Connecting Research to Teaching: Slope, Rate of Change, and Steepness: Do Students Understand these Concepts?
NCTM, March 2010, Volume 103 Issue 7,
This article's intended audience is high school math teachers. It has a reading level 10.5. This article investigates how teachers introduce their students to the concept of rate of change since research has shown that many students struggle with comprehending rates of change. Although this article follows an AP Calculus class, I chose it because students not fully understanding rates of change is not an isolated phenomena to Calculus. This problem exists in my Algebra 1 classes, and this is a great resource for teachers to counteract this dilemma.
How to Use the Slope Intercept Form (in Algebra)
http://www.wikihow.com/Use-the-Slope-Intercept-Form-(in-Algebra)
This article is intended to help Algebra 1 students who are struggling with slope intercept form. It has a reading level of 6.7, and it is organized into 5 different methods for representing a linear function into the slope intercept form. I chose this because it is a very easy read that explicit writes out each step for students to see. This section is very important because it makes up about 50% of the EOC for Algebra 1. For each step there is one paragraph describe the process.
Slope of a Line: The Angle form the Horizontal- Rise Over Run
http://math.about.com/library/weekly/aa120502a.htm
This article is intended for high school students who are just learning about slopes. The reading level is 5.1, and this article explains to the students how to calculate your slope from two points. Moreover, it explains the difference between a slope of 0 and an undefined slope. Also, I really like that this article explains that the tangent of an angle is equal to your slope. This is a concept not often taught in a textbook, but it is a very rich idea. I chose this article because I think it does a good job describing to the readers the significance of slope, and it provides some great really world problems.
Books:
Authors: Prindle, Anthony; Prindle, Katie
Ages: 9th grade and up
This book is intended to be a self-guided manual for students and adults who need additional help with Algebra. It consists of notes, quizzes, tests, answers, charts and other diagrams that are geared toward providing a detailed explanation of how Algebra works. I chose this book because I think it is a great resource for people that learn at their own pace. It might be more geared toward adults and high-school graduates, but reviews say that it has been very beneficial for homeschooled students.
Author: Rappaport, Josh
Ages: 7th grade and up
This book makes math fun again! It is written similar format as a conversation. It uses humor to make to question/answer style entertaining. It covers a wide range of topics that tend to be the more challenging material in Pre-Algebra and Algebra. I chose it because I think it is important for students to have a wide variety of reading material, and this is not your traditional math textbook. Too often textbooks are very boring and dull, but this book tries to give a little bit of life to Algebra.
Authors: Long, Lynette Ph.D
Age: 7th grade and up
This book is another book that tries to present Algebra in a untraditional manner, it tries to make it fun and entertaining. It covers a large range of topics and has a large selection of entertaining activities. I choose this book because once again I think it is important for students to be exposed to a large variety of text, especially if the text makes math look cool to students. This book is more geared toward middle school and high school students, but I think it is able to be used by adults who are learning Algebra on their own.
Authors: LearningExpress Editors
Ages: 9th grade and up
This book is a great resource for students who are practicing algebra at their own at home (or anywhere). It is very direct in its explanations and provide ample amount of practice problems to help students learn the various topics. It does not offer extensive explanations. This book appears to be used more like a workbook rather than a textbook; however, the activities seem to be very enriching for the various topics. I chose this book because I think it is direct enough to help my students who get caught up in extensive details.
I'm So adorable
Authors: Yang, Rong
Ages: 8th grade and up
This book is a great resource for students who are learning Algebra and students who are in Pre-Algebra (although some of the reviews said that this is more appropriate for intermediate to advance pre-algebra students instead of beginners). I chose this book because I think it does a good job explaining the basics of Algebra while also doing a good job at explaining the more complicated material. It is full of examples and word problems that are accompanied by a summary explaining everything that is important to the problems or theorems. All in all I think it is a great resource.
Webpages:
http://www.regentsprep.org/regents/math/algebra/ac1/rate.htm
This webpage is a great resource for students who are learning Algebra 1. The reading level is 5.7 and I chose it because it is a wonderful reference page if students need additional help at home. It requires no adult supervision (if you trust a kid with the internet). It has powerful visual aids that explicit explains what is slope. The text is separated by font style and color to differentiate really important information. It goes through several examples and explains step by step how to solve the problem.
http://www.mesacc.edu/~marfv02121/readings/average/
This webpage is intended for college students, but I think it may be suitable for an Algebra 1 honors class. The reading level is 7.3 and it is very organized, thus making it easy to read. I chose this webpage because it does a very good job describing the average rate of change as a function, which is a very powerful thought for a student learning algebra. It provides several examples of rates of change that is familiar to the reader. It models for the reader how to solve several problems. It lists all the steps for the first example; however, the rest of the examples are less detailed.
http://www.sparknotes.com/math/calcab/applicationsofthederivative/section1.rhtml
This webpage provides notes for AB Calculus students. There are several webpages separated into various topics such as terms, applications, and example problems. The reading level is 9.9. I chose this site because rate of change is not unique to just Algebra. It plays a very important role in Calculus as well. This site explains the difference between instantaneous and average rate of change. It gives the classic example of position, velocity, and acceleration as different rate of change. It does not go into great detail explaining the underlying concepts; therefore, if a student struggles with reading, then this site will be challenging. However, it is a great resource for students learning calculus and possibly Algebra 1 honors.
http://www.algebra-class.com/rate-of-change.html
This webpage is a helpful resource for students learning Algebra 1. The reading level is 5.7, and like the previous websites, this is a reference page students can access at home if they need additional help. It starts with an essential question "Why do I need to find the slope of a line?" It provides real-world problems that can be modeled by a linear function. I chose it because it has 4 good examples, and it has a video clip embedded into the webpage that provides even more explanation of calculating the slope of a line. The only catch is the webpage designer liked to use a lot of red text, which does not appeal to my eyes.
http://clinton.k12.mo.us/cms/lib2/MO01001720/Centricity/Domain/385/2.2%20Slope%20and%20Rate%20of%20Change.pdf
This webpage is intended for Algebra 2 students. I was unable to directly check the text for the reading level, but if I was allowed to guess I would say it is close to a 6th grade reading. It has arrows connecting terms to their definitions. It has only one page of notes and the rest of the text is word problems with example work solving each question. I chose this webpage because I think it is always important for students to have good direct notes along with example problems that follow the same format as the type of questions the students will be tested over. It is very easy to follow along as you read. All in all, it is a good webpage for students to study with at home.
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