Foundations of Mathematical Reasoning

The NMP Implementation Guide
Appendix I: Foundations of Mathematical Reasoning
This is a quantitative literacy-based course designed to provide students with the skills and
conceptual understanding to be successful in a college-level statistics or quantitative literacy course.
It will also provide the foundation for students going into the NMP STEM Prep Algebraic Reasoning
Prerequisite Skills and Placement
For the first implementation of Foundations of Mathematical Reasoning in Fall 2013, placement will
be based on the college’s requirements for enrollment in Beginning Algebra or the local equivalent.
This allows for students who have previously failed Beginning Algebra, new students who place
directly into the course, or students who have successfully completed a pre-requisite to Beginning
Algebra. [Note: The State Implementation Team will discuss whether any other common placement
standards should be set.]
The curricular materials are designed based on the assumption that students will be able to
Demonstrate procedural fluency with real-number arithmetic operations (e.g., basic operations,
comparing, contrasting), use arithmetic operations to represent real-world scenarios, and use
those operations to solve problems.
Use graphical representations on a real number line to demonstrate fluency when ordering
numbers, representing operations (e.g., addition, subtraction, doubling, halving), and
representing fractions and decimals.
Demonstrate a basic understanding and familiarity with fractions, decimals, and percentages.
Procedural competency for representing each number form and moving from one to the other is
desired upon enrollment in this course, but out-of-class materials may be needed to review basic
concepts and build basic skills.
Course Structure and Contact Hours
The course is designed for 4 contact hours, i.e., 4 contact hours per week in a semester system or an
equivalent number of contact hours in a quarter system. Colleges may choose to offer this as a 4credit course or as a combination of course credits and lab credits. In the latter case, it is important
to note that the curriculum is not designed for a separate “lab time” from an instructional point of
view. For example, if the course is scheduled as a 3-credit course with a 1-hour lab, the instructor will
use all 4 contact hours for classroom instruction and activities.
Since this course is a developmental math course, colleges may choose how to number it. With the
exception of Intermediate Algebra, developmental math courses do not currently have standard
outcomes and course numbers in the Academic Course Guide Manual that colleges must use.
Each lesson in the course will be designed to implement the design principles of active learning as
described in the NMP Curriculum Design Standards. All lessons will expect students to “do”
mathematics and statistics, such as analyze data, construct hypotheses, solve problems, reflect on
their work, and make connections among and between mathematical concepts.
Foundations of Mathematical Reasoning is organized around big mathematical and statistical ideas
and concepts. A primary goal of the curriculum is the development of conceptual understanding
and building multiple strategies for solving problems (see the NMP Curriculum Design Standards)
supporting students to make connections between concepts and apply previously learned material
The Charles A. Dana Center at
The University of Texas at Austin
October 2013
Page 61
The NMP Implementation Guide
to new contexts. The course will prepare students for success in future courses and help them
develop skills for the workplace and as productive citizens.
The curricular materials are offered through on online platform supported by McGraw-Hill. There is a
student fee for the materials. There is no need for an additional text or materials. Contact the Dana
Center for information on how to get access to the materials.
Course Description
This course surveys a variety of mathematical topics needed to prepare students for college level
statistics or quantitative reasoning or for algebra-based courses. Topics include: numeracy with an
emphasis on estimation and fluency with large numbers; evaluating expressions and formulas; rates,
ratios, and proportions; percentages; solving equations; linear models; data interpretations including
graphs and tables; verbal, algebraic and graphical representations of functions; exponential models.
This course is not for college-level credit. Students in this course are required to take a co-requisite
student success course.
The Charles A. Dana Center at
The University of Texas at Austin
October 2013
Page 62