• What place does social justice teaching and learning have in a math class? 
• How can I promote productive and respectful exploration of social justice topics and concepts with my students?
• How can I help my students see the connection between the math we’re learning and its application in society?

These are some of the key questions addressed in Carnegie Math Pathways’ new guide, Mathematics With, About, and For Social Justice, and the accompanying designers’ webinar.

Developed by leading experts organized by Carnegie Math Pathways and with support from Strong Start to Finish, this new guide and webinar present a framework to understand how mathematics and social justice are intertwined as well as strategies and resources to help you create productive and impactful social justice-focused math learning experiences. 

Gain tools and tips to:

• create an equitable classroom culture that values different perspectives, supports student agency and belonging, and enhances the critical thinking of each and every student;
• manage and focus challenging conversations on the instructional goals; and
• help students see mathematics as a tool to address real-world issues.

We’d like to thank our expert panel for their work to develop these resources:

• Shandy Hauk, Associate Professor of Mathematics at San Francisco State University and Senior Researcher at WestEd
• Lily Khadjavi, Chair and Professor of Mathematics, Loyola Marymount University
• David T. Kung, Director, Policy at the Dana Center
• Victor Piercey, Professor of Mathematics and the Director of General Education at Ferris State University
• John Staley, Coordinator, Baltimore City Public Schools

We encourage you to explore the guide and check out the webinar recording for a walk through of the elements of the guide.

VIEW THE GUIDE

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.

To stay informed about how Carnegie Math Pathways supports faculty with training and professional development, subscribe to our monthly newsletter, In Sum.

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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. 

* * *

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.

To stay informed about this work, subscribe to our monthly newsletter, In Sum.

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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.

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. 

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 online courses engage students, 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.

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!

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.