Webinar: Introducing Carnegie's Work in Developmental Mathematics

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Statway and Quantway: Mathematics Pathways to Student Success in Community Colleges

On April 1, 2011, Carnegie hosted a one hour webinar to introduce the foundation's work in developmental mathematics. The panelists were Karon Klipple and Jane Muhich of the Carnegie Foundation, and Julie Phelps, Carnegie's Pathways Networking Liaison. Carnegie Senior Partner Uri Treisman introduced the problem via audio recording.

Webinar Description

Carnegie and its partners are addressing the low success rate of developmental mathematics students by providing alternatives to the current community college mathematical sequence and content. The Statistics Pathway (Statway) is designed to take developmental math students to and through transferable college statistics in one year. Quantway provides an alternate and accelerated pathway with an innovative quantitative literacy focus in which students use mathematics and numerical reasoning to make sense of the world around them.

During the broadcast, the presenters:

  • Discussed how the Carnegie Foundation in partnership with the Charles A. Dana Center and 27 community colleges around the country are on the leading edge of a movement to disrupt the system that has been an impediment for our developmental mathematics students for decades.
  • Described the new pathways for non-STEM students that focus on the quantitative literacy and statistical reasoning skills needed in today's society and for college success.
  • Outlined Carnegie’s approach to building a networked improvement community centered around increasing student success in developmental mathematics.







Contact Information

The Carnegie Foundation for the Advancement of Teaching
51 Vista Lane
Stanford, CA 94305
Phone: 650-566-5100


The following questions were posted during the April 1st webinar. While we weren’t able to answer all of your questions, we did get to quite a few. Responders included Karon Klipple and Jane Muhich on general Statway and Quantway queries, Guadalupe Valdés  on language questions and Kay Merseth on professional development. Some of your questions about design principles and outcomes can be found within our pages on Statway and Quantway.

Cece Cunningham (not verified) on Tue, 05/03/2011 - 11:13am

This conversation is very exciting. Really good forum for sharing the best thinking. Cece Cunningham

Jane Muhich on Wed, 04/13/2011 - 11:08am

Quantway-related questions


Q: Give us examples of quantitative reasoning at this level?

The Quantway quantitative reasoning outcomes are the same whether we are talking about a college level course or a developmental mathematics class. For example, “Communicate quantitative results both in writing and orally using appropriate language, symbolism, data and graphs.” An example of the developmental mathematics level might be using housing costs or health care costs as a context for analyzing measures of center. A college level course would have more advanced mathematics content and more complex authentic contextual applications.

Q: The word "lesson" is confusing to me. How are the "lessons" organized...around a context or around a mathematical topic? Can you give a few examples of lessons in Quantway?

The lessons are intended to be taught in a typical 50 minute class period. The lessons around explicit mathematical outcomes, for example using proportional reasoning to make sense of larger numbers or comparing linear and exponential growth.

Q: Do you see the Quantway being attached to a college level course to make it a cohort?

We believe strongly in the persistence benefits of a cohort experience and also developing quantitative reasoning skills overtime. With that in mind, we are seeking funding to develop the college level Quantway course, Quantway II. The Carnegie Foundation believes in creating clear relevant academic pathways for students.


Course Formats, Class Size, Cohort drop out issues

Q: Will these courses be available through e-learning?

The initial pathways’ curricula are being developed for class instruction. The out of class materials are being housed in an online platform.

Q: Have your restricted class size, etc. to help ensure success?

To create the greatest flexibility and ease of adoption, we have left many implementation choices up to the individual participating institutions. With that in mind, we have not restricted the class size in any way, but left it up to the individual institutions to create the optimal conditions for their students to succeed.

Q: What is the term length (e.g., weeks) of Statway and Quantway?

The Statway is intended to bring developmental students to and through a college level statistics course within one year. Some institutions are breaking the Statway curriculum into three quarters, some two semesters, some are accelerating the entire course to fit within one semester. The Quantway, though currently a one semester developmental mathematics course, would follow the same structure when the college level Quantway course is developed.

Q: Will these courses have textbooks, computer assisted instruction? How are they delivered?

The Pathways are designed to be taught without a textbook and have a portion of the class materials, including out of class activities located with a computer based platform.

Q: My institution is very interested in this model, but is limited by factors. We currently have a 1-sem. Stats course, but are not able to make the 2-sem. Statway commitment - will there be a 1-sem condensed option or a way to adopt the 2 sems independently?

All of our current colleges began in a similar situation, with a one semester/quarter college level statistics course. Some of the colleges have created a Statway developmental mathematics prerequisite course followed by their college level statistics course, some of the colleges sought approval for a new two semester sequence, other colleges ventured into other creatively structured course options. The curriculum is intended to offer colleges the flexibility to fit within their institution specific needs and organization structures.

Q: How do students proceed who are in a cohort and fail a course or drop out and want to re-enter the pathway?

For the Statway colleges, individual institutions would be able to make decisions whether students who dropped out would be able to rejoin an existent cohort in progress, for example the second semester of a two semester sequence. The Quantway Pathway when fully developed will have clear course delineations and won’t present the same issues.

Q: Earlier there was mention of cohorts; will students remain with the same group of students for their entire class sequence?

Yes, the intention is for students to stay with the same students throughout the year, deriving the persistence benefits of participating in a cohort

Q: Could you discuss implementation strategies for the Statway or Quantway project in an 8-week semester format?

Currently we have no colleges on an 8-week semester. The lessons, however, are intended to fit into a 50 minute class period and could be parsed in such a way to fit into a myriad of scheduling formats, as is currently happening with our current Statway colleges.

Q: Will the pilot classes be face-to-face or only online or hybrid? or how is the delivery going to be for the pilots?

The first instantiation of the Statway and Quantway curricula will be face to face. This is not to say that online and/or hybrid models may not be developed moving forward.

Q: Have you actually implemented these programs at any colleges?

No, the 2010–2011 is the co-development year where we are developing these pathways with researchers and community college faculty. Lessons are currently being piloted across 27 colleges around the country, and we are gathering feedback from those lesson pilots. The entire curriculum will be launched during the 2011-2012 academic year.

A similar concept to Statway, Statpath, has been taught by Myra Snell at Los Medanos College, which has had very successful results. She is part of the curriculum design team working on developing the Statway.

Math Competencies Needed

Q: What math competencies do students need prior to taking these courses? What happens to students who do not have the necessary math skills for an algebra course?

Students should have tested into Elementary/Introductory Algebra to enroll in the Pathways. If a student didn’t have pre-algebra proficiency he would have to go through the necessary prerequisite material before entering the Statway/Quantway or enter into the pathway through some institution specific mechanism.

Policy Issues, placement exam, wide range of dev. ed. Learners, STEMPATH - options

Q: Do any of your states have the legislated requirement that all college-level math classes must require students to be proficient in high school algebra two? Have SW and QW been adopted/approved by the higher ed authorities in the states of the participating colleges? Would a program of courses such as Statway be acceptable for transfer students desiring a 4 year degree?

Yes, many of the participating colleges have algebra requirements for college-level math courses. The Statway is the equivalent of a college-level introductory statistics course. The Statway would fulfill the program requirement of any 4 year degree program with a similar requirement.

Carnegie Foundation has successfully been working with the colleges and state boards to ensure the articulation of the Statway as a college level statistics course.

In certain states, a hold-harmless agreement has been brokered for the initial first few years of the Statway to have time for the initiative to be evaluated for effectiveness, while not harming any students participating in the program.

Q: Have you developed placement tests for these pathways? If there is no pre/post assessment, how do you plan to measure success of the program?

We are not currently developing a placement or diagnostic tool for colleges to use and are leaving course placement up to the individual institutions.

We are developing summative end of module, mid-course and end of course assessments which will be used assess student understanding in the Pathways.

We will also track students for persistence to completion, college-level mathematics or quantitative reasoning requirement completion for Quantway, and other student success measures.

Q: Currently we do get students who may have struggled in high school but "find their mathematical voice" in a developmental course and decide to pursue an engineering degree or go on to medical school. How would being placed in a Statway course affect their future? What would that pathway look like going from Statway to Stemway?

Students being empowered by initial successes in mathematics then wanting to change careers is a crucial engineering problem in these pathways. The Carnegie Foundation in conjunction with the Dana Center is looking to develop a bridge course to take students who change their minds from the Statway to the Stemway.

Until this bridge course is developed, it is important we carefully advise students enrolling in the Statway and Quantway.

Q: Do you know if at the participating colleges for this project ... is it just the developmental math departments that have embraced this project or have the entire math departments embraced this concept?

It is not only the developmental math departments who have embraced this initiative. To become a Statway college, there needed to be departmental commitment to the initiative.

Karon Klipple on Wed, 04/13/2011 - 11:07am
Title: Statway

Statway questions


Special Topics, Roadblocks, Ideas and Research

Q: ­Who’s the researcher at UCLA?­ 

Jim Stigler

Q: If a fireman shouldn't factor, why should he/she learn Chi-squared?

A: We believe that the statistical and quantitative reasoning skills developed in the pathways serve our students far better than the disconnected content in traditional developmental mathematics courses. Though these firemen may never use a chi-square test, they will use the logic and reasoning skills and the statistical acumen developed throughout the course.

Q: Based on the information I've heard thus far, technology seems to be a big part of this curriculum (right?), how to get the buy in from those instructors who do not allow calculators in developmental mathematics?

A: see below

Q: What role do you see technology playing in these new pathways? My college is still set on paper/pencil algorithms in the college level classes, which puts a serious restriction on what we can do at the developmental level?

We encourage and support the use of technology in our pathways, particularly when the use of technology to complete procedures supports the understanding of underlying concepts.

Q: What path would you expect an elementary education major to follow?

We believe that there may well be a need to develop an additional pathway specifically for these students.

Q: With all the institution-specific cutoff scores and stuff, will the programs work for everyone?

That’s an open question. We’ll be collecting data on the performance of students at various institutions (with various cutoff scores and stuff) and comparing the results. We also recognize and encourage faculty to implement modifications to support the particular needs of their campus population. So, while we are provided a core set of curricular materials we recognize that there will be some variability in implementation based on local needs. We are capturing that variability to include in the analysis of the program results.

Q: How does the rigor of these courses compare with that of College Algebra?

The Statway is at the same level of rigor as a traditional college-level introductory statistics. We have no intention of making these pathways less rigorous.

Lesson Study videos

Q: ­Are these videos currently available to watch? If not yet, where will we be able to view videos of the Lesson Studies?

We will make these available online as we launch the pathways, probably by next July. 

Q: In some of the videos, students are working on group activities. Is there a common set of activities for each pathway?

Both pathways embody the same learning theory, which includes productive struggle, as we talked about in the webinar.


General Pathways Questions

Q: So, in your view, an ideal developmental math curriculum (in the future) would have to include not only a STATWAY and a QUANTWAY course, but also a course to prepare them for College Algebra (STEM path)? Have I interpreted your comments correctly?

We envision ‘STEM-way’ that would prepare students for calculus (rather than college algebra.)

Q: Will the proposed Quantway path connect with the work that is being developed for Stemway as well?

At this point, STEM-way is a theoretical idea. We haven’t yet planned for its development.

Q: ­To clarify, why is one being conducted in West and SW samples and the other with midwest and East coast samples rather than at similar/more comparable institutions.

We were careful to pilot the two pathways in different states, so as not to confuse the articulation issues within a given state. The two groups of schools are quite comparable in terms of innovation and variability. 

Q: We have many community college students who are not prepared for elem. alg. Are there plans for examining the needs of these students?

Excellent question. Right now our focus is on students who already have a background in arithmetic and pre-algebra.

Q: How are you going to deal with one of the key barriers to development sequences as documented by Bailey - that 30-35% of students placed into a developmental sequence never take the first course in the sequence?

This is where counseling and advising play a crucial role. It is our hope (and hypothesis) that students will see the benefit in an ‘accelerated’ cohort experience that focuses on meaningful content and includes student support. Much work is being done among administrators within the collaboratory and on individual campuses to make students aware of this new opportunity. We’ll be testing this hypothesis over the coming years.

Q: What if there are more deficiencies in a person's math background that are just too much for this condensed (compressed time) version of teaching allows.  Do you allow them to catch up?

A: We know that not all students who place into elementary algebra (the requirement for both pathways) actually have the necessary mastery of pre-algebra skills needed to succeed. We anticipate and are planning for faculty to provide some just-in-time remediation in those cases.

Q: One of the biggest problems with the way many current DE courses are taught is transferability beyond the course. How is Pathway addressing this perpetual problem?

The pathways will likely be the culmination of a student’s mathematics courses, as they are to-and-through a college-level math course for non-STEM majors. We need to work to address the needs of students for whom success in the pathways emboldens them to take additional math courses or even switch to STEM majors.

View Curriculum? Course Materials?

Q: ­Where would I be able to view the StatWay curriculum? ­

You can currently view the course level outcomes vetted by several professional societies.  Later in the year we will also share with you the topic level outcomes for this course. In 2012 we will post an initial version of the open source lessons being developed for the pathways.

Q: ­How do you determine the textbooks? I see a lot of open source material being used in these course?­

For the SW we are working to develop open source reference/out-of-class materials that coincide not only with our content but also with our design principles.

Kay Merseth on Wed, 04/13/2011 - 11:06am

Professional Development questions


Q: What types of professional development will help faculty improve their instruction?

A variety of professional development tools and activities are being planned to help faculty implement Statway. In fact we are calling it the "Pathway Way." These activities and tools may include webinars on teaching practices, video cases and interviews with Statway faculty AND students about what it takes to feel successful in Statway classrooms, written cases on classroom practice to be used in summer workshops, observation tools for use in Statway classrooms by colleagues, the eventual development of a gallery of videos of Statway instructors teaching various lessons, a blog for discussion/sharing of teaching hints/ideas, written cases on difficult math concepts to teach to both explore the mathematics as well as teaching approaches, creating and maintaining website with references for alternative data sets that can be used with lessons and soon. The question, of course, is that we can't do this all of this at once. So we are currently involved in an analysis around feasibility, impact, resources, cost and time to implementation. 


Q: Is there any work being done to adapt these "course" strategies for learning centers and academic support areas?

 Not at the moment as far as I know

Q: Will Quantway be verifying that the instructors of the program are qualified? It seems to me that many student failures are caused by failed teachers. 

We are exploring the creation of a Pathway certification program which instructors would attend (online) and be certified as Pathway instructors.

Guadalupe Vald├ęs on Wed, 04/13/2011 - 11:05am

Language-related questions


Q: How are language barriers overcome? Earlier slides indicate the teaching of math and statistics is embedded in problems posed in authentic context. That sounds good, but also seems it would increase problems related to language barriers.­

We hypothesize that within the Staway and Quantway lessons, we can minimize language barriers in several ways. One way is by making certain that the materials that we are using attend carefully to possible unnecessary complexities within the texts themselves. For example there is no reason to write complicated, dense paragraphs or to use colloquialisms (e.g., piece of cake) that may be unfamiliar to students who come from non-English backgrounds. We want to make certain that the text materials that we use are accessible in that they make the content and the focus of the instruction clear.

For example, Guadalupe revised the first paragraph of lesson 9.1.1 as follows:


A newly discovered chemical can be developed into a beneficial medical drug. However, even if a new drug has medical benefits, it may have serious side effects. Before it is tested on humans, the new chemical is tested for safety on rats.


 Medical drug companies can develop beneficial drugs using newly discovered chemicals. These new beneficial drugs, however, may have serious side effects, that is, they may cause unexpected problems in addition to desired benefits. For that reason, drug company scientists test drugs on rats before they test them on humans to make sure that they are safe.

Guadalupe changed most of the paragraph to the active voice. That means that she stated specifically who carried out the actions (e.g., drug companies, company scientists). The authors here sought to embed the problem in an authentic context, which indeed is exactly what is done in statistics most of the time. However, Guadalupe conjectured that if students had limited background knowledge about how experiments are carried out and why experiments are carried out, they might have difficulty making sense of the task and the rich problem. So, she provided more information. The principle followed here had to be: Don’t simplify when background knowledge may be lacking, amplify instead.

In her revision, Guadalupe also explained a possibly unknown term (side effects) immediately after the term saying: that is, they may cause unexpected problems in addition to desired benefits. The principle followed here is: paraphrase what may be unknown general usage terms.

We are currently being guided by guidelines on plain language that are part of the federal government’s effort to provide clear and readable texts in the military, and the government itself, and in the legal arena. We are working to develop our own document that has mathematics examples such as those provided above. The plain language guidelines have been sent to the Statway authors, and we expect to carry out revisions of  a number of lessons (we are deciding how many we can actually do). The trick is that we have to make sure that in revising for language, we don’t introduce errors in the statistics. So we will need a math review that follows the language revision.

Most of the time, difficult language has less to do with mathematical vocabulary (which instructors do a good job of explaining) than it has to do with the way that texts are written. Key problems include: wordiness (it is my intention versus I intend to), long and unnecessarily complex sentences with many dependent clauses, use of dummy subjects (it appears that students drink too much versus students drink too much) and other similarly avoidable and unnecessarily complicated expressions.

Another way that we can reduce language barriers is to make certain that instructors are aware of the language backgrounds of their students. We want to do quick surveys once students are in class that will give instructors some idea about how students rate their language strengths and weaknesses (I like to talk a lot, English is my only language, I never talk in class, I studied math in English and in another language. My other language is my dominant language). This will help instructors to know how much to attend to things like ordinary meanings of words versus technical meanings of the same words (e.g., significant other versus significant difference). We have created a glossary of a number of such terms that has already been posted. Additionally knowing the language background of students can help instructors figure out how best to group students as they work on rich problems. It will be important not to group together students who do not like to talk, those who feel very insecure about their English, or those students who love to monopolize all interactions.

Finally, language barriers can be somewhat overcome if there is clarity about what we are assessing when we ask students to express their reasoning either orally or in writing. We definitely want to make certain that they learn how to express their reasoning but in most cases our evaluation need not focus on the grammatical correctness of their responses.


Q. Will the language and literacy rubric for writing lessons be available at some point?

Some of the early Statway lessons appeared to require quite a bit of writing. What was not clear was exactly what kind of writing was actually required for the purposes of the lesson. In some cases, it is possible that a mere jotting down of ideas in list form would have sufficed. The question simply sought to give students an opportunity to note what they had done so far.

In other cases, the expectation seemed to involve the production of a well developed paragraph. However, it was not clear whether the expectation was that both the quality of the thinking AND the quality of the writing be evaluated.

It will be important in moving forward to think very carefully about the purposes of requiring writing and about the ways in which writing must be modeled if students are to develop a sense of what a good explanation or a good justification of a position looks like. Once we decide what the purpose of writing is and once we make certain that we have modeled the writing in the lessons themselves, then we can certainly develop a literacy rubric.

In years past, writing across the curriculum efforts were very popular. They fell out of favor because it became clear that subject matter teachers are experts in their subject matter and not in the teaching of writing. We want to make certain that we do replicate the problem in either the Statway or the Quantway, so it will be important to take a good look at what can be taught by giving examples of brief good written explanations and what cannot be taught (e.g., thesis development, paragraph development, coherence) in a mathematics class that is already doing many other important things in a very short time.

Melissa Ward (not verified) on Fri, 04/01/2011 - 10:18am

I had a few lingering questions after viewing/listening to this webinar. 1. I know a similar assessment question was asked during the Q&A section. But, could you tell me if there is any sort of diagnostic assessment to determine skill gaps for the incoming students? Also, how is the course designed to address a variety of skill gaps that various students may possess? 2. What sort of measurement tool do you plan to use for the course to show effectiveness of student achievement? Is there a pre/post assessment to report this data? If not, what measurement tool do you plan to use? Thanks!

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