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Pre-Transfer Mathematics at Berkeley City College:An Adaptive ApproachPresenter: Mary Jennings October 31, 20131:50-2:40 p. m.

1In California, all paths to graduation or transfer pass through intermediate algebra.2

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

3and every student seeking transfer to a four-year college must satisfy a minimum mathematics requirement of a transfer-level course.4

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

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

Traditional Berkeley City College Mathematics PathwaysMath 203 Intermediate AlgebraAA/AS area 4bMath 202 Geometry AA/AS area 4bMath 201 Elementary AlgebraMath 253 Pre-AlgebraNon-degree applicableMath 250 ArithmeticNon-degree applicable* Math 1 Pre-CalculusAA/AS area 4b; CSU area B4;IGETC area 2Math 13 StatisticsAA/AS area 4b;CSU area B4; IGETC area 2Math 50 TrigonometryAA/AS area 4b; CSU area B4 STEM Math 3A Calculus IAA/AS area 4b; CSU area B4; IGETC area 2 Math 3B Calculus IIAA/AS area 4b; CSU area B4; IGETC area 2 Math 2 Pre-CalculusAA/AS area 4b; CSU area B4; IGETC area 2 Math 3E Linear AlgebraAA/AS area 4b;CSU area B4; IGETC area 2 Non-STEM Math 16A Calculus IAA/AS area 4b; CSU area B4; IGETC area 2 Math 3C Calculus IIIAA/AS area 4b; CSU area B4; IGETC area 2 Math 3F Differential EquationsAA/AS area 4b; CSU area B4; IGETC area 2 Non-Stem Math 16B Calculus IIAA/AS area 4b; CSU area B4; IGETC area 2Math 18 Real Number SystemsAA/AS area 4b; CSU area B4NOTE: Red boxes indicate courses required for AS-T degree in Mathematics. 7

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

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

These students enter our pre-transfer mathematics curriculum one or more levels below intermediate algebra.

The ramifications are striking:10

Math 203 Intermediate AlgebraAA/AS area 4bMath 202 Geometry AA/AS area 4bMath 201 Elementary Algebra

Math 253 Pre-AlgebraNon-degree applicable

Math 250 ArithmeticNon-degree applicable

47% success62% successApproximately 29% of students who begin with elementary algebra succeed at intermediate algebra,

11

Math 203 Intermediate AlgebraAA/AS area 4bMath 202 Geometry AA/AS area 4bMath 201 Elementary Algebra

Math 253 Pre-AlgebraNon-degree applicable

Math 250 ArithmeticNon-degree applicable

47% success62% success50% successapproximately 15% who begin with pre-algebra succeed at intermediate algebra,

12

Math 203 Intermediate AlgebraAA/AS area 4bMath 202 Geometry AA/AS area 4bMath 201 Elementary Algebra

Math 253 Pre-AlgebraNon-degree applicable

Math 250 ArithmeticNon-degree applicable

47% success62% success50% successand approximately 14% who begin with arithmeticsucceed at intermediate algebra.

48% success13

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

The pre-transfer curriculum can amount to as many as14 units of coursework for students and 16 units of instruction for faculty.

In fact, 15

during any given semester, the mathematics department invests approximately47% of its resources in runningpre-transfer-level arithmetic and algebra classes*:

*This figure does not include proof-based geometry.16

Traditional Berkeley City College Mathematics PathwaysMath 203 Intermediate AlgebraAA/AS area 4bMath 202 Geometry AA/AS area 4bMath 201 Elementary AlgebraMath 253 Pre-AlgebraNon-degree applicableMath 250 ArithmeticNon-degree applicable* Math 1 Pre-CalculusAA/AS area 4b; CSU area B4;IGETC area 2Math 13 StatisticsAA/AS area 4b;CSU area B4; IGETC area 2Math 50 TrigonometryAA/AS area 4b; CSU area B4 STEM Math 3A Calculus IAA/AS area 4b; CSU area B4; IGETC area 2 Math 3B Calculus IIAA/AS area 4b; CSU area B4; IGETC area 2 Math 2 Pre-CalculusAA/AS area 4b; CSU area B4; IGETC area 2 Math 3E Linear AlgebraAA/AS area 4b;CSU area B4; IGETC area 2 Non-STEM Math 16A Calculus IAA/AS area 4b; CSU area B4; IGETC area 2 Math 3C Calculus IIIAA/AS area 4b; CSU area B4; IGETC area 2 Math 3F Differential EquationsAA/AS area 4b; CSU area B4; IGETC area 2 Non-Stem Math 16B Calculus IIAA/AS area 4b; CSU area B4; IGETC area 2Math 18 Real Number SystemsAA/AS area 4b; CSU area B4NOTE: Red boxes indicate courses required for AS-T degree in Mathematics. 17Yellow totals 47% of department resources

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

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 2012.19That was six semesters.

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

California Community Colleges Chancellor's OfficeBasic Skills Progress Tracker ReportFall 2011-Spring 2012Entry Two Levels Below Transfer into MATH 201 Elementary Algebra StudentsAttemptsSuccessSuccess RateBerkeley City Total15816084Mathematics158160840.532Report Run Date As Of : 2/24/2013 11:40:00 AMMath 201-Math 203A Fall 2011 elementary algebra cohort success rate of 53.2% looks promising, but

21

California Community Colleges Chancellor's OfficeBasic Skills Progress Tracker ReportFall 2011-Spring 2012Entry Two Levels Below Transfer Success One Level Below Transfer MATH 201 Elementary AlgebraMATH 203 Intermediate AlgebraStudentsAttemptsSuccessSuccess StudentsAttemptsSuccessTwo-term Success Berkeley City Total15816084494939Mathematics158160840.5324949390.247Report Run Date As Of : 2/24/2013 11:40:00 AMMath 201-Math 203the cohorts Spring 2012 intermediate algebra success rate tells a less encouraging story:22

California Community Colleges Chancellor's OfficeBasic Skills Progress Tracker ReportFall 2011-Spring 2012Entry Two Levels Below Transfer Success One Level Below Transfer MATH 201 Elementary AlgebraMATH 203 Intermediate AlgebraStudentsAttemptsSuccessSuccess StudentsAttemptsSuccessTwo-term Success Berkeley City Total15816084494939Mathematics158160840.5324949390.247Report Run Date As Of : 2/24/2013 11:40:00 AMMath 201-Math 20323Question: How did students get from a 53% elementary algebra success rateto a 25% intermediate algebra success rate?

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

California Community Colleges Chancellor's OfficeBasic Skills Progress Tracker ReportFall 2011-Spring 2012Two Levels Below Transfer One Level Below Transfer MATH 201 MATH 203 StudentsAttemptsSuccessSuccess StudentsAttemptsSuccessTwo-term Success Berkeley City Total15816084494939Mathematics158160840.5324949390.247Report Run Date As Of : 2/24/2013Math 201-Math 20325Students did not continue!

26Thirty-five students - 22% of the cohort and 42% of those who succeeded at elementary algebra -

did not continue immediately into intermediate algebra.

California Community Colleges Chancellor's OfficeBasic Skills Progress Tracker ReportFall 2011-Fall 2012 CohortTwo Levels Below Transfer One Level Below Transfer MATH 201 Elementary AlgebraMATH 203 Intermediate AlgebraStudentsAttemptsSuccessSuccessStudentsAttemptsSuccessThree- to Four- Semester SuccessBerkeley City Total158160840.5325252420.266Mathematics158160840.5325252420.266Report Run Date As Of : 2/24/2013 11:50:27 AMUnfortunately, even giving students three to four terms to complete the traditional Math 201-203 sequence makes little difference.27

California Community Colleges Chancellor's OfficeBasic Skills Progress Tracker ReportFall 2011-Fall 2012 CohortTwo Levels Below Transfer One Level Below Transfer MATH 201 Elementary AlgebraMATH 203 Intermediate AlgebraStudentsAttemptsSuccessSuccessStudentsAttemptsSuccessThree- to Four- Semester SuccessBerkeley City Total158160840.5325252420.266Mathematics158160840.5325252420.266Report Run Date As Of : 2/24/2013 11:50:27 AMUnfortunately, 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

California Community Colleges Chancellor's OfficeBasic Skills Progress Tracker ReportFall 2011-Fall 2012 CohortEntry Two Levels Below Transfer: MATH 201 Elementary Algebra Three-Semester Success at TransferableMATH 001 Pre-Calculus StudentsAttemptsSuccess997 Students4.4%as well as for students seeking to transfer:29

California Community Colleges Chancellor's OfficeBasic Skills Progress Tracker ReportFall 2011-Fall 2012 CohortEntry Two Levels Below Transfer: MATH 201 Elementary Algebra Three-Semester Success at TransferableMATH 013 Statistics StudentsAttemptsSuccess252610 Students6.3%30

California Community Colleges Chancellor's OfficeBasic Skills Progress Tracker ReportFall 2011-Fall 2012 CohortEntry Two Levels Below Transfer: MATH 201 Elementary Algebra Three-Semester Success at TransferableMATH 050 Trigonometry StudentsAttemptsSuccess110 Students0%31

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

Fall 2009-Spring 2012 CohortEntry Two Levels Below CollegeElementary Intermediate Algebra Six-Semester Transferable Course Success Rate for Cohort of 264:24.2%76 Students114 Attempts64 Successes29%24%33

The Fall 2009 Elementary Algebra CohortOne 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

AttemptsFall 2009-Spring 2012Two Levels Below Transfer MATH 201Elementary Algebra Attempts313Fall 2009-Spring 2012One Level Below Transfer MATH 203Intermediate Algebra Attempts135Another thing that is striking is the number of attempts it shows.35

It took448 attemptsand 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

California Community Colleges Chancellor's OfficeBasic Skills Progress Tracker ReportFall 2009-Spring 2012 CohortTwo Levels Below Transfer One Level Below Transfer MATH 201 Elementary AlgebraMATH 203 Intermediate AlgebraStudentsAttemptsSuccessSuccessStudentsAttemptsSuccessSix-Semester SuccessBerkeley City Total26431315653.2%1171358231%Report Run Date As Of : 2/24/2013 11:50:27 AM37

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

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

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

Berkeley City College Mathematics Pathways to Transfer: Accelerated Path* to StatisticsMath 206 Algebra for Statistics6 unitsMath 13 StatisticsMath 253 Prealgebra or Multiple Measures Assessment into Math 201Math 250 ArithmeticMath 203 Intermediate Algebra4 unitsMath 13 StatisticsMath 253 Prealgebra Math 250 ArithmeticCompare thisto thisMath 201 Elementary Algebra4 units 41

Berkeley City College Mathematics Pathways to Transfer: Accelerated Path* to StatisticsUnfortunately 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

becauseMath 206, Algebra for Statistics, does not fulfill the AA degree requirementand 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

These limitations led us to explore another option:An adaptive delivery system* for the pre-transfer curriculum:

*Piloted experimentally duringFall 2012-Summer 2013 terms

44

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

Redundancy in the Pre-Transfer-Level Mathematics Curriculum: Arithmetic and Pre-AlgebraDecimals Math 253 PrealgebraRatio and ProportionPercentsMixed NumbersFractionsWhole NumbersMath 250 ArithmeticStatistics and ProbabilitySigned NumbersIntroduction to AlgebraGeometry46

Redundancy in the Pre-Transfer-Level Mathematics Curriculum: Elementary and Intermediate AlgebraRational Expressions and Equations Math 203 Intermediate AlgebraFunctions, Graphs and LinesSystems of EquationsFactoring PolynomialsOperations on PolynomialsGraphs of Linear EquationsMath 201 Elementary AlgebraRadical Expressions and EquationsQuadratic Equations and Functions Exponential and Logarithmic FunctionsAbsolute Value Equations and Inequalities47

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

Adaptive Pre-Transfer-Level Mathematics Sequence:Modular Pre-AlgebraMath 348UG Decimals Math 253 PrealgebraMath 348UH Ratio and ProportionMath 348UK PercentsMath 348UF Mixed NumbersMath 348UE FractionsMath 348UD Whole NumbersMath 250 ArithmeticMath 348UM Statistics and ProbabilityMath 348UN Signed NumbersMath 348UO Introduction to AlgebraMath 348UL Geometry49

Adaptive Pre-Transfer-Level Mathematics Sequence:Modular Elementary and Intermediate AlgebraMath248VD Rational Expressions and Equations Math 203 Intermediate AlgebraMath 248VE Functions, Graphs and LinesMath 248VF Systems of EquationsMath 248VC Factoring PolynomialsMath 248 VB Operations on PolynomialsMath 248VA Graphs of Linear EquationsMath 201 Elementary AlgebraMath 248VH Radical Expressions and EquationsMath 248VJ Quadratic Equations and Functions Math 248VK Exponential and Logarithmic FunctionsMath 248VG Absolute Value Equations and Inequalities50

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

Berkeley City College Mathematics Pathways to Graduation or Transfer with Adaptive Modular Pre-Transfer Sequence Math 1 Pre-CalculusAA/AS area 4b; CSU area B4;IGETC area 2Math 13 StatisticsAA/AS area 4b;CSU area B4; IGETC area 2Math 50 TrigonometryAA/AS area 4b; CSU area B4Math 202 Geometry AA/AS area 4b STEM Math 3A Calculus IAA/AS area 4b; CSU area B4; IGETC area 2 Math 3B Calculus IIAA/AS area 4b; CSU area B4; IGETC area 2 Math 2 Pre-CalculusAA/AS area 4b; CSU area B4; IGETC area 2 Math 3E Linear AlgebraAA/AS area 4b;CSU area B4; IGETC area 2Non-STEM Math 16A Calculus IAA/AS area 4b; CSU area B4; IGETC area 2 Math 3C Calculus IIIAA/AS area 4b; CSU area B4; IGETC area 2 Math 3F Differential EquationsAA/AS area 4b; CSU area B4; IGETC area 2Non-StemMath 16B Calculus IIAA/AS area 4b; CSU area B4; IGETC area 2Math 18 Real Number SystemsAA/AS area 4b; CSU area B4NOTE: Red boxes indicate courses required for AS-T degree in Mathematics. Math 348UD 348UO: Arithmetic and Pre-AlgebraMath 248VA 248VK: Elementary and Intermediate Algebra*52

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

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

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

Modular Pre-Transfer Mathematics was aCompression Model:

Removing redundancy shrank the pre-transfer curriculum: from 14 credit hours to 10 credit hoursfrom 16 teaching hours to 10 teaching hours.56

Avoidance Model

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

Modularization Model

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

Stretching and Skipping Model,

arranged so that students could work ahead into more advanced courses upon completion of the current semesters work and/or skip over topics they had already mastered.59Modular Pre-Transfer Mathematics was a

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.60Modular Pre-Transfer Mathematics was a

mixed students working at various levels in each section (all levels met concurrently in each modular math section*).

61Modular Pre-Transfer Mathematics

*Creating these combined sections served two deep purposes:

It enabled students to progress smoothly from module to module during each academic term independently of the rest of their schedules.

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

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.63Modular Pre-Transfer Mathematics

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

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

Reasons Students Drop or DelayInadequate academic preparation for collegeNot being able to afford educational expensesNeeding to help provide for a familyFamily care-taking responsibilitiesHealth issuesNeighborhood violenceHomelessnessCollege is not what they want

66

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

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

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 geometry69

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

Homelessness

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

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

Health issues

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

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

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

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

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

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

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

79

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

Students never had to start the sequence all over again.

81

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

82

Adaptive Pre-Transfer-Level Mathematics Sequence:Modular Pre-AlgebraMath 348UG Decimals Math 253 PrealgebraMath 348UH Ratio and ProportionMath 348UK PercentsMath 348UF Mixed NumbersMath 348UE FractionsMath 348UD Whole NumbersMath 250 ArithmeticMath 348UM Statistics and ProbabilityMath 348UN Signed NumbersMath 348UO Introduction to AlgebraMath 348UL Geometry83

Adaptive Pre-Transfer-Level Mathematics Sequence:Modular Elementary and Intermediate AlgebraMath248VD Rational Expressions and Equations Math 203 Intermediate AlgebraMath 248VE Functions, Graphs and LinesMath 248VF Systems of EquationsMath 248VC Factoring PolynomialsMath 248 VB Operations on PolynomialsMath 248VA Graphs of Linear EquationsMath 201 Elementary AlgebraMath 248VH Radical Expressions and EquationsMath 248VJ Quadratic Equations and Functions Math 248VK Exponential and Logarithmic FunctionsMath 248VG Absolute Value Equations and Inequalities84

How these classes workedWe 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

How these classes workedAssignments for each course consisted of86

AssignmentMinimum Performance LevelCommentsTaking an optional challenge exam90%Optional: A grade of 90 or higher permitted the student to skip to the next module immediately

AssignmentMinimum Performance LevelCommentsTaking an optional challenge exam90%Optional: A grade of 90 or higher permitted the student to skip to the next module immediatelyWatching video tutorialsC/NCNo grade was attached to this

AssignmentMinimum Performance LevelCommentsTaking an optional challenge exam90%Optional: A grade of 90 or higher permitted the student to skip to the next module immediatelyWatching video tutorialsC/NCNo grade was attached to thisWorking concept check exercises80% (100%)Prerequisite for doing homework

AssignmentMinimum Performance LevelCommentsTaking an optional challenge exam90%Optional: A grade of 90 or higher permitted the student to skip to the next module immediatelyWatching video tutorialsC/NCNo grade was attached to thisWorking concept check exercises80% (100%)Prerequisite for doing homeworkDoing homework problems80%Prerequisite for doing practice final

AssignmentMinimum Performance LevelCommentsTaking an optional challenge exam90%Optional: A grade of 90 or higher permitted the student to skip to the next module immediatelyWatching video tutorialsC/NCNo grade was attached to thisWorking concept check exercises80% (100%)Prerequisite for doing homeworkDoing homework problems80%Prerequisite for doing practice finalTaking a practice final exam80%Could be taken as many times as needed from any location with internet accessPrerequisite for final exam

AssignmentMinimum Performance LevelCommentsTaking an optional challenge exam90%Optional: A grade of 90 or higher permitted the student to skip to the next module immediatelyWatching video tutorialsC/NCNo grade was attached to thisWorking concept check exercises80% (100%)Prerequisite for doing homeworkDoing homework problems80%Prerequisite for doing practice finalTaking a practice final exam80%Prerequisite for final exam. Could be taken as many times as needed from any location with internet accessTaking a final exam70%Proctored and password-protected. Taken in math lab under supervision of section instructor. Double-graded (by computer and by instructor)

AssignmentMinimum Performance LevelPercent of Course GradeTaking an optional challenge exam90%100%Watching video tutorialsC/NCNoneWorking concept check exercises80% (100%)Together with homework 5%Doing homework problems80%Together with concept checks 5%Taking a practice final exam80%10%Taking a final exam70%85%

How these classes workedTwo 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

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

How these classes workedIn 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 Mathematics96

How these classes workedOutside 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 Mathematics97

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

from their colleges perspective, things look somewhat like this:99

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

100

less than twenty progress into an intermediate algebra class,

101

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

102

about twelve pass,

103

and of every twelve who pass intermediate algebra,

104

about nine go on to succeed in a transfer-level course105in six semesters or less!

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

106

fewer than ten go on tosatisfy math requirements fortransferring to a four-year college 107

fewer than ten go on tosatisfy math requirements fortransferring to a four-year college 108in six semesters or less.

We also provided students with progress benchmarks, for example:

109

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

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

DataThe data for these classes is not straightforward to interpret for many reasons.

112

DataOne 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

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

DataDespite persistent reminders from instructors, many students who did not purchase the codes did not drop in a timely fashion. Most of them received Ws.

This resulted in negative consequences for the students, the program and the school. 115

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. 116Data

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.117Data

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

118Data

(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.)119Data

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.)

120Data

Outcomes: Elementary-Through-Intermediate Algebra Sequence121Across all modules the average success rate for the Fall 2012 cohort is approximately 60% counting Ws and 81% not counting Ws

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

The progress that these students made raise hopes of a 3-semester elementary-through-intermediate algebra success rateof

at least 40%

and possibly much more.*123

Math 203 Intermediate AlgebraAA/AS area 4bMath 202 Geometry AA/AS area 4bMath 201 Elementary Algebra

Math 253 Pre-AlgebraNon-degree applicable

Math 250 ArithmeticNon-degree applicable

47% success62% successApproximately 29% of students who have begun with elementary algebra have succeeded at intermediate algebra

124Recall recent six-semester success in lecture-based classes:

125Across all modules the average success rate for the Fall 2012 cohort is approximately26% counting Wsand 52% not counting Ws.Outcomes Arithmetic-Through-Pre-Algebra Sequence

Outcomes Arithmetic-Through-Pre-Algebra Sequence126Across all modules the average success rate for the Spring 2013 cohort is approximately51% counting Ws and 76% not counting Ws.

Math 203 Intermediate AlgebraAA/AS area 4bMath 202 Geometry AA/AS area 4bMath 201 Elementary Algebra

Math 253 Pre-AlgebraNon-degree applicable

Math 250 ArithmeticNon-degree applicable

47% success62% success50% successApproximately 15% who have begun with pre-algebra have succeeded at intermediate algebra,

127Recall recent six-semester success in lecture-based classes:

Math 203 Intermediate AlgebraAA/AS area 4bMath 202 Geometry AA/AS area 4bMath 201 Elementary Algebra

Math 253 Pre-AlgebraNon-degree applicable

Math 250 ArithmeticNon-degree applicable

47% success62% success50% successand at most 14% who have begun with arithmetichave succeeded at intermediate algebra.

48% success128Recall recent six-semester success in lecture-based classes:

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

129

Interpreting outcomesOne 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

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

131

Module 4: Decimals Hybrid Math 253 Pre-AlgebraModule 5: Ratio and ProportionModule 6: PercentsModule 3: Mixed NumbersModule 2: FractionsModule 1: Whole NumbersHybrid Math 250 ArithmeticModule 8: Statistics and ProbabilityModule 9: Signed NumbersModule 10: Introduction to AlgebraModule 7: GeometryModules in bold boxes are redundant: They occur in both Math 250 and Math 253.132

Interpreting outcomesWhen 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

Interpreting outcomesWhat 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

The Challenges This Model PosedAt system level:EnrollmentCommunicating with the campus and district community about the system: Students, A&R, counseling, financial aid, assessment, ...Resolving the schedule conflicts that the enrollment system sawSize: 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 AidTimingStudents not using financial aid for purchasing access codes?

Veterans benefits and load requirements135

The Challenges This Model PosedAt student levelAccess code purchasesPace: An average of 2.5 modules completed per student (counting Ws) and 3.4 modules completed per student (not counting Ws) 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

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 137The Challenges This Model Posed

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

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

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

Module 1: Whole NumbersModule 2: FractionsModule 3: Mixed NumbersModule 4: DecimalsModule 5: Ratio, Proportion and MeasurementModule 6: PercentModule 7: GeometryModule 8: Statistics and Probability (not in Math 201)Module 9: Signed NumbersModule 10: Introduction to AlgebraModule 11: Graphs of Linear EquationsModule 12: Operations on PolynomialsModule 13: Factoring PolynomialsModule 14: Rational Expressions and EquationsModule 15: Functions, Graphs and LinesModule 16: Systems of EquationsModule 17: Absolute Value Equations and InequalitiesModule 18: Radical Expressions and EquationsModule 19: Quadratic Equations and FunctionsModule 20: Exponential and Logarithmic FunctionsHybrid Math 250ArithmeticHybrid Math 253Pre-AlgebraHybrid Math 201Elementary AlgebraHybrid Math 203Intermediate Algebra

Hybrid Pre-Transfer MathematicsRedundant 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, so142

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

Module 4: Decimals Hybrid Math 253 Pre-AlgebraModule 5: Ratio and ProportionModule 6: PercentsModule 3: Mixed NumbersModule 2: FractionsModule 1: Whole NumbersHybrid Math 250 ArithmeticModule 8: Statistics and ProbabilityModule 9: Signed NumbersModule 10: Introduction to AlgebraModule 7: GeometryModules in bold boxes are redundant: They occur in both Math 250 and Math 253.144

Hybrid Pre-Transfer MathematicsThis 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

Hybrid Pre-Transfer MathematicsSince 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

Module 1: Whole NumbersModule 2: FractionsModule 3: Mixed NumbersModule 4: DecimalsModule 5: Ratio, Proportion and MeasurementModule 6: PercentModule 7: GeometryModule 8: Statistics and Probability (not in Math 201)Module 9: Signed NumbersModule 10: Introduction to AlgebraModule 11: Graphs of Linear EquationsModule 12: Operations on PolynomialsModule 13: Factoring PolynomialsModule 14: Rational Expressions and EquationsModule 15: Functions, Graphs and LinesModule 16: Systems of EquationsModule 17: Absolute Value Equations and InequalitiesModule 18: Radical Expressions and EquationsModule 19: Quadratic Equations and FunctionsModule 20: Exponential and Logarithmic FunctionsHybrid Math 250ArithmeticHybrid Math 253Pre-AlgebraHybrid Math 201Elementary AlgebraHybrid Math 203Intermediate Algebra147

Hybrid Pre-Transfer MathematicsThe potential economy of this hybrid system is very clear,

148

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

Hybrid Pre-Transfer MathematicsFrom 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

Hybrid Pre-Transfer Mathematicsgo through assessment and counseling,

select the entry point that the students 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

Hybrid Pre-Transfer MathematicsThe modules are now internal to the hybrid courses and invisible to the enrollment system, and to students until they begin doing coursework, so152

Does the Hybrid Model Address the Challenges the Modular Model Posed?At system level:EnrollmentCommunicating with the campus and district community about the system: Students, A&R, counseling, financial aid, assessment, ...Resolving the schedule conflicts that the enrollment system sawSize: 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 AidTimingStudents not using financial aid for purchasing access codes?

Veterans benefits and load requirements

153

Does the Hybrid Model Address the Challenges the Modular Model Posed?At system level:EnrollmentCommunicating with the campus and district community about the system: Students, A&R, counseling, financial aid, assessment, ...Resolving the schedule conflicts that the enrollment system sawSize: 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 AidTimingStudents not using financial aid for purchasing access codes?

Veterans benefits and load requirements

154

Does the Hybrid Model Address the Challenges the Modular Model Posed?At student level

Access code purchases

155

Does the Hybrid Model Address the Challenges the Modular Model Posed?At student level

Access code purchases are still a problem156

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

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.

Benefits of Hybrid Pre-Transfer MathematicsFrom the students 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

Working independently through these hybrid courses provides students with most of the advantages of the modular system. For example,

160Benefits of Hybrid Pre-Transfer Mathematics

Hybrid Pre-Transfer Mathematicsallows students to skip over material they already know 161

Hybrid Pre-Transfer Mathematicsallows students to avoid redundancy in the pre-transfer curriculum162

Hybrid Pre-Transfer Mathematicsallows students a measure of attendance flexibility163

Hybrid Pre-Transfer Mathematicsallows students a measure of flexibility in pace164

Hybrid Pre-Transfer Mathematicsallows students who have to drop during one semester to carry credit for completed modules forward into a future semester165

Hybrid Pre-Transfer Mathematicsdevelops an independent mindset and work ethic166

Hybrid Pre-Transfer Mathematicsengenders a strong sense of proprietorship and confidence at mathematics167

Hybrid Pre-Transfer Mathematicsrewards maturity and self-discipline168

Hybrid Pre-Transfer Mathematicsrequires that students master every concept in the pre-transfer curriculum

169

Hybrid Pre-Transfer Mathematicsapplies 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. Reasons Students Drop or DelayInadequate academic preparation for collegeNot being able to afford educational expensesNeeding to help provide for a familyFamily care-taking responsibilitiesHealth issuesNeighborhood violenceHomelessnessCollege is not what they want

171

College is not what they want?Coming soon to Berkeley City College:

Contextualization!We are still looking for answers.172

173A recent study conducted at Community College Research Center, Teachers College, Columbia University*** with

256,672 students

and

57 colleges

participating found that

173174of students who entered a developmental mathematics sequence one level below college, approximately

27%

successfully completed a gatekeeper course in mathematics;

174175of students who entered a developmental mathematics sequence two levels below college, approximately

20%

successfully completed a gatekeeper course in mathematics;

175176and of students who entered a developmental mathematics sequence three levels below college, approximately

10%

successfully completed a gatekeeper course in mathematics.

176 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 isthe % of students who successfully complete a college-level gatekeeper course in mathematics is1 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&pbMode=normalReferral, 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

177Pre-Transfer Mathematics at Berkeley City College:An Adaptive Approach*Mary Jennings mjennings@peralta.eduOctober 31, 2013*This presentation is also available for viewing at http://www.mnemosyne.cc/

178