Executive Summary
         Beyond Crossroads

Dear Colleague,
The American Mathematical Association of Two-Year Colleges (AMATYC) is proud to present Beyond Crossroads: Implementing Mathematics Standards in the First Two Years of College. This second standards document from AMATYC is intended to stimulate faculty, departments, and institutions to examine, assess, and improve every component of mathematics education in the first two years of college. AMATYC is committed to promoting improvement in mathematics education and has collaborated with its members, its affiliates, and other national organizations on the development of Beyond Crossroads. We invite you to read this executive summary, to examine Beyond Crossroads, and to view the electronic resources that extend and enrich this document.

Susan S. Wood, Project Director, Virginia Community College System (VA)
Sadie C. Bragg, Project Co-Director, Borough of Manhattan Community College (NY)
Philip H. Mahler, Project Co-Director, Middlesex Community College (MA)
Richelle M. (Rikki) Blair, Editor, Lakeland Community College (OH)

                                                                    November 2006

Background

As part of its mission to promote and improve mathematics education in two-year colleges, AMATYC published its first standards document, Crossroads in Mathematics: Standards for Introductory College Mathematics, in 1995. This was the first publication to communicate principles and standards for the teaching and learning of mathematics in two-year colleges. It emphasized desired modes of student thinking and provided guidelines for selecting content and instructional strategies. These standards were widely accepted and are as important today as they were in 1995.

With the 2006 publication of Beyond Crossroads, AMATYC reaffirms and builds upon the principles and standards set forth in 1995. In its five Implementation Standards, Beyond Crossroads advocates for informed decision-making and outlines expectations, responsibilities, recommendations, and action items for students, faculty, departments, and institutions. Beyond Crossroads is a call for continuous improvement in content, pedagogy, and professionalism.

Changing Environments

Informed citizens in today’s global society need to be quantitatively literate. Technological advances continue to influence both the mathematics that is used in the workplace and the career opportunities available to college students. Between now and 2012, the number of high-skilled jobs as a percentage of the workforce is expected to increase and the number of unskilled jobs is expected to decrease.

Further, the environment for learning and teaching mathematics in higher education continues to experience significant changes. Advances in technology affect the mathematics that should be taught and the pedagogy that should be used to teach it. These changes create new challenges for faculty development, recruitment, and preparation of replacement faculty.

Faculty, with support from their institutions, shoulder the day-to-day responsibility for responding to this changing environment. They must continue to grow in their mathematical and pedagogical knowledge, contribute to their profession, address the learning needs of their diverse students, and prepare quantitatively literate citizens for the future. Creating a learning environment that responds to our ever-changing technological society requires the active involvement of every faculty member, department, and institution.

Basic Principles and Implementation Standards

Mathematics courses taken during the first two years of college offer students an opportunity to acquire mathematical to use technology as a learning tool, and to improve their ability to solve problems. It is important that students develop a greater appreciation for mathematics and an increased confidence to use mathematics. Improving the undergraduate mathematical experience and increasing the number of graduates in science, technology, engineering, and mathematics programs is widely accepted as essential to our nation’s ongoing vitality.

Basic Principles. The foundation of all the standards presented in Beyond Crossroads:

• Assessment The assessment of student learning in mathematics should be a fundamental tool for the improvement of instruction and student learning.
• Broadening Mathematics courses and programs in the first two years of college should broaden students’ options in educational and career choices.
• Equity and Access All students should have equitable access to high-quality, challenging, effective mathematics instruction and support services.
• Innovation Mathematics programs should be thoughtfully constructed to approach content and instruction with appropriate use of traditional and innovative methods.
• Inquiry Effective mathematics instruction should require students to be active participants.
• Quantitiative Literacy Quantitative literacy should be integrated throughout the mathematics program and the college curricula.
• Relevance The mathematics that students study should be meaningful and foster their appreciation of the discipline.
• Research into Practice The practice of mathematics teaching should be guided by research on teaching and learning.
• Technology Technology should be integral to the teaching and learning of mathematics.

Implementation Standards

Beyond Crossroads introduces five Implementation Standards that extend the Standards for Intellectual Development, Content, and Pedagogy presented in the 1995 Crossroads in Mathematics. These five standards, with accompanying implementation recommendations and action items, are intended to guide the decision making of professionals in selecting and putting strategies into practice to meet the challenges of improving student learning in mathematics.

Implementation Standards. Guidelines for faculty, departments, and institutions for improving mathematics education: Student Learning and the Learning Environment Mathematics faculty and their institutions will create an environment that optimizes the learning of mathematics for all students. Assessment of Student Learning Mathematics faculty will use the results from the ongoing assessment of student learning of mathematics to improve curricula, materials, and teaching methods. Curriculum and Program Development Mathematics departments will develop, implement, evaluate, assess, and revise courses, course sequences, and programs to help students attain a higher level of quantitative literacy and achieve their academic and career goals. Instruction Mathematics faculty will use a variety of instructional strategies that reflect the results of research to enhance student learning. Professionalism Institutions will hire qualified mathematics faculty, and these faculty will engage in ongoing professional development and service.

Embracing Change and Continuous Improvement

Implementing the standards outlined in Beyond Crossroads includes making a commitment to continuous improvement in instruction, student learning, and professional development. Improvement may involve changing actions and philosophies of faculty, departments, and institutions. The Beyond Crossroads Implementation Cycle is a process for continuous improvement used to assess and improve any activity or project. AMATYC advocates the use of the principles and standards of Beyond Crossroads for guiding discussions and decision making about the direction of change in mathematics education.

Embracing the call to continuous improvement is a component of professional growth. Indeed, the challenges of making and embracing change are numerous. For some professionals, implementing change is energizing. For others, any change can be challenging. Embracing change in mathematics education should be a thoughtful process of planning, implementing, evaluating, and documenting, followed by redefining, implementing again, and improving the action(s) in the future to enhance student learning in mathematics. Continuous improvement in mathematics instruction is essential to improving student learning.

Moving from Vision to Reality

Beyond Crossroads sets forth ambitious goals and outlines key implementation roles for institutions, departments, faculty, students, and other stakeholders to reach these goals. Mathematics faculty should take the lead but will need the active cooperation of the entire mathematics community to implement changes to improve their teaching, student outcomes, and the mathematical abilities of future citizens. To move from vision to reality, faculty, departments, institutions, and students need to respond to each of their respective accountabilities:

Faculty

• accept responsibility for continuing to learn about mathematics and effective mathematics instruction
• use a multifaceted approach to instruction, not only to address a variety of learning styles, but also to reveal the richness and interconnectedness of mathematics
• determine desirable quantitative literacy outcomes for each mathematics course and promote quantitative literacy as an appropriate general education outcome.

Mathematics Departments

• incorporate workplace skills into all programs
• seek input from business and industry and require students to solve realistic problems with technology available in the workplace
• place K-12 teacher recruitment and preparation as high priorities of the department and cooperate with four-year institutions to provide supervised field experiences for future teachers.

Higher Education Institutions

• recruit and hire qualified mathematics faculty and then provide them with mentoring and ongoing professional development
• promote quantitative literacy across the curriculum and in general education courses
• cooperate with business and industry to collect information about the skills and knowledge that their employees need and use this information when assessing courses and programs.

Students

• accept responsibility for their learning and seek the resources that can help them attain their academic goals
• take their mathematics courses early in their program and set high mathematical expectations for themselves
• examine mathematical concepts from multiple perspectives and employ a variety of problem-solving strategies
• communicate mathematics, both orally and in writing.

Standards for Intellectual Development, Content, and Pedagogy

The 1995 Crossroads in Mathematics presented the three sets of standards listed below. Putting all these standards into practice has a greater effect on the improvement of student learning and professionalism of faculty than implementing any single standard in isolation.

Standards for Intellectual Development. Guidelines for desired modes of student thinking and goals for student outcomes:

• Problem solving
• Modeling
• Reasoning
• Connecting with other disciplines
• Communicating
• Using technology
• Developing mathematical power
• Linking multiple representations

Standards for Content. Guidelines for the selection of content in courses and programs:

• Number sense
• Symbolism and algebra
• Geometry and measurement
• Function sense
• Continuous and discrete models
• Data analysis, statistics, and probability
• Deductive proof

Standards for Pedagogy. Guidelines for instructional strategies in active student learning:

• Teaching with technology
• Active and interactive learning
• Making connections
• Using multiple strategies
• Experiencing mathematics

Roles of Stakeholders

The complex issues surrounding learning, assessment, curriculum, teaching, and professionalism can only be fully addressed through actions of all stakeholders, including leaders of K-16 education, business and industry, publishers, government, and society. Thoughtful collaboration among the stakeholders can produce greater results than any action taken alone. Faculty and institutions cannot accomplish their goals for improving mathematics education alone-the principles and standards in Beyond Crossroads are best served when two-year college mathematics faculty and institutionscollaborate with the following entities:

• the broader mathematics community to build public understanding of and support for improvements in mathematics education
• K-12 school districts and four-year institutions to align exit and entrance requirements, instructional strategies, and curricula
• publishers and developers of instructional materials to create standards-based instructional resources
• faculty in other disciplines to infuse mathematics across the curriculum
• business and industry so that desired employee skills and strategies for achieving them are outlined and incorporated into mathematics courses and programs
• professional societies, government agencies, and educational institutions to build consensus and provide guidance to practitioners.

Electronic Resources

The following electronic resources, available to AMATYC members at http://bc.amatyc.org, extend and enhance the messages of Beyond Crossroads.

Beyond Crossroads Live! is a Web-enhanced version of the Beyond Crossroads document featuring the following:

• links to Web sites referenced in the written document
• a searchable index with hyperlinks to relevant text references
• printable PDF versions of Beyond Crossroads
• a portal for the other Beyond Crossroads electronic resources.

Beyond Crossroads Outreach Kit is a set of presentation materials communicating the messages of Beyond Crossroads to a variety of audiences using a variety of formats. The outreach kit will facilitate the following:

• provide an assortment of easy-to-use presentation materials
• address the five Implementation Standards and a history of Beyond Crossroads, among other topics
• include adaptable presentation slides and a speaker's guide.

Beyond Crossroads Electronic Resources on Quantitative Literacy and Assessment will provide additional materials in a variety of formats that extend and enhance the messages of Beyond Crossroads. Components of these electronic resources include presentation materials that align with the written document.

The preparation of this document was assisted by contributions from Pearson Addison-Wesley and Pearson Prentice-Hall. Partial funding for the development of Beyond Crossroads was provided by the ExxonMobil Foundation. Planning for Beyond Crossroads' electronic resources was assisted by a grant from the National Science Foundation (DUE 0410842).

© 2006 American Mathematical Association of Two-Year Colleges.