetic Tech Business Office Management Liberal Arts Art History Business Retail Management Theater Business Management Education English Interior Design Asst Liberal Arts English Communication Media Arts American Sign Language HVAC Hotel & Retail Mgmt Infor Tech Web Construction Tech Communcation Studies Education History Liberal Arts Pol Sci Liberal Arts Creative Writing Fitness Specialist Understanding Our Developmental Students Areas of Study 2500 2000 1500 1000 500 0 22,197 General Studies Students (some counted twice) There were 184 STEM students versus 17,991 Non-STEM students or 1.02% STEM students

Understanding Our Developmental Students Accuplacer CPA Score versus Success Rate Probability of Passing MAT001 Accuplacer CPA (Algebra) Score 0.800 0.700 Probability 0.600 0.500 f(x) = 0.03x + 0.41 R² = 0.95 0.400 0.300 0.200 0.100 0.000 20 25 30 35 40 45 50 55 60 Score Probability of Passing MAT007 Probability Accuplacer CPA (Algebra) Score 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 f(x) = 0.03x + 0.41 R² = 0.99 20 25 30 35 40 45 Score 50 55 60 65 70 75

Understanding Our Developmental Students Accuplacer CPM Score versus Success Rate Probability of Passing MAT001 Accuplacer CPM (Arithmetic) Score 0.700 Probability of Passing 0.600 0.500 f(x) = 0.0266910519x + 0.3810248563 R² = 0.8477280298 0.400 0.300 0.200 0.100 0.000 20 25 30 35 40 45 50 55 60 65 70 CPM Score Probability of Passing MAT007 Accuplacer CPM (Arithmetic) Score f(x) = 0.0014x + 0.4944 R² = 0.3542 0.700 Passing Probability 0.600 0.500 0.400 0.300 0.200 0.100 0.000 10 20 30 40 50 60 Accuplacer CPM Score 70 80 90 100

Providing the Right Content Developmental math means many things to many instructors. Currently we lack a coordinated, consistent, and well-defined set of course content topics for our developmental courses. We have departmental syllabi for MAT001, MAT006, and MAT007, but the level at which to teach a particular topic is often not precisely spelled out. This is fine for the upper level courses, to an extent, but for the developmental courses this can be very problematic. There should be NO ambiguity in what should be taught, and at what level, in a developmental course. This isn't an issue for the MALA sections of the course, since the material is limited by ALEKS, and the tests are standardized. This, however, is not the case for the lecture courses, which are highly dependent upon the textbook. We need to reach a consensus on exactly what we should teach these students and to what level of mastery. Since NYS has adopted common core*, we propose aligning what we teach with common core, but at the same time tailoring it to the needs of college students taking developmental math. The courses need to satisfy two types of students, one that takes either MAT101, or MAT102 (liberal arts students), and one that takes either MAT103, or MAT111 (students who require more mathematics training based upon their chosen major) * www.engageny.org

Providing the Right Content (cont.) One of the most successful models on what to teach, and at what level, is the Singapore Mathematics Curriculum and its associated textbooks. The textbook is actually more important than the stated curriculum, since it alone defines what is taught. Singapore Math has found a successful blend of Number, Algebra, Geometry, Measurement Systems, Statistics and Probability concepts, needed by all students, but taught at the proper level and not too fast. They redesigned their curriculum around Quality and not Quantity, and their textbooks reflected it.* Singapore Math Three Tracks Normal (Technical) (10%) Normal (Academic) (25%) Express (O-Level) (60%) Where should we place our developmental students? * http://www.iea.nl/fileadmin/user_upload/irc/irc_2013/papers/irc-2013_kaur.pdf www.engageny.org

Delivering the Best Pedagogy While proper course content is required to set limits and expectations, proper pedagogy is more critical for a student's success. Proper pedagogy has two important aspects; Cognitive, where you focus on how to teach a concept in the best way, and Non-Cognitive, where the focus is on engaging and motivating the student to put the necessary effort in to succeed. In all the attempts by other colleges to address the developmental math problem, it is the non-cognitive aspects of pedagogy that has proven to have the largest impact on student success. The most successful attempts at getting developmental students to succeed, were the ones that were able to successfully connect to the students, so that the student's can and do control their own learning. This is the most critical component for the atrisk student's. It is also the primary reason that the students succeed in their subsequent courses (not just math). The real question then, is how to standardize this in all developmental courses. This should not be teacher nor course dependent, since it is so critical.

Proposed Holistic Solution Ideas to Discuss and Debate Have only one developmental math course that a student needs to take before moving on to a college level course. A student can take either MAT006 or MAT007 depending upon their level of preparedness. Remove the multiplication rule for loosing students: (50% pass MAT001) X (50% Pass MAT007) = 25% available to take a College Level Math Have different tracks of MAT006 and MAT007 based upon student capabilities, with the lower track courses having fewer students and a teacher (or student) aide assigned to the class. By track we mean the same material, but we separate the higher risk students from the lower risk students, and give the higher risk students more individualized and customized instruction to help them succeed. This requires proper placement of students which could come from Accuplacer or DyscalculiUM Screener (we're testing it this semester). Define the precise goals/objectives of MAT006 and MAT007. For example, prepare a student to take either MAT101, MAT102, MAT103, MAT111, or a science class. However, a grade of SB or higher is required for MAT103 or higher and for certain science classes.

Proposed Holistic Solution Ideas to Discuss and Debate Revise the syllabi for MAT006 and MAT007, based upon the course definitions mentioned above (choose the precise topics and define the level of mastery for each). Revise along the lines of Common Core (the Singapore version), since this is what is currently being taught in high school. Modify topics to meet the specific needs of the 99% of developmental student not planning on going into STEM. NOTE: The course content of MAT006 and MAT007 have not changed in over 40 years, but the secondary school curriculum has undergone numerous sweeping changes over that time period. They are long overdue for a major revision. Come up with best practices for teaching all the topics in the newly defined MAT006 and MAT007 courses and share with all faculty teaching the courses. Develop special training for faculty to properly teach developmental students. Perhaps only certain (certified?) faculty should be allowed to teach the lower track courses with the highest risk students. Include non-cognitive approaches.

Proposed Holistic Solution Ideas to Discuss and Debate Have a departmental (or college-wide) coordinator (given 3 or 4 released credit hours per semester) assigned to monitor, assess and revise/improve the developmental program on a regular basis. The coordinator must be faculty (NOT administration) and the approach must be data driven. Expand the MLC with a special developmental component and resource room. Adopt or create a proper textbook (covering only the approved topics and at the approved level) for both courses used by ALL faculty to set a common standard.

Real, Concrete, and Practical Approaches

How to Address Student Motivation Non-Cognitive Approaches to Developmental Students

Reinforcing Non-Cognitive Skills in Developmental Math Courses

The Five Non-Cognitive Skills In their review of the existing research, the University of Chicago scholars identify five non-cognitive skills that contribute to students academic success. They are: Academic Behaviors observable behaviors that show students engagement and effort Academic Mindsets - students attitudes and beliefs about their academic work and ability Academic Perseverance the ability to overcome distractions, obstacles and challenges to complete academic work Learning Strategies tactics that students use to help them remember, think and learn Social Skills behaviors that allow students to interact with peers and adults in positive and productive ways Farrington, C.A., Roderick, M., Allensworth, E., Nagaoka, J., Keyes, T.S., Johnson, D.W., & Beechum, N.O. (2012).Teaching adolescents to become learners. The role of noncognitive factors in shaping school performance: A critical literature review. Chicago: University of Chicago Consortium on Chicago School Research.

David Conley, author of College, Careers, and the Common Core, shares a Four Keys framework for understanding college and career readiness, and one of those keys consists entirely of the non-cognitive skills listed below: goal setting; persistence; self-awareness; motivation; progress monitoring; help seeking; and self-efficacy.

Practices to implement: goal setting; Written contracts for completion persistence; Exercises, homework, bonus work self-awareness; Assessment of Dyscalculia results motivation; Manipulatives, varied lesson approach progress monitoring; Course calendar help seeking; Group work, outside study groups, encouraging student to attend office hours, classroom PA self-efficacy; One-on-one teacher-student rapport to bolster confidence (smaller class size)

How to Address the At-Risk Students Dyscalculia What it is, and how best to teach a dyscalculic.

Dyscalculia Also called number blindness, is severe difficulty in making arithmetical calculations, as a result of a brain disorder. It affects 3-6% of the general population. Dyscalculia is a specific learning disability that affects a person s ability to acquire arithmetical skills. It can manifest itself as a person s inability to understand basic number concepts and/or number relationships, recognize symbols, and comprehend quantitative and spatial information. Many people liken the effects of dyscalculia with numbers to that of dyslexia with words, and while there are many characteristics that overlap, however, there is no proven link between the two Screening for Dyscalculia DysCalculiUM is the first web-based solution for screening for dyscalculia in adults and learners in post secondary education. It is effective in both further and higher education, but can also be used to screen adults in the workplace who are struggling with mathematics. Diagnosing Dyscalculia Only a trained psychiatric professional can diagnose a person with dyscalculia

Dyscalculia Study (Preliminary Results) The Screening Test Special thanks to Dr. DeLongoria the Associate Vice-President of Academic Affairs for funding the study

DyscalculiUM Sample Questions

DyscalculiUM Sample Questions

DyscalculiUM Sample Report

DyscalculiUM Sample Report Categories Assessed Conceptual Comparative Verbal Comparative Symbolic Comparative Visual Spatial Graphical Tabular Symbolic Abstraction Spatial Directional Spatial Temporal Operational Conceptual Operational Inferential

Dyscalculia Study (Preliminary Results) DyscalculiUM Results All Courses 30 25 Frequency 20 15 10 5 0 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 90-9595-100 Overall Percentage Score 109 Students Tested Severely at Risk At Risk Not at Risk 15.6% 66.1% 18.3%

Dyscalculia Study (cont.) DyscalculiUM Results Al-Hihi DyscalculiUM Results Chu 7 6 4 Frequency Frequency 5 3 2 1 0 10 9 8 7 6 5 4 3 2 1 0 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 90-95 95-100 Overall Percentage Score Overall Percentage Score DyscalculiUM Results Fulton DyscalculiUM Results Millings 7 6 6 5 5 4 4 Frequency 7 3 2 3 2 1 1 0 0 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 90-95 95-100 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 90-9595-100 Overall Percentage Score Overall Percentage Score DyscalculiUM Results Young 4 3 Frequency Frequency 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 90-95 95-100 2 1 0 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 90-95 95-100 Overall Percentage Score

Dyscalculia Study (cont.) Although we can not say for certainty the exact percentage of students in developmental math that have dyscalculia, it seems reasonable from these results that it is significantly above the 3-6% level of the general population. It is most probably closer to 25% (or higher), with a fixed percentage being difficult to assign, since it will be highly dependent upon the cut-off point for the student's level of severity. It is, obviously, a significant problem for making progress with Suffolk developmental math students, and needs to be considered and addressed in any developmental math reform. This is something that is NOT considered in any other developmental reform programs! Dyscalculia is not something that can be cured, but there are techniques that are more effective for dyscalculic students, and they should be understood and utilized by instructors.

Dyscalculia Potential Teaching Techniques AlgeDisks and more

Sample of disks that we use in our class :

Video showing how these disks are used in the classroom.

Using manipulatives to show students how to multiply two binomials:

Using manipulatives to show students how to multiply two binomials:

Next Steps

Questions/Comments?