Text Set Collection #2: Rate of Change

Articles:

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:

E-Z Algebra

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.

Algebra Survival Guide: A Conversional Guide for the Thoroughly Befuddled

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.

Painless Algebra 3rd Edition

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.

Algebra Success In 20 Minutes a Day

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.

A-Plus Notes for Beginning Algebra: Pre-Algebra and Algebra 1
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.

Reading Reflection # 11

Dear peoples,
The main idea behind Teaching Learners to Think, Read, and Write More Effectively in Content Subjects by Richard C. Sinatra is in order to make students better thinkers, readers, and writers, teachers must implement an effective construct that utilizes text structure, concept mapping, and a shift in teaching-style. Sinatra claims that a teacher can implement this construct in three easy steps. The first step is modeling for the students; however, Sinatra does point out that one should be considerate of the fact that concept maps are appropriate after students have been introduced to all the topics. For some teachers, this can be a great closure activity after only one lesson. However, other teachers may say this activity is most appropriate after two or three lessons. Either way the beauty behind a concept map is that the students mental arrange ideas and make connections between the ideas for themselves. The teacher is there to help direct the students, not give answers. A concept map is a great review activity. In fact, tomorrow during my evaluation my students will create a concept map about multiple representations of linear equations. I chose this activity because it is open-ended in the sense that the students can connect the ideas however they pleasure (even if it is incorrect). Also, it is a great activity to start a classroom discussion. In fact, I think this article left out a major aspect of being a student, speaking. The same construct would benefit the students' ability to communicate effectively along with the three other skills the author mentions. The second stage of implementation is guided practice. This goes back to the idea that a teacher is more like a navigator through the land of knowledge, but it is the students job to make the discoveries between the ideas. The teacher can continuously have students write a paragraph or two about a topic. Of course it is important to ask to write about a purposeful question. The hope is that students will begin to practice this construct on their own for future use. The author points out that this construct has proven to benefit students at all grade levels. Therefore, if you are a teacher you should probably try this strategy in your classroom. The data shows that not only does it improve the students' ability to think read and write, but it also has a positive impact on the different content areas too. I personally like it for a closure to a unit, but at any rate give it a try.

Sincerely,
Me (a genuinely good guy)

Reading Reflection # 10

Hello and welcome back to another exciting issue of typing about what I read,

After watching The Millennials: The Dumbest Generation or the Next Great Generation, I agree with both speakers to a certain extent. I believe that students today have the potential to be the next great generation; however, students today are able to fall through the cracks and become possible some of the dumbs people ever. Mark Bauerlein points out that there has been a drastic drop in reading amongst people between the ages of 18-23 despite the increase in the number of public libraries, schools and universities, and the Internet. For many, the primary source of the Internet is  a venue for social networking. More and more, high school seniors are deemed not ready for college, and more entering freshmen are taking remedial classes. The various forms of technology in every one's everyday life is continuously distracting students. The accumulation of these factors puts students today at the risk of being the dumbest generation. However, it is also true that because of the continuous advancements made in technology and science, students today can become the next great generation. Neil Howe explains that there has actual be a steady positive change in almost every category for today's students.
There has been an increase in voters between the ages of 18- 30 in recent years. Also, there has been a decrease in anti-social movements and violence, while categories such as child-parent relationships and community service have seen a steady increase over the years. Howe claims that kids are smarter today than ever before because of the emergence of technology in classrooms. So are students become dumbing? Well statistics can be tricky because Howe only spoke in terms of percentages, but there are more people today than there was during the 70's and 80's. Therefore, percentages can be misleading. Also, there are more students attending college then ever before in the U.S., but should all of these students attended college? Perhaps the reason why there are more students needing to take remedial classes is because there are many students who should not go to college that do go because our society views college as a necessity to be successful. If technology is distracting our students, then why are so many schools going 1-1? Howe points out that we are always comparing today's students the standards of students in previous generations. However, it is impossible to see how student's from the past would perform under our current standards in education. Howe also made an interested example when he compared science fairs from the 50's and today. Back then science fairs had volcanoes that foamed over the top, and today students create machines that do a number of various operations. Also, games cannot be such a bad thing when they are becoming more and more popular as a method of teaching. The SIMS is a much more accurate way to teach kids about life than the board game Life. There is a steady trend worldwide that kids today are much more informed than any other group of students throughout history. However, this really is about the smarter kids of today, because the students on the bottom of the spectrum still could be considered the dumbest kids ever.

Web Resource #2: TenMarks

Attention all blog readers,

I have a great online resource you can use in your classrooms. It is called TenMarks.com, and I am currently using this in my Algebra 1 classroom. This site does require you to purchase a license, but if you can convince your school to buy the students a subscription, it is a great tool to use to help get assessment data about your students. You can easily create a class roster for each of your sections, and you can assign specific problems that are centered on a particular standard. When you login into the website it displays the class results, and it shows you the distribution of comprehension amongst your classes. I use it for my Algebra 1 students, but it is designed for all grade levels up to Algebra II. We currently use this at least every other Friday, and the kids like it. It is very easy to navigate through and it offers hint and video tutorials if you answer a question incorrectly (do be warned that the man in the video has a very thick accent and students complain about the clarity of his voice). The site is very professional and has minimal advertisement. It does not have lots of flashy colors or any other kind of distraction. Also, it requires minimal adult supervision. Once students have there login information they can hop right on and start their assignments. The data it gives you does an excellent job representing the students' comprehension of the material. The students like working on the site, but to be honest it does not seem very engaging. It is just question after question. It has a built in library of standards for each subject, which is pretty nice. There is not anything I can readily find about this site that I do not like. If your school chose to buy a bunch of licenses and you are wanting to have a relaxing Friday afternoon, then get a TenMarks account and assign your students a few standards to practice. This way everyone is happy and students are still practicing math.

Signing out,
Michael Vargas (Me)