Carnegie Math Pathways

Carnegie Math Pathways Launches New Webinar Series on Quality Instruction

Marley Arechiga

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.

A Toolkit to Support Equity-based Corequisite Design and Implementation

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Diablo Valley College (DVC) in California and University of Wisconsin-Milwaukee (UWM) have both seen success rates in gateway mathematics dramatically increase after implementing and scaling math corequisites, including Quantway and Statway Corequisites. Not only have their corequisite programs helped more students directly enroll in college-level math courses, they are closing equity gaps in outcomes as well.

Case studies of DVC and UWM corequisite implementation are among the Practice Profiles featured in the Corequisite Mathematics Toolkit. Sponsored by Strong Start to Finish, this toolkit was developed by Dana Center in partnership with Carnegie Math Pathways.

It is designed to guide institutions through the process of adopting and scaling corequisites that enable all students to access gateway mathematics in their first year and ensure that students receive the supports they need to be successful. With clear design principles, planning and implementation tools, and studies from the field, this toolkit offers college educators a comprehensive resource to design corequisites for scale and build equity into each phase of the work.

Download the toolkit

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

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

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Knocking down the ‘brick wall’ for students

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

Launching dual enrollment at Fremont High School

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

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

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

Expanding access to 4-year colleges and making math empowering

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

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

The 74: For Free Community College to Work, HS Students Must be College-Ready. Some Programs that Can Make that Happen

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With the possibility of free community college on the horizon, the best way to guarantee the success of the free college initiative is to ensure that students who enroll are college-ready.

Programs like Carnegie Math Pathways’ Quantway and Statway can better prepare more students for college-level work and help ensure this success, argue Stanley Litow, professor at Duke and Columbia universities, and Tina Kelley, a former New York Times reporter and co-author, with Stanley Litow, of “Breaking Barriers: How P-TECH Schools Create a Pathway from High School to College to Career.”

Read the Op-Ed

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

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

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

The search for a new approach

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

Improvements in outcomes and the student experience

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

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

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

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

Building the infrastructure for institutional improvement

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

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

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

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

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

Increasing Student Success with Corequisite Solutions

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Carnegie Math Pathways Quantway and Statway corequisite solutions are helping students succeed in gateway mathematics at 3-4 times the rate of the traditional math sequence, and in a fraction of the time—saving students time and money on their educational path.

Since their launch in 2017, Quantway and Statway corequisites have provided students with targeted, just-in-time supports to successfully complete college-level math in a single term while offering institutions the flexibility to implement in a variety of models.

Read the impact brief for an overview of our corequisite course design and the results to date.

Read the brief

Transforming Student Learning with Online Course Solutions

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Carnegie Math Pathways Quantway and Statway online course solutions are changing the way students experience learning math remotely.

Since their launch in 2019, Quantway and Statway online courses have served over 5,000 students at 50 institutions. In that time, they’ve demonstrated the same high success rates as in-person Quantway and Statway courses, even as implementation scaled in the fall of 2020.

Learn about our approach to online learning and the results so far in our latest impact brief.

Read the brief