Transition to College Mathematics and Statistics
Mathematical Modeling

Transition to College Mathematics and Statistics is designed so that students engage in the modeling process. Students also engage in the mathematical behaviors identified in the Common Core State Standards for Mathematics (CCSS) Mathematical Practices and other mathematical habits of mind as the primary vehicle for learning the mathematics and statistics elaborated in the CCSS content standards.

Even prior to the era of the Common Core State Standards for Mathematics, many mathematics educators have encouraged learning mathematics through modeling of problems. Problems that engage students in mathematical modeling have the following features and benefits (Dewey, 1929, 195; Hiebert, Carpenter, Fennema, Fuson, Human, Murray, Olivier, & Wearne, 1996):

  • Problems are identified in context.
  • Problems are studied through active engagement
  • Conclusions are reached as problems are (at least partially) resolved.
  • The benefits lie not only in the solutions to the problems, but the new relationships that are discovered.

Process of Mathematical Modeling: Mathematical modeling in the CCSS for high school mathematics is a conceptual category and is also one of eight mathematical practices. The diagram below describes the modeling process and the mathematical practices engaged in during each phase of the process. Connecting Mathematical Practices (MP) and Content Standards (CS) MP1 and MP4 are the overarching focal points of the entire process.

Instructional Model

The manner in which students encounter mathematical ideas can contribute significantly to the quality of their learning and the depth of their understanding. Transition to College Mathematics and Statistics is designed so that students are engaged in the mathematical behaviors identified in the Common Core State Standards Mathematical Practices as the primary vehicle for learning mathematics and statistics. Each unit includes multi-day lessons centered on big ideas. Each lesson includes two to four focused mathematical investigations that engage students in a four-phase cycle of classroom activities—Launch, Explore, Share and Summarize, and Self-Assessment. This cycle is designed to engage students in investigating and making sense of problem situations, in constructing important mathematical concepts and methods, in generalizing and proving mathematical relationships, and in communicating, both orally and in writing, their thinking and the results of their efforts. Most classroom activities are designed to be completed by students working collaboratively in groups of two to four students. See the front matter of the TCMS Teacher's Guide for more detail on the instructional model designed into the curriculum materials. Also, see the available video clips from a TCMS field-test classroom of students working on a modular arithmetic investigation.

Meeting Students' Needs and Interests

Transition to College Mathematics and Statistics is flexibly designed to meet students' present and future needs. In addition to the core sequence as presented in the text, selected units can be organized into courses that focus on either statistics or discrete mathematics while continuing to strengthen students' quantitative and algebraic fluency essential for college readiness or career apprenticeships. See recommended Statistics and Algebra Pathway and Discrete Mathematics and Algebra Pathway.

Teaching Resources

The TCMS Teacher's Guide has been developed to support teachers in facilitating classrooms where students consistently engage in authentic, cognitively demanding problems. The Teacher's Guide includes each student page and a facing page containing problem solutions and helpful teaching notes.

Features include:

  • unit and lesson overviews and objectives;
  • unit planning guides with suggested assignments;
  • notes related to instruction: possible student approaches, possible incorrect or partial thinking, mathematical practices, technology, and differentiation embedded at point of use;
  • sample student and teacher discourse scenarios for whole-class lesson launches and investigation summarizing discussions; and
  • links to additional online printable resources such as student activity and unit summary masters, technology tips, lesson quizzes, unit tests, take-home assessments, projects, and college-readiness assessments.

See the front matter of the TCMS Teacher's Guide for an explanation of the formative and summative assessment program.

Supplemental Resources

College Readiness Assessment Sets: In addition to continuing use of important competencies in the student text, you will find College Readiness Assessment (CRA) sets in the unit resource masters for each lesson in the course. The exercises will help students build skills in strategic areas. The exercises are in multiple-choice format as is commonly found on mathematics placement tests.

The 10 exercises in the CRA sets are drawn from 10 general areas. The exercises are in the same order in each set. In the Unit Resource Masters, you will find a record sheet that students can use to keep track of their progress and performance on the CRA sets. This record sheet shows the 10 categories. If students are consistently missing the same numbered items in these sets, you may wish to suggest extra work on similar exercises.

To help students develop test-taking strategies, discuss how items are often written in novel ways, but still assess mathematical understandings they have or should be able to reason about. TCMS students should develop or refine the habit of reasoning numerically, graphically, and algebraically. This skill, as well as general test-taking strategies such as estimating and eliminator some multiple-choice options, should be periodically discussed. Answers to the CRA sets for each unit are found at the end of each lesson in the Teacher's Guide. An online version of the CRA sets is available on ConnectED.

Student Help: Resources have been developed to assist students with homework. Hints, scaffolding, selected answers, and occasional full solutions are provided for student use.

Professional Development Providers: For onsite professional development facilitated by experienced TCMS facilitators, contact your McGraw-Hill sales representative or any of the facilitators listed here.

Developing a Collaborative Classroom: To assist students in learning how to collaborate effectively, you may wish to engage them in some skits as outlined in Dysfunctional Group Skits.