Transition to College Mathematics and Statistics

Developed with funding from the National Science Foundation. Transition to College Mathematics and Statistics (TCMS) is a problem-based, inquiry-oriented, and technology-rich fourth-year high school mathematics course. It was developed to help ensure student success in college and careers in an increasingly technological, information-laden, and data-driven global society.

TCMS was specifically designed for the large number of students whose intended undergraduate programs of study do not require calculus—such as business; management; the environmental, information, life, health, and social sciences; and many teacher preparation programs.

The development of TCMS involved a collaborative effort among the author team, an international advisory board, and content and evaluation specialists.


According to the most recently available reports from the Conference Board of Mathematical Sciences (2010) and the National Center for Educational Statistics (2011), it is estimated that about 5.8% of undergraduate students nationwide are enrolled in calculus or advanced courses with calculus as a prerequisite. At community colleges, that number drops to 1.8%.

All too often, college-bound noncalculus-intending students are enrolled in an inappropriate precalculus course or opt out of mathematics their senior year. But research has repeatedly shown that students who are not enrolled in an appropriate mathematics course their senior year are much more likely to be placed in a remedial (non-credit bearing) course in college.

In some schools, students may elect to take a statistics or discrete mathematics course—courses that frequently do not provide the mathematical content to be successful on current college placement tests.

TCMS Scope and Sequence

The TCMS course consists of the eight units:

  • Unit 1   Interpreting Categorical Data
  • Unit 2   Functions Modeling Change
  • Unit 3   Counting Methods
  • Unit 4   Mathematics of Financial Decision-Making
  • Unit 5   Binomial Distributions and Statistical Inference
  • Unit 6   Informatics
  • Unit 7   Spatial Visualization and Representations
  • Unit 8   Mathematics of Democratic Decision-Making
TCMS Features

Key content and instructional features as outlined below have been informed by the latest research on student learning and recommendations from client disciplines on the focus of undergraduate non-calculus based mathematics and statistics courses.

  • Balanced Content Transition to College Mathematics and Statistics reviews and extends students' understanding of important and broadly useful concepts and methods from algebra and functions, statistics and probability, discrete mathematics, and geometry. These branches of mathematics are connected by CCSS mathematical practices and by mathematical habits of mind such as visual thinking, recursive thinking, searching for and explaining patterns, making and checking conjectures, exploiting use of multiple representations, providing convincing explanations, and a disposition towards strategic use of technological tools.
  • Flexibility TCMS consists of eight focused and coherent units, each of which is generally self-contained with attention to content prerequisites provided by "Just-in-Time" review tasks in lesson homework sets. The course has been organized to be as flexible as possible. The organization permits teachers to tailor courses that best meet the needs and interests of their students. For example, some teachers may choose to use the unit on Mathematics of Democratic Decision-Making as the second or third unit of the course to parallel state or national elections.
  • Mathematical Modeling TCMS emphasizes mathematical modeling including the processes of problem formulation, data collection, representation, interpretation, prediction, and simulation. The modeling perspective supports students in connecting mathematical content with important mathematical practices and habits of mind.
  • Technology Numeric, graphic, and symbolic manipulation capabilities such as those found in TCMS-Tools and on many graphing calculators are assumed and appropriately used throughout the course. TCMS-Tools is a suite of software tools that provide powerful aids to learning mathematics and solving mathematical problems. This use of technology permits the curriculum and instruction to emphasize multiple linked representations (verbal, numerical, graphical, and symbolic) and to focus on goals in which mathematical thinking and problem solving are central.
  • Active Learning The instructional materials promote active learning and teaching centered around collaborative investigations of problem situations followed by teacher-led whole-class summarizing activities that lead to analysis, abstraction, and further application of underlying mathematical ideas and principles. Students are actively engaged in exploring, conjecturing, verifying, generalizing, applying, proving, evaluating, and communicating mathematical ideas.
  • Multi-dimensional Assessment Comprehensive assessment of student understanding and progress through both curriculum-embedded formative assessment opportunities and summative assessment tasks support instruction and enable monitoring and evaluation of each student's performance in terms of mathematical practices, content, and dispositions.

A companion suite of mathematical and statistical software tools, called TCMS-Tools, is freely available for Transition to College Mathematics and Statistics.

Further Information

For further information about the Transition to College Mathematics and Statistics program and implementation support, contact


Transition to College Mathematics and Statistics is published by McGraw-Hill Education in both print and digital formats. For sample review copies or digital access, contact the publisher, your regional/local McGraw-Hill sales representative, or call 1-800-334-7344.

This material is based upon work supported, in part, by the National Science Foundation under grant no. DRL-1020312. Opinions expressed are those of the authors and not necessarily those of the Foundation.

Copyright 2019 Transition to College Mathematics and Statistics