1. Streamlining Math Pathways in Florida
Presenters:
Wendy Carden, Irma Cruz-White,
Thomas Flanagan, Angelina Kuleshova

2. Proposed Recommendations Discussed
Recommendation #1: Create common mathematics pathways by aligning mathematics courses to programs, meta-majors and careers in Florida.
Recommendation #3: Ensure mathematics prerequisites align with mathematics pathways.
Recommendation #5: Encourage colleges and universities to implement instructional models (such as the co-requisite model) that place students, when appropriate, directly into college-level mathematics courses carrying general education credit.

3. Key Ideas Alignment: Acceleration:
Mathematics course requirements are aligned to programs of study (Recommendation #1).
Support course content is aligned with the content of gateway courses (Recommendation #3).
Acceleration:
Place students, when appropriate, directly into college-level mathematics courses carrying general education credit, and
Implement co-requisite instruction to improve academic outcomes in the gateway course (Recommendation #5).
Two themes/guiding principles

4. Recommendation #1: Create common mathematics pathways by aligning mathematics courses to programs, meta-majors and careers in Florida.
What is the definition of Math Pathways?
Math pathways enable students to take different paths through the math curriculum, depending on their course of study, so the math they learn is relevant and aligned to their goals (Ganga & Mazzariello, 2018).
There is national consensus (including within mathematics community), that students need different math skills depending on their programs of study and are not well served by traditional algebra-based calculus sequence.

5. Math Pathways... ...are more than sequences of math courses
...they are also aligned to meta-majors & programs of study

6. Create Common Math Pathways in Florida
Our huddle group is suggesting commonality
A general common pathway.
A pathway appropriate for one school may not be appropriate for another school

7. Creating Common Math Pathways in Florida:
Focusing on academic disciplines using a survey
Example: Arkansas Mathematics Task Force
Focusing on mathematics course sequencing
Example: North Carolina’s Brunswick Community College

8. Focusing on Academic Disciplines
Identify mathematics competencies needed for specific programs of study, relying on upper-division discipline-specific faculty to identify the competencies.
Use the identified mathematics competencies to recommend common transferable mathematics course requirements for each program of study and corresponding meta-major.

9. Focusing on Academic Disciplines: Example Arkansas
Survey of Departmental Leadership at 2-Year and 4-Year Colleges in Arkansas to Identify Mathematics Competencies Necessary for Student Success in Non-STEM Disciplines administered using Survey Monkey.
The survey presented a comprehensive list of mathematics skills and sub-skills asking the respondent to check the main topics or mathematical skills they felt were important for students in their majors to comprehend.

10. The graph shows the percentage of respondents from 4-yr non-STEM degree programs who chose required topics that are traditionally associated with and taught in a College Algebra course.
Linear functions were identified by 41% of the non-STEM programs as being needed for success in a degree program. All other topics were identified as essential by less than 40% of the respondents.

11. The graph shows the percentage of respondents from 4-yr non-STEM degree programs who chose required topics that are traditionally associated with and taught in an Introduction to Statistics course.
All of the topics identified as topics addressed in Introduction to Statistics were selected by 30% or more of the respondents. Thus, more respondents found the topics addressed in Introduction to Statistics to be relevant compared to those topics listed in College Algebra

12. The graph shows the percentage of respondents from 4-yr non-STEM degree programs who chose required topics that are traditionally associated with and taught in a Quantitative Literacy course.
All topics with only one exception (Mathematical Modeling) were selected by over 40% of the respondents as essential to non-STEM majors. Thus, more respondents found the topics addressed in Introduction to Statistics to be relevant compared to those topics listed in College Algebra

13. Arkansas Math Pathways Task Force Recommendations Based on the Survey Results
Programs of study that do not require Calculus should not require students to take College Algebra.
Instead, students should be expected to take Quantitative Literacy or Introduction to Statistics, which are courses more relevant to their degree programs, future careers, and civic responsibilities.
American Mathematical Association of Two-Year Colleges (AMATYC), American Mathematical Society (AMS), the American Statistical Association (ASA), Mathematical Association of America (MAA), and Society for Industrial and Applied Mathematics (SIAM)

14. Focusing on Mathematics Course Sequencing
STEM: College Algebra, Calculus and Beyond according to major
Business: College Algebra, Statistics, Business Calculus according to major
Integration of business skills into lower-division mathematics courses for business majors.
Statistics/Liberal Arts Pathway
Broaden access to STA2023 through new placement and prerequisite policies.
Liberal Arts Pathway
Quantitative Reasoning/Literacy Pathway
Broad learning outcomes: Argumentation/Communication, Proportional reasoning, Probability & Statistics, Modeling, Application
Additional info to consider and explore (see links):
STEM: College Algebra, Trig/Precalc, Calc and beyond.
Business: College Algebra (call to contextualize the course for business majors by creating a College Algebra for Business Majors course), Stats, Business Calc.
Stats: broaden access to STA by avoiding algebra-intensive courses as pre-reqs., placing students directly into the course & providing co-req. Support. In FL, Stat pathway would also have to use another course (ex. MGF)
Liberal Arts: MGF1106, MGF1107
Despite recommendations to develop and utilize courses with specialized content and delivery for business programs, many institutions rely on general education college algebra and calculus courses, especially at 2-year colleges. Consequently, students are not encountering specialization-specific curriculum until their upper-division coursework, despite research indicating that requirements of prerequisite math courses could potentially increase student success in consecutive business math courses (Green et al., 2007).
Business faculty, mathematics faculty, and professional associations should collaborate to design lower-division mathematics courses that provide a coherent and rigorous foundation of quantitative skills needed for success in associated programs and careers.

15. Brunswick Community College, NC - An Example
They have two main pathways...
Quant/Stat pathway, and
STEM Calculus pathway with prerequisite courses labeled “Precalculus Algebra”, rather than “Intermediate/College Algebra”:
MAT 001P - Math Skills Support
MAT Quantitative Literacy
MAT Statistical Methods I
MAT Precalculus Algebra
MAT Precalculus Trigonometry
MAT Brief Calculus (Prerequisite: MAT 171)
MAT Calculus I (Prerequisites: MAT 171 and 172)
MAT Calculus II

16. Brunswick Community College, NC - An Example
The benefits of this system…
“Intermediate/College Algebra” courses are labeled “Precalculus”.
The “Precalculus Algebra” label, rather than “College Algebra”, more accurately describes for advisors, students, and program directors, the roles these courses play in the system – preparation for calculus.
In my opinion, MAC1105 could just as well be called “High School Algebra”, since so much of it overlaps with what is being taught in Algebra 2, a high school level course.

17. Brunswick Community College, NC - An Example
Labels matter…
Leaders of programs of study that do not require calculus will conclude that a “Precalculus” pathway is not best suited for them.
Quant/Stat pathway would address more relevant real-world mathematics, including dimensional analysis, finance, modeling, problems solving, etc.
This could help with over reliance on MAC1105:
in FCS

18. Fitting this System into Florida’s System…
Two main pathways...
STEM Calculus
non-STEM with Quant/Stat/MGF
Developmental Mathematics
MGF 1106 – Explorations in Mathematics I
MGF 1107 – Explorations in Mathematics II
MAT 11xx – Quantitative Reasoning (3 General Education credits)
STA 2023 – Statistics
MAT 1033 – Precalculus Algebra I
MAC 1105 – Precalculus Algebra II
MAC 1147 – Precalculus Algebra III with Trigonometry
MAC 2233 – Survey/Business Calculus (Prerequisite: MAC 1105)
MAC 2311 – Calculus I (Prerequisites: MAC 1147)

19. Recommendation #3: Ensure Mathematics Prerequisites Align with Mathematics Pathways.
Key Assumptions:
Prerequisite course must improve students’ success rate in a gateway course.
Prerequisite course content must align with the content of a gateway course.
We assume that a prerequisite must be a support course for the gateway course - it must work to improve students’ success rate in a gateway course.

20. FCS Prerequisite Course Enrollment in Fall 2014
In Fall 2014, about 50% of FCS students enroll in a prerequisite course as their first math course. Only 23% enrolled directly into college level course as their first math course.

21. MAT1033 Intermediate Algebra Enrollment in FCS
About 92% of FCS students, who enrolled in one of the three prerequisite courses in school year, enrolled in MAT1033 course:
~92% of students
Let’s look at MAT1033 enrollment in particular. MAT1033 is a “safe option” according to advisors since it doesn’t not limit students’ choice of major.

22. MAT1033 as a Common Prerequisite in the
State Coursewide Numbering System in FL
High enrollment in MAT1033 is potentially motivated by the State Coursewide Number System use of the course as a common prereq for all gateway courses.

23. MAT1033 Intermediate Algebra Pass Rates in FCS
However, MAT1033 is not such a safe option when it comes to student success rates. MAT1033 creates a bottleneck that contradicts the spirit of multiple math pathways.

24. Examine the use of MAT1033 as a Prerequisite for STA and MGF courses
“Prerequisite courses other than Intermediate Algebra can adequately prepare students for courses of study that do not lead to Calculus” (AMATYC, 2014).
Thus, MAT1033 may not be the best prerequisite course for STA and MGF courses.
In the Florida Statewide Course Numbering System, we recommend to reconsider the use of MAT1033 as a prerequisite for STA and MGF courses.
If we assume that a prerequisite course content must align with the content of a gateway course & improve students’ chances of success in a gateway course, then MAT1033 is not a good option...

25. Non-MAT1033 Prerequisite Options for STA2023 Across FCS

26. Evidence of Success: Introductory Statistics Course
Logue, Watanabe-Rose and Douglas (2016) randomly assigned 907 students to (a) remedial elementary algebra, (b) that course with workshops, or (c) college-level statistics with workshops (corequisite remediation). Students assigned to statistics passed at a rate 16 percentage points higher than those assigned to algebra (p < .001), and subsequently accumulated more credits.
56% of students assigned to the college-level statistics with a two-hour workshop support passed the course.
39% of students assigned to traditional developmental algebra course prior to taking statistics passed the course.
44% of students assigned to traditional developmental algebra course with a two-hour workshop support prior to taking statistics passed the course.

27. Evidence of Success: MGF1106 & 1107 Courses
In school year, St. Johns River State College changed the prerequisite for MGF1106 and MGF1107 courses from MAT1033 to developmental education exemption.
Success rate for MGF1106 decreased from 76% in to 71% in However, since enrollment increased from 285 to 508, more students were successful.
Success rate for MGF1107 increased from 61% in to 69% in Enrollment has also increased from 77 to 216.

28. Examine the Use of MAT1033 as a Prerequisite for MAC1105
Recent study suggests that MAT1033 may not increase the likelihood of successful completion of MAC1105 (Center for Postsecondary Success, 2018).
Within the sample of Fall 2014 FTIC, AA degree-seeking FCS students, researchers identified a group of students with a PERT score range that would have placed them into MAT1033. Within this group, some students took MAT1033 and others enrolled into MAC1105 (possibly due to other placement measures [SAT scores, etc.])
So, while all of the students had similar PERT scores, we observed higher passing rates of MAC1105 for those who enrolled directly, compared to those who first enrolled in MAT Therefore, examine content alignment between MAT1033 and MAC1105 AND consider co-requisite model.

29. Examine the Use of MAT1033 as a Prerequisite for MAC1105
So, while all of the students had similar PERT scores, we observed higher passing rates of MAC1105 for those who enrolled directly, compared to those who first enrolled in MAT Therefore, examine content alignment between MAT1033 and MAC1105 AND consider co-requisite model.

30. Recommendation #5: Encourage colleges and universities to implement instructional models (such as the co-requisite model) that place students, when appropriate, directly into college-level mathematics courses carrying general education credit.
What is the definition of a Co-Requisite?
Co-requisite developmental instruction or tutoring that supplements credit instruction while a student is concurrently enrolled in a credit-bearing course. (FL Statute )
Working definition: ...the placement of students who have been designated as underprepared directly into college-level courses and providing additional supports. (Charles A. Dana Center 2019)
SB1720: instruction or tutoring that supplements credit instruction while a student is concurrently enrolled in a credit-bearing course.

31. Investigation of Math Pathways in the Florida College System by the Center for Postsecondary Education (CPS) at FSU

32. Investigation of Math Pathways in the Florida College System by the Center for Postsecondary Education (CPS) at FSU

33. Co-Requisite Success

34. Co-Requisite Success

35. Three Main Objectives of a College Algebra Co-Requisite Course
Remediate
Reinforce
Practice

36. Co-Requisite Design Considerations
Consideration 1: Existing Campus Supports
Consideration 2: Co-requisite model (placement, credit hours, financing)
Student structures
Calendar structures
Just in time remediation
Prerequisite support
Grades
Staffing
Credit hours
Financing
Dana Center Mathematics Pathways: Co-Requisite Supports Narrowing the Gap Between Instruction and Support

37. Co-Requisite Design Considerations
Consideration 3: Co-requisite content
Consideration 4: Cultural shift
Collaborative work
Early referral
Explicit instruction
Ongoing formative assessment
Dana Center Mathematics Pathways: Co-Requisite Supports Narrowing the Gap Between Instruction and Support

38. Miami Dade College: Implementation of Co-requisite Model with MAC1105
Five faculty at Miami Dade College (MDC) are piloting a MAC1105 College Algebra co-requisite course in the Fall of Students who are exempt and have been placed into MAT1033 will have a choice to go directly into MAC1105 as long as they opt to enroll into a co-requisite lab that meets two hours per week.
Students will only pay for 3 credits total.
Each professor will pilot 1 Intervention (experimental) class and 1 Control class. Students have the co-requisite lab after the lecture course. Students meet with the Learning Assistant (Not Professor) to facilitate the dialogue about the topics learned in class.
The co-requisite lab is worksheet-based/active learning.
Who’s teaching the lab? the instructor
Students earn one credit hour for lab
Do students earn elective credit for the lab component?
How is the instructor compensated?
What is a student fails the lab but passes 1105?
Grading (A-F or satisfactory/unsatisfactory)? Assignments in corequisite?
To audience:
What are you doing at your institution? What are you considering? What have you heard about at conferences, other states, etc.?

39. Critical Takeaways
Students should engage in a mathematic pathway that directly relates to their academic and career goals.
Students should complete their first transferable mathematics course within their first year of study.

40. Contact Information
Wendy Carden:
Irma Cruz-White:
Thomas Flanagan:
Angelina Kuleshova:
References are available upon request