An essential component of undergraduate education is the development of the mathematical skills and knowledge that enable students to fully contribute to society and to succeed in their chosen professions. At Michigan State University (MSU), we believe that all of our students can develop the necessary mathematical skills and knowledge regardless of their quantitative fluency when they enter the University. We also know that students with different professional goals require different types of quantitative literacy, with some majors requiring a knowledge of calculus and others not.

At MSU we are committed to constructing realistic pathways for students to develop mathematical skills and knowledge and to providing guidance for students in finding the right paths for them. The Department of Mathematics, the Department of Statistics and Probability, the Program for Mathematics Education (PRIME), and the Hub for Innovation in Learning and Technology, have collaborated to revise our gateway mathematics curriculum to better meet the needs of our students.

## Creating More Effective Gateway Math Courses: Moving Beyond MTH 1825

Traditionally, the centerpiece of MSU’s mathematics graduation requirement has been MTH 103: College Algebra. About half of our entering undergraduate students arrive to campus needing to take MTH 103, while the other half have demonstrated proficiency in algebra and can therefore go immediately to calculus if it is needed for their major. However, roughly a thousand incoming students - more than 10% of each year’s starting class - do not have the high school math background to succeed in MTH 103 without more foundational mathematics knowledge and skills. In the past, these students have been assigned to take a remedial course, MTH 1825: Intermediate Algebra.

Remedial mathematics courses are ubiquitous at American universities, and their logic is obvious: students who are missing some necessary knowledge or skills must learn them before moving on. However, these courses far too frequently fail to provide students with successful pathways to graduation. Nationally it is estimated that only one-third of the students who begin in a remedial mathematics course successfully complete the course. At MSU ^{1} we have done much better; from 2013 through 2017, MTH 1825 had a DFW rate (the rate at which students who begin the class drop, fail, or withdraw) of 18.2% during the fall semesters. Furthermore, for the same semesters MTH 1825 had a repeatable grade rate (the rate at which students receive a grade of less than 2.0) of 11.7%. At MSU, therefore, more than 80% of students in fall offerings of MTH 1825 passed the course, and about 70% earned a grade of 2.0 or higher.

While the rate of success in MTH 1825 is much higher than for remedial math courses nationally, it is not high enough. The DFW and repeatable grade rates for MTH 1825 were three to four times higher than the average of all other 100-level courses at MSU. Furthermore, failing to succeed in MTH 1825 is a serious stumbling block for many students, and it prevents their progress toward graduation. For example, in previous years only 6% of students who placed into MTH 1825 and entered MSU intending to study a STEM field (which requires calculus) succeeded in graduating with a STEM degree (compared to an approximately 60% or higher STEM degree completion rate for those who entered and placed directly into calculus).

One challenge with a remedial course like MTH 1825 is that the review topics are not directly related to the more advanced material in MTH 103, which makes it difficult for students to see the connection of MTH 1825 to their educational goals. Furthermore, because it is a remedial course, credit in MTH 1825 does not count toward an undergraduate degree, even though students pay for the cost of three credits to take the class. Finally, for historical reasons, MSU has taught most MTH 1825 students via an online course in which it is difficult to provide the focused and individualized support that many of the students need.

We are committed to revising our math pathways to help every student learn the math skills and knowledge needed to graduate. At MSU we have taken three complementary approaches to enhance student success in gateway mathematics: the development of quantitative literacy courses (MTH 101 and MTH 102), the creation of a two-semester version of college algebra (MTH 103A and 103B), and coordinated refinements of our math placement system.

## Ensuring Quantitative Literacy – MTH 101 & 102

While necessary for calculus-bound students, MTH 103 is not appropriate for all students, especially for students who do not intend to pursue a major that requires advanced use of algebra. For these students, MSU has developed MTH 101 and 102, led by Dr. Bronlyn Wassink in the Department of Mathematics in collaboration with PRIME. MTH 101 and 102 constitute a two-semester “quantitative literacy” sequence in which students develop and use mathematical skills in real-world contexts. Students in MTH 101 explore the mathematics relevant to health and risk, science, and the environment, and those in MTH 102 study applications to finance, economics, and politics. Furthermore, revisions to our undergraduate mathematics requirement allow MTH 101 and 102 to fulfill MSU degree requirements. Together, these changes enable students whose fields of study do not require calculus to obtain the relevant quantitative skills and the knowledge needed for them to succeed in their subsequent courses at MSU and in their chosen professions.

Over the last three years, MTH 101 and 102 have proved extremely successful. Students in the fall semesters (the semester in which most students taking the course enter MSU from high school) of MTH 101 had a DFW rate^{2} of 5.9% (over three years, Fall 15, Fall 16, & Fall 17) and a repeatable grade rate of 8.2%. MTH 102 has only been taught over the last two years and had a DFW rate of 4.4% (Fall 16 & Fall 17) and a repeatable grade rate of 5.6%. These number are comparable to or even better than the the DFW (6.2%) and repeatable grade rates (5.3%) for all 100-level fall courses at MSU during Fall 17.

Important new changes for MTH 101 and 102 are planned for Fall 2018. When the courses were initially designed, students were required to first pass (or place out of) MTH 1825. We have tested the hypothesis that MTH 1825 is necessary by, in selected cases and with appropriate oversight, allowing some students to proceed directly into MTH 101 and 102 without having taken or having placed out of MTH 1825. The results are unequivocal: students of all backgrounds perform well, and MSU students can succeed in MTH 101 and 102 without taking MTH 1825.

Beginning in Fall 2018, therefore, we will open MTH 101 and 102 to all incoming students, allowing many to begin to immediately fulfill the mathematics requirement, save on tuition, and reduce their time to a degree. We will also be expanding the capacity in MTH 101 and 102 from approximately 800 students to 1000 students per semester. With the changes being made for Fall 2018, all students who need the quantitative literacy courses will be able to take them starting in the semester they enter, enhancing their educational experience and success at MSU.

## Enhancing the Path to Calculus – Replacing MTH 1825

The changes above address the needs of students who are not required to take calculus. We are also reforming the pathway for calculus-bound students who need additional foundational skills and who would previously have taken MTH 1825. For these students, we are introducing a new two-semester sequence (MTH 103A and 103B) that will be based on a “growth mindset”, the understanding that students’ most basic abilities can be developed through dedication and hard work and that the ability to learn is not fixed (Dweck^{3}). These new courses, which are designed to help every student learn algebraic concepts, will be taught in-person (not online), incorporate just-in-time focused review of foundational material, and utilize a new pedagogical model that emphasizes mastery and allows students to develop new skills over the course of both semesters.

The design of MTH 103A and 103B is based on work done by Ms. Jane Zimmerman (Department of Mathematics) with the Dow/STEM scholars hybrid summer bridge program. The summer component of that program was similar to what will be covered in MTH 103A, and most Dow/STEM students continued with Ms. Zimmerman in the fall in what was essentially MTH 103B. The results of that program, using a “standards-based,” ongoing teaching/learning cycle that allowed for development of skills over time, were impressive. Of the 49 Dow/STEM students who completed “MTH 103B” with Ms. Zimmerman in FS17, over half received grades of 4.0, and the overall grade average in the course exceeded 3.5. These results are outstanding, especially since these are students who had placed into MTH 1825 based on their math placement examination. Dr. Teena Gerhardt (Department of Mathematics), and Dr. Becky Matz and Mr. Ryan Yang (Hub), and a team of graduate students are working with Dr. Zimmerman to enhance and extend this work. With the support of the Provost’s Office, we are replacing MTH 1825 with MTH 103A for all students entering in FS18 – and we are confident students will benefit greatly from these changes.

## Finding the Right Placement – Improving Accuracy Using HS Transcript Information

Just as important as curriculum reform in our gateway mathematics program is the placement system that can affect mindset and helps us guide students to initially take the right courses. With the elimination of MTH 1825 as a prerequisite, we need no longer be concerned about placement for students planning to take MTH 101 & 102. Placement continues to be an issue, however, for students bound for calculus, where proper placement is necessary to determine whether they start with MTH 103A, MTH 103, or a subsequent course.

The MSU Math Placement Exam (MPE) will continue to be the primary tool we will use to guide calculus-bound students in making placement decisions. No placement exam is perfect, however, and not all students take the MPE in time to be properly enrolled during MSU’s Academic Orientation Program. Of particular concern is the under-placement of students, which can be demoralizing, trigger stereotype threat, and delay their progress toward a degree.

With the help of Dr. Susan Richter (Institutional Research in the Office of Planning and Budgets), we have analyzed the patterns of success of students in mathematics courses based on their high school transcript. Using this information, we find that approximately 10%-20% of students who place into MTH 1825 via the MPE would have likely succeeded in MTH 103 without any additional preparation. Conversely, based on our analysis of patterns we have seen in the high school transcripts of incoming students, we have a reasonable sense of where students without MPE scores should be placed. This information will be used starting in the Fall 2018 to enhance the accuracy of our placement process and start more students in MTH 103. Students in MTH 103 will also be provided with an “off-ramp” after the first few weeks of class that will allow them to move into MTH 103A if their placement in MTH 103 was inappropriate. Augmented by the professional and personal assessment of our advisors, the enhanced MPE score, the use of high school transcripts, and the “off-ramp” to MTH 103A will allow us to more effectively find the right mathematics pathway for every student.

## The Path Forward

These changes will move MSU much closer to fulfilling our commitment to construct realistic pathways for students to develop mathematical skills and knowledge and to help students in finding the right paths. The faculty from the Department of Mathematics, and PRIME, along with collaborators from the Hub and Institutional Research, deserve our thanks for all they have done. Success will require faculty, staff, advisors, and students to work together to realize the potential of the changes being made as well as a commitment on the part of all of us to the continuous improvement of our gateway mathematics program in the future.

## Summary of changes are being made to MSU gateway mathematics in FS18

Beginning in FS18, MTH 1825 will no longer be a prerequisite for MTH 101 and 102 regardless of a student’s Math Placement Exam (MPE) score, and we will expand the number of seats available.

For entering students needing to take college algebra and who would have previously placed into MTH 1825, we will create a two-semester credit-bearing sequence, MTH 103A (graded P/F) and 103B, which will together serve the role of MTH 103 for the purposes of prerequisites, corequisites, and the University mathematics requirement.

We will use HS transcript information to improve accuracy of placement, and in particular to avoid underplacement, and provide an “off-ramp” from 103 to 103A.

## References

^{3 }Dweck, Carol S. (2008) Mindset: The new psychology of success. New York: Ballantine Books.