Carnegie Math Pathways Glossary

Advancing Quality Teaching (AQT)

The faculty development component of the Pathways program.The aim of AQT is to provide instructors with the knowledge, skills, and habits necessary to experience efficacy in initial use of the Pathways and develop increasing expertise over time.

Alpha Labs

Alpha Labs engages academic researchers in helping to improve community college students’ success in developmental mathematics courses. Researchers in Alpha Labs network and partner with Pathways faculty members to work on priorities set by the community of practice.

Bridge Courseware

The Pathways Bridge Courseware is designed to help Quantway or Statway students pursue even broader educational opportunities, including those in STEM and Business.These materials have been collaboratively designed to bridge the material learned in Statway and/or Quantway to college algebra, business math, and pre-calculus courses. The courseware includes five modules:

  1. Linear equations and inequalities, including systems
  2. Functions
  3. Exponent rules
  4. Polynomials expressions including quadratic equations
  5. Rational expressions

Carnegie Foundation for the Advancement of Teaching

Founded by Andrew Carnegie in 1905 and chartered in 1906 by an act of Congress, the Carnegie Foundation for the Advancement of Teaching has a long and distinguished history. It is an independent policy and research center, whose primary activities of research and writing have resulted in published reports on every level of education. The current work of the Foundation is focused on using the tools and tenets of improvement science in Networked Improvement Communities to accelerate how the field learns to improve.

CarnegieHub

The “one-stop shop” collaborative online platform for Pathways NIC members.
http://pathways.carnegiehub.org

Carnegie National Faculty (CNF)

The Carnegie National Faculty are a group of network members identified for their exceptional leadership, exemplary teaching practice, and commitment they have shown within the Pathways Networked Improvement Community. The CNF play a central role in the self-governance structure of the Pathways network. New CNF are elected annually to a 3 year membership; the CNF work with Carnegie staff to identify new candidates and then vote to elect new candidates.

Carnegie Math Pathways

Carnegie Math Pathways is the name of the entire operation. This includes Statway and Quantway, as well as Productive Persistence.

Community College Pathways (CCP)

We have retired this name and replaced it with Carnegie Math Pathways

Collaboratory

A Collaboratory is a “center without walls” in which researchers work without regard to physical location, interacting with colleagues through a networked community; a networked organizational form that includes social processes, collaboration techniques, formal and informal communication. – Wulf 1989, Cogburn 2003.

Collaboratory Colleges

The original 27 founding colleges of the Statway and Quantway Networked Improvement Communities: American River, Austin, Borough of Manhattan, Cuyahoga, Foothill, Capital, East Georgia, El Paso, Gainesville, Gateway, Housatonic, Houston, Miami-Dade, Mt. San Antonio, Naugatuck Valley, Northwest Vista, Onondaga, Pierce, Richland, San Diego City, Seattle Central, Sinclair, South Georgia, Tacoma, Tallahassee, Valencia, and Westchester.

Contextualized Lessons

Educators and researchers from UCLA and the Northeast Resiliency Consortium (composed of Achieving the Dream, The Carnegie Foundation for the Advancement of Teaching, and seven Community Colleges in the Northeast) have developed a version of the curriculum that includes 12 modified lessons. Designed to meet the needs of specific workforce programs, the modified lessons are designed employing authentic contexts from one of three disciplines: Applied Health Care, Environmental Technologies, and Information Technology. They include situations with real-world challenges frequently faced in the discipline, enhanced language and literacy supports, and reinforcements for the language, operations, and non-math skills specific to the discipline.

Curriculum Materials

In addition to the Online Homework Platform (see below), the Quantway and Statway curricula include:

Quantway

  • Student lessons: Students handouts for each lesson that present the in-class problematic situations and related tasks. Instructors can download lesson handouts individually or as workbooks for the course. Each lesson handout includes two sections for students to do at home:
    • Out-of-Class Exercises (OCE): Homework that builds upon and extends the learning objectives of the in-class lesson.
    • Preparing for the Next Lesson (PNL): Homework that introduces concepts in the next lesson and includes student self-assessment of readiness for the next lesson.
  • Instructor Notes: Elaborated instructional notes for every lesson that provide support for preparing and teaching the lesson. In addition to suggestions for teaching the lesson, each lesson’s Instructor Notes includes an introductory section detailing: lesson topics, primary context, Productive Persistence focus, level of productive struggle, prerequisite assumptions, learning goals, explicit connections to prior lessons, section to create ‘notes to self’, suggested timeline for teaching the lesson, and special notes.

Statway

  • Student lessons: Students handouts for each lesson that present the in-class tasks and highlights of the main ideas of the lesson. Instructors can download lesson handouts individually or as workbooks for the course. Each lesson handout includes a Take It Home section for homework.
  • Instructor Notes: Elaborated instructional notes for every lesson that provide support for preparing and teaching the lesson. In addition to suggestions for teaching the lesson, each lesson’s Instructor Notes includes an introductory section detailing: estimated time for the lesson, materials required, brief summary, learning goals, and introduction tips.
  • In addition, both curricula provide:
    • Alternative Lessons: Contextualized lessons (QW only) and Framework for Improving Teaching lessons are included as replacement options (see glossary entries).
    • Course timeline: The course timeline provides a brief overview of each lesson and shows the estimated time required for each. It is designed to help instructors plan their syllabus/timeline for the entire course.
    • Glossary: The glossary is included in the student books and provides definitions for important words and concepts in the books.
    • Learning Outcomes: A detailed Learning Outcomes document that shows the conceptual framework and learning goals for the course.
    • Materials checklists
    • Productive Persistence resources: The curricula include a plethora of guidelines, instructional routines, activities, and resources for how to introduce, demonstrate, and support growth in all the corresponding psycho-social factors. (see Productive Persistence glossary entry).

Driver Diagram

A tool that visually represents a Network’s working theory of practice improvement.

Faculty Facilitators

Faculty facilitators are a key to the strength and vibrancy of Pathways Networked Improvement Community. Facilitators are campus leaders, serving as a resource for their team members and a critical point of contact with the Carnegie Foundation. Each campus team appoints a faculty member to serve this role on campus and to join twice a term facilitator calls.

Faculty Support Program (FSP)

An AQT program designed to prepare and support new Pathways faculty before and during their first year of teaching Statway/Quantway.

Framework for Improving Teaching (FIT)

The Framework for Improving Teaching, developed by the AQT team, is a tool that supports faculty to improve their teaching using the Problem Cycle, an instructional routine for supporting students’ productive struggle. Selected Statway and Quantway lessons have been developed and tested that better provide structure for the Problem Cycle (called the FIT lessons). Additionally, a rubric to support faculty in using the lessons and the Problem Cycle is available to support instructional improvement in enacting the Problem Cycle.

IMathAS

The homework platform – developed by University of Washington’s David Lippman – used to build the online portion of the Quantway pathway. IMathAS was used as a stand alone tool from 2011-2014. It is now integrated into Canvas using LTI to allow a seamless student experience.: legacy platform for MyQW from 2011-2014

Instructional Kernel

The Pathways can only be assessed and improved reliably if all participating institutions adhere to common elements that we call the “Kernel”. The Kernel of both the Statway and the Quantway Pathways consist of the following three components:

  • Statistics and/or mathematics content component (includes learning outcomes, lesson materials, online homework platform, and assessments)
  • Productive Persistence, the student motivation and engagement component (includes classroom materials, instructional routines and practices, and surveys)
  • Data component (includes collecting, analyzing and reporting data on student demographics, student performance, and faculty background)While the Pathways are designed to allow for local contextualization, it is imperative that all institutions implement the instructional kernel. The effectiveness of the Pathways can only be assessed if comparable data is collected across institutions, which is possible only when the kernel is used uniformly.

Math Conceptual Knowledge (MCK)

The MCK is a measure of Pathways students’ incoming math conceptual understanding as assessed by a math background survey that all Pathways students take during their first week of class. Instructors receive reports on their students’ MCK scores.

Online Homework Platform

The online platform for students’ work outside the classroom used to complete homework, complete quizzes, respond to surveys, and (in some sections) complete the summative assessment. The online platform is built on a set of underlying technologies – Google Apps, Instructure’s Canvas, and iMathAS (for Quantway).

OLI (Online Learning Initiative)

The legacy online homework platform for Statway from 2011-2014.

Model for Improvement

model_for_improvementThis framework guides the change activity of an improvement community. Hypotheses for change are articulated using the three disciplining questions and changes are tested using an explicit methodology to learn whether they are actually improvements. The framework guides individual change efforts as well as structuring a larger community’s shared learning.

The Plan-Do-Study-Act (PDSA) cycle is a method for testing the changes you would like to introduce into your system as you seek improvement. At its core, it is about facilitating learning: your existing theory directs your testing cycles, but the new information you learn from testing informs your theory. The PDSA cycle can be used to structure small scale tests that are common in the early stages of an improvement effort and larger more complex tests as changes are scaled to multiple contexts. The disciplined introduction of changes and study of results allows you to build knowledge to advance towards your aim.

Networked Improvement Community (NIC)

A community committed to solving a common problem, using a common theory of action, and common assessments/measures in order to achieve efficacy with reliability at scale.

Northeast Resiliency Consortium (NRC)

A group of seven Pathways colleges located in the northeast part of the U.S. who have joined the Pathways as part of a Department of Labor TAACCCT grant. In particular these seven colleges are interested in customizing Quantway to support the health care, information technology, and environmental workforce sectors.

Plan-Do-Study-Act (PDSA)

An improvement science tool used for documenting a test of change. Involves testing a change idea by developing a plan (Plan), carrying out the plan (Do), observing and learning from the consequences (Study), and determining what modifications should be made to the test (Act).

Problem Cycle (PC)

An instructional routine that supports Pathways instructors to create opportunities for students to learn through productive struggle on rich problems and to engage in meaningful collaborative learning. It consists of four phases that can be used flexibly in lessons: Launching the Problem, Working the Problem, Discussing the Problem, and Conclusion.

Productive Persistence (PP)

Productive Persistence is defined as tenacity plus good strategies. To help more students successfully complete their academic goals, we want them to both persist in their studying and attendance (tenacity) and to do so efficiently and effectively (good strategies). The work in Productive Persistence has focused on identifying the critical psycho-social factors which impede student learning, and developing activities and instructional routines designed to enhance persistence and productivity.

Quantway (QW)

Quantway is an alternate and accelerated pathway that motivates and engages students through an innovative quantitative reasoning focus where students use mathematics and numerical reasoning to make sense of the world around them. Quantway is designed as two courses. Quantway 1 is the first term and fulfills the requirements for students’ developmental mathematics sequence. Quantway 2 is the second term that results in college mathematics credit.

Quantway Contextualized lessons

Educators and researchers from UCLA and the Northeast Resiliency Consortium (composed of Achieving the Dream, The Carnegie Foundation for the Advancement of Teaching, and seven Community Colleges in the Northeast) have developed a version of the curriculum that includes 12 modified lessons. Designed to meet the needs of specific workforce programs, the modified lessons are designed employing authentic contexts from one of three disciplines: Applied Health Care, Environmental Technologies, and Information Technology. They include situations with real-world challenges frequently faced in the discipline, enhanced language and literacy supports, and reinforcements for the language, operations, and non-math skills specific to the discipline. The modified lessons also include corresponding OCE/PNLs (both on paper and online).The new lessons available are:

  • Six lessons about applied healthcare: 1.4, 2.3, 2.4, 3.1, 3.7, 4.3
  • Four lessons about environmental science: 1.8, 1.9, 3.2, 4.7
  • Two lessons about information technology: 2.7, 4.2

Six Principles of Improvement

  1. Make the work problem-specific and user-centered
  2. Variation in performance is the core problem to address
  3. See the system that produces the current outcomes
  4. We cannot improve at scale what we cannot measure
  5. Anchor practice improvement in disciplined inquiry
  6. Accelerate improvements through networked communities

Starting Strong

The Starting Strong Package provides faculty the resources to proactively help students develop the mindsets and skills needed to succeed in a college setting. By implementing these activities in the first three to four weeks of class, you can establish a culture of high academic expectations and social assurance that prevent students from disengaging and withdrawing.

Statway (SW)

Statway is an alternate and accelerated pathway that motivates students through an innovative statistics curriculum, engaging them in relevant content and authentic contexts. Statway is designed as a one academic year course that allows students to simultaneously complete their developmental mathematics requirements and receive college mathematics credit in statistics. The course concentrates on statistical content with requisite algebraic concepts taught and applied in the context of statistics.

Staying Strong

The Staying Strong Package provides faculty the resources to proactively help students maintain the mindsets and skills needed to succeed in a college setting. By reinforcing and building on the expectations and norms that you established in the first month of the course, you can sustain a culture of high academic expectations and social assurance that prevent students from disengaging and withdrawing. According to recent research, there are five critical times when students come to know or perceive their faculty members’ theories of their students:

  • Initial messages about whether abilities are fixed or can be developed
  • During all learning opportunities
  • Feedback after poor performance
  • Messages and perceived attitudes about the importance of class participation and attendance
  • Encouragement for students to seek additional help

The Learning Opportunities

The Learning Opportunities are the principles of learning that undergird the curriculum and pedagogy of the Pathways. They were developed based on research on mathematics teaching and learning about the kinds of experiences are important for deep learning.

  • Productive Struggle: expending effort to make sense of mathematics to figure something out that is not immediately apparent
  • Explicit Connections: making explicit the mathematical relationships among concepts, procedures, ideas
  • Deliberate Practice: increasing variation and complexity of tasks over time

Translational Research

Translational research is engineering research that aims to make findings from basic science useful for practical applications that enhance human health and well-being. It is practiced in fields such as environmental and agricultural science, as well as the health, behavioral, and social sciences.

Triple Aims of Educational Improvement

  • Engaging education for all students
  • Effective in advancing learning
  • Efficient in its use of resources

Explore the Pathways

Our holistic approach includes a robust faculty professional development program including faculty mentors, instructor access to all the curriculum and assessment materials, rich data analytics for your faculty and institution, and a community of engaged faculty, administrators, advisors, and institutional researchers working collectively to continuously improve the Pathways program and promote student success. To become a part of this accelerated Networked Improvement Community, sign up as an Explorer.

Become an Explorer