Monday, December 2, 2013

So What?

So What?

Adams, A. E., & Pegg, J. (2012). Teachers' Enactment of Content Literacy Strategies in Secondary Science and Mathematics Classes. Journal Of Adolescent & Adult Literacy, 56(2), 151-161.

Purpose:  Adams and Pegg want to illustrate how effective strategies and modifications can improve student literacy in the mathematics and science contents.

What was studied/discussed:  They studied the ways in which teachers incorporate content literacy strategies into their instruction.  The 26 teachers for this study were taken from “high-needs” (pg. 153) schools and taught math and/or science in grades ranging from 6-12.  The teachers participated in workshops and classes pertaining to content literacy, literacy strategies, and “tools to support student construction of content understanding” (pg 153).  The teachers then were observed, their lesson plans evaluated, and asked to reflect on their experiences.  The teacher reflections and discussions were used to “triangulate” (pg. 154) the data collected.

Important terms:  Rehearsal, Reorganization, and Transitional; literacy strategies; Frayer Model;  VVWA (Verbal Visual Word Association)

Results:  All of the teachers incorporated the strategies they learned into their lessons, but they did so in differing manners.  Adams and Pegg found that the teachers were enacting these strategies in either rehearsal, reorganizational, or transitional manners.  The observations also shed light on the modifications of the strategies that each teacher enacted.  Many of the teachers modified the strategies so that they “aligned with their instructional goals and current practices” (pg 158), which resulted in minimal conflict between strategies.  The modifications often resulted in helpful strategies for students.  However, there was not enough data to suggest that the modifications of the tools were used “in ways that enhance student learning” (pg 159).

So What? :  The study may not have come to a clear conclusion on whether the literacy-instructional adaptations are truly helpful, but there are many aspects that would certainly be beneficial for our students.  The article details the Rehearsal, Reorganization, and Transitional approaches to literacy strategies, and I really like them.  I think utilizing aspects of each approach in our math and science classes would most certainly enhance student learning.  The saying goes, “everything is good in moderation,” so what is considered moderation when adapting these approaches for instructional purposes? 
            The rehearsal and reorganizational approaches contain strategies that help students in three phases of the class:  writing, reading, and vocabulary, with emphasis being placed on the writing and vocabulary.  Mathematics education hinges on how well students reproduce the information they have learned and how well they understand the concepts and terms.  We must be able to utilize both approaches, passive and active, and blend them so that our students are challenged and learn from those challenges.  How do we balance between the two differing approaches, so that we are not monotonous to our students?
How can we use these approaches in the near future?  The reorganizational approach is everywhere in Common Core.  Our students are being asked to discuss their knowledge with one another.  This would certainly engage the students, and help them to “construct meaning” and “draw on background knowledge” (pg 158).  The students would be active in their learning, rather than sitting back and memorizing (i.e. rehearsal approach).  The reorganizational approach also promotes technology, which is ever-growing in our society.

How do we attain success?  These approaches are highly adaptable, which is the point of the article.  Teachers must be able to modify the approaches in order to align the goals of the strategy with the goals of the instruction.  The approaches should be modified with goals in mind and incorporated with our student’s knowledge for maximum effectiveness.  And only then can we utilize the tools in ways that genuinely enhance student understanding.

Monday, November 25, 2013

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

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

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.

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.

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.

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.

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.

 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.

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.

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.

 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.


Sunday, November 17, 2013

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

Monday, November 4, 2013

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

Sunday, November 3, 2013

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.

Monday, October 28, 2013

Text Set #1 - Probability

General Resources pertaining to the many aspects and figures of Probability:

Books

  • Leonhard Euler and the Bernoullis:  Mathematicians from Basel
    • MBW Tent
    • ages 12 and up
This book is a collection of tales about men who were integral in the creation of the mathematical principles in Probability.  This book is a fictional dialogue that is actually historically accurate.  Its contents give students a firm basis of life in the 16th and 17th centuries and tell of how these men discovered their name-bearing theorems.



  • A Very Improbable Story:  A Math Adventure
    • Edward Einhorn & Adam Gustavson
    • ages 7 and up
This book is a picture book that details a young boy's day and the many challenging and improbable things he must complete in order to get a cat off his head.  The boy must complete games of daunting probability from the time he brushes his teeth until late in the evening.  The book contains hilarious depictions of the scenes and details the mathematics used in each situation.




  • The Cartoon Guide to Statistics
    • Larry Gonick & Woollcott Smith
    • ages 14 and up
This book has an uncanny ability to provide informational and often humorous depictions of instances in which probability and statistics are prevalent in the real world.  The material covered in this work are of higher level, yet are written in a manner understandable by early high school students.  Theories of probability are easily portrayed in this work.



  • Probability Demystified
    • Allan Bluman
    • Ages 14 and up
This book is another example of a work that presents the difficult material of a probability course in a manner easily understood by beginner students.  The work contains the major theorems of the course as well as topics that are often taken for granted (sample space, events, etc).  The book contains all of these and up to the many higher-level aspects of probability.  



  • Math Made Easy:  Combinations and Permutations
    • Dawn LaBuy-Brockett
    • Ages 5 and up
This book teaches the many aspects of combinations and permutations, from the basics to the more in-depth concepts that entail.  The work contains easily understood explanations and pictures detailing factorials, groups, ordered sets, and more.  The pictures are clear and concise and provide a great "hands up" for the reader.



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Websites

An in-depth look at the life and accomplishments of one of math's greatest minds.  Bernoulli is the mind behind the Bernoulli Trials, an integral aspect of the probability curriculum.  The work also notes the other, maybe less-known discoveries of Jacob Bernoulli.

This website is perfect for the beginner probability student as it details, in layman's terms, how to calculate permutations and combinations.  The terminology used in this site is very simple yet very forth.  It tells the reader exactly what is needed in a very direct manner.  The site also has multiple images that depict the situations perfectly.

Cram.com is a site in which the general public can post files for subjects across the board.  This particular file is a set of flashcards that detail multiple key vocabulary terms for an introductory probability course.    The site allows students to cycle through the "front" of the flashcards to quiz themselves and allows the students to flip from front to back when studying.

This site is actually an in-depth example of experimental probability.  The girls in this situation are vying to win at "Horse".  The students are then given the outcomes of ten games and are asked to derive the probability of many other situations.  This would be perfect to provide a real world application of the concept.

In this website, readers are given multiple resources through which we can teach probability to our students.  There are many lessons that teachers can freely access and utilize.  There is also a great description of Nrich's ideal classroom in which a problem is the basis for a classroom and not a technique.

Mathwords is a site that has an incredibly extensive selection of mathematics vocabulary.  Each term has its own page that delves deep into its meaning.  This particular page pertains to Bernoulli Trials.  The site gives many examples in which a Bernoulli Trial is prevalent and also gives a great definition of the term.  The page also defines what each variable in the equation means, in easy to understand terminology.

This site is a deeper look into Bernoulli Trials and Binomial Distributions.  Stat Trek is built for upper high school to collegiate level students and the terminology used is equivalent in level.  The students are subject to a more academic-specific vocabulary set in the description, but it is still an easy to understand site with tons of information.

This particular portion of the Math Forum details "Probability in Our Lives".  It is a good scope into how the basic ideals of probability and statistics are evident in many everyday activities.  One of the best instances outlined on the website is in weather forecasting.  Though weather probability is much more than what is detailed on the math forum, we are still given a great look into how the job is done.  There are also many other instances that bring about many other aspects of probability.

This site on the EMathZone is dedicated to one of the most basic ideas in all of probability:  the sample space.  Without a sample space, however, there are no odds or likelihoods.  This site gives great and very simple definition of a sample space.  It also gives good, concrete examples of sample spaces in multiple formats (Bernoulli, binomial, etc).  The spaces are even depicted as images so the reader is given multiple medias from which to learn.

WikiHow somewhat receives a bad rap because it can be edited by any person imaginable (credentials or any Joe off the street).  However, this particular wiki is great because it is accurate.  The wiki is also very easy to follow along and easy to learn from.  The only drawback is the author's decision to use higher-level vocabulary to describe the action necessary.  The wiki also has great pictures that enable the reader to see the discovery of the expected value.  The situation is also a game, so the reader is more apt to follow to see if he/she should even play the game (applicable to their lives).



Sunday, October 27, 2013

Bromley Article

The Bromley article was a bit different than previous readings.  This article detailed certain facts about vocabulary and the English language in general.  I found it incredibly interesting to read about the language.  I knew English was a large and expansive language, but I did not know it was THAT much larger than French or German.  I knew that a bunch of words had multiple meanings, but 70% of our most used words?  I was astonished by that figure.  However, the one fact that took me aback was the one that stated that the rules of English are more consistent and simpler than other languages.  I always thought English was the toughest language to learn because of the nuances and rules.  Apparently not.  I guess I could see how this is the case, especially when compared to Chinese.  All in all, I thought it was cool to learn more about my language.

In regards to my classroom, the bullet point that I noticed was number four, "Words are learned because of associations that connect the new with the known."  I think, especially in math, students must be able to draw connections between words to understand the vocabulary.  There are multiple roots and affixes of math vocabulary that are prevalent in many, many words.  As I have said before in this blog, I can utilize that aspect of math vocabulary via word clouds or other strategies.  Focusing on those common words/parts of words can certainly build student vocabulary.