Carnegie Math Pathways

A Guided Pathways Approach to Improving Learning and Teaching in Introductory College Mathematics

Case Study

A Guided Pathways Approach to Improving Learning and Teaching in Introductory College Mathematics

by

In 2019, Milwaukee Area Technical College (MATC) embarked on a campus-wide Guided Pathways reform effort to create more equity-minded, student-centered systems to improve the learning experience and help more students reach their completion goals. MATC’s math department took advantage of this opportunity to rethink their introductory math offerings, which were proving to be a barrier to many students. Using a Guided Pathways lens to focus on both the structure of the offerings and the way they were taught, the math department was able to make dramatic changes to better serve students.

MATC students collaborate

MATC is the largest technical college in Wisconsin, serving a diverse population of 25,000 students annually. Each term, MATC was seeing up to 1,500 students — a large majority of whom were from low-income households, first-generation, and/or traditionally underrepresented students in higher education — enroll in their developmental math courses. For these students, the courses extended their time to graduation and were an expense that didn’t count toward their major. And with perpetually low outcomes, these courses were contributing to achievement gaps between White students and students of color at the college.

MATC’s math department decided to do away with their developmental algebra sequence entirely and instead offer more credit-bearing paths to success. They introduced a math reasoning option for college credit that did not require prerequisites and better aligned with many of MATC’s applied programs of study.

Alongside the shift toward more credit-bearing math options, the department also worked to move away from lecture-style teaching to evidence-based active and collaborative instructional practices that could better engage and support students. They sought a solution that would build on the investigative and group-based instructional model of their Math for Elementary School Teachers course, an approach they hoped to apply across all their entry-level courses.

This led to the adoption of Quantway Core for their math reasoning course. They believed the collaborative, discovery-based learning approach and relevant contextualized curriculum of the Carnegie Math Pathways design would better engage non-STEM students with math that is meaningful to their college and career goals. Additionally, they’d seen how the use of Quantway at neighboring schools like Madison College and the University of Wisconsin-Milwaukee had drastically improved outcomes.

Since launching Quantway Core in fall 2019, MATC has served over 800 students and seen their course outcomes increase substantially. Previously, only 50% of students passed pre-algebra, the first step on their path to college-level mathematics. Now, 74% of students are earning college credit directly in Quantway Core. The new approach is not only helping more students enroll directly in and succeed in credit-bearing math, it’s also reshaping students’ relationship with math.

Faculty are seeing students in Quantway Core gain greater confidence in their mathematics abilities than in previous courses. MATC’s math faculty attribute this to the curriculum itself, which they believe empowers students. The embedded social emotional supports strengthen students’ beliefs in their abilities while the relevant problem contexts connect math concepts to issues related to students’ lives and decision-making.

This change is also having a positive impact on faculty. As MATC has expanded sections and increased the number of instructors teaching their Quantway Core course, they’ve seen more math faculty come to value group learning and recognize this approach as improving their practice.

As math instructor Eric Hagedorn, who leads the Quantway Core implementation, puts it, “What I see [Quantway] doing is not only powerfully impacting our students, but I feel like every member of our team is a better teacher. Because this curriculum requires you to learn how to interact with your students in a way that facilitates the learning, rather than just doing the math for them. It’s not about us lecturing.”

By engaging in Guided Pathways planning, MATC’s math department has eliminated a system of courses that weren’t working for their students. With a greater focus on the students’ learning experience, MATC has not only introduced new pathways to student success, they’re scaling a solution that is helping all of their students build a more positive and productive relationship with mathematics.

In fall 2022, MATC will expand their math pathways with the introduction of Quantway College–a transfer-level course option to support those students looking to advance to a 4-year institution. According to MATC’s Dean of General Education Academic & Career Pathway, Dr. Sadique Isahaku, the impact of this program has been powerful and worth the investment: “This is closing equity gaps and giving more students a fair chance to advance academically toward their goals.”

Increasing College Readiness With Quantway Dual Enrollment Partnerships in Wisconsin

by

Bucking the trend – rethinking the path to student success in college mathematics

For years, Madison College had been seeing a disturbing trend common to many 2-year colleges across the country–incoming students were arriving underprepared in mathematics and most who were placed in developmental math never advanced to college-level math. In fact, just 12% of our students were completing the developmental math sequence in a single year.

We realized we needed to do better and redesign our foundational math offerings—both the content and the instructional approach. Our college introduced a math reasoning course using Carnegie Math Pathways’ Quantway Core in 2012. With a relevant, applied curriculum taught using a group-based, active learning approach, Quantway gave students a meaningful and rigorous alternative to our algebra developmental sequence and shortened the path to our college-level quantitative reasoning course. The impact was undeniable. With Quantway Core, success outcomes increased from an average of 58% to 74%.

Yet, while this had an impact on enrolled students, these changes still didn’t stop the fact that the majority of new students entering from high school were not eligible to enroll in our college-level math courses and were being directed to enroll in prerequisite courses. This system was costing our students time and money, and in many cases, thwarting their entire academic aspirations. This motivated my colleagues and me to develop a plan to support students in college math before they even graduated high school.

Partnering with high schools is key for our college’s student success strategy

We knew that to increase readiness for college-level math, we needed to collaborate with educators at our local high schools. We presented a plan to our dean, our college’s K-12 partnership office, and local high school instructors to use Quantway Core as a dual enrollment math reasoning course for high school juniors and seniors. The course offered students an alternative option to algebra and would prepare students for and provide college credit for many of Madison College’s applied technical programs. And for those wishing to pursue other programs, it would ensure they could enter college ready to enroll in college-level quantitative reasoning.

We also made the case that using Quantway Core brought the opportunity to establish instructional partnerships between college and high school educators. While the high school teachers were already familiar with group learning strategies, we proposed offering professional mentorship and support as they became familiar with the Pathways curriculum and pedagogy.

In the end, several of the high schools in the Madison College district were on board, seeing this as a way to improve student outcomes and increase high school graduation. We began working with high school instructors and administrators to align the course for approval for high school and Madison College credit, and with high school counselors to prepare for student recruitment.

Outcomes from our first year

In fall 2020, we launched Quantway Core dual enrollment programs with 10 teachers at eight schools. Still very much in the height of the Covid-19 pandemic, these courses were taught almost completely remotely.

Between fall 2020 and spring 2021, the math reasoning dual enrollment courses served 281 students and students achieved a 45% success rate. Though slightly lower than the historical average success rate of the elementary algebra dual enrollment course, these are encouraging initial outcomes, particularly amid Covid-related disruptions. There was notable variation in success rates across schools, with some reporting similar outcomes to those we’ve seen at the college, while others reported lower outcomes due to complications with remote access and online learning during the pandemic.

Despite the challenges, instructors’ survey responses at the end of the academic year were positive, noting several benefits for students. For one, students were interacting with one another during the learning process and were engaging positively with the curriculum. Students also demonstrated the ability to advocate for themselves and seek help, as well as enhanced reading and math skills. And because the content is relatable and meaningful to students, they built deeper connections to and could see the value of math.

Critical to the success of our launch and implementation was our investment in partner high school instructors. We worked with Carnegie Math Pathways to provide high school teachers with training on the Pathways instructional approach and courseware platform. We also established a peer mentorship program, connecting high school instructors to an experienced Quantway mentor instructor at Madison College. And perhaps most importantly, we formed a community connecting the dual enrollment educators and enabling them to share experiences and engage in professional development to enhance their practice and effectiveness in the classroom.

Looking ahead

The preliminary evidence of how this program is improving the learning experience and helping students build a new, more positive relationship to math while preparing for college has us optimistic about the power of this endeavor. We’re further encouraged because every school that taught Quantway this year has confirmed they are going to continue to offer the course again in the coming school year. And we’ll be working with three additional high schools making a total of 11 schools and 14 high school faculty in the 2021-22 academic year.

At Madison College, we offered six sections of math reasoning on campus in fall 2021 as we continued to scale our dual enrollment implementation. We believe our investment in high schools is an important way to expand college access and prepare students to enter Madison College. We look forward to continuing to learn from our partnerships and expanding this math learning opportunity to students across all 40 high schools in our district.

A Dual Enrollment Story: Expanding Postsecondary Options for Fremont High School Students with Statway

by

Knocking down the ‘brick wall’ for students

At a 2016 board of education meeting, I represented Fremont High School’s Algebra 2 course with an image of a brick wall. In California, two years of math are required for high school students to graduate, yet three years are required for admission to 4-year colleges. So many of our students were failing or not enrolling in their third year of math, Algebra 2, that a brick wall seemed to me to perfectly symbolize the dead end this course had become for these students. Approximately 40% of students enrolled in Algebra 2 did not pass with a C or higher, and for those who came from our most economically disadvantaged feeder school, an alarming 80% received Ds and Fs. We knew that something needed to change if we wanted to give more students the opportunity to continue studying math and the option to pursue a degree at a 4-year institution after high school.

Launching dual enrollment at Fremont High School

At the same time that Fremont was searching for a solution for our Algebra 2 challenge, a local community college, Mission College, was exploring ways to both increase their college completion rate by replacing their remediation math sequence with an accelerated, credit-bearing pathway and to better connect with local high schools as a means to increase enrollment at Mission. Statway, the statistical reasoning math pathway from Carnegie Math Pathways, proved to be a good match for Mission’s own effort to reform remediation, offering an accelerated route for students to fulfill their college math requirement while engaging them in relevant content through collaborative learning. While partnering with Carnegie Math Pathways to implement Statway as their solution, Mission simultaneously connected with us on launching a dual enrollment program that would prepare students for success in college, provide high school and college credit upon successful completion, and also create a pipeline of Fremont students to their campus. Recognizing the opportunity to offer Statway as an alternative to Algebra 2, we were eager to partner with Mission to better prepare students for college and make a 4-year education a viable option for more students.

To successfully bring Statway to our high school, we involved a host of our stakeholders, including educators and administrators from our high school, partner college, and our school’s district administration. Over the course of more than three months, this team worked to coordinate who would teach the course and what the credit structure would look like. We have chosen to offer Statway as a year-long course. As long as students achieve a C grade or higher in both semesters of the course, they earn both high school and college-level credit. In our district, students are advised about which math courses to take based on their interests, but ultimately have the agency to decide for themselves which course is right for them, and they have the opportunity to drop if they feel it isn’t right for their goals. Statway has become an important addition to the math course offerings at Fremont because it provides students with an alternative to Algebra 2.

Since its launch, our dual enrollment program has seen various iterations as we learned what worked and what we needed to adjust in response to unforeseen challenges. Initially, the course was co-taught at Fremont by myself and an adjunct faculty member from Mission, but the following year I was hired as a part-time instructor at Mission in order to teach Statway at Fremont. Over the years, funding sources have changed and even our college partnership has shifted. While our school’s relationship with Mission remains strong, we’ve since transitioned our dual enrollment partnership to Foothill College. While changes have been made behind the scenes, the experience the program has provided for students and faculty, and the outcomes they’ve produced have been consistently meaningful.

Expanding access to 4-year colleges and making math empowering

Dual enrollment Statway at Fremont has welcomed almost two hundred of our students “back to math” and helped create access to 4-year institutions for many who otherwise would have gotten stuck because of Algebra 2. It has dramatically improved the way students perceive themselves—as capable of learning and doing mathematics. And it has created a culture of inclusion: I regularly hear my students coaching each other on note taking and study strategies and checking in on each other’s understanding of the material. Although the vast majority of our Statway students struggled in at least one foundational high school math course, 60–80% of students in the program have earned college math credit through Statway each year.

By helping us knock down the “brick wall” of Algebra 2, our concerted effort with Mission, and now Foothill, to offer Statway as a credit-bearing option at Fremont has helped us convince our students to give math another chance and significantly increased access to 4-year institutions. We are excited to continue offering Statway to expand postsecondary options for our students.

Transforming Math Learning Through Faculty-Driven Change at the State University of New York (SUNY)

by

suny facultyFacing the challenge of math as a gatekeeper to college completion

At the State University of New York (SUNY), we are committed to ensuring that every student graduates and is well prepared for success in the workforce. We know that strengthening and accelerating student learning in mathematics is critical to achieving our goal. Our data show that mathematics, and developmental mathematics in particular, has been a primary gatekeeper to college completion for thousands of our students. We had to radically change how we approach mathematics education if we were going to help more students reach their college and career goals.

The search for a new approach

We began by working with faculty in our system to investigate new alternative approaches within our system and across the field. As part of our investigation, we learned about Carnegie Math Pathways and their quantitative and statistical reasoning pathways – Quantway and Statway. Impressed by the evidence of the Pathways’ impact in other systems and states, as well as the philosophy behind their student-centered approach and dedication to professional learning, our faculty made the case for adoption and our system decided to formally partner with Carnegie Math Pathways to bring these course options to SUNY colleges and universities.

Improvements in outcomes and the student experience

Our partnership with Carnegie Math Pathways has given SUNY colleges the tools to transform the way they serve students who need support in mathematics, laying the groundwork for increased graduation and completion rates. Originally piloted at two SUNY colleges, Quantway and Statway has now been used at more than half of the community colleges across our system.

Our Pathways-implementing colleges have demonstrated a noticeable improvement in student outcomes compared to students in traditional course sequences. Several of our schools have also made important advances in addressing equity gaps in success rates.

The relevant curriculum, combined with a collaborative learning approach and embedded social emotional learning support have truly made a difference to students. Our faculty are seeing improved attendance, engagement, and success in their classes. And students are telling us that they really feel like their math course has a purpose. Students have shared that Carnegie Math Pathways has helped them overcome math anxiety and helped them develop skills they never thought possible.

Our students’ success through Quantway and Statway is bringing both personal and institutional benefits. Students are achieving their gateway math credit within one year and building confidence that is supporting them as they advance in their studies and beyond. By investing in math instruction and providing math options that are meaningful to students’ studies and careers, our colleges are seeing improved and more equitable outcomes.

Building the infrastructure for institutional improvement

suny group photoOur partnership has helped us catalyze a system-wide network of faculty, administrators, and advisors committed to institutionalizing math pathways and supporting faculty learning and development.

Through this professional network, our educators have benefited from robust professional learning including Pathways trainings, mentorship development, and opportunities to share resources and support each other in improving practice. In partnership with Carnegie Math Pathways, we’ve coordinated large bi-annual learning forums that bring research and practitioner expertise together to improve students’ experiences in learning mathematics.

The result is a transformation in learning and teaching at 28 SUNY institutions that has impacted more than 20,000 students and over 475 faculty, administrators, advisors, and support staff.

Carnegie Math Pathways has also helped us build the infrastructure for our culture of student success that is integral to our corresponding efforts in corequisite English, multiple measures placement, and Guided Pathways.

Thanks to the early work of dramatically rethinking our math programs and our partnership with Carnegie Math Pathways, SUNY has begun making a real difference in our students’ success in math, and valuable strides towards ensuring the success of all our students.

How We Reimagined College Readiness Courses at RIDE with WestEd’s Carnegie Math Pathways & Reading Apprenticeship

by

Seeking a new path to increase college retention

At the Rhode Island Department of Education (RIDE), we strive to prepare our graduates for success in postsecondary education, work, and life. Like so many education systems across the country, however, each year, we at RIDE have seen thousands of our high school graduates drop out of college before even reaching their second year. By examining the data, we identified that students were consistently dropping out of college once they encountered remediation courses.

Nearly half of Rhode Island students who enroll in one of our three public colleges are placed into developmental courses. Of those, around 70% drop out of college within a year. Intensifying these bleak outcomes is the reality that while students in Rhode Island can earn a degree for free at local community colleges, developmental education courses are excluded from that deal, catching many of our students off guard with unexpected bills.

Recognizing the urgent need to change our approach, we set out to form a partnership between our high schools and colleges to ensure that students arrive at college prepared for college-level coursework.

Building evidence-based high school and college readiness courses in partnership with WestEd

To do this, we partnered with our state’s three public colleges, who recognized that the status quo was not serving our students and whose collaboration was key to better aligning K-12 and college standards. Together, we searched for partners in the field who could help us design quality, student-centered readiness content that focused not just on the skills that students were missing, but on the college-level work that we were preparing them for.

WestEd’s Carnegie Math Pathways and Reading Apprenticeship offered the evidence-based content and student-centered approach that we were searching for. With input from our local educators, administrators, and professors, they also worked with us to create custom courses to meet our students’ specific needs. With the onset of the COVID-19 pandemic, we took advantage of WestEd’s adaptive learning platform to provide effective distance learning opportunities, and we expanded our programming to rising 9th-graders. Our goal was to mitigate learning loss caused by the disruption from COVID-19 and to ensure that our students were well prepared for high school and college.

Our four, 8-week-long remote readiness courses—English and math courses for rising 9th-graders, rising 12th-graders, and departing high school seniors—launched in the summer of 2020. Each course was designed with synchronous and asynchronous components, enabling students to work both independently and with their classmates during live collaboration sessions. By bringing these courses online, we were also able to offer students the flexibility to learn at the pace that best suited their learning styles.

And the demand was overwhelming. Within five days, more than 2,000 students had registered for the courses, with 10% of the entire 9th-grade cohort statewide registering for the courses. This response has shown that this shift is something our community desperately needs from us and is already benefiting from.

High impact courses that are boosting engagement and achievement

The impact in both English and math was game-changing, with students demonstrating growth in critical reading areas and in post-math test results. Twelfth-grade students who took the pre and the post math test improved their SAT scores, on average, by 55 points. Even more impressive, students who had enrolled in the math courses below grade level were improving their SAT scores, on average, by 100 points. In the high school math readiness course, students improved their post-math test scores by an average of 15 percentage points.

In their reading courses, students demonstrated gains in comprehension of complex texts, positive self-concept as readers and students, and explicit approaches to reading complex texts. Students across all courses reported feeling engaged and connected to their peers and teachers.

The benefits of the readiness courses extended to our teachers as well. Our staff reported finding the course content engaging and high-quality, and many teachers appreciated the opportunity to gain experience and skills with new teaching styles and tools that could be used both online and in person.

Key takeaways and next steps

A variety of factors contributed to the success of our readiness courses. The broad coalition between RIDE, our public colleges, and WestEd enabled us to remove siloes that unwittingly interfered with our students’ success. With WestEd’s balanced focus on readiness as well as developmental education, we were able to confidently promote these courses not as remedial but as foundational to college success, helping us reduce the stigma for students who were a grade level behind and boost recruitment. And the robust training and professional development provided for RIDE educators, which included one-on-one coaching and a community of practice, supported our teachers as they embraced an innovative instructional approach.

Perhaps most important to our students’ success was the relevant, contextualized curricula that students could connect with real-world situations in their lives. The English and math lessons helped students develop critical thinking skills important not only to their future studies and careers, but also to helping them process and interpret the challenging events happening around them at the time, including the social justice movements in response to George Floyd’s death and the pandemic.

With heartening outcomes from our summer effort, we are even more optimistic about continuing our partnership with WestEd to improve and expand our math and literacy readiness courses. We are offering similar courses year round and aim to eventually expand to elementary school, with the hope of capturing students at critical junctures to prepare them for the next step in their learning journeys. We’re excited because our kids and teachers love these courses, and they’re making a real difference in student achievement.

Serving Students Better and More Equitably with Coreqs at the University of Wisconsin-Milwaukee

by

The problem we needed to solve

uwm classThe University of Wisconsin, Milwaukee is steadfastly committed to increasing college completion and doing so equitably. For years, though, we found math to be a significant barrier to students’ progress toward graduation. Gateway math completion outcomes in our traditional algebra-based developmental sequence were low, with only a 55% pass rate.

UWM serves roughly 25,000 undergraduate students each year, and on average 40% of incoming first-year students are deemed as needing additional support to prepare for college-level math. With our low success rate in gateway math, we knew that a sizeable number of our students were falling through the cracks and not advancing toward their goals.

Seeking a new approach to provide students more relevant options and an engaging learning experience

We worked to address this by adopting math pathways – a STEM-focused algebra path and a quantitative reasoning math literacy path, both designed to reduce the 2-3 term developmental math sequence to just two terms and to give students math options better aligned with their areas of studies and career paths. As a department, we also committed to an active instructional model to better engage students.

In our search for an effective curriculum to improve instruction and our students’ learning experience in math literacy, I learned about Carnegie Math Pathways Quantway. Following our team’s participation in a Pathways orientation workshop, we decided to adopt it to replace our textbook, and were so pleased with it. I loved the idea of the problem situations and not having a prescriptive textbook. Along with the rich, contextualized curriculum, Quantway gave us access to high-quality peer-based professional training around an evidence-based active teaching approach and ongoing opportunities to improve these resources.

And the results of this decision were impressive. We saw gateway course success rates dramatically improve to 73% and 77% respectively for our two-term math literacy and algebra pathway sequences.

Embracing deeper reform with a coreq solution in partnership with Carnegie Math Pathways

In 2017, our department took our developmental reform effort a step further. Recognizing that we were still losing students in the gap between our developmental course and the credit-bearing gateway course, and seeing the growing evidence behind the national coreq movement, our department decided to redesign our math options. I began to reach out to the Pathways community to explore reworking Quantway Core and College offerings into a single-term corequisite course.

Working collaboratively with the Carnegie Math Pathways team as well as math faculty in the Pathways national network, we deconstructed the Quantway College content and built in the Quantway Core scaffolded supports alongside the embedded Pathways Productive Persistence supports, creating a coreq course that I piloted with my students in spring 2018.

Powerful results thanks to a well designed solution

uwm studentsThe pilot was a tremendous success. Since Spring 2018, we have enrolled 373 students in our Quantway coreq course and achieved an average success rate of 86%. This is a 13% improvement from the previous two-term sequence, and a 30% increase from outcomes prior to our math pathways implementation. Further, coreq implementation has positively impacted outcomes across groups as well. With the Quantway corequisite implementation, we’ve narrowed a 32 percentage point gap in success rates between Black and White students to just 5 points. In fact, UWM’s Quantway corequisite course has been recognized by the Wisconsin system as having some of the strongest improvements in terms of equitable passing rates across all demographic groups.

This really demonstrates for us the power of a coreq solution. By not allowing students to fall through the cracks of remediation courses, we believe the Quantway coreq is better serving our students. By providing our students the ability to directly enroll in a college-level math course designed with the supports they need to be successful, we’re giving all students more equitable access to college math and a better chance at success in college, career, and beyond.