About the Cover

The image is from https://www.britannica.com/science/algebra/Islamic-contributions#ref762052 and shows the homeland of Persian mathematician Muhammad Al-Khwarizmi, among other ancient mathematicians in the area.  Muhammad Al-Khwarizmi wrote Al-Kitab al-mukhtasar fi hisab al-jabr wa’al muqabalah (The Compendious Book on Calculation by Completion and Balancing) in 825 AD.  This book introduced methods for solving equations.

Overview

This text was originally created to use as an OER text/workbook for MATH 1600 Informal Mathematical Modeling at Fitchburg State University by adapting a combination of relevant existing OER materials as well as some original material from the project lead and colleagues who have taught this course over the years.  MATH 1600 is an algebra, functions, and modeling course designed for future K-8 educators; The resulting text will serve as an open resource for any such course at other universities.  The text aims to use a universal language with clarity of expression that is reader friendly for all.  It also includes word problems and activities (in various formats) that strive to be relevant to a variety of cultures and genders.  Mathematical concepts are defined in multiple ways and extra explanations and scaffolding are included.  A variety of examples and activities are incorporated to accommodate different learning types.  The text includes corresponding mathematics standards from both the National Council of Teachers of Mathematics (NCTM) and the Massachusetts Mathematics Curriculum Framework which is based on the Common Core State Standards (CCSS).  Users should cross check these with their own state standards as they see fit.  The text is meant to be used as a workbook for students to fill in as corresponding concepts are covered in class.  It currently includes material on algebra, patterns, functions (properties, linear and quadratic) and statistics as they relate to elementary and middle school mathematics, and beyond.  It is a work in progress and instructors are encouraged to adapt it to their needs.  Additions, edits and updates will be made in the future.  Hopefully, this open textbook will provide a resource for other such courses in Massachusetts and eventually across the United States.

What is an OER textbook?

OER stands for Open Educational Resource and OER textbooks are books that are publicly available online free of charge (and at low-cost in print).  They also have an open license that allows others to reuse it, and in some cases revise it. This book has a Creative Commons Attribution license and allows reuse, revision, and redistribution so long as the original creator is attributed (please see the licensing information for this book for more information). In addition to saving students money, an OER textbook can be revised to be better contextualized to one’s own teaching.

Format and How to Use this Book

Each chapter begins with National Council of Teachers of Mathematics (NCTM) mathematics standards and/or Massachusetts Mathematics Curriculum Frameworks standards that correspond to the material in that chapter.  Concepts are introduced and/or reinforced through  activities and examples (without solutions) which are meant to be worked through together as a class, in groups or individually and then discussed.  Questions are posed throughout the text as points for discussion.  Space is left after examples, activities and questions to enable students to fill in the blanks as in a workbook.  At the end of each section there are exercises that may be worked on in class and/or used for homework.  Some chapters include extra activities and/or exercises at the end. Pre-class work activities are meant to be completed before the material is covered in class and serve as points for discussion in class.

Motivation

To create a single OER text appropriate for MATH 1600.  The previous text used was not an OER and is out of print.  It also required supplemental material to be used for this course.  Other texts designed for future K-8 educators attempt to cover number sense, geometry, algebra and statistics all in one book and do not go into enough depth on the algebra, functions and modeling to be used for this course.  In the past a traditional college algebra textbook was used for this class but these do not have the pedagogical connections for future educators.  Furthermore, these text options are expensive.  This text is not only free but was also created with a DEI (Diversity, Equity and Inclusion) lens.  In particular, scaffolding is included in many  examples and multiple representations of certain concepts is addressed to accommodate various learning types.  The terminology used aims to be clear for neurodiverse learners and avoids slang that some cultures may not understand. Videos and images are provided to enhance understanding and cultural backgrounds were considered when creating scenarios for applications.

Audience

This text will be used in MATH 1600 Informal Mathematical Modeling at Fitchburg State University.  MATH 1600 is an introductory level algebra, functions and modeling course designed for future K-8 educators.  The resulting text will serve as an open resource for any such course at other universities.

Learning Outcomes

• Significantly deepen each student’s knowledge of and ability to work with algebra, patterns and functions, their multiple representations and explain how these concepts are used in a variety of problem solving situations.
• Enable students to solve problems using various methods and to understand and appreciate the equivalence of the different methods.
• Improve each student’s analytical and problem solving skills.
• Enable students to think logically and precisely and to successfully present their work clearly in written and oral form with accurate mathematical language.
• Give each student the confidence and competence to communicate and reason mathematically.
• Help each student obtain a deep understanding of the fundamental mathematics that they will one day teach to others.
• Demonstrate a math curriculum that is diverse, inclusive and accessible to all and help students to develop such material.