Chapter 2

Guiding Principles

Embracing Change

LinksImplementing the standards of Beyond Crossroads includes making a commitment to continuous improvement and professional development.  It may also involve changing actions and philosophies of faculty, departments, and institutions.  These changes may involve a relatively small, piecemeal change, or may be a large-scale, systemic change.  “Systemic change is a cyclical process in which the impact of change on all parts of the whole and their relationship to one another are taken into consideration…it is not so much a detailed prescription for improving education as a philosophy advocating reflecting, rethinking, and restructuring.”(1) Systemic change may be incremental (small operational changes), substantial (key functions are overhauled), or transformational (changing the entity irreversibly).(2

excellence has
become a moving
target. While basic
skills such as
reading, writing and
math will likely
remain at the core of
the curriculum, the
abilities built on this
foundation continue
to change with our
National School
Boards Foundation,
Education Leadership
Toolkit: Change and
Technology in
America’s Schools,
2005, p. 1

Indeed, the challenges of making and embracing change are numerous.  Beyond Crossroads advocates developing goals and objectives based on input from all stakeholders, so that all students can be successful learners of ambitious learning outcomes in mathematics.  A small, piecemeal change might be appropriate in a particular activity.  In another situation, large-scale systemic change might be necessary to completely define new goals, objectives, and strategies, and essentially start over. 

For some professionals, embracing and implementing change is natural or even intuitive.  They look for ways to improve and revise instructional strategies and curricula on a regular basis.  For them, this process is comfortable.   For others, any change can be challenging.  They feel most comfortable and confident when they can predict what will happen in their classroom and are familiar with student responses and difficulties.  Regardless of whether the process of change is natural or challenging, continuous improvement in mathematics instruction is essential to improving student learning. 

Embracing the challenge of continuously improving student learning is a component of professional growth.  To continue to grow professionally, faculty need to look inward and engage in a process that assesses their own teaching practice regularly.  Then they need to use that information to redesign goals, objectives, and student learning activities.  Implementing standards may involve stepping outside of one’s comfort zone, experimenting with new methods, and building confidence.  Embracing change and continuous improvement are reflective processes of planning, implementing, evaluating, and documenting, followed by redefining, implementing again, and refining the action in the future to improve student learning in mathematics. 

Basic Principles of Beyond Crossroads

Addressing the issues and challenges facing mathematics education in the first two years of college begins by adopting a set of basic principles.  These principles are the foundation upon which all of the Crossroads standards are built.  The Basic Principles outlined in Crossroads in Mathematics in 1995 have been revisited, updated, and expanded to form the philosophical underpinnings of Beyond Crossroads and are presented here in alphabetical order.

Assessment should support mathematics learning and instruction.  An effective assessment program includes assessment of learning outcomes at the class, course, and program levels of instruction.

The mathematical content, reasoning skills, and communication skills developed in mathematics courses should open doors for students to pursue future work in a variety of fields.

The mathematics education community must reach out to all students.  Active participation of all students in mathematics and the pursuit of mathematics-intensive careers by many are critical goals of our society.

Mathematics content and instruction should include opportunities for students to engage in inquiry, problem solving, modeling, and collaborative learning, using appropriate technology. Thoughtfully crafted, interactive lectures can highlight meaningful mathematics and inspire students to learn. 

Students learn through investigation.  Advances in neuroscience confirm that students’ active involvement in learning mathematics is important in the process of building understanding and modifying the structure of the mind.(3)

Quantitative literacy is “the capacity to identify, understand and engage in mathematics as well as make well-founded mathematical judgments about the role that mathematics plays in individual’s current and future life as  a constructive, concerned and reflective citizen.”(4)  Students’ insight and skills for solving quantitative problems in context should be developed throughout the entire college curricula.

Mathematics should be presented in the context of realistic, understandable, applied problems that help students develop an appreciation of the nature, history, and usefulness of the discipline.

Faculty are best prepared to design effective mathematics instructional strategies and assessment tools when they have an understanding of the results of pertinent educational research, particularly in cognitive science and learning theory, and when they use those results to make informed decisions about their teaching.

Technology continues to change the face of mathematics and affect the relative importance of various concepts and topics of the discipline.  Advancements in technology have changed not only how faculty teach, but also what is taught and when it is taught.  Using some of the many types of technologies can deepen students’ learning of mathematics and prepare them for the workplace.


To address the challenges facing mathematics education in the first two years of college, Beyond Crossroads focuses on implementation of the Crossroads in Mathematics Standards and advocates for informed decision-making.  Faculty need to embrace change and use a multi-faceted approach to instruction, not only to address a variety of student learning styles, but also to reveal the richness and interconnectedness of mathematics. Beyond Crossroads introduces five Implementation Standards in the next chapter, extending the Principles and Standards for Intellectual Development, Content, and Pedagogy presented in Crossroads in Mathematics. These standards, collectively, call for all faculty to challenge themselves professionally and to empower students quantitatively to be successful in their lives and careers.