# Core objective #2: Quantitative reasoning

**Objective:** Fundamental practice

**Brief description of learning objective: ***Students will be able to apply quantitative reasoning and mathematical analysis methodologies to understand and solve problems*.

## Standards or requirements for verification

**Only Core Math courses may be verified for CO2. These should be lower-division (100-200 level) general education courses, for three or more units each.**

**NOTE:** Core Objectives 1-3 will not be satisfied in the same manner as subsequent Core Objectives. These three objectives are not satisfied by a single course. Instead, a foundation for these objectives is built in Core Writing and Core Math requirements, and developed in other General Education courses. A discipline-specific competency should then be developed within the major and integrated into the Core Capstone course. These objectives should be assessed in the Core Writing, Core Math, and Core Capstone courses.

The foundation for this objective is built by the Core Math requirement and should be developed by courses that require Core Math as a prerequisite, beginning with the Core Natural Sciences requirement. If possible, this objective should also be integrated into the Core Capstone course.

This objective aims to ensure that students learn to think critically about mathematical models for relationships between different quantities and use those models effectively and accurately to solve problems and reach sound conclusions about them. Students should be able to comprehend, work with, and apply general mathematical techniques and models to different situations, not just plug problem-specific data into a given formula.

These skills will enable students to effectively use and interpret data, formulas, and graphs in the workplace, in the news media, and when making personal finance, health, and other types of decisions as informed citizens.

Courses that build a foundation for this objective may examine various types of mathematical techniques (including those related to uncertainty, probability, random events, and statistics) provided they include meaningful study of the methods, not simply applications of certain mathematical or statistical methods to another discipline. These courses should have assignments and exams that include significant components of several of the following activities:

- manipulations with algebraic formulas
- critical thinking about graphical representation of data
- practice assigning variables to quantities in order to describe relationships between the quantities
- application of mathematical or statistical models to different real-world contexts

The courses should ensure that students are synthesizing the material, understanding key concepts, and making abstract connections through testing of a comprehensive nature.

Courses building a foundation in this Core Objective will meet the expectations for the Core Mathematics requirement and should:

- include the Core Objective, together with its brief description, on the course syllabus in its original form
- include three or more student learning outcomes addressing this Core Objective on the course syllabus, along with other student learning outcomes appropriate to the course
- identify in the course syllabus the teaching techniques and student experiences that will help students acquire the competencies described in the Core Objective
- assess whether students have acquired the competency described in the student learning outcomes and use methods for collecting and analyzing data that can be reported to the Core Curriculum Board

Capstone courses that integrate CO2 should emphasize models appropriate to the discipline that are grounded in sound mathematical techniques, or apply appropriate statistical methods in testing hypotheses against observed data.

## Suggested student learning outcomes and assessment methods

Faculty may incorporate one or more of the examples from this list or propose their own student learning outcomes and methods of assessing the objective.

Students will be able to apply quantitative reasoning and mathematical analysis methodologies to understand and solve problems.

Courses *building* CO2 might feature outcomes like this:

Students will be able to:

- apply general mathematical models to solve a variety of problems
- solve problems and correctly arrive at meaningful conclusions regarding their answers
- manipulate equations and formulas in order to solve for the desired variable
- interpret given information correctly, determine which mathematical model best describes the data, and apply the model correctly
- correctly apply mathematical language and notation to explain the reasoning underlying their conclusions when solving problems using mathematical or statistical techniques.

Capstone courses *integrating* CO2 might feature outcomes like this:

Students will be able to:

- apply mathematical tools and methods to formulate relationships between different quantities, in fields such as the physical and social sciences
- apply appropriate statistical methods to test hypotheses against observed data
- assign variables to quantities and formulate mathematically sound relationships between them to build mathematical models in a real world problem
- after using a mathematical or statistical model for a real-world situation, interpret numerical answers derived from a mathematical or statistical model of a real-world situation to reach sound conclusions.

All courses that are verified as satisfying a Core Objective will be assessed on a regular basis to determine how well students are learning the knowledge and skills described in the objective. Instructors are expected to develop ways of directly measuring student learning (through evaluating the work students produce in the course) and to report these measurements to the Core Board upon request.

Direct assessment of student mastery of the stated outcomes should be measured primarily through exams. For assessment purposes, item analysis on selected exam questions (sufficiently similar across the different sections) should be collected and analyzed. In addition, longitudinal analysis of success of students applying more foundational quantitative skills in more advanced courses should be performed where appropriate.