wamathpathways.files.wordpress.com · Web viewMath Pathways Report: Math Course-Taking Patterns...

Math Pathways Report:

Math Course-Taking Patterns for Successful Washington Transfer Students

Michael DavisEducational Researcher

Devin DuPreePolicy Research Associate

State Board for Community and Technical Colleges

Bill MooreDirector, K-12 Partnerships

State Board for Community and Technical Colleges&

Washington Math Pathways to Completion state facilitator

Data Highlights

Course Enrollments and Completions1. Transfer students pass math at community and technical colleges (CTC) at relatively high

rates (table 1), while the pass rates at the baccalaureate institutions (BIs) are relatively lower (table 2)

2. STEM sequence and pre-college math courses have the lowest pass rates at both CTCs and BIs (tables 1 and 2)

3. 47% of all math enrollments are in STEM sequence courses (table 5), of the 2011-2012 transfers 19% of students completed in STEM fields (table 6)

Transfer Patterns and Baccalaureate Degree Completions1. Students who complete a baccalaureate degree are more likely to have taken math at CTC

than those that do not complete a degree at a BI (graph 1) 2. Students who complete a baccalaureate degree are more likely to have taken no additional

math after transfer than those who do not complete a degree at a BI (graph 2)3. There are a variety of sequence patterns for students in terms of last CTC math course to

first BI math course; some of them make clear sense and others are unclear or in some case potentially problematic for students. (tables 8-10)

4. An analysis of a) the variety of CTC math courses students take prior to BI statistics and b) the variety of BI math courses following CTC statistics indicates that “Statistics” serves disparate purposes for a diverse student population, raising some questions about to what extent the course as currently defined is meeting those needs. (tables 11-12)

5. The vast majority of students who transfer do so using the general Associate of Arts Direct Transfer Agreement (DTA) or no degree (35% and 48%, respectively) rather than any specifically-defined degree (e.g., AS-T) (table 13)

6. Of the math pathway courses defined by the DTA, students taking Statistics are among the most likely to complete a baccalaureate degree while students taking Pre-calculus are the least likely (tables 14 and 15)

7. Students who take STEM math sequence courses as their last CTC math or their first math course at a BI are less likely to complete a baccalaureate degree than students who take other math courses (tables 14 and 15)

8. Students taking Calculus 1 and Calculus 2 complete a baccalaureate degree at about the same rate as students taking Precalculus courses (table 15)

Washington Math Pathways to Completion Project Report (working draft) 2

Background of Study and Data Explanations

Our project began by asking what can we learn about math pathways for transfer by looking at the records of students that have transferred from a CTC to a BI. The full data set contained all students with a CTC record and a BI record between the years 2008 and 2015 (N > 80,000). In order to analyze transfer pathways we had to conduct analyses by course. But the data set did not have courses categorized in roughly equivalent bins. Several factors made this categorization process complicated:

1) each college designs its own courses and sequences independently, so equivalency can be difficult to assess 2) the courses offered change with relatively frequency 3) names for courses are not standardized (outside of the common courses designated with an ‘&’) so even nearly identical courses might have various names and abbreviations.

When we began coding classes into standardized bins, we found that coding courses that are no longer offered at the colleges is challenging. Reliable information about the course curriculum and place in the department sequence was often unavailable. We also realized that inferences about the effectiveness of transfer pathways for these legacy courses would not necessarily be helpful. For these reasons we limited the application of the coding scheme to the last three years of the data set. This smaller data set included those students that had their last year at CTC between 2011 and 2014 (N = 42,095). In order to explore the viability of mathematics pathways we also wanted to examine completion rates at the BI for students in different pathways. These analyses ran into issues related to time to completion. The last year in the data set from the BI is 2014-2015. Thus, for most years of transfer, students would not necessarily be expected to have graduated (e.g, a 2013 transfer would only have had two years to complete). It is possible that although limited time to completion reduces completion rates, these time pressures apply equally to all groups under analysis such that we could make inferences about relative success. However, It was unclear to what extent we should expect that particular mathematics pathways and major areas might take longer to complete than others under normal circumstances and thus might be relatively more affected by time limitations. For these reasons, we focus our analyses of degree completion on those students that earned a Direct Transfer Agreement (DTA) in the 2011-2012 school year. For this sub-population we have three more years of data at the BI, providing the standard amount of time for completion analyses. The data do not provide conclusive evidence or support claims about causality. That said, they inform important impending observations about math pathways and transfer. Nobody every demonstrated a causal link between tobacco smoking and cancer—but most agree smoking is a bad health decision and would advise their children accordingly. Perhaps a similar frame may be helpful when considering the data and questions below. Do certain pathways appear more likely to lead to success or difficulty? Are any of the observed patterns providing information that could help guide students who start at a Washington community or technical college and transfer in order to complete a baccalaureate degree? How might these data inform policy and practice at the colleges?


Data Analyses

What is the final math course for community and technical college students who transfer, and how did they do (pass/fail) in those courses?

Table 1:Enrollment and Pass Rates Final Math Course at CTC

Course Enrolled Pass Fail Percent PassingArithmetic (three levels below) 302 228 74 75.5%Algebra (two levels below) 931 674 257 72.4%Algebra Intermediate 1 (non-precalculus qualifying) 359 285 74 79.4%Algebra Intermediate 2 (precalculus qualifying) 2251 1697 554 75.4%Applied Algebra 347 316 31 91.1%Elementary Ed Math 798 776 22 97.2%Stats 7888 7509 379 95.2%Math in Society 4283 4168 115 97.3%Business Precalculus 974 899 75 92.3%Business Calculus 2330 2187 143 93.9%Precalculus 6244 5778 466 92.5%Calculus I 2102 1791 311 85.2%Calculus II 1768 1551 217 87.7%Calculus III 1953 1812 141 92.8%Calculus IV 1261 1197 64 94.9%Differential Equations 917 860 57 93.8%No Code 599 549 50 91.7%

Total Enrolled 353683233

6 3032 91.4%No Math 6773 NA NATotal Students 42095

NOTE: Color coding reflects distinct math pathway alternatives: Statistics, Quantitative reasoning, Elementary Education, Business, and STEM[Back to Highlights]


Summary1. The entry-level college math courses have the most students, followed closely by business

calculus, intermediate algebra, and the calculus sequence. 2. The pass rates across the board are high, with the lowest pass rates in pre-college courses.

(intermediate algebra courses that were “non-precalculus qualifying” showed a slightly higher pass rate than pre-calculus qualifying).

3. This sample reflects CTC students who had ambitions to transfer to a BI and followed through on those ambitions and is likely non-representative of CTC students overall.

Some Questions1. There are 7211 students who enrolled in Calculus or more advanced courses as their final

CTC math course. How many of these students have aspirations for a STEM major? 2. Of the 5778 students in pre-calculus courses how many have aspirations for majors that

require Calculus? What percent of these students are planning to earn degrees in STEM fields?

Data Cautions There were some challenges determining the proper coding for historic courses not listed in catalogs. Further increases to the accuracy of the coding would likely yield even greater differences between precalculus and non-precalculus qualifying versions of intermediate algebra (some qualifying courses are likely coded non-qualifying courses and the reverse to a lesser extent).


What is the first math course these students take at their baccalaureate institutions after transferring, and how did they do (pass/fail) in those courses? [Back to Highlights]

Table 2: Enrollment and Pass Rates First Math Course at BI

Course Enrolled Pass FailPercent Passing

Algebra (two levels below) 253 75 178 29.6%Algebra Intermediate 2 (precalculus qualifying) 691 198 493 28.7%Elementary Ed Math 562 521 41 92.7%Intro Statistics 1721 1572 149 91.3%Advanced Statistics 426 407 19 95.5%Logic 229 191 38 83.4%Math in Society 1547 1298 249 83.9%Business Calculus 336 267 69 79.5%Business Precalculus 1016 847 169 83.4%Precalculus 3567 2501 1066 70.1%

Course Enrolled Pass FailPercent Passing

Calculus I 2472 1982 490 80.2%Calculus II 494 371 123 75.1%Calculus III 2190 1887 303 86.2%Calculus IV 626 574 52 91.7%Differential Equations 542 478 64 88.2%No Code 395 320 75 81.0%Total in Math 17098 13529 3578 79.1%No Math 24997 NATotal Students 42095

Summary1. Precalculus has the largest enrollment with more students than Math in Society and

Statistics combined; Calculus and Calculus 3 have the next highest enrollments. 2. Pass rates for all courses are lower at BI than at CTC, and pre-college courses have much

lower pass rates at BI than at CTC. 3. Precalculus courses have the lowest success rates among all college-level courses. Further,

30% of all student failures in the first BI math are from students in Pre-calculus. Calculus I and Intermediate Algebra contribute the second largest number of failures, each with 14%.


Some Questions 1. Why are pass rates lower at BI? Are the students taking math at BI relatively weaker for the

course-level? To what extent are the lower pass rates at BIs attributable to students with failures at CTC moving into the BI system?

2. Why are so many of the failures coming from pre-calculus and calculus I? To what extent are students under-prepared for the courses in which they enroll?

3. What is contributing to the disparities in pass rates such that differences between institutions are not equivalent across courses (e.g., Calculus I, Calculus IV and Stats are relatively close between BI and CTC while Math in Society and Pre-Calculus show larger disparities)?

Available data can help explore some of these questions. Table 3 below shows pass/fail result of all students in their first BI math course by their pass/fail result in their last CTC math course.

Data Cautions1. Some courses had very low enrollment. 2. Rows with small sample sizes were removed for clarity. 3. The totals shown includes all courses.

Table 3: Pass/fail at CTC by Pass/Fail at BI

BI Math ResultsCTC Math Results No math Fail Pass Grand TotalNo Math 3308 785 2624 6717Fail 1574 578 890 3042Pass 20016 2305 10015 32336Grand Total 24898 3668 13529 42095

Summary1. More students failing their first mathematics course at BI have passed their last CTC math

course than have failed or taken no math; only 15.8% (578/3668) of the failures in BI mathematics courses among CTC transfer students come from students who failed their last math at CTC.

2. However, students who fail in their last CTC math course are less likely to pass their first BI math course (61%, 890/1468 attempts) compared with students that pass their last CTC math course (81%, 10015/12320 attempts).

3. Of the 3409 students with no math at CTC who actually enrolled in math after transfer, 77% (2624) passed that first BI math course.

4. Given that students passing CTC math are only slightly more likely to pass BAI math than those students taking no CTC math, these data suggest that success at CTC math contributes to success at BI math but may be playing a relatively small role in the differences of pass/fail rates for these students.


Some Questions 1. Is failure at the CTC an indication of some student-level characteristics that contribute to

lowering the likelihood of passing BI math?


Does it matter where students take their mathematics courses?

Given, the above differences in pass rates between CTC math courses and BI math courses it might seem advantageous for students to take mathematics at CTC (unless the observed disparities in pass rates are attributable to differences in student characteristics of those enrolling in a given course at each institutional level). Overall, it seems that most successful transfer students take their math at the CTC rather than at the BI (see Table 4 below).

Table 4: No Mathematics Enrollments by Institution Level

Where do transfer students take math?N No Math N Transfers Percent

CTC 6779 42095 16.1%BAI 24997 42095 59.4%No Both CTC and BAI 3353 42095 8.0%Total No Math CTC or BAI 28423 42095 67.5%

At CTCs the enrollment rate in some math is 83.9% (16.1% no math) versus the enrollment rate of 40.6% at BI (59.4% no math). More than 3.5 times as many students take no math at BI compared with CTC.

To control for time-to-degree issues and explore these issues further we examined the mathematics enrollment patterns of students from the 2011-2012 cohort only, comparing those who earned a degree and those who had not yet earned a degree by spring 2015.

Graph 1: Enrollment in mathematics at CTC and BI for 2011-2012 BI completers


Graph 2: Enrollment in mathematics at CTC and BI for 2011-2012 transfers Non-completers

[Back to Highlights]

Summary1. The graphs show that students who complete degrees at BI are more likely to enroll in

mathematics courses at the CTC than students who do not earn a degree. 2. Degree earners are also less likely to enroll in mathematics at the BI. 3. Many transfer students who complete degrees at BI take no math following transfer (as

shown below greater than 90% of completers in some majors take no math at BI).

There are likely both individual differences and structural issues that contribute to these observations. For example, students enrolling in CTC immediately after high school can also minimize time away from mathematics by enrolling in mathematics at CTC and thus may experience more math success.

Some Questions1. Could it be that those students who seek to complete requirements as soon as possible

have more information or are more diligent or determined than those students who would delay facing a perceived challenge in math?

2. Could students facing uncertainty regarding their aims or lacking information about requirements delay taking math until transfer? These students may be uncertain about their intended academic path or they may lack confidence about where they will be accepted and requirements for their intended major(s) may vary across potential destinations.


Are students enrolling in the mathematics courses relevant to the requirements of their intended majors?

Above we saw that there were a considerable number of failures in mathematics at both CTC and BI. These failures may restrict completions and likely add to time to completion. Given these findings, we wondered to what degree students are taking mathematics required and relevant for their intended academic path.

Table 5: All enrollments CTC and BI by Area Pathway

Area Students PercentMath/STEM Sequence 23682 46.5%Statistics 9849 19.3%Quantitative Reasoning 5839 11.5%Business Math 4419 8.7%Elementary Ed 1294 2.5%Pre-college 4862 9.5%#N/A 996 2.0%Grand Total 50941


From Table 5 it would seem that the majority of students are planning on majors requiring mathematics courses in the STEM sequence. Pending the completion of a full inventory of mathematics requirements across degree programs in the state, it is still possible to provide a rough estimate of expected mathematics enrollments based on completed majors. Estimates of this type cannot account for changes to aspirations in response to difficulty (e.g., wanted to be an engineer but ended up in communications). Nonetheless, they can be a helpful addition to efforts to understand enrollment patterns.

A cursory look at the top majors show that STEM majors are not quite so popular. Table 6 below shows the completion areas of the 2011-2012 transfer students and the percentage of students earning degrees in each of the top ten areas.


Table 6:Distribution of Majors for the 2011-2012 CTC Transfers

Transfer Year Rank Major Area N

Percent of Completions

2011-12 NA No Completion 8699 NA 1 Business Mgmt & Admin 1423 16.6% 2 Social Sciences 877 10.3% 3 Health Professions 727 8.5% 4 Psychology 592 6.9% 5 Engineering 590 6.9% 6 Education 480 5.6% 7 General Studies/Unknown 467 5.5% 8 Biological Sciences 463 5.4% 9 Computer Science 408 4.8% 10 Communications 391 4.6%

Total Completions* 8555 100.0%Total* 17254Completion Rate 49.6%

* Totals include majors not shown. [Back to Highlights]


Using a rough coding scheme to classify the math courses taken into levels, what’s the pattern of movement in levels from CTC to BI?

The following table shows all students that passed their last CTC math course by course level and the course level of their first BI math enrollment.

Table 7:Course level of CTC by BI Course Level (for students with CTC pass only)

BI Level

CTC Level 1 2 3 4 5 6

No Math*

TotalCTC

1 219 896 16 1 2 2 1748 28842 229 3858 1305 69 281 30 13682 194543 7 371 452 181 98 4 2865 39784 1 185 143 86 418 17 701 15515 377 68 38 1108 341 740 26726 157 15 14 529 187 295 1197

No Math* 26 119 15 7 39 20 374 600Total BI 482 5963 2014 396 2475 601 20405 32336

* including 600 students with courses not assigned codes at CTC and 395 at BIKeyLevel 1 = pre-collegeLevel 2 = entry-level (gateway) mathLevel 3 = gateway math with at least one college-level prerequisiteLevels 4-6 = successive levels of advanced math (mostly Calculus)

The rows display the CTC math-course level and the columns display BI math-course level. The green cells indicate students moving up a level following transfer: from pre-college to college-level (N = 896) and from entry-level college courses to more advanced classes (N = 1305). The yellow cell shows students staying at the same level (N = 3858). The red cell indicates student that have passed a college-level course and enroll in a pre-college course following transfer (N = 229). Levels 1, 2, and 3, which represent pre-college, entry-level, and courses with one college-level prerequisite respectively are the easiest to interpret because they represent the clearest categories. The sequence and content of upper division courses shows relatively more variability across campuses.

Summary1. Most of the students (63.1 %) who pass math at CTC do not take math at BI following

transfer.


2. Students taking entry-level math courses (level 2) and courses that follow entry level (Level 3, e.g., Calculus and Business Calculus) as their last course at CTC are the most likely to not enroll in math at BI (more than 70% do not).

3. Students taking more advanced courses are relatively more likely to enroll.

Some Questions1. Why do many students without a college math credit at CTC not enroll in mathematics

following transfer? Perhaps some may delay addressing mathematics requirements before stopping out or may pursue degrees that do not require mathematics beyond intermediate algebra.

2. Why are so many students repeating the same class or staying at the same level (many upper levels have only one course)?

Data Cautions1. Many students do not advance in level, but this is not necessarily problematic as there are

multiple legitimate reasons students might take courses at the same level. First, many of the levels contain multiple courses that might be taken in sequence (e.g., level 1 contains all pre-college).

2. Also, students changing intended major or selecting a major for the first time may have to take a course at the same level as their last passed math course at CTC to meet requirements. Those students who passed a college mathematics course at CTC and then enrolled in pre-college mathematics after transfer may be in a similar situation of facing new requirements (or be ignorant of existing requirements).

The above table helps examine broad trends; for a more close-grained analysis, we explored course-by-course transfer patterns to find examples of course sequences across transfer we identified as positive, questionable, and concerning. Below are examples of each type with relatively large sample sizes.

Table 8: Examples of Positive Sequencing

CTC Math

N Enrolled in Any BI Math

BI Math CourseDestination

N For Specific BI Math

% of Students Enrolled in Math at BI in this course

Intermediate Algebra 697 Pre-calc 219 31.4%Precalc 2754 Calc I 786 28.5%Calc I 867 Calc II 172 19.8%Calc II 870 Calc III 372 42.8%

Summary1. These students seem to be progressing in the sequence of courses.2. Only one CTC math course had more than 1/3 of those passing at CTC and taking math at BI

enroll in a more advanced math course (Calc II).


Some Questions1. What are the factors that determine whether students advance to the next course or repeat

—are students with higher grades more likely to advance? 2. What role does confidence play in the process? What about advising?

Table 9: Examples of Questionable Sequencing

CTC MathN Enrolled in Any BI Math

BI Math Course Destination


% of Students Enrolled in Math at BI in this course

Precalc 2754 Math in Society 185 6.7%Stats 1458 Math in Society 102 7.0%Precalc 2754 Intro Stats 315 11.4%Precalc 2754 Precalc 785 28.5%

Summary1. These pathways are potentially evidence that students plan inadequately or lack an

understanding of requirements as it is unclear why a student would take a “Math in Society” type course following success in a Statistics or Pre-calculus course.

2. Many students follow CTC pre-calculus with BI pre-calculus. Given the diversity in the ways that colleges divide the material in the courses that prepare students for Calculus, perhaps many of the students taking Pre-Calculus at CTC and Pre-Calculus at BI are advancing within a pre-calculus sequence. Perhaps despite being qualified for Calculus enrollment these students do not feel confident that they are prepared to succeed in Calculus.

3. Pre-calculus at CTC followed by statistics at BI may be more easily explained. Perhaps students are changing areas or selecting an area that requires statistics or they were unaware of statistics requirements for their major at the time they took pre-calculus. It is also possible that these students intended majors are in areas that require both Statistics and Calculus.

Some Questions

1. Are there programs that require “Math in Society” but would not accept other college-level math classes?

2. Does it make sense for students to follow Pre-calculus with Statistics if their majors required both Calculus and Pre-calculus?

Table 10:Examples of Concerning Sequencing

CTC Math

N Enrolled in Any BI

BI Math Course Destination


% of Students Enrolled in Math at BI in


Math this courseStats 1458 Stats 134 9.2%Int. Algebra 697 Int. Algebra 973 13.9%Calc I 867 Calc I 366 42.2%Calc II 870 Calc I 141 16.2%Calc II 870 Calc II 86 9.9%

Summary1. The students in these pathways are repeating a course or taking less advanced

mathematics courses following transfer. These enrollment patterns are relatively harder to explain than the repetitions seen in Table 9.

2. The most common mathematics enrollment for students passing CTC Calculus I after transfer to a BI is Calculus I.

Some Questions1. To what degree is a lack of continuity in math pathways across institutions contributing to

the observed patterns? (e.g., students who have passed a class called Calc I at CTC have not learned the material required for entrance into Calc II at BI).

2. Are students enrolling in Calc I at BI following successful completion of Calc II at CTC trying to improve their GPA in major-related courses?



How are courses with high enrollment part of a coherent sequence?

The above tables provided some examples of different types of course taking patterns. Below we look more thoroughly at a single pathway (statistics) to examine the full range of courses that students take prior and following the main pathway course. This approach allows to more fully consider the ways a course fits into a sequence. We selected statistics because it is a high-enrollment course and because the data raise some interesting questions. The table on the following page shows the CTC courses that students passed prior to enrolling in Intro Statistics courses at BI.

Table 11:Last CTC Math Courses Prior to Enrolling in Intro Statistics at BI

Not Assigned/AssignableAlgebra

Algebra (two levels below)Algebra Intermediate 1 (non-precalculus qualifying)

Algebra Intermediate 2 (precalculus qualifying)Applied Algebra

Arithmetic (three levels below)Business Calculus

Business PrecalculusCalculus I

Calculus IICalculus IIICalculus IV

Differential EquationsElementary Ed Math

Honors StatisticsIntro Statistics

LogicMath in Society

Precalculus

0 100 200 300 400

CTC Course Passed before BI Intro Sta-tistics

Intro Statistics

Table 12 (next page) shows the relationship in the opposite direction: the BI math courses that students enrolled in after passing intro statistics as their last CTC math course.


Table 12: BI Mathematics Enrollment Following Intro Statistics Pass at CTC

Not Assigned/AssignableAdvanced Statistics

Algebra (two levels below)Algebra Intermediate 2 (precalculus qualifying)

Arithmetic (three levels below)Business Calculus

Business PrecalculusCalculus I

Calculus IICalculus IIICalculus IV

Differential EquationsElementary Ed Math

Intro StatisticsLogic

Math in SocietyPrecalculus

0 50 100 150 200 250 300 350 400

BI Math Course Following Intro Statistics at CTC

Intro Statistics

Summary1. While many students move from Calculus to Intro Statistics (145) and from Calc II (124)

and Calc III (116) into Intro Statistics, many also go from Statistics at CTC into Calculus at BI (229), and into other upper division mathematics courses beyond Calc 1 (200+).

2. At the same time, for most transfer students it appears that Intro Statistics is a terminal mathematics course (5652/7110 that pass the course at CTC take no math at BI1).

3. Taken together, these data suggest that the students taking intro statistics courses have great diversity in their mathematical knowledge, intended applications for statistical skills, and needs and interest for technical proficiencies. They also suggest that Intro Statistics may be required or at least considered part of the training for highly technical STEM fields, while also being a way to fulfill QSR for social science, heath, and other majors. This diversity of prior knowledge and future uses of statistics among students enrolling in statistics would appear to be a challenge for course design and instruction.

1 The data under analysis only pulled math courses taken so courses in statistics departments not co-listed do not appear. Further investigations will be needed to incorporate these data and get a more accurate account of the statistics pathways.


Some Questions1. Is it possible that some students would benefit from more discipline specific training in

statistics rather than a general Intro Statistics course? Such an approach would not require students to transfer abstract statistical techniques to areas of interest, which is a well-recognized hurdle for learners.

2. What can we learn about how many such courses exist but aren’t reflected in this dataset because they are not co-listed as mathematics courses?

Those students without an identified area of interest (unlikely to be a large group with a pathways approach) and those students interested in continuing to more advanced study of statistics (also likely a small group) could potentially opt for a more general and abstract statistics course. [Back to Highlights]


How many students are using each of the DTA pathways? How effectively is the DTA supporting student completions at BI?

The DTA pathways allow students to advance toward a BAI degree in particular areas. Examining the degree to which students avail themselves of these various opportunities and the relatively success rates of students in these pathways can help inform policy. To allow for adequate (150% time) time to graduate our completion analysis of DTA pathways is restricted to the 2011-2012 data. The distribution of students across the various DTA pathways was similar across other years.

Table 13:2011-2012 CTC Completion and BI Completion Percent

CTC CompletionTotal

Number

Number Completing BI

Degree

Percent Completing BI Degree

No CTC completion 8325 2769 33.3%DTA: Associate in Arts 6078 3856 63.4%General Studies Degree 678 418 61.7%DTA: Business 625 511 81.8%AS-T 621 463 74.6%Applied Associates 112 83 74.1%Certificate, 1-2 years 133 71 53.4%Certificate, less than 1 year 228 110 48.2%High School Completion 188 110 58.5%Total* 17254 8555 49.6%

*Includes completion types with smaller N not displayed

Summary1. The DTA: AA is by far the most commonly used of the DTAs; more than three times as many

students use the DTA: AA than all the other DTAs combined. 2. Students who complete a DTA: Business are the most likely to complete within 150% time,

followed by AS-T and then DTA: AA. 3. The students who earned a general studies degree completed at a similar to student in the

DTA: AA. 4. Relative to students with no completion at CTC and those with less than a two year degree,

students in all of the DTAs completed at higher rates. However, this comparison is confounded because these populations, having earned fewer credits at CTS have not had adequate time to complete at BI in the time-window of our data set.

Some Questions1. What are the programmatic feature of the business DTA that allow for better performance?2. What are the system challenges with having such a large percentage of students use the

general DTA agreement?


Considering the first BI math course that transfer students take, what are the rates of BI completion by course? Which math pathways are most common for popular majors?

The table on the following page shows the last math CTC math for common courses of students that earned a DTA: AA by BI major area. For each CTC math course the table displays the percentage of students enrolling in that course that completed a degree at BI.


Table 14:Last CTC Math Course by BI Completion Major (DTA: AA students only)

Major Int. Algebra Precalc Calc I Calc II Bus Calc Elem. Ed Math

Stats Math in Society

No Math Total* % no math at CTC

No Completion 154 544 140 116 67 57 406 414 83 2222 3.7%Social Sciences 52 94 32 11 16 4 121 93 28 509 5.5%Business Mgmt 6 50 39 21 128 1 182 32 3 503 0.6%Psychology 34 75 15 5 6 7 129 69 20 393 5.1%Education 15 26 5 3 2 119 24 52 7 265 2.6%Communications 29 55 7 4 12 1 40 67 14 252 5.6%Health Professions 9 40 4 1 1 105 16 9 201 4.5%General Studies/Unknown

18 26 5 2 3 7 37 65 9 182 4.9%

Biological Sciences 2 49 21 24 5 31 10 8 177 4.5%Multi/Interdisciplinary Studies

9 36 4 3 3 3 23 29 5 130 3.8%

English/Letters 8 25 4 1 4 2 13 42 7 120 5.8%Public Affairs 4 23 3 34 29 3 111 2.7%Computer Science 4 12 6 14 1 21 12 6 109 5.5%Total* 404 1231 339 263 261 214 1309 1105 236 6078 3.9%% Degree Earned 61.9% 55.8% 58.7% 55.9% 74.3% 73.4% 69.0% 62.5% 64.8% 63.4%*Totals for majors include courses not shown and totals for courses include majors not shown. Full table available in digital form.



Summary1. Almost all students earning the DTA: AA take mathematics at CTC (96.1 %). 2. Stats, Math in Society, and Precalculus have roughly equivalent enrollments

and together they comprise more than half of the total enrollments; among these three courses students taking statistics have the highest completion rate at BI and those taking precalculus the lowest rate (the precalculus rate is lower than the rate for those students taking intermediate algebra, as is the rate for students in Calculus I and Calculus II).

3. Business calculus and Elementary Ed Math have the highest completion rates but much smaller enrollments than three major pathways courses. Completers in several majors—sociology and psychology in particular—are distributed across multiple math pathways courses.

Some Questions

1. Why are the completion rates for students taking courses in the STEM sequence lower than for students taking other courses?

2. In particular, we expected that students taking courses such as Calculus I and II at CTC would show better outcomes. What factors account for completion rates equivalent to Precalculus in those courses?

3. Is the diversity in mathematics enrollment in social science and psych majors a function of varying aspirations (e.g., some psych careers need very little math and some are math intensive) or is access to information the major cause?


Considering the first BI math course that transfer students take, what are the rates of BI completion by course, and which math pathways are most common for popular majors?

The table on the following page shows the first BI math course for all students that earned a DTA: AA displayed by their BI major area. For each BI math course the table displays the percentage of students enrolling in that course who actually completed a degree at a BI.


Table 15:First BI Math Course by BI Completion Major (DTA: AA Completers Only)

Major Int. Algebra

Precal Calc I Calc II Bus Calc Elem. Ed Math

Stats Math in Society

No Math

Total* % no math at BI

No Completion 39 253 176 36 30 51 71 47 1265 2222 56.9%Social Sciences 2 22 19 3 5 44 10 364 509 71.5%Business Mgmt 23 5 3 36 5 12 368 503 73.2%Psychology 2 22 5 9 14 328 393 83.5%Education 1 7 5 90 2 2 147 265 55.5%Communications 1 5 2 1 3 234 252 92.9%Health Professions 4 2 19 1 175 201 87.1%General Studies/Unknown

1 7 1 3 22 1 134 182 73.6%

Biological Sciences 3 29 31 2 21 5 58 177 32.8%Multi/Interdisciplinary Studies

1 3 5 1 2 3 1 3 105 130 80.8%

English/Letters 1 4 1 113 120 94.2%Public Affairs 1 1 1 107 111 96.4%Computer Science 2 9 7 1 4 2 58 109 53.2%Total* 58 418 300 62 78 149 238 111 4043 6078 66.5%% degree 32.8% 39.5% 41.3% 41.9% 61.5% 65.8% 70.2% 57.7% 68.7% 63.4%*Totals for majors include courses not shown and totals for courses include majors not shown. Full table available in digital form.



Summary1. Approximately 2/3 of those students who earn DTA: AA do not take mathematics following transfer to BI; 69% of those

who take no math at BI completed a degree. 2. Among those who did not complete a degree at a BI, 57% did not take math. 3. For all math courses except for statistics the completion rates are higher for students taking that course at CTC rather

than at a BI (the statistics rates were roughly identical rates across sectors, 69% at CTC, 70% at BI). The largest differences in completion rates across sectors were for Intermediate Algebra, Precalculus and Calculus I.

Some Questions1. Why are the completion rates for students taking courses in the STEM sequence lower than those taking other courses? 2. What can account for the differences between completion rates for the same course across the sectors?3. The full analysis of course-level data showed that the BI degree completion rates for Calculus III and IV were

progressively higher compared with Calculus I and Calculus II. Are students lower down in the STEM sequence somehow stuck in the middle?

4. Are there student-level characteristics that distinguish these sub-populations?


wamathpathways.files.wordpress.com · Web viewMath Pathways Report: Math Course-Taking Patterns...

Documents

Transcript of wamathpathways.files.wordpress.com · Web viewMath Pathways Report: Math Course-Taking Patterns...