# Transition to Quantitative Reasoning (TQR)

## Overview

This course provides a pathway for students who may not be interested in pursuing a STEM and/or math- intensive major and would typically not take math their senior year. These students traditionally complete the 2-year math graduation requirement and often take three years to do so.

## TQR At-A-Glance

The units of study build upon previous math concepts, such as functions, inequalities, and exponents, to provide opportunities for students to develop a greater perspective of the underlying structures of mathematics and how to connect mathematical topics. This enables students to continue to persevere through problem-solving and begin to develop their quantitative reasoning skills for success in college-level courses or the workplace. The course culminates with a relevant, in-depth unit about financial mathematics. The National Common Core Standards for Mathematical Practice are an integral part of each lesson, and specific high school Common Core State Standards are the focus of the mathematical content. Through a facilitative teaching approach, the lessons and tasks provide students with opportunities to solve challenging problems in which they gather, analyze, and evaluate information, work effectively in groups to make decisions using critical reasoning skills, as well as opportunities to communicate concisely through written and oral language.

• UNIT 1 | Team Building & Problem Solving
• UNIT 2 | Linear Functions
• UNIT 3 | Quadratic Functions
• UNIT 4 | Exponential Functions
• UNIT 5 | Logarithmic Functions
• UNIT 6 | Systems of Equations & Inequalities
• UNIT 7 | Absolute Value & Piecewise Functions
• UNIT 8 | Financial Mathematics

• Algebra I and Geometry or Integrated Math I and II with a passing grade
• May have also taken a third year of math (e.g. transition course, 2-year course, etc.

Intended for high school seniors who place into:

• Level 3 “Standard Met” on CAASPP
• Level 2 “Standard Nearly Met” on CAASPP

Students who typically enroll in this course:

• May not have planned on taking a senior-year math course.
• May have originally been placed into Algebra II or IM III.
• Could move beyond a “just-got-by” status from IM III or Intermediate Algebra II and improve their preparation to succeed in college-level mathematics.

• Students are immediately engaged in a Daily 2 and a Number Sense activity developed specifically for 4th-year math students.
• A task is launched using a variety of strategies, such as real-world context, video, or group activity. Students proceed in groups to complete the task while the teacher facilitates the learning by providing questions, giving structure to think time and group collaboration, and selecting and sequencing student work to be presented during the whole class discussion.
• Each task is debriefed by the entire class through various methods. Some examples include students presenting their work, making comparisons and connections with the work of others or questions from the teacher that ensure complete understanding.
• Students write and reflect about their reasoning and work, as well as the work of their peers, through exit slips or journal entries.

## QRAT & TQR Professional Learning Program

The professional learning program offers background and instruction in using facilitation as the classroom approach to helping seniors in high school think more critically, solve problems in different ways, and be able to apply their learning to real-world contexts. Teachers who attend will read about growth mindset and apply this notion in the classroom. Similarly, teachers will examine authentic student work, using formative assessment to guide their instruction, and understand how to differentiate their instruction to meet the needs of all learners.

### Learning Outcomes for Teachers

1. Demonstrate their new understanding of what comprises good teaching: moving teachers from lecture and direct instruction to a facilitative approach.
2. Use a variety of formative assessment tools and practices to plan and evaluate their instruction to better meet the needs of all learners in the classroom. Teachers will guide and support students to use standards for mathematical practice such as the ability to make sense of problems and persevere in solving them; reason abstractly and quantitatively; construct viable arguments and critique the reasoning of others; model with mathematics; use appropriate tools strategically; attend to precision; look for and make use of structure; look for and express regularity in repeated reasoning.
3. Use a variety of facilitative teaching and questioning strategies to provide opportunities for students to access, investigate, and reason through the mathematical content of the TQR/QRAT courses.
4. Learn the value of engaging with teachers in the professional learning program and in their own schools to discuss and practice a growth mindset.
5. Demonstrate the ability to gather, evaluate, and apply important and useful contextual qualitative and quantitative data as a means for understanding the students’ academic abilities in math with a greater foundation of conceptual understanding. Hence, students taught by teachers in this professional learning program will be able to solve conceptual and pragmatic mathematics questions in the 12th-grade course.

To accommodate teachers' busy schedules, the Professional Learning Program is offered twice a year: once in the summer, over the course of a week, and once in the winter, over the course of several months.

## Continuing Education Units (CEUs)

Continuing Education Units are available to teachers upon successful completion of the TQR/QRAT Professional Learning Program. Registration and payment must be received no later than two weeks following the last class meeting.

Complete this Registration Agreement and follow the instructions listed.

The cost is \$65.00 for 2 units.

Liz Arellanes
Sacramento State College of Continuing Education
(916) 278-6249
arellanl@csus.edu

## Other CSU Mathematics Bridge Courses

In addition to Quantitative Reasoning with Advanced Math Topics (QRAT), there are other mathematics courses and projects within the CSU that focus on supporting mathematics and quantitative reasoning readiness among K-12, CSU, and community college educators.

#### The Projects in the CSU Focus On:

• Principles in preparing teachers for 12th-grade mathematics and/or quantitative reasoning
• Content and pedagogical practices
• Topics in mathematics and quantitative reasoning that develop and address K-12, community college, and CSU requirements