Professional learning is important.
Schools have taught Algebraic Reasoning, the high school math course in Texas, since 2016. The Algebraic Reasoning textbook was adopted by the Texas State Board of Education in 2017. We’ve been working with teachers across the state since then and have learned a few things about what helps make teachers successful. In this brief online course, we guide you through some of the essential knowledge that successful Algebraic Reasoning teachers have.
Finite Differences and Common Ratios: Course Outline
If you’re teaching Algebraic Reasoning this year, or if you support teachers who are, you’ve come to the right place.
The cornerstone of the Algebraic Reasoning course, as it is defined in the TEKS for the course, is looking at functions through the lens of finite differences for polynomial functions and common ratios for exponential functions. If you’re using the Cosenza & Associates, LLC, book, Algebraic Reasoning, by Paul Gray, Jacqueline Weilmuenster, and Jennifer Hylemon, then this is particularly true.
The purpose of this short course of study is to provide an overview of what finite differences and common ratios are. Our goals are:
- Understand what finite differences are and how they relate to polynomial functions.
- Understand what common ratios are and how they relate to exponential functions.
- Learn about patterns in data sets that can be used to write polynomial or exponential functions.
If you taught Algebra 1, you may have used this approach. We used it in back in the 1990s and early 2000s in the TEXTEAMS institutes from the Charles A. Dana Center at the University of Texas at Austin and that legacy lingers in many districts in both their math leaders and curriculum documents. 20 years later, they are germane not only to this course, but also to Algebra 1 and Algebra 2 because they show how rates of change define linear, quadratic, and cubic functions and successive ratios define exponential functions.
The material used in this short course comes directly from the Algebraic Reasoning textbook. You are free to use this material both for professional learning purposes and with your students. It does not replace the textbook but our goal here is to help support all teachers who are teaching this course, particularly with the chaos in the 2020-2021 school year induced by COVID-19.
To navigate through this course, click or tap on the Topic title. Depending on your browser settings, you may need to right-click and select “Open in New Tab” in order for the topic to open in a new tab. Otherwise, just use the back-arrow to return to this page.
Learn more about the connections among arithmetic sequences, linear functions, and finite differences.
Learn more about the connections among geometric sequences, exponential functions, and common ratios.
Learn more about the connections between quadratic functions and finite differences.
Learn more about the connections between cubic functions and finite differences.
Why do finite differences work? How are they related to polynomial functions?