Carnegie Math Pathways

Greater Student Success Calls for Greater Investment in Faculty

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Greater Student Success Calls for Greater Investment in Faculty

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Recently, Jasmine Prasad, vice president of legislative affairs for the Student Senate for California Community Colleges, urged the many colleges still placing students in remedial courses to stop presenting this as a positive option and instead enroll students in transfer-level courses that provide the best possible path for college success.

We couldn’t agree more because we’ve seen firsthand the power corequisites have in providing students supportive transfer-level options that improve college math completion rates. Students in Carnegie Math Pathways corequisites, for example, earn college credit at over three times the rate of students in traditional remedial math sequences, and in a fraction of the time. But achieving these outcomes takes more than just a shift in course structure. It takes investing in faculty and supporting them with the resources they need to successfully teach corequisite courses.

When institutions adopt corequisite math programs, they’re undertaking a fundamentally different, more equitable approach than traditional remedial math sequences. Corequisite education, in particular, is enabling thousands of students to enroll directly into college-level courses while receiving the targeted supports they need to earn college credit in a single term. While coreq models have shown tremendous promise at leveling the playing field for many more college students, we must acknowledge that they are intensive and demand new skills of educators. It is for this reason that Carnegie Math Pathways provides educators with professional training and development opportunities to ensure their experience in the classroom is successful.

In Pathways corequisite courses, specifically, educators use evidence-based active and collaborative learning methods to have students work through real-world math problems together—a wholly different approach from the rote, lecture-based approach to math teaching. But we don’t simply hand off materials to educators and expect them to become experts overnight. Through a structured system of peer-led training, faculty mentorship, and ongoing professional development, we help educators build the skills, strategies, and comfort they need to command this new and impactful instructional approach. And perhaps most importantly, we help foster a community across institutions in which educators are able to connect with and support one another in their practice.

In more than a decade of working with educators, we’ve learned that investment in faculty training and professional development is vital for ensuring that proven reforms like corequisite math remediation can succeed at scale. The results of this community of support for faculty have been profound. With robust resources and a community rallying behind them, educators not only see higher course outcomes, but they develop stronger connections with their students, observe deeper learning and greater persistence in their classroom, and have a more positive teaching experience.

“The mentor assuaged my fears and helped me understand and refine the active learning and group management techniques that I was using. Then, after a little more professional development, I was ready to be a mentor myself. This experience enabled growth and change that made my classroom teaching a lot more rewarding.”

Such was the case with Read Vanderbilt, a Statway corequisite instructor and math faculty at Diablo Valley College in California. Vanderbilt says that while educators may have taken a professional development course on group learning, putting the approach fully into practice can be really challenging. Yet with dedicated, ongoing support, educators can build their confidence as facilitators of group learning and help their students reach new heights.
“Carnegie Math Pathways provided me with weekly communication with a mentor in my first year, which made all the difference,” he said.

“The mentor assuaged my fears and helped me understand and refine the active learning and group management techniques that I was using. Then, after a little more professional development, I was ready to be a mentor myself. This experience enabled growth and change that made my classroom teaching a lot more rewarding.”

The adoption of accelerated corequisites to expand access to transfer-level math is a change for educators, but the prospects they hold for helping thousands more students advance in their education, particularly those most harmed by the status quo, cannot be denied. California colleges owe it to their students to provide them with the best course options to help them reach their goals, but they also owe their faculty and instructors the resources and supports they need to successfully implement these courses.

 

3 Things We’ve Learned About Designing Effective Dual Enrollment Math Programs

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How can we get high school students who feel shut out from higher education to even consider applying to college? One way is to enroll them directly in a college-level course while still in high school. That’s what we’re learning through newly imagined dual enrollment partnerships between high schools and colleges. 

Typically, dual enrollment math programs are seen as another form of advanced placement, reserved only for those students deemed “accelerated” or who are already on a path to college. And in many districts, racial participation gaps between White students and their Black and Latino peers persist. Over the past several years, however, Carnegie Math Pathways has collaborated with educators to make dual enrollment math programs more equitable by expanding eligibility to enroll and making course content more relevant and engaging to high school students.

Throughout these experiences, we’ve learned important lessons that could help you design or rethink your dual enrollment math program to create more equitable opportunities for students to attend and succeed in college. Below, we outline just some of our learning, shared during a recent webinar hosted by Transforming Post-Secondary Education in Mathematics (TPSE).

Dual enrollment math content can be more than algebra and calculus

Although an increasing number of colleges, if not most, offer alternative math pathways such as statistics or quantitative reasoning, many dual enrollment math programs are still reserved for students on a path to calculus. But imagine how many more students could discover their potential to succeed in college if they could choose from more math options than just algebra.

Consider Fremont High School in California. At Fremont, two years of math are required for graduation, but three are required for admission to California universities. Because failure rates in Algebra II, Fremont’s third-year math offering, were so high, students were not earning enough math credits to qualify for local college admission. And its reputation discouraged students from even enrolling in Algebra II. 

To give students more options to choose from and encourage them to continue their math education, Fremont implemented a dual enrollment math program with statistical reasoning content using Statway. This led to greater enrollment in third-year math and more students earning college math credit while still in high school. By offering topics other than algebra, statistical and quantitative reasoning courses like Statway and Quantway can appeal to students who previously thought college was out of reach, and even help them get ahead in their college-level math studies. 

We must build students’ identities as college students both in and out of the classroom

Students who haven’t considered college as an option or hadn’t considered themselves as potential college students generally have much to learn about the expectations and requirements of the college setting. It is incumbent upon us as educators to clearly communicate course expectations, norms, and grading requirements and make content and pedagogy inclusive. Further, the entire system built around a dual enrollment program—advising and placement, for example—needs to be ready for students who may not be comfortable or familiar with the college registration process and may not have anyone to assist them with it.

Both the in-class environment and out-of-classroom supports are crucial to building students’ identity as college students and their self-confidence and self-efficacy as math learners.

Anticipate and prepare for the administrative planning of your dual enrollment program

Even with the most dedicated high school and college administrators working together to increase college access and success, policy and bureaucracy can get in the way. We have encountered two common challenges in this arena. The first is cost. Even if the course itself is paid for, student materials may not be. In many cases, this has left institutions scrambling to find grant funding to pay for student materials. It is important to consider cost at the outset of a dual enrollment program, and it is vital to aim for a program that comes at no cost to students. This is an issue that goes beyond what individual educators and administrators can undertake on their own and needs to be addressed at the state policy level. Ample research, such as The Dual Enrollment Playbook, can help you make the case to your school district leaders or state representatives to support you with lowering costs to students for dual enrollment programs.

The second is the decision about whether high school or college instructors should teach the course and where. College instructors may not have experience teaching high school students and may not be paid to participate in activities outside of instruction, such as coordinating with the high school teacher. Meanwhile, having high school students on college campuses may expose them to the college experience but transportation obstacles can dramatically reduce participation for many of the students we’re trying to reach. There are many approaches schools can take. At Fremont, the dual enrollment course is taught at the high school by a math teacher who is also an adjunct faculty at the partner college. 

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While we can tell students repeatedly that they’re capable of going to and succeeding in college, the dual enrollment experience can show them they can. We can appeal to students’ interests with real-world curricula. We can support them in and out of the classroom to meet college-level expectations. And we can work behind the scenes to ensure that the program’s administrative aspects—like where to teach a dual enrollment class—are designed to support student success. 

A carefully designed dual enrollment program can show students who’ve never dreamed of attending college, let alone succeeding in that setting, that they are capable of doing just that. The ripple effects could be transformative—more equitable access to college, more diversity at college campuses, and more educated citizens.

 

What Carnegie Math Pathways Research is Revealing About Scaling Reform Successfully

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Too often, education initiatives that can drastically improve student outcomes succeed in a contained setting but fail to achieve those same results at scale. A study by Carnegie Math Pathways at WestEd is examining what conditions and support are needed for institutional leaders to implement promising innovations at scale effectively and sustainably.

Funded by the National Science Foundation and launched in 2018, the six-year Scaling Up through Networked Improvement (SUNI) project is providing leadership coaching to teams in two cohorts of two institutions to scale Carnegie Math Pathways course programs. The resulting evidence from the cases in the project is intended to shed light on effective approaches to implementing reform and change management at higher education institutions more broadly.

Early findings from this study have revealed several factors critical to enacting large-scale change effectively. These findings have practical value to college administrators seeking to scale proven solutions to bolster student success.

Rally support and buy-in from all stakeholder groups to ensure strong implementation.

Implementing reform at scale is more likely to happen when key decision-makers in multiple departments of the campus organization agree that the change is a worthy investment of effort and resources. For institutions participating in the SUNI study, it was clear that significant changes were needed to increase student success rates in developmental math, where many students’ education journeys were being derailed. Learn your department’s pain points and wishlists to develop ambitious but realistic goals that everyone can rally behind. 

Develop an implementation plan that defines and guides the scaling effort and helps minimize disruption amid leadership turnover.

Documenting shared goals, roles, and responsibilities can help leadership teams understand the scope of the work to be done, how it will get done, and by when. Using an implementation planning tool that project coaches introduced to the teams, institutions developed a guide to define and help steer the implementation of their reform. Inspired by the A3 management process developed by Toyota, this tool helps leaders develop shared goals, measures of success, and a means to communicate those goals and progress towards meeting them.

Since each leadership team created its implementation and scaling guide, the buy-in for the initiative was high. During times of change, such as when leaders transitioned to new positions, this guide has given new leaders a road map of the project, allowing them to quickly orient and keep the initiative on track. 

Nurture authentic engagement among your team with strong relationships and mutual trust.

Because scaling reform requires buy-in, it’s perhaps not surprising that fostering relationships built on trust and mutual respect is a key aspect of effective scaling. As we saw at one institution, when a key administrative leader consistently honored the contributions and positive impact of his team, it made them more willing and trusting participants in the reforms. Additionally, open and honest communication about the challenges and barriers that they faced along the way, and a willingness to consult with and accept input from colleagues, also helped strengthen support for the scaling effort. Before and throughout undertaking reform, evaluate relationships among your team and explore the resources available to strengthen them, such as professional development and coaching for leadership on team-building.

Ensure quality of communication and coordination between departments to maintain effective implementation.

Quality communication that supports transparency and coordination across stakeholders is essential to any reform endeavor. Early in the study, leaders at one institution discovered they were struggling with a lack of clarity about their roles and responsibilities for their reform initiatives, which led to unclear expectations. Through coaching and professional development facilitated by the project, these leaders identified ways to more concretely organize and communicate their needs, roles, and expectations to fulfill their program goals. As you consider embarking on reforms, evaluate the quality of communication among and between departments. What channels are they using, and are these channels effective at keeping your team(s) informed? What steps can be taken to improve the effectiveness of communication and the quality of coordination?

Continuously improve processes to sustain reform efforts.

With goals, challenges, and potential solutions subject to change quickly and at any moment, it’s critical to practice continuous improvement to sustain reform. When conditions that impact reform arise, recalibrating with colleagues is crucial not just for delivering the best possible outcome for students, but for keeping teams engaged, proactive, and joyful in their work of serving students. Continuous improvement means the regular evaluation and reevaluation of the considerations described above—maintaining buy-in, refining the implementation plan, nurturing strong relationships, and ensuring effective communication. Build in time to regularly monitor and assess what’s working and what isn’t so that the right improvements can be made at the right time.

In addition to these factors, the research reveals that engaging in coaching and networked learning (collaborative professional learning with peers), and extending these supports to entire leadership teams, is linked to the successful scaling of Carnegie Math Pathways programs. These insights remind organizational leaders that trust, communication, and shared goals are vital for sustaining large-scale reforms and building leadership capacity.

Throughout the next and final year of the study, participating leadership teams will continue to receive coaching and professional development support as they scale their Pathways programs. At the end of the study in 2023, the research team will publish the results to support institutional leaders in scaling ambitious reforms that can drastically improve student outcomes. 

 

 

New Grant Will Help Carnegie Math Pathways Support Instructors with Teaching Social Justice-Themed Math Lessons

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Carnegie Math Pathways has received a grant from Strong Start to Finish to develop a publicly available instructional guide to help educators effectively facilitate social justice-themed math lessons. 

The grant will fund an expert consultant to help design the guide, which will include strategies and frameworks to support educators with equitably engaging students to explore mathematics concepts contextualized in social justice themes and topics. The grant will also support a workshop—open to all educators—later this summer to explore the ideas and recommendations in this guide.

“We’re grateful to have SSTF’s support to help us advance more equitable instruction,” Karon Klipple, Executive Director of Carnegie Math Pathways, said.

“Math is a powerful means of helping students understand the world around them, including issues of social justice, and these resources will help teachers make mathematics more empowering and relevant for their students.” 

The grant builds on work that began in 2017 with the formation of Carnegie Math Pathways’ Social Justice Curriculum Committee. Comprised of educators within the Pathways’ national network of math practitioners, researchers, and administrators, the group developed a set of quantitative and statistical reasoning lessons situated in social justice contexts, such as gerrymandering and race and incarceration.

Since that time, lessons have been continuously improved and made available to educators in the Pathways network. With support from Strong Start to Finish, Carnegie Math Pathways will not only be able to support the implementation of Pathways-specific social justice lessons, but social justice-themed lessons more broadly.

The value of such lessons and guidance on how to facilitate them is clear—students learn how they can use math concepts to understand contemporary issues relevant to their lives, interests, and identities. And instructors receive the support they need to create welcoming learning environments that promote productive discourse around such complex topics. By understanding and applying equitable and culturally sustaining instructional practices, we can help more students feel empowered to participate in these types of lessons and feel like their perspectives and experiences are valued.

For students of color, adult learners, and other marginalized students, who may not see themselves or their communities represented in math curriculum or how math applies to problems they face, this is an important way to elevate visibility and help students feel that what they are learning in class can make a difference in their lives. And we know that when students feel supported and can engage in learning that they see as relevant, they are more likely to participate, persist, and succeed in their math course.

 

Online But Not Alone: Tips for Fostering Inclusion and Belonging in Online Math Courses

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Evidence shows that building students’ sense of belonging in the classroom is crucial to their success, particularly in math, one of the most feared and maligned subjects. These anxieties and negative outlooks on math can be exacerbated in online courses, where students can feel even less connected to the instructor and their classmates as they learn at a distance. 

In our latest Quality Instruction webinar, we discussed the supports and interventions that the Pathways community has found to be effective in fostering students’ sense of belonging, and how these have been adapted online to support learners from the beginning of the term, right to the end. Below, we offer some of the practical strategies you can use to build up your students’ sense of belonging in online courses and help them feel ready to succeed.

Provide a welcome package

The start of the term can set the tone for the rest of the course, and thoughtfully considering how you’ll first engage students in your course is critical to establishing a welcoming learning environment. In Pathways courses, we think of the elements that support student belonging at the start of each course as being part of a package—what we call “Starting Strong.” This package supports students in the first weeks of the course to develop the mindset and skills needed to succeed in a college course. The following are key elements of a course welcome package that we’ve found most impactful for creating an inclusive and connected online learning community.

A clear, intuitive course landing page. The course landing page presents an opportunity to clearly establish expectations and lay foundations on which to build community and belonging with and among your students. On this page, we suggest including a welcome video to introduce yourself and the course to your students; activities such as a syllabus scavenger hunt to orient students to the platform and a “get to know you” activity in which students can meet one another; and clear next steps on how to begin the course.

Predictable and visible course structure. A “learning cycle” describes learning as happening in phases, where students improve their skills by engaging in a predictable, and repeatable cycle of learning activities. In Pathways courses, students follow the same learning cycle in every unit of each module, establishing a predictable pattern that enables them to focus their energy on the content and working with their peers rather than on navigating the course structure. By mapping the learning cycle and representing it visually in your courseware, you can make the course environment familiar for students, which can contribute to their continued engagement.

Course orientation. Instructor-led orientation sessions scheduled during Week 1 of your courses provide a chance to talk through course expectations and give students another opportunity to be visible in the learning space, ask questions, and strengthen connections with you, their peers, and the key course processes. 

Investing in these early measures to welcome students and create an inclusive learning community sets the stage to help students productively engage throughout the course and feel like they belong.

carnegie math pathways learning cycle

Promote a growth mindset

Beyond Starting Strong, or the course welcome package, Pathways courses implement Staying Strong, a package of resources and interventions to help students maintain their confidence and motivation beyond the first weeks to successfully complete the course. An important component to ensuring students “stay strong” is an emphasis on growth mindset.

A growth mindset describes the belief that one is capable of learning a given subject and even excelling at it. Because students who have previously struggled with math tend to believe they can’t master the content, it’s important to show them evidence to the contrary and instill a growth mindset*—especially in online courses where students spend less time with the instructor, who can provide encouragement. One way we do this in Pathways courses is by sharing an article with students that describes the malleability of the brain, even in adulthood, and that individuals can improve their abilities in anything as long as they practice and use good learning strategies. Students have reported experiencing a newfound outlook on their ability to do math after reading the article.

Provide wise feedback

Another important factor to helping students persist in the course is ongoing, constructive feedback. Because online courses are more limited in their face-to-face interactions, the feedback given to students carries even more weight. Consequently, we must be mindful that our well-intentioned feedback does not inadvertently convey low expectations for our students. In Pathways courses, we promote “wise” feedback, which consists of phrases that communicate that the class has a high standard and that you believe that the student is capable of meeting that standard. By communicating to students that they’re capable of excelling in a rigorous course, wise feedback fortifies for students the belief that they can achieve and do belong in your course. 

examples of wise and unwise feedback

Share emotion regulation and metacognitive learning strategies

Students’ sense of belonging in online classes is also strongly influenced by how they respond to everyday learning activities of the course, and how comfortable they feel engaging with them. Learning in an online environment can present new challenges to students and we can support them by proactively discussing strategies to learn in an online setting.

The first set of strategies we introduce in Pathways courses is emotion regulation strategies to respond to stress in a healthy way. Engaging with rigorous material can be frustrating at times and may even heighten existing levels of anxiety if the student believes that stress is a sign of impending failure. In our Stress Reappraisal intervention, we share research with students that shows that the physiological signs of stress are also signs that you are preparing to take on a challenge, as opposed to running from one. Engaging in this reading and writing activity, relative to a similar control article, significantly boosted students’ performance on exams. By presenting information to your students about how stress works and how they can regulate it, you can help them discover healthy ways of managing it that benefit them throughout the course and beyond. 

The second set of strategies focuses on developing metacognitive awareness. Metacognition refers to how students are thinking about their thinking. Being able to identify and then address gaps in their learning can bolster a student’s confidence and identity as a learner. We have integrated self-regulation prompts in all online assignments as well as before synchronous collaboration sessions that challenge students to assess their confidence with specific math concepts.

Recap

As more students seek to carry out their education online, it’s incumbent upon us to move beyond the message board or comments section to engage them in meaningful online learning that welcomes them and makes them feel they have a place in class. By fostering students’ sense of belonging with strategies such as these, we can move toward online courses that build a stronger sense of community and lead to greater student success.

 

To learn more about other ways Carnegie Math Pathways courses engage online learners, read our learning brief Narrowing the Distance in ‘Distance Learning’: Lessons from Carnegie Math Pathways on Designing for Student Success Online. And be sure to sign up for our monthly newsletter, In Sum, to stay informed about additional research and learning from Carnegie Math Pathways.

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*It’s important to note that promoting a growth mindset does not imply that students can succeed just by changing their beliefs. Much more factors into their success, including quality of instruction. We recommend exploring the research of Carol Dweck, the originator of the growth mindset framework, for further learning in this area.

New Brief | Narrowing the Distance in ‘Distance Learning’: Lessons from Carnegie Math Pathways on Designing for Student Success Online

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Students are increasingly pursuing their education online. Although wide-ranging distance learning options offer learners flexibility and increased access to education, research shows that failure and withdrawal rates are sharply higher in online courses than in equivalent in-person courses, including for developmental math. For distance learning to fulfill its promise to students, online math learning must be rethought.

Carnegie Math Pathways has designed and tested a new approach to online learning that moves away from the traditional asynchronous learning model, which provides few supports to enable student success. Adapting principles that have proven to be effective in in-person course models, Carnegie Math Pathways has developed online courses focused on promoting connection and belonging.

This new brief highlights some of the key learnings from the design and implementation of online Carnegie Math Pathways courses as well as recommendations for how educators can support community and collaboration online in order to narrow the distance and promote student success.

Read the Brief

View the recording of our webinar, Online But Not Alone, to explore this topic further!

WestEd’s Carnegie Math Pathways and World Education, Inc. are Awarded a $3.8M IES Grant to Expand Adult Numeracy and Digital Literacy

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WestEd’s Carnegie Math Pathways and World Education, Inc. have been awarded a four-year, $3.8M grant by the Institute of Education Sciences (IES) to increase numeracy and digital literacy among adult learners. This partnership is part of a multi-year effort through the IES-funded Building Adult Skills Network to develop and test interventions to support millions of adults in the United States with strengthening their basic skills and overcome academic attainment gaps.

Numeracy and digital literacy skills are essential for educational and career opportunities and informed, productive citizenry, but according to the Organisation for Economic Co-operation and Development (OECD), 16 percent of the adult population in the United States is not digitally literate and nearly a third does not have the numeracy skills to complete common quantitative tasks such as calculating with whole numbers and percentages. This grant will generate evidence on how to best support adult learners with gaining these critical skills.

“Adult numeracy in the U.S. is a significant barrier to individuals’ advancement of quality of life, as well as to societal progress more generally.” Ann Edwards, Pathways’ Director of Research and Implementation and the grant’s principal investigator, said.

“With this project, we are aiming to contribute to knowledge and practice addressing the challenge of improving levels of adult numeracy and digital literacy in the United States.”

Working in partnership with the Pennsylvania Department of Education, the Pathways and World Education, Inc. will develop a 10-week course designed to improve adult basic numeracy and digital literacy in Pennsylvania, which has a diverse adult education population.

The approach will draw from the success of Carnegie Math Pathways’ adaptive technologies to address specific learning gaps, provide supports for English Language Learners (ELLs), and incorporate routines that promote positive self-identities as learners. By designing the course to be delivered fully online or in blended formats, the research team will also explore how a personalized and adaptive online learning experience can help cultivate the development of numeracy and digital literacy.

Another aspect of the project is professional development support for educators of adult learners. According to a 2015 study by the American Institutes of Research, most educators of adult learners have less experience teaching adults than their full-time counterparts and have less access to professional development. By providing a professional development component, the research team will equip educators of adult learners with strategies and skills necessary to design and teach rigorous adult learning programs.

The project will work with approximately 45 adult numeracy instructors to serve more than 1,600 adult basic education learners across rural and urban learning sites in Pennsylvania. Findings will contribute and link to the overarching goals of the Adult Skills Network, funded by IES, to gather research and evidence to improve adult basic skills and academic attainment using technology.

Learn more about this project as well as the Adult Skills Network here.

All California Community Colleges Can Meet the Requirements of AB 705. Here’s How.

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A central goal of California’s AB 705, passed in 2017, was to ensure that all students complete transfer-level English and math classes within a year, without first taking remedial courses. In fact, it requires that colleges place students into courses where they have the greatest likelihood of completing transfer courses, and restricts them from requiring remediation that delays students’ progress toward a degree. In July, EdSource reported that a majority of the state’s community colleges are still not yet fully implementing the requirements of this law.

It can be challenging for colleges to wade through uncharted waters and make the systemic changes needed to meet the law’s requirements. But proven solutions and resources are available to help institutions rise to the challenge. At a number of schools, these waters have already been charted, mapped, and skillfully navigated through partnerships with research-based organizations, and the implementation of solutions shown to help students succeed directly in transfer-level math courses.

Over the past decade, tens of thousands of students have succeeded in Carnegie Math Pathways Quantway and Statway courses, regardless of their original math placement level. We’ve served nearly 80,000 students, with 3 to 4 times as many of those students earning college math credits as those in traditional math sequences. We’ve helped institutions achieve these outcomes with a holistic approach. Our pedagogy centers student collaboration and provides social-emotional support to elevate students’ confidence and sense of belonging. We also build strong relationships with faculty, assist administrators with rethinking placement, and critically examine our student data.

And we’re not the only organization helping colleges transform their approaches to traditional math remediation. The California Acceleration Project (CAP), is a professional development network that exists specifically to support California’s community colleges with increasing completion and equity by transforming remediation. CAP has worked with all 115 California community colleges to implement reforms aimed at increasing student completion of transferable, college-level math and English requirements.

The Dana Center provides support to help educators successfully implement math pathways, with targeted efforts at the institution and state levels. Recently, Dana created a toolkit designed to help institutions successfully implement corequisite math courses. This comprehensive resource, supported by Strong Start to Finish, provides practical tools and profiles of institutions that have made this change. (Carnegie Math Pathways served as a contributor and on the national board of advisors for this toolkit.)

We owe it to our students to give them the best possible chance of success in college. It’s true that AB 705 has prompted the need for big change. But the evidence shows that this type of change is not just possible, it can lead to greater success for students. And while change isn’t necessarily easy, a wide array of supports from organizations like ours, CAP, the Dana Center, and others exist to help institutions with everything from placement, to advising, to instruction. Choosing to not meet the requirements of AB 705 is choosing to uphold the status quo, which has barred hundreds of thousands of students, especially Black, Latinx, and Indigenous students and those experiencing poverty, from completing their degree simply because well-intentioned, but ill-designed remediation courses hold them back. We owe it to our students to do what we so often ask of them in class—to dispassionately evaluate quantitative evidence and act on it.

Advancing Equity in Math Classrooms: What We Mean When We Say ‘Reimagine Math Teaching and Learning’

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A little over a year after the killings of George Floyd, Breonna Taylor, and Ahmaud Arbery, we’re reflecting on the commitment to equity we reaffirmed in our statement after their deaths. We continue to believe that “educated citizens are key to a just and equitable society.” Yet we continue to see persistent barriers to math education that impact who has access to and succeeds in postsecondary education. These barriers continue to hold back students—especially Black, Latinx, Indigenous, and low-income students—from reaching their full potential not just in college and the workforce but as citizens. Students can earn higher salaries with a degree, but what more could they accomplish equipped with and empowered by a firm grasp of statistical or quantitative reasoning? What systems, institutions, or policies could they make more just or transform to benefit their communities?

Our contribution to the fight to make math education more equitable has been proving that all students, regardless of demographics, can succeed directly in college-level math, saving students time, money, and morale. But the impact of high quality math education can be so much more far-reaching than the degree our students earn. It can influence decisions big and small that affect our lives and those around us, from choosing a credit card to evaluating climate change data.

Developed over the course of our first 10 years of operation, here are some of the components of high quality math education that we’ve learned can not only make student success in math and college more equitable but can make math an empowering tool for students to grow self-sufficiency and to advocate for themselves in their lives.

Culturally relevant curricula

When students see themselves in culturally relevant curricula, they can gain a firmer understanding of how math can be applied to the real world and how they can use it to empower themselves and their communities. It also reaffirms the reality that their lived experiences have a place in their math classrooms, despite what previous math learning experiences may have led them to believe.

Too often, “rigor” in math is associated with abstract, decontextualized algebra or calculus content. But if, instead, rigorous math challenges students to be involved in their own learning and to think critically, then what we think of as rigorous math should include contextualized statistical and quantitative reasoning. Positioning algebra and calculus as the gold standard of mathematical rigor reinforces dominant narratives about ability and race by framing inequitable experiences and outcomes as meritocratic. 1 2

By providing content that is more accessible (yet no less rigorous than algebra or calculus), students can begin to see how they are capable of excelling in complex math. Jennifer Morris, a Quantway instructor at the College of Menominee Nation, which in any given semester serves students representing 12 to 16 different Native American tribes, summed it up this way: “Students know that they’re not represented in the textbooks, and they’ve known it all along. But until they see themselves represented, they don’t realize what an impact that has.”

Showing students they’re capable of doing math

Social-emotional activities that promote growth mindset, or the belief that ability can be strengthened through hard work and the right support, are crucial to helping students unlearn the deeply ingrained messaging they’ve received about who is and isn’t a “math person.” We regularly hear from students who discontinued their studies because they simply could not earn the math credit needed to graduate.

One concrete way we help foster students’ growth mindset is by assigning a reading in each Pathways course about the neuroscience of learning and how we can grow our brains. Following the reading, students complete a short set of activities reflecting on the article. In a randomized control study, 20% of the students in the control group withdrew from the course, compared to only 9% of the students who read the growth mindset article.

While research shows we can positively build up students’ beliefs about themselves as math learners and doers, we can’t rely on growth mindset alone to make math classrooms more equitable. Doing so can place disproportionate responsibility on students for their success when a significant portion of it depends on one key person–their instructor.

Showing instructors that their students are capable of doing math

Students benefit from a growth mindset but many may not come to believe they have a high capacity to learn if their instructor doesn’t believe it first. Racial and gender-based stereotypes about math talent and ability can have profound negative effects on minoritized students. This is why a significant, ongoing commitment to examining how we perceive students is essential if we want to see more equitable outcomes.

In Pathways courses, we prepare educators by helping them expand their thinking about what students can achieve. This is put into acute focus when they encounter the collaborative learning aspect of Pathways courses for the first time, wherein instructors play more of a facilitator role, allowing students to struggle productively to arrive at their answers. It’s not uncommon for educators to be surprised by how much students can learn without their guidance, especially in the online versions of our courses where students collaborate on Zoom, often without the instructor.

“The thing that surprised me the most about teaching (Quantway online),” George Hurlburt, math faculty at SUNY Corning Community College, said, “is how successful the students could be without the teacher being in the room. I really thought it would be a problem and that I would have to regularly join the collaboration to help the students get through…But they didn’t quit and that’s what impressed me the most about them.”

Reimagining math teaching and learning

Truly reimagined math teaching and learning ensures that pedagogy and curricula do not perpetuate the harm that traditional math models inflict, from stereotyping to tracking to cutting down students’ confidence. The devastation of last year’s killings and the gross inequities laid bare by the pandemic continue to challenge us to examine how to dismantle systems that hold back minoritized students.

We’re looking critically at our course assessments—can we better align them with the collaboration and communication skills students have built in Carnegie Math Pathways courses? We’re examining our social emotional supports—can they be more robust in the online space? And we’re finding ways to provide better scaffolding for students to have conversations about math lessons contextualized with social justice issues.

A generation of students is grappling with how to move forward after experiencing deeply traumatic moments in our country’s history. Everyone has a part to play in how we help our students respond. Making math more equitable and more empowering is ours, and we’re honored to continue this mission in the next decade.

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1 Battey, D., & Leyva, L. A. (2016). A framework for understanding whiteness in mathematics education. Journal of Urban Mathematics Education, 9(2), 49–80. https://doi.org/10.21423/jume-v9i2a294

2Leyva, L. A., McNeill, T., Marshall, B., & Guzmán, O. (2021, March). “It seems like they purposefully try to make as many kids drop”: An analysis of logics and mechanisms of racial-gendered inequality in introductory mathematics instruction. The Journal of Higher Education. https://doi.org/10.1080/00221546.2021.1879586

Key Takeaways from a Decade of the Math Pathways Movement

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Earlier this year I had a wonderful conversation with three key education reform leaders on the movement to create math pathways. As I reflect on that discussion and particularly how Carnegie Math Pathways has helped shape this field, a few things stand out in terms of what has been most impactful and where there is further work to be done in reshaping mathematics to better serve our students and ensure success.

1. Data is essential to understanding the problem we are trying to solve, to motivating the will to make change, and to helping us identify potential solutions.

Thinking back to the early 2000’s, most of us understood from our own experiences on campuses that mathematics was a barrier to success. But it wasn’t until Tom Bailey’s work at the Community College Research Center (CCRC) in 2010 that the problem was put into sharp relief. CCRC’s research demonstrated that once students were placed in remedial or developmental mathematics, only 20% completed a single college level math class within three years. And this system of remediation particularly disadvantages marginalized students, including Black, Latinx, Indigenous students, and students experiencing poverty.

Developmental mathematics is a well intended solution to a very real problem; yet its design actually prevents students from learning and succeeding in college level mathematics. The system of developmental mathematics has stopped half a million students a year from graduating or transfering. Knowing this has forced all of us as educators to ask hard questions about our current approaches. It’s spurred us to examine our own institutional data to understand how these national statistics relate to what is actually happening with our own students. As we begin to understand the impact of this system within our own institutions, it becomes clear that the status quo is unacceptable, that a more just and equitable solution is needed.

By taking a more comprehensive, data-informed view of the system that generates these outcomes, we are better able to understand our students’ experiences, the factors impacting their experiences, and how best to address them.

2. Reimagining mathematics education so that it is a gateway to college success for every student requires systems change, not mere tweaks to existing structures.

Through critically examining the system, it became clear that multiple factors affect student success, namely, how students are placed into classes, the sequence of developmental courses students must pass before being allowed to enroll in college level mathematics, and what mathematics content students actually need to know to meet their college, career, and life goals.

We learned that traditional placement methods overplace students into developmental mathematics courses (often a sequence of courses) before allowing them to enter a credit-bearing college level course, financially burdening students and significantly lengthening their educational journey.

Data from the Carnegie Math Pathways showed that students performed just as well with college level mathematics content regardless of whether they were assessed as needing intermediate algebra, elementary algebra, or even pre-algebra.

In fact, Carnegie Math Pathways programs, Quantway and Statway, showed that sequences of developmental courses were not necessary. Students could succeed in college level mathematics if simultaneously given the right supports. This evidence has helped spark the movement of corequisite remediation, which is now in place in roughly half the states across the country.

At the same time, the math pathways approach has ensured that more students are learning mathematics relevant to their careers and interests such as statistics and quantitative reasoning. No longer are all students, regardless of interest or major, on a single trajectory to calculus inspired by our nation’s race to space against the Soviets in the 1950s. Instead, mathematics departments are following the advice of the mathematics and statistical professional societies in offering differentiated pathways that give students the skills and knowledge they need to be successful in their careers and lives in the 21st century.

3. Developing confident and successful learners requires transforming their learning experience inside the classroom.

The structural changes of redesigning placement, implementing corequisite remediation, and aligning math pathways with majors are essential to improving student outcomes and experiences. But they are not sufficient. Developing confident and successful learners and doers of mathematics requires changing how students engage with mathematics inside the classroom. Carnegie Math Pathways has shown that by actively engaging in contextualized mathematics in a supportive and inclusive environment, students develop deep conceptual knowledge, build confidence, and gain transferable hard and soft skills they need to be successful in mathematics and beyond. Because of Quantway and Staway, and programs like them, students are pursuing mathematics-based careers that they never before thought possible.

faculty at a carnegie math pathways event

Every student deserves the chance to succeed and advance, and nowhere can students feel an institutions’ commitment to them more than in the classroom. Creating powerful and effective learning experiences that help students build a growth mindset and foster a sense of belonging in class and in college requires investment in faculty professional development. For example, the State University of New York, through its partnership with Carnegie Math Pathways, has exemplified this commitment to professional learning by establishing a network of mathematics educators across their institutions who are focused on sharing learning and advancing instructional practice. And this investment has led to sustainable change for their students.

Our path forward

In the last 10 years, the Carnegie Math Pathways network of researchers and practitioners has played a leading role, alongside the Charles A. Dana Center and Complete College America, in launching a movement that has supported educators in transforming the educational lives of hundreds of thousands of students nationwide and abroad. While the Covid pandemic has made plain and even exacerbated the inequities in our educational system, math pathways continue to be a proven and sure step in dismantling some of these inequities.

Carnegie Math Pathways remains committed to our goals of improving math learning experiences for every student through innovative course solutions and by strengthening faculty development in equitable and inclusive instruction, and more. Progress toward this goal is possible because educators and administrators who are deeply passionate about making math teaching and learning more equitable are taking action.

So what actions can you and your institution take?

  • Begin by understanding your students’ experiences. Increasingly, many of us know the hard quantitative data about how our current systems serve our students. But knowing their personal stories makes the impact of those facts and figures all too real and impossible to ignore. Talk to them, interview them, ask them about their journey in deciding to come to your school, the process of enrolling, selecting and attending classes, and preparing for their future beyond your school. What do they hope to achieve? What are their pain points? Where could the system serve them better?
  • Then take the time to examine and understand the system that is responsible for the current outcomes so you can take steps to change it. Some key things you can ask include:
    • Are all the students who could benefit from college math able to take it based on your school’s placement method?
    • Do students have the option to engage in mathematics courses that are aligned to their majors? And how quickly is it possible to progress through their required courses?
    • Are students given the individualized support they need to be successful?
    • And are their experiences showing them the relevance of mathematics to their lives and futures and building their confidence as learners?
  • Reach out and connect with others. You don’t have to do this alone. Form a community of like-minded colleagues with whom you can share practices and ideas. Math faculty can connect with faculty in related disciplines to understand the specific mathematics skills students need to be successful in these disciplines. Faculty can connect with advisors to understand how incoming students are guided in selecting course pathways. Understanding each others’ perspectives may lead to new solutions for students. It may be that more can be done to prepare students for placement, that simple additional supports could significantly boost students’ identity and confidence as math learners, or that an alternative pathway would better meet the needs of non-STEM majors, saving them time and money and making it more likely they successfully advance academically.

We acknowledge that these tasks are complex and require time, resources, and commitment. Yet, the hard work has tremendous payoff. All of us need to understand our students’ goals and their experiences within the systems we create. It is incumbent upon all of us to create institutions and systems worthy of the students we serve. Together, the Carnegie Math Pathways network of educators has made tremendous progress over the last 10 years in transforming student’s learning experience and increasing success in gateway college mathematics. In the next 10 years I am confident we can do even more.