Contextualized Mathematics: Teaching and Learning Math with Contextualized Mathematics

Contextualized Mathematics

Teaching and Learning Math with Contextualized Mathematics

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Copyright © 2022 Hector R. Valenzuela, Ph.D.

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ACKNOWLEDGEMENTS

This book is dedicated to my wonderful and amazing kids Cooper, Ellie, and Sophie. I also want to dedicate this book to my loving parents Julia Valenzuela and Martimiano Valenzuela. This dedication extends to my siblings Maria, Jesse, Julio, Lorenzo, Jose, Martha, and Juan. My kids, parents, and family are all an inspiration and foundation for my success, eternal joy, and infinite ∞ happiness.

Dr. Hector Valenzuela, Ph.D.

TABLE OF CONTENTS

Acknowledgements

1. Introduction

2. Constructing Math Knowledge

3. Research on Learning Mathematics

4. College Math Education

5. Linking Mathematics and Learning

6. Contextualized Mathematics Teaching

7. A New Mathematics Curriculum

8. Recommendations and Applications

References

Chapter One

INTRODUCTION

I DISTINCTLY REMEMBER in grade school how easy mathematics was for me, and yet how challenging it was for many of the other children in the same classroom. The same scenario would also appear both in my junior high years, and then off to my high school years where I distinctly remember not even having to study math. Studying at different universities left me with the same impression of why some students found math easy and most found it increasingly challenging. As I went on to graduate school and studied higher mathematics, I then began to see a pattern in myself. As the math became increasingly theoretical in graduate school, the less I became aware of its implications and applications. I then realized how difficult it was to learn math at a high level that was solely based on theory. This was the theme played out before my eyes as I worked my way through graduate school to get a graduate level degree in mathematics.

It was clear that there was something missing in math curriculum. I could see that when math curriculum was theoretical and general in nature, students had a difficult time learning the math concepts. When math was more applied and structured to real life, students became more interested in math and had a higher interest in solving the math problems. I particularly remember finishing graduate school, thinking I really needed to be in an industry that uses math, so I could see how math works in real life. After graduate school, I then went on to work for a large insurance company where I worked in their management information systems department just north of San Francisco, California. Having worked for this insurance company for 15 years, I saw how math was used in a business and application setting. During my tenure in the insurance industry, I started teaching math at a junior college in central California. It was then that I realized I needed to shift my focus and begin a journey that would lead me to teach and research contextualized mathematics at the college and university levels.

At that point in my career, I could see that there was certainly a need to begin to reflect and think about how math could be applied and used in a new type of math curriculum. I was fortunate enough to do research at a college in Kirkland, Washington i.e., Lake Washington Institute of Technology. My work centered around the research and development of contextualized math curriculum that was applied within technical fields. The key for my research centered on developing math that students could apply in their technical fields. I then went on to research other applied math curricula at other colleges in the state of Washington. My research, my teaching experience, and my love of teaching and learning mathematics form the impetus for this book.

There is a definite need for a new type of math curriculum. From a broader perspective, students are entering colleges and universities with a skill deficiency in mathematics which affects their ability to complete their college math requirements successfully. College students are struggling to complete required college mathematics standards after they enter college (Albritton, Gallard, & Morgan, 2010; Bonham & Boylan, 2011; Hern, 2012).

The reason students need to complete their college and math courses is that getting their degree requires them to successfully complete these specific courses. Furthermore, students who have previously taken face-to-face math classes are now enrolling in online math courses with the use of new technologies, which investigators should consider when researching student completion rates (Ashby, Sadera, & McNary, 2011; Jones & Long, 2013). According to research by the Community College Research Center of online education within the state of Washington and the state of Virginia, the completion rate for online remedial math was 19% lower than completion rates in face-to-face classes (Crawford & Persaud, 2013). Furthermore, in 2008, three-fourths of students who started remedial math in college never finished their remedial math successfully (George, 2010).

One of the challenges college students face is the linking of math concepts, organizing mathematical ideas, and solving math problems to complete their college remedial math and college math courses successfully (Albritton et al., 2010; Bonham & Boylan, 2011; Diaz, 2010). If educators fail to address this student math problem through new curricula such as college contextualized math curriculum, this will likely lead to high failure rates in college and university math classes, which affects students’ ability to complete their certificate or degree requirements for graduation (Howard & Whitaker, 2011; Sheldon & Durdella, 2010).

In my research, I focused on developing contextualized mathematics in math curriculum. Therefore, it is first important to understand the concept of contextualization. Contextualization is a method used for math curriculum design within lesson plans and as a pedagogical practice in face-to-face math classes. Many researchers are studying the effects of using contextualization in the teaching and the learning process for mathematics learning (Bottge & Cho, 2013; Perin, 2011; Young, Hodge, Edwards, & Leising, 2012).

Contextualized math refers to the teaching of mathematics problems that emphasize real-life situations. For example, an instructor could develop a contextualized math assignment on exponential functions and equations by having students work on an Internet-based problem to determine the monthly payment for a new car at a