Text Set #2 - Logarithms

General Resources pertaining to logarithms and the figures that coined logs.

Books

• Higher Mathematics:  Exponentials and Logarithms Revision
• A Forrest
• Ages 18 and up

This book is an overview of logarithms and exponential functions.  It is written to suit a higher mathematics course and the students within that course.  There are real-world examples that also draw from higher level courses (i.e. macro-economics).

• Math is Super Cool:  The Ultimate Guide for Understanding Exponent and Logarithm
• Peta-Gaye Reid
• ages 13 and up

This book is an introduction to logarithms and exponentials.  The book provides an easy to follow instruction on the basics and the general principles behind logs and exponentials.  It also provides a fun commentary between the author and characters from the other Math is Super Cool books.

• Algebra II for Dummies
• Mary Jane Sterling
• ages 15 and up

Everyone has heard of the Dummies books, and they have a bad rap as being a very low level book for its readers.  However, the fact is that the Dummies books are really great resources that provide easy to understand explanations.  They are a very good resource for basic knowledge on its content.  This book is no different.  Algebra II for Dummies provides instruction on everything within the  Dummies model.

• Math, Better Explained
• Kalid Azad
• ages 15 and up

This book, like the Dummies book, provides a ground-level explanation of many mathematical concepts, including logs.  The book is unconventional, as the author explains the abstract concepts in a concrete manner.  Readers are able to see how things work via examples and real-life applications.

• Essentials:  Math Made Nice & Easy #2
• The Editors of  the Research & Education Association
• ages 10 and up

This book shines light on the fun side of mathematics via simple and interesting instruction on the subject.  Each step given in instruction is noted and the notes are specific as to the reason.  The book goes in depth on each concept, so many levels can benefit from this resource.

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Websites

• History of Logarithms
• http://www.westcler.org/gh/outtda/pdf_files/History_of_Logarithms.pdf
• ages 14 and up  

This site is a pdf file that details the 'invention' of logarithms.  The article goes into detail on the three inventors' escapades in discovery.

• Burgi Biography
• http://www-history.mcs.st-and.ac.uk/Biographies/Burgi.html
• ages 18 and up

This site details the life and accomplishments of Jost Burgi, one of the founders of logarithms.  The site talks of how the Swiss mathematician came of age in the mathematics realm and how he came about discovering logarithms.

• John Napier and Logarithms
• http://ualr.edu/lasmoller/napier.html
• ages 17 and up 

This website also details the life of a co-founder of logarithms, John Napier.  The site goes in depth on the society in which Napier lived and how he founded logs.  There are quotations by Napier that shine light on his thinking, as well.

• Logarithms:  Introduction to “The Relationship”
• http://www.purplemath.com/modules/logs.htm
• ages 14 and up 

PurpleMath.com is a site that has thousands of mathematical concepts on file.  The site explains its content with ease and puts emphasis on the procedure.  The site is very easy to navigate and is free for all users.  Purple Math is a great tool for remediation and enrichment.

• What on Earth is a Logarithm?
• http://www.math.utah.edu/~pa/math/log.html
• ages 11 and up

The University of Utah's page on logarithms is also a site that provides further explanations on logarithms.  This site, however, provides solid examples to go with explanations.  The thing that sets this one apart is the "Special Bases" portion of the site.  In this part, the site talks about how logarithms connect to the e function, or natural logs.

• Logarithms
• http://hyperphysics.phy-astr.gsu.edu/hbase/logm.html
• ages 14 and up

HyperPhysics provides solid examples of four basic operations pertaining to logarithms.  Each operation is explained thoroughly and provides an example.  Each portion is east to follow and make connections from operation to operation.

• Pauls Online Notes:  Algebra – Logarithm Functions
• http://tutorial.math.lamar.edu/Classes/Alg/LogFunctions.aspx
• ages 12 and up

 This is another site that provides its visitors with in-depth explanations for each step in solving a logarithmic problem.  The site also contains a "how to graph" portion that plots an example on the x-y coordinate plane.

• Interactive Logarithmic Function Graph
•  https://sites.google.com/site/mathmaine/home/logarithmic-grapher
• ages 11 and up

This Google site has a Java embed that presents Geogebra.  Geogebra is a great tool to use no matter the concept.  In logarithms, Geogebra has pre-loaded the basic equation for a logarithmic curve and students can adjust the values in the equation.  Doing so, they can see how each coefficient influences the graph of the curve.  This is a highly interactive resource that is immensely helpful in transformations.

• Simple Logarithmic Equations
• http://www.brightstorm.com/math/precalculus/exponential-and-logarithmic-functions/solving-simple-logarithmic-equations/
• ages 16 and up

This site contains a video that introduces students to logarithms.  The video is very helpful, as the instructor is knowledgable and clear with his explanations.  The site also has example problems for visitors/students to work on their own, or with the help of the instructor via another video.

• Logarithms | Algebra | Khan Academy
• http://www.khanacademy.org/math/algebra/logarithms-tutorial
• ages 17 and up

 Ah, Khan Academy.  Khan Academy helped me get through many courses in undergrad and it is incredibly useful for our students now.  The videos that Khan Academy produces are spectacular.  They are easy to follow and highly informational.  There are 25 videos pertaining to logarithms alone.  Each of them are in-depth, so no matter what aspect of logarithms a student needs help with, Khan Academy has a video to alleviate the problem.

BBR Chapter 7

In this chapter, BBR wrote about strategies to aid students' independent learning.  They detail how crucial this skill is in their future and I could not agree more.  If our students want to go and be successful in college, they will certainly have to learn a lot of material independently.  They will have to hone their study skills for tests as well.

The strategy that I believe would be most effective in aiding their independent learning, is PLAE.  PLAE is preplan, list, activate, and evaluate.  I like this strategy because it enables students in all three phases of the reading process.  It also is so simple that we could use it without even knowing.  BBR details how students must continually ask questions to better their understanding.  That aspect is also befitting of the Common Core Standards.  I like how the questioning is present in each aspect of the PLAE, too.  The questioning is what drives our learning, and what drives us to do what we do.  The PLAE model helps with studying because it makes students ask "What is most important?"  If they can answer that with a mini-discussion in their heads, they certainly understand the material.

WA

Web Resource #2 - Khan Academy

In the second installment of this blog's web resource reviews, I will talk about a site that helped me get through undergrad.  Khan Academy is a free resource that is suitable for students in 3rd grade through the collegiate level.  The site contains thousands of videos that detail many aspects of the mathematics curriculum.  In each subject area, there are many subgroups and topics that contain videos.  The videos are very simple to follow and are highly informational.  The creators break down the concepts into smaller and easy-to-swallow tidbits that allow the students to go at a slower pace and allow them to understand each step.  The step-by-step aspect of Khan Academy is the part I like best.  With my own experiences, I could get the material up to certain points; the steps caught me up to speed with the remainder of the material and allowed me to do substantial remediation and ready for the next lesson.

Students in my classes now would greatly benefit from supplementing my lessons with the Khan Academy lessons.  They do not have to sign up, but doing so allows for more interaction.  Parents need not be present when students are learning on Khan Academy and there aren't any commercial advertisements to divert attention or anything of the sort.  

The site has many pros:  interactive, highly informational, step-by-step solutions, and many subject areas to choose from.  There are few cons, one of which is the length of the videos.  Rather than short spurts, many of the lessons take up to 15 minutes.  But I can see how that con can certainly transform into a pro.

Overall, I would definitely recommend Khan Academy to students.  I often tell my students to utilize the videos on the site when they are still unsure about a concept.  I really like this site, stemming from my own successes when using it.

WA

Long Article - CCSS Implementation

This article stirred a lot of emotion in me, as I am sure it did in many other teachers/interns.  With the implementation of Common Core, there are a lot of questions that remain unanswered.  The ones making decisions pertaining to the CCSS don't know the answers either many times.  But they do know that there will be shock and push-back.  The implementation of Common Core will take time, and the standards and evaluations don't allow time.  As said in the article, many states are looking at revoking the CCSS or are holding off on implementing them.  I know Georgia is following the CCSS but is not going to require the taking of the PARCC exam.  I also know that Tennessee is following the CCSS from now on and will be requiring the PARCC in the future.  However, the PARCC is not going to be administered until the 2014-2015 school year.  Which basically makes this year a wash when it comes to state test scores (I think this is where most teachers get irate over the implementation of CC).

There are many problems with this whole implementation process of the Common Core State Standards.  The problems detract the fact that the standards are, in my opinion, a good step in the right direction.  There are many aspects that will prove highly beneficial in the long run.  However, the confusion overshadows the benefits that lie with the CCSS.