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Pre-Transfer Mathematics at Berkeley City College: An Adaptive Approach Presenter: Mary Jennings October 31, 2013 1:50-2:40 p. m.

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In California, all paths to graduation or transfer pass through intermediate algebra. 2

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Every student seeking an AA or AS degree must satisfy a minimum mathematics requirement of intermediate algebra, 3

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and every student seeking transfer to a four-year college must satisfy a minimum mathematics requirement of a transfer-level course. 4

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Intermediate algebra is a prerequisite to every transfer-level course. 5

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In the context of the Berkeley City College mathematics curriculum, we see intermediate algebra for the vital subject that it is: 6

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Traditional Berkeley City College Mathematics Pathways Math 203 Intermediate Algebra AA/AS area 4b Math 202 Geometry AA/AS area 4b Math 201 Elementary Algebra Math 253 Pre-Algebra Non-degree applicable Math 250 Arithmetic Non-degree applicable * Math 1 Pre-Calculus AA/AS area 4b; CSU area B4; IGETC area 2 Math 13 Statistics AA/AS area 4b; CSU area B4; IGETC area 2 Math 50 Trigonometry AA/AS area 4b; CSU area B4 STEM Math 3A Calculus I AA/AS area 4b; CSU area B4; IGETC area 2 Math 3B Calculus II AA/AS area 4b; CSU area B4; IGETC area 2 Math 2 Pre-Calculus AA/AS area 4b; CSU area B4; IGETC area 2 Math 3E Linear Algebra AA/AS area 4b; CSU area B4; IGETC area 2 Non-STEM Math 16A Calculus I AA/AS area 4b; CSU area B4; IGETC area 2 Math 3C Calculus III AA/AS area 4b; CSU area B4; IGETC area 2 Math 3F Differential Equations AA/AS area 4b; CSU area B4; IGETC area 2 Non-Stem Math 16B Calculus II AA/AS area 4b; CSU area B4; IGETC area 2 Math 18 Real Number Systems AA/AS area 4b; CSU area B4 NOTE: Red boxes indicate courses required for AS-T degree in Mathematics. 7

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According to district institutional research, during the past five years, intermediate algebra students at Berkeley City College have been succeeding at an average rate of approximately 62%. 8

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This success rate is disappointing in itself, but unfortunately many students come to Berkeley City College unprepared even for intermediate algebra. 9

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These students enter our pre-transfer mathematics curriculum one or more levels below intermediate algebra. The ramifications are striking: 10

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Math 203 Intermediate Algebra AA/AS area 4b Math 202 Geometry AA/AS area 4b Math 201 Elementary Algebra Math 253 Pre-Algebra Non-degree applicable Math 250 Arithmetic Non-degree applicable 47% success 62% success Approximately 29% of students who begin with elementary algebra succeed at intermediate algebra, 11

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Math 203 Intermediate Algebra AA/AS area 4b Math 202 Geometry AA/AS area 4b Math 201 Elementary Algebra Math 253 Pre-Algebra Non-degree applicable Math 250 Arithmetic Non-degree applicable 47% success 62% success 50% success approximately 15% who begin with pre-algebra succeed at intermediate algebra, 12

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Math 203 Intermediate Algebra AA/AS area 4b Math 202 Geometry AA/AS area 4b Math 201 Elementary Algebra Math 253 Pre-Algebra Non-degree applicable Math 250 Arithmetic Non-degree applicable 47% success 62% success 50% success and approximately 14% who begin with arithmetic succeed at intermediate algebra. 48% success 13

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This poses a significant challenge to the mathematics department and the college. 14

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The pre-transfer curriculum can amount to as many as 14 units of coursework for students and 16 units of instruction for faculty. In fact, 15

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during any given semester, the mathematics department invests approximately 47% of its resources in running pre-transfer-level arithmetic and algebra classes*: *This figure does not include proof-based geometry. 16

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Traditional Berkeley City College Mathematics Pathways Math 203 Intermediate Algebra AA/AS area 4b Math 202 Geometry AA/AS area 4b Math 201 Elementary Algebra Math 253 Pre-Algebra Non-degree applicable Math 250 Arithmetic Non-degree applicable * Math 1 Pre-Calculus AA/AS area 4b; CSU area B4; IGETC area 2 Math 13 Statistics AA/AS area 4b; CSU area B4; IGETC area 2 Math 50 Trigonometry AA/AS area 4b; CSU area B4 STEM Math 3A Calculus I AA/AS area 4b; CSU area B4; IGETC area 2 Math 3B Calculus II AA/AS area 4b; CSU area B4; IGETC area 2 Math 2 Pre-Calculus AA/AS area 4b; CSU area B4; IGETC area 2 Math 3E Linear Algebra AA/AS area 4b; CSU area B4; IGETC area 2 Non-STEM Math 16A Calculus I AA/AS area 4b; CSU area B4; IGETC area 2 Math 3C Calculus III AA/AS area 4b; CSU area B4; IGETC area 2 Math 3F Differential Equations AA/AS area 4b; CSU area B4; IGETC area 2 Non-Stem Math 16B Calculus II AA/AS area 4b; CSU area B4; IGETC area 2 Math 18 Real Number Systems AA/AS area 4b; CSU area B4 NOTE: Red boxes indicate courses required for AS-T degree in Mathematics. 17 Yellow totals 47% of department resources

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Even so, for example, of students who began at pre-algebra level in Fall 2009, only about 12% had successfully completed intermediate algebra by the end of Spring 2012. 18

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Even so, for example, of students who began at pre-algebra level in Fall 2009, less than 12% had successfully completed intermediate algebra by the end of Spring 2012. 19 That was six semesters.

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Students working through the elementary-through-intermediate algebra sequence generally fare somewhat better: 20

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California Community Colleges Chancellor's Office Basic Skills Progress Tracker Report Fall 2011-Spring 2012 Entry Two Levels Below Transfer into MATH 201 Elementary Algebra StudentsAttemptsSuccessSuccess Rate Berkeley City Total15816084 Mathematics158160840.532 Report Run Date As Of : 2/24/2013 11:40:00 AM Math 201-Math 203 A Fall 2011 elementary algebra cohort success rate of 53.2% looks promising, but… 21

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California Community Colleges Chancellor's Office Basic Skills Progress Tracker Report Fall 2011-Spring 2012 Entry Two Levels Below TransferSuccess One Level Below Transfer MATH 201 Elementary AlgebraMATH 203 Intermediate Algebra StudentsAttemptsSuccess StudentsAttemptsSuccess Two-term Success Berkeley City Total 15816084 49 39 Mathematics158160840.53249 39 0.247 Report Run Date As Of : 2/24/2013 11:40:00 AM Math 201-Math 203 the cohort’s Spring 2012 intermediate algebra success rate tells a less encouraging story: 22

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California Community Colleges Chancellor's Office Basic Skills Progress Tracker Report Fall 2011-Spring 2012 Entry Two Levels Below TransferSuccess One Level Below Transfer MATH 201 Elementary AlgebraMATH 203 Intermediate Algebra StudentsAttemptsSuccess StudentsAttemptsSuccess Two-term Success Berkeley City Total 15816084 49 39 Mathematics158160840.53249 39 0.247 Report Run Date As Of : 2/24/2013 11:40:00 AM Math 201-Math 203 23 Question: How did students get from a 53% elementary algebra success rate… …to a 25% intermediate algebra success rate?

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24 Almost 80% of students in this cohort who attempted intermediate algebra succeeded at it, but note what happened not during but before intermediate algebra:

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California Community Colleges Chancellor's Office Basic Skills Progress Tracker Report Fall 2011-Spring 2012 Two Levels Below TransferOne Level Below Transfer MATH 201MATH 203 StudentsAttemptsSuccess StudentsAttemptsSuccess Two-term Success Berkeley City Total 15816084 49 39 Mathematics158160 84 0.532 49 39 0.247 Report Run Date As Of : 2/24/2013 Math 201-Math 203 25 Students did not continue!

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26 Thirty-five students - 22% of the cohort and 42% of those who succeeded at elementary algebra - did not continue immediately into intermediate algebra.

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California Community Colleges Chancellor's Office Basic Skills Progress Tracker Report Fall 2011-Fall 2012 Cohort Two Levels Below TransferOne Level Below Transfer MATH 201 Elementary AlgebraMATH 203 Intermediate Algebra StudentsAttemptsSuccess StudentsAttemptsSuccess Three- to Four- Semester Success Berkeley City Total 158160840.53252 420.266 Mathematics15816084 0.532 52 42 0.266 Report Run Date As Of : 2/24/2013 11:50:27 AM Unfortunately, even giving students three to four terms to complete the traditional Math 201-203 sequence makes little difference. 27

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California Community Colleges Chancellor's Office Basic Skills Progress Tracker Report Fall 2011-Fall 2012 Cohort Two Levels Below TransferOne Level Below Transfer MATH 201 Elementary AlgebraMATH 203 Intermediate Algebra StudentsAttemptsSuccess StudentsAttemptsSuccess Three- to Four- Semester Success Berkeley City Total 158160840.53252 420.266 Mathematics158160840.53252 42 0.266 Report Run Date As Of : 2/24/2013 11:50:27 AM Unfortunately, even giving students three to four terms to complete the traditional Math 201-203 sequence makes little difference. These results have obvious implications for students seeking an AA degree … 28

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California Community Colleges Chancellor's Office Basic Skills Progress Tracker Report Fall 2011-Fall 2012 Cohort Entry Two Levels Below Transfer: MATH 201 Elementary Algebra Three-Semester Success at Transferable MATH 001 Pre-Calculus StudentsAttemptsSuccess 997 Students4.4% …as well as for students seeking to transfer: 29

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California Community Colleges Chancellor's Office Basic Skills Progress Tracker Report Fall 2011-Fall 2012 Cohort Entry Two Levels Below Transfer: MATH 201 Elementary Algebra Three-Semester Success at Transferable MATH 013 Statistics StudentsAttemptsSuccess 252610 Students6.3% 30

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California Community Colleges Chancellor's Office Basic Skills Progress Tracker Report Fall 2011-Fall 2012 Cohort Entry Two Levels Below Transfer: MATH 201 Elementary Algebra Three-Semester Success at Transferable MATH 050 Trigonometry StudentsAttemptsSuccess 110 Students0% 31

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The Fall 2009 Elementary Algebra Cohort To get a sense of six-semester success we direct our attention to the Fall 2009 elementary algebra cohort: 32

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Fall 2009-Spring 2012 Cohort Entry Two Levels Below College Elementary Intermediate Algebra Six-Semester Transferable Course Success Rate for Cohort of 264: 24.2% 76 Students114 Attempts64 Successes 29%24% 33

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The Fall 2009 Elementary Algebra Cohort One thing that is striking about this cohort is that, over a period of six semesters, out of 264 students, only 76 (29%) attempted a transfer-level course and only 64 (24%) succeeded at one. 34

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Attempts Fall 2009-Spring 2012 Two Levels Below Transfer MATH 201 Elementary Algebra Attempts 313 Fall 2009-Spring 2012 One Level Below Transfer MATH 203 Intermediate Algebra Attempts 135 Another thing that is striking is the number of attempts it shows. 35

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It took 448 attempts and 6 semesters to get 31% of a beginning cohort of 264 students through the elementary-intermediate algebra sequence between Fall 2009 and Spring 2012. 36

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California Community Colleges Chancellor's Office Basic Skills Progress Tracker Report Fall 2009-Spring 2012 Cohort Two Levels Below TransferOne Level Below Transfer MATH 201 Elementary AlgebraMATH 203 Intermediate Algebra StudentsAttemptsSuccess StudentsAttemptsSuccess Six- Semester Success Berkeley City Total 26431315653.2%1171358231% Report Run Date As Of : 2/24/2013 11:50:27 AM 37

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Some speculate that reducing the number of exit points on the path to graduation or transfer will improve student success rates. 38

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We recently added a new course, Math 206, Algebra for Statistics, to our curriculum in an effort to address this possibility. 39

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Algebra for Statistics provides Berkeley City College students with an acceleration option that reduces the number of algebra units on the path to statistics from eight to six. 40

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Berkeley City College Mathematics Pathways to Transfer: Accelerated Path* to Statistics Math 206 Algebra for Statistics 6 units Math 13 Statistics Math 253 Prealgebra or Multiple Measures Assessment into Math 201 Math 250 Arithmetic Math 203 Intermediate Algebra 4 units Math 13 Statistics Math 253 Prealgebra Math 250 Arithmetic Compare thisto this Math 201 Elementary Algebra 4 units 41

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Berkeley City College Mathematics Pathways to Transfer: Accelerated Path* to Statistics Unfortunately this accelerated pathway is restricted to students who intend to transfer and do not intend to major in: science, technology, engineering, mathematics, business, nursing, or nutrition, 42

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…because Math 206, Algebra for Statistics, does not fulfill the AA degree requirement and does not satisfy the “intermediate-algebra-as-prerequisite” requirement for transfer-level courses. (Similar offerings on other campuses have been challenged and this matter is still under review by University of California Office of the President…) 43

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These limitations led us to explore another option: An adaptive delivery system* for the pre-transfer curriculum: *Piloted experimentally during Fall 2012-Summer 2013 terms 44

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We were prompted to consider this approach by noting the significant amount of redundancy in the traditional pre-transfer curriculum: 45

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Redundancy in the Pre-Transfer-Level Mathematics Curriculum: Arithmetic and Pre-Algebra Decimals Math 253 Prealgebra Ratio and Proportion Percents Mixed Numbers Fractions Whole Numbers Math 250 Arithmetic Statistics and Probability Signed Numbers Introduction to Algebra Geometry 46

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Redundancy in the Pre-Transfer-Level Mathematics Curriculum: Elementary and Intermediate Algebra Rational Expressions and Equations Math 203 Intermediate Algebra Functions, Graphs and Lines Systems of Equations Factoring Polynomials Operations on Polynomials Graphs of Linear Equations Math 201 Elementary Algebra Radical Expressions and Equations Quadratic Equations and Functions Exponential and Logarithmic Functions Absolute Value Equations and Inequalities 47

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Accordingly, the modular sequence consisted of twenty stand-alone half-unit modular courses: 48

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Adaptive Pre-Transfer-Level Mathematics Sequence: Modular Pre-Algebra Math 348UG Decimals Math 253 Prealgebra Math 348UH Ratio and Proportion Math 348UK Percents Math 348UF Mixed Numbers Math 348UE Fractions Math 348UD Whole Numbers Math 250 Arithmetic Math 348UM Statistics and Probability Math 348UN Signed Numbers Math 348UO Introduction to Algebra Math 348UL Geometry 49

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Adaptive Pre-Transfer-Level Mathematics Sequence: Modular Elementary and Intermediate Algebra Math248VD Rational Expressions and Equations Math 203 Intermediate Algebra Math 248VE Functions, Graphs and Lines Math 248VF Systems of Equations Math 248VC Factoring Polynomials Math 248 VB Operations on Polynomials Math 248VA Graphs of Linear Equations Math 201 Elementary Algebra Math 248VH Radical Expressions and Equations Math 248VJ Quadratic Equations and Functions Math 248VK Exponential and Logarithmic Functions Math 248VG Absolute Value Equations and Inequalities 50

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which provided an alternate pathway into transfer-level courses, 51

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Berkeley City College Mathematics Pathways to Graduation or Transfer with Adaptive Modular Pre-Transfer Sequence Math 1 Pre-Calculus AA/AS area 4b; CSU area B4; IGETC area 2 Math 13 Statistics AA/AS area 4b; CSU area B4; IGETC area 2 Math 50 Trigonometry AA/AS area 4b; CSU area B4 Math 202 Geometry AA/AS area 4b STEM Math 3A Calculus I AA/AS area 4b; CSU area B4; IGETC area 2 Math 3B Calculus II AA/AS area 4b; CSU area B4; IGETC area 2 Math 2 Pre-Calculus AA/AS area 4b; CSU area B4; IGETC area 2 Math 3E Linear Algebra AA/AS area 4b; CSU area B4; IGETC area 2 Non-STEM Math 16A Calculus I AA/AS area 4b; CSU area B4; IGETC area 2 Math 3C Calculus III AA/AS area 4b; CSU area B4; IGETC area 2 Math 3F Differential Equations AA/AS area 4b; CSU area B4; IGETC area 2 Non-StemMath 16B Calculus II AA/AS area 4b; CSU area B4; IGETC area 2 Math 18 Real Number Systems AA/AS area 4b; CSU area B4 NOTE: Red boxes indicate courses required for AS-T degree in Mathematics. Math 348UD – 348UO: Arithmetic and Pre-Algebra Math 248VA – 248VK: Elementary and Intermediate Algebra * 52

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reduced the number of algebra units on the path to an AA degree or transfer from eight to six, and, 53

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in contrast to the newly adopted Algebra for Statistics course, prepared students for both STEM and non-STEM pathways. 54

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Modular pre-transfer math at Berkeley City College merged a variety of new methods being tried on campuses across the United States: 55

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Modular Pre-Transfer Mathematics was a… Compression Model: Removing redundancy shrank the pre-transfer curriculum: – from 14 credit hours to 10 credit hours – from 16 teaching hours to 10 teaching hours. 56

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Avoidance Model Students had the option of testing out of any part of the sequence at any time. 57 Modular Pre-Transfer Mathematics was an…

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Modularization Model Students undertook small courses that felt manageable. This made deciding to continue less difficult. 58 Modular Pre-Transfer Mathematics was a…

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Stretching and Skipping Model, arranged so that students could work ahead into more advanced courses upon completion of the current semester’s work and/or skip over topics they had already mastered. 59 Modular Pre-Transfer Mathematics was a…

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Flipped Classroom Model Students undertook the study of each topic in each course independently online and brought their questions to the classroom for an instructor to address. 60 Modular Pre-Transfer Mathematics was a…

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mixed students working at various levels in each section (all levels met concurrently in each modular math section*). 61 Modular Pre-Transfer Mathematics …

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*Creating these combined sections served two deep purposes: 1.It enabled students to progress smoothly from module to module during each academic term independently of the rest of their schedules. 2.It placed students who engaged in successful behaviors in a position to model them for those who had not yet adapted to the college academic culture. 62

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Made curricular adaptation to student pathways straightforward. Students on STEM pathways might need a more rigorous pre-transfer curriculum than those on non-STEM pathways. 63 Modular Pre-Transfer Mathematics …

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Part of the challenge we face is encouraging students to stay in school. We noted above how many students dropped not during semesters but between them. Recall for example that between Fall 2011 and Spring 2012 we “lost” 35 members (22%) of a 158-student cohort. 64

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The decision to leave or delay school is not one that students take lightly. Here are some of the challenges our students face and how the modular system addressed them: 65

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Reasons Students Drop or Delay Inadequate academic preparation for college Not being able to afford educational expenses Needing to help provide for a family Family care-taking responsibilities Health issues Neighborhood violence Homelessness College is not what they want 66

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Inadequate academic preparation for college The modular system spanned the entire pre- transfer curriculum and met students wherever they needed to begin and it was capable of acknowledging and granting detailed credit for pre-transfer-level topics that students had already mastered. 67

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Not being able to afford educational expenses The modular system allowed students to enroll in one half-unit module at a time, thus enabling them to stretch payment for their mathematics courses across the semester. Students paid only for coursework they were ready to undertake and complete. 68

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Not being able to afford educational expenses The purchase of a single workbook and access card bought each student access to the instructional materials needed for the entire pre-transfer mathematics curriculum,* all the way from the beginning of arithmetic to the end of intermediate algebra. The total price of these materials was approximately $140. * Excepting proof-based geometry 69

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Not being able to afford educational expenses This could reduce the cost of pre-transfer textbook purchases for arithmetic and algebra courses by up to 75%, depending on where students entered the sequence. 70

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Homelessness The Berkeley City College math lab provided students who were homeless a safe, clean, comfortable place where they could study and concentrate. 71

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Needing to help provide financial support or personal care for family The modular courses were hybrids and did not require that students attend every class. Students who needed to work for a living or to take care of other family members were able to integrate these courses into their schedules with relative ease. 72

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Health issues Students with physical or mental disabilities or health issues could work from home except for taking proctored final exams. 73

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Neighborhood violence The almost sequestered manner in which these courses operated in the Berkeley City College math lab provided students with a safe, quiet, peaceful environment in which to study and concentrate. 74

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Addressing these matters is crucial to helping students succeed in a community college environment: 75

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Students often come to community college expecting to graduate in two years, but making up for math deficiencies and coping with personal issues can add years to the time it takes to satisfy graduation requirements. 76

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Loss of time translates into loss of money, loss of confidence, loss of hope, …. 77

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An important advantage of the modular classes was that if for any reason a student’s academic progress was interrupted during a semester, the student kept credit for all modular courses that he or she had completed. 78

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A student never risked losing more than half a unit of credit for work undertaken but not completed. 79

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When the student returned to school he or she began working at the beginning of the last modular course he or she had undertaken. 80

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Students never had to start the sequence all over again. 81

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How these classes worked The pre-transfer sequence consisted of twenty half-unit modular courses, each covering one major pre-transfer mathematics topic: 82

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Adaptive Pre-Transfer-Level Mathematics Sequence: Modular Pre-Algebra Math 348UG Decimals Math 253 Prealgebra Math 348UH Ratio and Proportion Math 348UK Percents Math 348UF Mixed Numbers Math 348UE Fractions Math 348UD Whole Numbers Math 250 Arithmetic Math 348UM Statistics and Probability Math 348UN Signed Numbers Math 348UO Introduction to Algebra Math 348UL Geometry 83

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Adaptive Pre-Transfer-Level Mathematics Sequence: Modular Elementary and Intermediate Algebra Math248VD Rational Expressions and Equations Math 203 Intermediate Algebra Math 248VE Functions, Graphs and Lines Math 248VF Systems of Equations Math 248VC Factoring Polynomials Math 248 VB Operations on Polynomials Math 248VA Graphs of Linear Equations Math 201 Elementary Algebra Math 248VH Radical Expressions and Equations Math 248VJ Quadratic Equations and Functions Math 248VK Exponential and Logarithmic Functions Math 248VG Absolute Value Equations and Inequalities 84

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How these classes worked We ran six combined sections during Fall 2012 and six during Spring 2013. Each section was deliberately composed of about twenty-five students as follows: Approximately 20% arithmetic students, 20% pre-algebra students, 30% elementary algebra students and 30% intermediate algebra students. 85

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How these classes worked Assignments for each course consisted of… 86

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Assignment Minimum Performance Level Comments Taking an optional challenge exam 90% Optional: A grade of 90 or higher permitted the student to skip to the next module immediately

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Assignment Minimum Performance Level Comments Taking an optional challenge exam 90% Optional: A grade of 90 or higher permitted the student to skip to the next module immediately Watching video tutorialsC/NCNo grade was attached to this

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Assignment Minimum Performance Level Comments Taking an optional challenge exam 90% Optional: A grade of 90 or higher permitted the student to skip to the next module immediately Watching video tutorialsC/NCNo grade was attached to this Working concept check exercises 80% (100%)Prerequisite for doing homework

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Assignment Minimum Performance Level Comments Taking an optional challenge exam 90% Optional: A grade of 90 or higher permitted the student to skip to the next module immediately Watching video tutorialsC/NCNo grade was attached to this Working concept check exercises 80% (100%)Prerequisite for doing homework Doing homework problems 80% Prerequisite for doing practice final

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Assignment Minimum Performance Level Comments Taking an optional challenge exam 90% Optional: A grade of 90 or higher permitted the student to skip to the next module immediately Watching video tutorialsC/NCNo grade was attached to this Working concept check exercises 80% (100%)Prerequisite for doing homework Doing homework problems 80% Prerequisite for doing practice final Taking a practice final exam 80% Could be taken as many times as needed from any location with internet access Prerequisite for final exam

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Assignment Minimum Performance Level Comments Taking an optional challenge exam 90% Optional: A grade of 90 or higher permitted the student to skip to the next module immediately Watching video tutorialsC/NCNo grade was attached to this Working concept check exercises 80% (100%)Prerequisite for doing homework Doing homework problems 80% Prerequisite for doing practice final Taking a practice final exam 80% Prerequisite for final exam. Could be taken as many times as needed from any location with internet access Taking a final exam70% Proctored and password- protected. Taken in math lab under supervision of section instructor. Double-graded (by computer and by instructor)

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Assignment Minimum Performance Level Percent of Course Grade Taking an optional challenge exam 90%100% Watching video tutorialsC/NCNone Working concept check exercises 80% (100%)Together with homework 5% Doing homework problems 80%Together with concept checks 5% Taking a practice final exam 80%10% Taking a final exam70%85%

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How these classes worked Two meetings per week, 75 minutes per meeting. Class size limit 35 but we only had 17 computers in the math lab, so students were assigned to attend on only one of their two meeting days.* Encouraged students who owned laptops to attend both days each week. 94

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How these classes worked *At first we were dismayed at the small number of students we could accommodate per class period but this has turned out to be something we appreciate now. It keeps the number of students in class at any given time reasonably manageable for an instructor who is simultaneously teaching and proctoring exams. 95

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How these classes worked In class, each student logged into the online learning system we were using* and worked independently while his or her instructor circulated among work stations answering questions and proctoring exams. *Squires and Wyrick, Developmental Mathematics 96

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How these classes worked Outside of class, students logged into the online learning system we were using* and worked independently from any location with internet access. Any assignment except the proctored (challenge and final) exams could be completed from any internet location. *Squires and Wyrick, Developmental Mathematics 97

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From the beginning we sent a message that made it clear to students that they would need to take their mathematics work seriously, explaining that … 98

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from their college’s perspective, things look somewhat like this: 99

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Of every 40 students who enroll in an elementary algebra class, 100

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less than twenty progress into an intermediate algebra class, 101

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and of every twenty students who enroll in an intermediate algebra class, 102

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about twelve pass, 103

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and of every twelve who pass intermediate algebra, 104

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about nine go on to succeed in a transfer- level course… 105 in six semesters or less!

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So, of every 40 students who enroll in an elementary algebra class, 106

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fewer than ten go on to satisfy math requirements for transferring to a four-year college… 107

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fewer than ten go on to satisfy math requirements for transferring to a four-year college… 108 in six semesters or less.

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We also provided students with progress benchmarks, for example: 109

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110 Finish (pass your final exam for) …By about… Your first module by aboutSeptember 9 Your second module by aboutSeptember 23 Your third module by aboutOctober 14 Your fourth module by aboutNovember 4 Your fifth module by aboutNovember 25 Your sixth module by about December 13 or 14 (last day of semester) To complete three units (six modules) during Fall 2012:

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111 For example, if you want to finish modules Math 348UD through Math 348 UH, then you need to finish… by about… Math 348UD by aboutSeptember 9 Math 348UE by aboutSeptember 23 Math 348UF by aboutOctober 14 Math 348UG by aboutNovember 4 Math 348UH by aboutNovember 25 Math 348UK by about December 13 or 14 (last day of semester)

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Data The data for these classes is not straightforward to interpret for many reasons. 112

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Data One confounding factor is that, in a very real sense, many of the students who did not complete their modules successfully never really got off the ground because they only went as far as a free seventeen-day access code permitted. They never purchased their $140 access codes and were, of course, eventually locked out of further participation in these courses.* 113

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Data *We attempted to negotiate a different purchasing system for the access codes with the publisher so that students who found the $140 purchase too much to handle all at once could purchase access to subsets of the internet materials but those efforts were not fruitful. 114

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Data Despite persistent reminders from instructors, many students who did not purchase the codes did not drop in a timely fashion. Most of them received W’s. This resulted in negative consequences for the students, the program and the school. 115

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Another confounding factor is that at the beginning of the Fall 2012 term students enrolled simultaneously in six modules (three units) and, if they completed the first six modules, they added more to their schedules. 116 Data

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Because the success rates we see in Fall 2012 are for the same subset of the same cohort during the same enrollment period, I do not feel that reporting the product of module success rates accurately describes student success. Instead I treat these students as I would members of a single class and report average success rates across modules as if they were for chapters in a course. 117 Data

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To be honest, I am not even sure how to evaluate overall system success without more longitudinal information because of incompletes and redundancy. 118 Data

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(Bear in mind that redundant modules were being completed not only by students who entered the system at elementary algebra level but also by students who entered at intermediate algebra level.) 119 Data

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To be meaningful, success in this system really has to be calculated at individual student level by means of detailed tracking. We have had no institutional research support for this project so I have had to do this personally, analyzing student progress across 240 rosters per semester. (More about this later.) 120 Data

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Outcomes: Elementary-Through-Intermediate Algebra Sequence 121 Across all modules the average success rate for the Fall 2012 cohort is approximately 60% counting W’s and 81% not counting W’s

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122 Across all modules the average success rate for the Spring 2013 cohort is 66% counting W’s and 86% not counting W’s. Outcomes: Elementary-Through-Intermediate Algebra Sequence

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The progress that these students made raise hopes of a 3-semester elementary-through-intermediate algebra success rate of at least 40% and possibly much more.* 123

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Math 203 Intermediate Algebra AA/AS area 4b Math 202 Geometry AA/AS area 4b Math 201 Elementary Algebra Math 253 Pre-Algebra Non-degree applicable Math 250 Arithmetic Non-degree applicable 47% success 62% success Approximately 29% of students who have begun with elementary algebra have succeeded at intermediate algebra 124 Recall recent six-semester success in lecture-based classes:

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125 Across all modules the average success rate for the Fall 2012 cohort is approximately 26% counting W’s and 52% not counting W’s. Outcomes Arithmetic-Through-Pre-Algebra Sequence

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126 Across all modules the average success rate for the Spring 2013 cohort is approximately 51% counting W’s and 76% not counting W’s.

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Math 203 Intermediate Algebra AA/AS area 4b Math 202 Geometry AA/AS area 4b Math 201 Elementary Algebra Math 253 Pre-Algebra Non-degree applicable Math 250 Arithmetic Non-degree applicable 47% success 62% success 50% success Approximately 15% who have begun with pre-algebra have succeeded at intermediate algebra, 127 Recall recent six-semester success in lecture-based classes:

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Math 203 Intermediate Algebra AA/AS area 4b Math 202 Geometry AA/AS area 4b Math 201 Elementary Algebra Math 253 Pre-Algebra Non-degree applicable Math 250 Arithmetic Non-degree applicable 47% success 62% success 50% success and at most 14% who have begun with arithmetic have succeeded at intermediate algebra. 48% success 128 Recall recent six-semester success in lecture-based classes:

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Interpreting outcomes Attaching meaning to these outcomes is premature, and interpreting them is a subtle business. 129

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Interpreting outcomes One thing we can definitely say is that persistence comes heavily into play in this population, and students taking these courses tend to continue. This is no doubt the result of a number of features of this system, but one notable factor is that students working at any level in the pre-transfer curriculum become invested in the next as soon as redundancy occurs. For example, 130

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Interpreting outcomes by the time a student has progressed two modules into arithmetic, that student has automatically undertaken the study of pre- algebra. 131

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Module 4: Decimals Hybrid Math 253 Pre-Algebra Module 5: Ratio and Proportion Module 6: Percents Module 3: Mixed Numbers Module 2: Fractions Module 1: Whole Numbers Hybrid Math 250 Arithmetic Module 8: Statistics and Probability Module 9: Signed Numbers Module 10: Introduction to Algebra Module 7: Geometry Modules in bold boxes are redundant: They occur in both Math 250 and Math 253. 132

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Interpreting outcomes When course modules are intermingled in the middle of a semester, students tend not to notice that they are passing from one course (say, elementary algebra) into the next (intermediate algebra) and once they have undertaken the next course, they tend to stay. *Persisting, in other words, becomes the default in this system, not the active choice.* 133

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Interpreting outcomes What is also the case, to quote an old truism, is that success breeds success. Students who succeed one module at a time are sometimes experiencing success at mathematics for the first time in their lives. This should not be underestimated as a driving factor in persistence. 134

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The Challenges This Model Posed At system level: – Enrollment Communicating with the campus and district community about the system: Students, A&R, counseling, financial aid, assessment,... Resolving the “schedule conflicts” that the enrollment system saw Size: 20 enrollment rosters per section plus 20 MyMathLab rosters per section plus 20 Moodle rosters per section… (Our IT department ultimately generated “meta-” Moodle rosters for us) – Financial Aid Timing Students not using financial aid for purchasing access codes? – Veterans’ benefits and load requirements 135

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The Challenges This Model Posed At student level – Access code purchases – Pace: An average of 2.5 modules completed per student (counting W’s) and 3.4 modules completed per student (not counting W’s) in the algebra sequence during Fall 2012 and less in the arithmetic- pre-algebra sequence At this rate it will take students about three semesters to complete the elementary-through-intermediate algebra sequence. 136

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These challenges led to the demise of the modular system at the end of the Summer 2013 session. It has since been replaced on our campus by 137 The Challenges This Model Posed

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Hybrid Pre-Transfer Mathematics, …which is basically the modular pre-transfer sequence described above, with one very important difference: We now have students enroll in full three- or four-unit arithmetic, pre-algebra, elementary algebra or intermediate algebra hybrid courses in order to participate in the modular system. 138

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Hybrid Pre-Transfer Mathematics, These hybrid classes are still combined sections that are composed of about 20% arithmetic, 20% pre-algebra, 30% elementary algebra, 30% intermediate algebra students. 139

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The hybrid pre-transfer mathematics sequence maps to the courses in our traditional lecture-based sequence exactly as the modular courses did: 140 Hybrid Pre-Transfer Mathematics

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Module 1: Whole Numbers Module 2: Fractions Module 3: Mixed Numbers Module 4: Decimals Module 5: Ratio, Proportion and Measurement Module 6: Percent Module 7: Geometry Module 8: Statistics and Probability (not in Math 201) Module 9: Signed Numbers Module 10: Introduction to Algebra Module 11: Graphs of Linear Equations Module 12: Operations on Polynomials Module 13: Factoring Polynomials Module 14: Rational Expressions and Equations Module 15: Functions, Graphs and Lines Module 16: Systems of Equations Module 17: Absolute Value Equations and Inequalities Module 18: Radical Expressions and Equations Module 19: Quadratic Equations and Functions Module 20: Exponential and Logarithmic Functions Hybrid Math 250 Arithmetic Hybrid Math 253 Pre-Algebra Hybrid Math 201 Elementary Algebra Hybrid Math 203 Intermediate Algebra

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Hybrid Pre-Transfer Mathematics Redundant modules represent work that a student does not have to repeat when proceeding from one course to the next. Credit for demonstrated mastery of redundant topics follows a student from one hybrid mathematics course into the next, so 142

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Hybrid Pre-Transfer Mathematics for example, when a student finishes arithmetic, he or she will have completed the first 5 of 9 modules in pre-algebra: 143

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Module 4: Decimals Hybrid Math 253 Pre-Algebra Module 5: Ratio and Proportion Module 6: Percents Module 3: Mixed Numbers Module 2: Fractions Module 1: Whole Numbers Hybrid Math 250 Arithmetic Module 8: Statistics and Probability Module 9: Signed Numbers Module 10: Introduction to Algebra Module 7: Geometry Modules in bold boxes are redundant: They occur in both Math 250 and Math 253. 144

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Hybrid Pre-Transfer Mathematics This means that the student needs only to complete four more modules to pass pre- algebra. This is a major incentive for students to persist. 145

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Hybrid Pre-Transfer Mathematics Since redundancy occurs in several parts of the pre-transfer sequence, this hybrid system provides students with many opportunities to accelerate their progress through the pre-transfer curriculum. Modules in bold below all occur in more than one pre-transfer mathematics course: 146

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Module 1: Whole Numbers Module 2: Fractions Module 3: Mixed Numbers Module 4: Decimals Module 5: Ratio, Proportion and Measurement Module 6: Percent Module 7: Geometry Module 8: Statistics and Probability (not in Math 201) Module 9: Signed Numbers Module 10: Introduction to Algebra Module 11: Graphs of Linear Equations Module 12: Operations on Polynomials Module 13: Factoring Polynomials Module 14: Rational Expressions and Equations Module 15: Functions, Graphs and Lines Module 16: Systems of Equations Module 17: Absolute Value Equations and Inequalities Module 18: Radical Expressions and Equations Module 19: Quadratic Equations and Functions Module 20: Exponential and Logarithmic Functions Hybrid Math 250 Arithmetic Hybrid Math 253 Pre-Algebra Hybrid Math 201 Elementary Algebra Hybrid Math 203 Intermediate Algebra 147

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Hybrid Pre-Transfer Mathematics The potential economy of this hybrid system is very clear, 148

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but does the hybrid model address the challenges the modular model posed? 149

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Hybrid Pre-Transfer Mathematics From the perspective of a student who wishes to enroll in a hybrid course, the process is the same as it is for students who are enrolling in lecture-based courses: 150

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Hybrid Pre-Transfer Mathematics go through assessment and counseling, select the entry point that the student’s background and assessment suggest, and enroll in a hybrid section of one of our traditional arithmetic, pre-algebra, elementary algebra or intermediate algebra courses. 151

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Hybrid Pre-Transfer Mathematics The modules are now internal to the hybrid courses and invisible to the enrollment system, and to students until they begin doing coursework, so… 152

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Does the Hybrid Model Address the Challenges the Modular Model Posed? At system level: – Enrollment Communicating with the campus and district community about the system: Students, A&R, counseling, financial aid, assessment,... Resolving the “schedule conflicts” that the enrollment system saw Size: 20 enrollment rosters per section plus 20 MyMathLab rosters per section plus 20 Moodle rosters per section… (Our IT department ultimately generated “meta-” Moodle rosters for us) – Financial Aid Timing Students not using financial aid for purchasing access codes? – Veterans’ benefits and load requirements 153

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Does the Hybrid Model Address the Challenges the Modular Model Posed? At system level: – Enrollment Communicating with the campus and district community about the system: Students, A&R, counseling, financial aid, assessment,... Resolving the “schedule conflicts” that the enrollment system saw Size: 20 enrollment rosters per section plus 20 MyMathLab rosters per section plus 20 Moodle rosters per section… (Our IT department ultimately generated “meta-” Moodle rosters for us) – Financial Aid Timing Students not using financial aid for purchasing access codes? – Veterans’ benefits and load requirements 154

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Does the Hybrid Model Address the Challenges the Modular Model Posed? At student level – Access code purchases 155

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Does the Hybrid Model Address the Challenges the Modular Model Posed? At student level – Access code purchases are still a problem 156

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Does the Hybrid Model Address the Challenges the Modular Model Posed? At student level – Pace is still a challenge: Students are on track to complete, on average, 3.5 modules during Fall 2013 under the hybrid system.* 157

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158 *Pace and the fact that students must now enroll in three- or four-unit hybrid courses makes reconsideration of the policy for Incompletes necessary. Students who progress through at least 50% of the coursework for a hybrid course will qualify for an Incomplete.

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Benefits of Hybrid Pre-Transfer Mathematics From the student’s perspective, the difference between the hybrid sequence and the lecture- based sequence is that students who study in the hybrid sequence work independently through the twenty modules that previously comprised the modular pre-transfer sequence rather than attending lectures and working in direct synchronization with other students in a class. 159

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Working independently through these hybrid courses provides students with most of the advantages of the modular system. For example, 160 Benefits of Hybrid Pre-Transfer Mathematics

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Hybrid Pre-Transfer Mathematics – allows students to skip over material they already know 161

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Hybrid Pre-Transfer Mathematics – allows students to avoid redundancy in the pre-transfer curriculum 162

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Hybrid Pre-Transfer Mathematics – allows students a measure of attendance flexibility 163

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Hybrid Pre-Transfer Mathematics – allows students a measure of flexibility in pace 164

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Hybrid Pre-Transfer Mathematics – allows students who have to drop during one semester to carry credit for completed modules forward into a future semester 165

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Hybrid Pre-Transfer Mathematics – develops an independent mindset and work ethic 166

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Hybrid Pre-Transfer Mathematics – engenders a strong sense of proprietorship and confidence at mathematics 167

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Hybrid Pre-Transfer Mathematics – rewards maturity and self-discipline 168

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Hybrid Pre-Transfer Mathematics – requires that students master every concept in the pre-transfer curriculum 169

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Hybrid Pre-Transfer Mathematics – applies standards of performance that are consistent, rigorous and demanding 170 As students progress through this system they become, more and more, products of the system.

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Reasons Students Drop or Delay Inadequate academic preparation for college Not being able to afford educational expenses Needing to help provide for a family Family care-taking responsibilities Health issues Neighborhood violence Homelessness College is not what they want 171

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College is not what they want? Coming soon to Berkeley City College: Contextualization! We are still looking for answers. 172

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173 A recent study conducted at Community College Research Center, Teachers College, Columbia University*** with 256,672 students and 57 colleges participating found that

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174 of students who entered a developmental mathematics sequence one level below college, approximately 27% successfully completed a gatekeeper course in mathematics;

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175 of students who entered a developmental mathematics sequence two levels below college, approximately 20% successfully completed a gatekeeper course in mathematics;

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176 and of students who entered a developmental mathematics sequence three levels below college, approximately 10% successfully completed a gatekeeper course in mathematics.

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A recent study conducted at Community College Research Center, Teachers College, Columbia University with 256,672 students, 57 colleges participating concluded that * For students whose initial placement in a developmental mathematics sequence is… the % of students who successfully complete a college-level gatekeeper course in mathematics is… 1 level below college (Intermediate Algebra)27% 2 levels below college (Elementary Algebra)20% 3 or more levels below college (Pre-Algebra or Arithmetic)10% *** Data drawn from very informative 3CSN webinar: http://drexelmeeting.adobeconnect.com/p9it1acl1h6/?launcher=false&fcsContent=true&p bMode=normal http://drexelmeeting.adobeconnect.com/p9it1acl1h6/?launcher=false&fcsContent=true&p bMode=normal “Referral, Enrollment and Completion in Developmental Education Sequences in Community Colleges” (CCRC Working Paper No. 15) By: Thomas Bailey, Dong Wook Jeong & Sung-Woo Cho, December 2008. New York: Community College Research Center, Teachers College, Columbia University (Revised November 2009). Achieving the Dream

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Pre-Transfer Mathematics at Berkeley City College: An Adaptive Approach* Mary Jennings mjennings@peralta.edu October 31, 2013 *This presentation is also available for viewing at http://www.mnemosyne.cc/

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