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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. In California, all paths to graduation or transfer pass through intermediate algebra. Every student seeking an AA or AS degree must satisfy a

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Pre-Transfer Mathematics at Berkeley City College: An Adaptive Approach


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

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

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

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

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

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

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

  8. 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%.

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

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

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

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

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

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

  15. 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,

  16. 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.

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

  18. 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.

  19. 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. That was six semesters.

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

  21. Math 201-Math 203 A Fall 2011 elementary algebra cohort success rate of 53.2%looks promising, but…

  22. Math 201-Math 203 the cohort’s Spring 2012 intermediate algebra success rate tells a less encouraging story:

  23. Math 201-Math 203 Question: How did students get from a 53% elementary algebra success rate… …to a 25% intermediate algebra success rate?

  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:

  25. Math 201-Math 203 Students did not continue!

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

  27. Unfortunately, even giving students three to four terms to complete the traditional Math 201-203 sequence makes little difference.

  28. 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 …

  29. …as well as for students seeking to transfer:

  30. 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:

  31. 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.

  32. Attempts Another thing that is striking is the number of attempts it shows.

  33. 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.

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

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

  36. 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.

  37. Berkeley City College Mathematics Pathways to Transfer: Accelerated Path* to Statistics Compare this to this Math 250 Arithmetic Math 250 Arithmetic Math 253 Prealgebra Math 253 Prealgebra or Multiple Measures Assessment into Math 201 Math 201 Elementary Algebra4 units Math 206 Algebra for Statistics 6 units Math 203 Intermediate Algebra4 units Math 13 Statistics Math 13 Statistics

  38. 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,

  39. …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…)

  40. 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

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

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

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

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

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

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