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

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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!

Rhode Island Department of Education Partnering with Carnegie Math Pathways as Part of $1M Gates Grant to Design New Algebra Course

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The Bill & Melinda Gates Foundation has selected the Rhode Island Department of Education (RIDE) as a $1M recipient of its “Balance the Equation — A Grand Challenge for Algebra I” grant. RIDE will work closely with Carnegie Math Pathways and other partners to pilot an “Algebra Readiness Course” to better prepare multilingual learners in Providence for Algebra I.

“We know that algebra tends to be a hurdle for students’ long-term success, and with this innovative program we are ensuring Rhode Island’s multilingual learners can get ahead,” Angélica Infante-Green, RIDE Commissioner of Education, said.

The new course will build upon a model created with WestEd’s Carnegie Math Pathways, piloted through its PrepareRI initiative in 2020. The proposed algebra readiness course will use student-centered pedagogy and a real-world curriculum to strengthen students’ pre-algebra skills while promoting their social emotional growth.

With experts from the English Learners Success Forum, Carnegie Math Pathways will help provide targeted and timely supports for multilingual learners to excel in algebra. These include curriculum modifications and expanded professional development opportunities for educators to tailor instruction for multilingual algebra students.

“We’re delighted for the opportunity to build on the impactful work we’ve done with RIDE so far to strengthen students’ math skills and knowledge. Multilingual learners have unique needs and we look forward to working with RIDE to provide them with the tailored support and attention necessary for their success in algebra,” Karon Klipple, Executive Director of Carnegie Math Pathways, said.

The “Balance the Equation” grant supports initiatives that make algebra more accessible, relevant, and collaborative for Black, Latino, and multilingual students and for those experiencing poverty. RIDE was selected along with 10 other grantees out of an initial pool of 416 applications from organizations across 26 countries and is the only government agency that won a grant. Other partners in the development of this initiative include the Providence Public School District, English Learners Success Forum, Young Voices, and Parents Leading for Educational Equity.

To learn more about the Balance the Equation grant, visit Balance the Equation Grand Challenge: Phase II.

Carnegie Math Pathways Launches New Webinar Series on Quality Instruction

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Instructors are perhaps the strongest touchpoint to students on a college campus. As educators, our instruction and the environment we create can help students feel welcome and see the value of what they’re learning. So how can we ensure that the learning experiences we’re working so hard to create in the classroom benefit every student, particularly in mathematics?

This fall, Carnegie Math Pathways is launching a new webinar series focused on exploring different components of quality instruction and deepening our understanding of how to practice them. We’ll cover timely topics and issues that impact instruction in the math classroom, including addressing inclusion and belonging, thinking critically about assessments, teaching in the context of Covid-19, and more. Each webinar will provide perspective, strategies, and tools to expand our thinking and enhance our ability to best serve all our students.

Our series kicks off on September 29th with a discussion of inclusive and equitable teaching practices. Together with researchers and educators, we’ll examine evidence-based practices that bring together curriculum, pedagogy, and professional development to promote the success of every learner. Join us!

Inclusive and Equitable Instructional Design: A Foundation for Student Success
Wednesday, September 29, 2021
12-1 PT / 3-4 ET
Cost: Free

View the Recording

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.

Increasing College Readiness With Quantway Dual Enrollment Partnerships in Wisconsin

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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.

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