Learning Opportunities: Productive Struggle, Explicit Connections and Deliberate Practice

If you were able to participate in the webinar, “It’s Not Just the Curriculum: Developing Pathways for Student Success in Community Colleges,” in January, you heard that Carnegie’s work in developmental mathematics in community colleges — the Statway™  and Quantway™ pathways — is not just another curriculum product or educational technology. Instead, the instruction includes six components. First, we are teaching the math that matters in students’ work, personal and civic lives. Second, given the diverse backgrounds of students in this sector, there are language and literacy supports interwoven through the materials and classroom activities and embedded in the instructional design. Third, we have introduced something called productive persistence to the pathways, science-based activities packaged to increase student motivation, skills and will to succeed in college. The fourth “ingredient” of this mix is learning opportunities: productive struggle, explicit connections and deliberate practice. Fifth, the advancing teaching component aims to provide instructors with the knowledge, skills and habits necessary to experience efficacy in initial use and develop increasing expertise over time. This dimension is essential in seeking to reduce the variability in outcomes among classrooms serving similar students. Finally, we seek to exploit how rapid informative analytics can inform continuous improvements by students, faculty, colleges and network-wide. Operating throughout the instructional system, we seek to tap technology as a powerful tool to advance efficacy, efficiency and personalization in the work of students and faculty alike.

These form a foundation for the lessons within these new innovative pathways for developmental math students. During last year’s Summer Institute, participants in Carnegie’s  Networked Improvement Communities attended a session on learning opportunities. In this session, Kay Merseth, a senior fellow working with Carnegie on a thread of work called Advancing Teaching, prepared an essay that beautifully explains what the three learning opportunities are and what they mean to both students and faculty.

Briefly, in Kay’s words:

“The focus of the productive struggle is on the mathematical learning goals embedded in the problem or situation — it’s not about guessing what the teacher wants to hear or about finding a particular answer. It is about the process of thinking, making sense, and persevering in the face of not knowing exactly how to proceed or whether a particular approach will work. Exploring, investigating one or multiple approaches, and articulating a chain of reasoning behind the approaches also characterize productive struggle.

Within the Pathway materials the idea of explicit connections refers to the linkages or relationships among and between mathematical and/or statistical facts, procedures, and concepts. Explicit connections generally reference math ideas and concepts and may be about context as well. Connections may be drawn by students or faculty, but most often are presented and reinforced by faculty.

Deliberate practice consists of a set of tasks for students that are created to overcome gaps in understanding, apply what has been learned, and/or deepen fluency with key concepts.”

To learn much more about these learning opportunities, read Kay’s essay, “Learning Opportunities for Pathway Classrooms.”

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Ed. note: This post has been revised from the original.

The original post did not include the fifth and sixth components of the pathways. These components — advancing teaching and rapid informative analytics — will be discussed further in future posts.

Community Colleges in the News

You might be interested in the release of a couple of reports on community colleges and a news article on the budget situation in California and how community colleges are affected.

OPEN-DOOR POLICIES AT TWO-YEAR COLLEGES FACE THREAT, REPORT SAYS
The nation’s college-completion agenda may be threatening open-door admissions policies at two-year institutions, says a report released by the American Association of Community Colleges. The organization is concerned that colleges may become more selective in admissions in an attempt to meet graduation goals, and will therefore limit college access for disadvantaged students. Community colleges are known for their open-door policies, which allow all types of students to enroll. The information is from The Chronicle of Higher Education.
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ACCELERATING COMMUNITY COLLEGE STUDENTS’ ENTRY INTO AND COMPLETION OF PROGRAMS OF STUDY
In this updated paper, originally released by the Community College Research Center in April 2011, Davis Jenkins and Sung-Woo Cho argue that to improve completion rates on a substantial scale, community colleges must ensure that new students enter a coherent college-level program of study as soon as possible. It presents a simple method for measuring program entry and completion rates using data on students’ actual course-taking behaviors rather than declared major or intent. The paper offers research-based suggestions for ways community colleges can rethink their practices at key stages of the student experience to accelerate program entry and completion.
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PROPOSAL WILL HURT COMMUNITY COLLEGE STUDENTS
The Institute for College Success posted that the dramatic changes proposed by California Governor Jerry Brown would lock out more than a third of applicants currently eligible for entitlement grants. These are students who have worked hard and earned the grades that the state has long promised entitled them to participate in California’s primary student aid program. These are also the students, research shows, for whom financial aid may make the biggest difference in terms of helping them persist and succeed in college. As they finally reach the point where they are ready to go to college, many will find their dreams shattered. Three out of four applicants cut out would be prospective Cal Grant B students, who on average have family incomes well below the poverty line. And the majority of these students go to community colleges, where students receive too little aid and already less likely to receive state grants.
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Webinar: Updates on Carnegie’s work in developmental math

Join us for a webinar, “It’s Not Just the Curriculum: Developing Pathways for Student Success in Community Colleges,” on Tuesday, January 24 at 11 a.m. Pacific, 2 p.m. Eastern time. Bernadine Chuck Fong, the senior managing partner for Carnegie’s Community College Program; Karon Klipple, who directs the Statway Networked Improvement Community (NIC); and Jane Muhich, who directs the Quantway NIC and our work in productive persistence, along with faculty members from participating institutions, are on the program. They will provide an update on what students and faculty members are experiencing with these new pathways and tell you how new institutions might get involved in the future.

Space is limited, so REGISTER NOW!

Lesson Study Revisited

You might find this article about lesson study from The Hechinger Report interesting. Carnegie is using lesson study, not exactly in the way outlined in this article, but to improve our mathematics pathways. Statway and Quantway faculty teams at each community college site will be organized into lesson study groups. They will work together to plan instruction, observe each other teaching, and identify the most difficult and high-priority obstacles that stand in the way of success of the pathways. The pathways curriculum materials are built upon three “learning opportunities” in the instructional design of the pathways — productive struggle, explicit connections to concepts, and deliberate practice. These learning opportunities are interconnected and not necessarily exclusive of each other and are designed to support a deep and more meaningful understanding of mathematical and statistical concepts. Lessons study provides a framework for rigorously and carefully improving the pathway in its entirety from curriculum development to implementation in the classroom.

“LESSON STUDY,’ JAPANESE STRATEGY FOR IMPROVING TEACHERS, CATCHING ON IN U.S.
Lesson study is a professional development strategy used extensively in Japan that essentially dissects a teacher’s lesson and the way it’s delivered. Here’s how it works: teachers come up with a detailed lesson plan and explain ahead of time to colleagues the goals of the lesson. Then, one teacher tries the lesson out on a group of students, while dozens of other teachers watch what happens. Finally, the observers offer feedback and ideas for improvement. “[We’ve been] doing lesson study more than 100 years in Japan,” says Toshiakira Fujii, a premier professor of math education in Japan who was among those teachers observing at Jorge Prieto Elementary on Chicago’s’ northwest side. “But lesson study in the United States is quite new.” “Traditional American professional development is somebody outside comes and then does for teachers,” says Takahashi. But he argues there is a lot that teachers can do on their own. “My goal is in every school teachers gather and then find a new way to improve lessons by themselves.”
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Juggling student access and success

An article by the Associated Press examines the way California community college leaders are struggling with the competing demands of student access and success.

CALIFORNIA COMMUNITY COLLEGE LEADERS CALL FOR OVERHAUL
California community college leaders have signed off on major policy changes aimed at boosting graduation and transfer rates in the 112-campus system, despite concerns measures could hurt disadvantaged students. The 22 recommendations will go to the state Legislature for review after the California Community Colleges’ governing board on Monday (1/10/11) endorsed the measures recommended by the state-appointed Student Success Task Force. Backers believe the proposals, if implemented, will help more students complete degree and certificate program and transfer to University of California and California State University campuses. That would help reduce the number of dropouts and create a more educated workforce.
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Exploring learning opportunities

This video showcases a panel discussion on learning opportunities from the Quantway™ and Statway™ 2011 Summer Institute. Hosted by Kay Merseth of the Carnegie Foundation and the Harvard Graduate School of Education, the panelists include: Jim Stigler, Carnegie Foundation, UCLA; Uri Treisman, Charles A. Dana Center, U. of Texas, Austin; Rachel Mudge, Carnegie Faculty in Residence; and Karen Givvin, Carnegie Foundation, UCLA.

Learning From Practice to Improve Practice

In a keynote address at the annual meeting of the Association of Community College Trustees in Dallas recently, Carnegie President Tony Bryk outlined for the Trustees how Carnegie is using improvement research in our work to improve the success rate of students in developmental math.

“We need to rethink how we innovate,” he said. “As educators, we are pragmatists. We see problems and we want to move quickly to solutions. But we also know from past experience that many solutions are rarely tested against evidence and we rarely rely on evidence to continuously improve them. We tend to put new programs in place and then move on.”

Bryk explained that Carnegie is challenging this way of working. He said that we know from 50 years of history at educational innovation that few things actually work as originally designed. That failures may occur is not the problem; that we fail to learn from them is.

In response, Carnegie embraces a quality improvement orientation, encouraging rapid cycles of change. If something doesn’t work, the process is to change it until we find something that does. “This entails a mind shift from seeing change as principally about managing the dynamics of large scale roll out toward seeing change as opportunities to learn to improve,” he said. “This learning from practice to improve is the surest mechanism for success.”

Resources

• Read the speech
• Download the presentation slides
• Listen to the speech:
  

Pathways Update: Good News from the Campuses

Good News from the Campuses
We now have 30 colleges participating in our two networked improvement communities—22 in Statway™ and eight in Quantway™. There are 1200 students enrolled in 60 sections of Statway™, and Quantway goes live in classroom beginning in January. Over 80 faculty members are now network members, all of whom have participated in some fashion in co-developing the materials with us and are beginning to engage in improvement projects seeking quality at scale.

The news coming from the Statway™ campuses is heartening, as is the reception from other sectors. From focus groups of the students on the campuses we’ve gotten comments that indicate that our work in productive persistence is having the effects we had hoped. As David Yeager posted here recently: “We recognize that in addition to pedagogical improvements, student motivation, engagement and skills must also be attended to. Keeping these factors in mind, Carnegie’s new math pathways include specific activities, support systems, and pedagogical approaches designed to encourage and build these skills and mindsets in order to increase a student’s self-efficacy, motivation, persistence, and ability to navigate college.”

Statway™ students are telling us that math and statistics are more interesting than the math they had before. They are less anxious and more likely now to believe that with hard work, they too can learn math. For example, we’re hearing things like, “It’s real world math. It’s realistic.”

Another student told us: “I just never really went past the basic math in high school. Then I went to college and just bombed it, never understood it. And it’s just very refreshing to be—not only grasping it—to actually be interested in math.” And another student said, “… We actually read an article about how we can learn math, in the statistics class—like how to grow your brain and stuff like that.  … It kind of gave me hope. It was something that we did at the beginning of this quarter. … I was like, ‘Okay, I can grow my brain.’”

Faculty members too are saying that the content is resonating with their goals for the class. Some who were doubtful when we first met a year a half ago, have showed up as faculty leaders within these communities. As one faculty member put it: “All of my comfort zones are deeply threatened, but it is like the comfort zones were exactly what has been wrong. The whole system is set up to protect us from being challenged to improve. …”

Statway™ In the News
“Statway, created by the Carnegie Foundation for the Advancement of teaching is a promising approach to remedial mathematics education. Built on the premise that statistics, data analysis and quantitative reasoning are essential for a growing number of occupations and professions.”

—The Hidden Costs of Community Colleges, American Institutes for Research, October 2011

A recently released report from the American Institutes for Research (AIR) found that nearly $4 billion was spent by federal, state, and local governments over five years on full-time community college students who dropped out after their first year without completing their certificate or degree programs. About a fifth of full-time students who enroll at a community college do not return for a second year. According to the report, for the 2008/2009 academic year, the most recent year for which data are available, nearly $1 billion of taxpayer money was spent on first-year, full-time students who dropped out, about 35 percent more than five years earlier. Mentioned in the report were initiatives that were attempting to address the completion rate of students in community colleges and Statway™ received a nod as a promising approach.

There Is More to College Success Than Test Scores and Lesson Plans: Carnegie’s Focus on “Productive Persistence”

Why do some college students persist while others don’t? David Levin asked this question about the alumni of the Knowledge is Power Program (KIPP)—a network of urban charter schools.  Instead of focusing on students’ test scores or college professors’ instructional styles, he found something different. Students who were successful “were the ones who were able to recover from a bad grade and resolve to better next time. …” That is, they weren’t just the ones who were “naturally smart.” Levin, who is co-founder of KIPP, and his ideas were the focus of a recent New York Times Sunday Magazine article, “The Character Test: Why our kids’ success—and happiness—may depend less on perfect performance than on learning how to deal with failure.” Optimism, persistence and social intelligence, according to the article, are the habits and mindsets that “seemed indispensable” to enable students who were from families without a lot of family resources to graduate from college. These characteristics help students navigate the transition from high school to college by helping them to bounce back from the new challenges that inevitably come up in college.

What are the characteristics that help students succeed and how can we promote them? Many psychologists have contributed to this question. Carnegie uses the term “productive persistence” to summarize these good ideas and to apply them to our initiative to improve student success in developmental mathematics in community colleges.

We do this because the work of social and developmental psychologists has convinced us that improved curricula and instruction are not sufficient to dramatically improve college-level math completion rates. Many students work hard in developmental math classes—studying long hours, nights and weekends—yet do so using ineffective strategies. Other students simply withdraw effort soon after the course begins. To help more students successfully complete the Carnegie initiated math pathways, we want them to both persist in their studying and attendance (tenacity) and to do so efficiently and effectively (good strategies). Productive persistence is core to our work.

We recognize that in addition to pedagogical improvements, student motivation, engagement and skills must also be attended to. Students placed in developmental math often come to the classroom with what our colleague from UCLA, Carnegie Senior Fellow Jim Stigler, calls “math scar tissue”—or the residue of years of failure in mathematics courses.  Such past failures can ossify and produce in students a belief that their mathematical ability is fixed and not improvable, thereby undermining their motivation following setbacks or failures. Students may also have crippling math anxiety that results in worsening cycles of procrastination and low performance, or they may lack basic study skills for successfully completing their work.  Moreover, because many community colleges are heterogeneous commuter campuses, students may feel only a weak sense of connection to their peers, to faculty, or to their institution. In the absence of these ties, motivation to attend and persist may suffer.

We believe that these mindsets, skills and social relationships can prevent student success. We also believe that when efforts are made to improve them, then the impact of otherwise effective curricula can be made manifest. In effect, we aim to do what our Senior Fellow Uri Triesman calls “reclaiming students’ mathematical lives.” We are committed to understanding the social and psychological drivers of developmental math student success and using our improvement processes to design and deliver effective interventions to address them.

In a recent Gates-funded white paper on “Academic Tenacity” by Carol Dweck, Geoffrey Cohen, and Gregory Walton of Stanford University, successful motivation is described as:

Students are engaged in learning, view effort positively, and are able and willing to forego immediate pleasures for the sake of schoolwork. For example, they seek challenging tasks that will help them learn new things, rather than tasks well within their comfort zone where they do not have to work hard or risk failure. Next, difficulty (confusion, setbacks, failures) does not derail them. They see a setback as an opportunity for learning or a problem to be solved rather than as a humiliation, a condemnation of their ability, a symbol of future failures, or a confirmation of their identity as a non-student. This is true at the level of a given task and at the level of their studies in general–they know how to remain engaged over the long haul and how to deploy new strategies for moving forward effectively.

Keeping these factors in mind, Carnegie’s new math pathways include specific activities, support systems, and pedagogical approaches designed to encourage and build these skills and mindsets in order to increase a student’s self-efficacy, motivation, persistence, and ability to navigate college.

Mathematics and Democracy and What We Know

LESSONS LEARNED FROM MATHEMATICS AND DEMOCRACY
“Indeed, as the twenty-first century unfolds, quantitative literacy will come to be seen not just as a minor variation in the way we functioned in the twentieth century but as a radically transformative vantage point from which to view education, policy, and work.”
Mathematics and Democracy (2001)

At a recent meeting of Carnegie partners and staff involved in the community college developmental mathematics initiative, we invited Bernard Madison, among others, to provide us with some insight into the current thinking around quantitative literacy (QL). Madison is a mathematician and mathematics educator with extensive experience in research, teaching, curriculum reform, university administration and science policy. He is at the University of Arkansas and currently his work in QL and teacher education is supported by grants from the National Science Foundation.  In advance of his visit, Madison directed us to reading material that included an article written with Lynn Arthur Steen of St. Olaf College, Reflections on the Tenth Anniversary of Mathematics and Democracy, published by the electronic journal of the National Numeracy Network, Numeracy: Advancing Education in Quantitative Literacy.

In the introduction, Steen explains that when the Woodrow Wilson Fellowship Foundation- sponsored report, Mathematics and Democracy (M&D),  was released in 2001, it became clear that “numeracy mattered for citizenship as much as for science; that effective strategies for analyzing problems were very similar across different contextual domains, and that civic rationale for quantitative literacy was both more urgent and more compelling than scientific ones.”  One editor wrote that the publication made QL respectable. Yet, the authors note that there still remains a major shortcoming in most mathematics education: the lack of connections to commonplace issues.

The article and an accompanying piece, Quantitative Reasoning in the Contemporary World, 1: The Course and It’s Challenges, by Madison and fellow Arkansas professor Shannon Dingman, look at the success of the News Math course at UA and find the course has a radical impact on students, not the least of which is the shift in the students’ views “regarding the relevance of the mathematics in their everyday life.”

This shift is an important one to Carnegie as we look at student persistence and attempt to address a significant factor that leads to disengagement and lack of motivation to persevere in math classes for many developmental students: that the students find the current developmental math course content irrelevant, dull and boring.

UNLOCKING THE GATE
MDRC just released a literature review by Elizabeth Zachry Rutschow and Emily Schneider, Unlocking the Gate: What We Know About Improving Developmental Education. The authors write in the overview: One of the greatest challenges that community colleges face in their efforts to increase graduation rates is improving the success of students in their developmental, or remedial, education programs — the courses that students without adequate academic preparation must take before they can enroll in courses for college credit. Emphasizing results from experimental and quasi-experimental studies, this literature review identifies the most promising approaches for revising the structure, curriculum, or delivery of developmental education and suggests areas for future innovations in developmental education practice and research. This analysis focuses on four different types of interventions for improving students’ progress through remedial education and into college-level courses, including (1) strategies that help students avoid developmental education by shoring up their skills before they enter college; (2) interventions that accelerate students’ progress through developmental education by shortening the timing or content of their courses; (3) programs that provide contextualized basic skills together with occupational or college-content coursework; and (4) programs that enhance the supports for developmental-level learners, such as advising or tutoring.