#9 - Article CCSS Implimentation

The article I read was written by Richard Long and discussed the implementation of CCSS. The author discusses the potential and the pushback of CCSS in the United States.  In the article, the author comments that "the Standards will change schools and provide the U.S. with more students who not only are ready to learn when they graduate high school and go to college but will not need remedial classes..."  If this comes true (we can only wait and see), it would be a wonderful thing for education.  However, as the author comments later in the article, this great idea for education, however the implementation amongst larger class sizes, higher poverty rates, and poor educational districts who cannot afford to redesign the educational curriculum brings a dark cloud over a successful execution of the CCSS.  Further, legislators claim that by educating our students with CCSS, "millions of manufacturing jobs that are expected to be open if there are more high school graduates with the academic abilities to learn these new jobs." is a bing 'ol full cup of cra...er -sh...-ahem- nasty stuff in the toilet.

Implementing CCSS to the math classroom is as easy as teaching physics - literally.  The critical thinking that is required to learn physics is now being applied to mathematics and is pushing that curriculum to highs that could be a great thing.  As for implementing it in my classroom?  I'm taking it one day at a time.

Web Resource Review #2

I will be reviewing the following site:
http://tutorial.math.lamar.edu/

This is commonly referred to as "Paul's online notes".  This is an amazing resource for calculus I, II, and III students.  This resource contains an educators notes from the classes he teaches complete with examples and solutions to check your work.  There's also a "contact me" link where you can ask for clarification if the notes are not clear enough.

Text Set - Proofs

Websites:

http://tutorial.math.lamar.edu/Classes/CalcI/LimitProofs.aspx

Readability - 10.3

 This site is called "Pauls online notes" to the average Calculus student.  It is a collection of notes a professor has posted to his website, specifically linked are his proofs for limits.  I like how he gives great in-depth examples and provides an extra resource for students on the whole.  

http://education.ti.com/en/timathnspired/us/home

Readability - 12.0

This site works in tandem wit h the Ti-Nspire app to provide great ways to teach subjects using technology - great for those honors courses.  When exploring this site also gives a list of textbooks that cover the material along with the standards that particular activity covers.  This makes an excellent teacher resource for teaching geometry proofs.

http://patrickjmt.com/

Readability - 9.6

This is a resource I have been using for years with my own schooling and with the students I am now tutoring.  It provides a great way to "flip" your tutoring sessions or even get ideas for how to create flip classroom videos!  The proofs on induction are particularly clear and concise with great expanations

https://www.khanacademy.org/math/trigonometry/seq_induction/proof_by_induction/v/proof-by-induction

Readability - 11.8

This is another site that is great for "flipped" instruction.  Khan academy offers a different format to their videos and provides less distraction by using technology to write directly on the writing surface.  This particular video gives a great explanation to using induction to prove a concept.

http://www.kutasoftware.com/freeige.html

Readability - 4.7

This is a semi-free teacher resource that geometry teachers can utilize to help their students prove geometry concepts.  Kuta offers free worksheets (pro), and for a one time payment (con), allows you to manipulate problems, restructure them, and change the format with which your student answers them -- essay, short answer, or even bubble are just some of the ways you can manipulate a normal worsheet o work for you (also great practice for the E.O.C.'s and ACT/SAT practice).

http://www.dummies.com/how-to/content/using-ifthen-logic.html

Readability - 8.6

While I don't like the "dummies" aspect of this site, it is clearly written with humorous touches thrown in.  I like how it gives numerous examples, and allows you to print the page for a quick resource.

Books

How to Prove It: A Structured Approach

by Daniel J. Velleman

Readability - 6.7

An overall great book for those getting ready to experience advanced mathematics.  This book can be a bit hard to read sometimes (the readability lies!), but definitely has great re-readability and is a great "quick" source for refreshing those proof skills.

Proofs without Words: Exercises in Visual Thinking (Classroom Resource Materials)

Readability – 8.4

BEHOLD! - One of the only words in the first few pages, this book provides a great resource for those visual learners to experience the many geometric proofs students encounter.  I like the minimalist language the book uses which will prompt the student to as their *teacher* questions.

Q.E.D.: Beauty in Mathematical Proof

by Burkard Polster

Readability - 11.9

I like this book because it gives a down to earth explanation of proofs and how to do them.  The writing within looks elegant while still providing an explanation that leaves you feeling more intelligent.

Math Girls 2: Fermat's Last Theorem (Volume 2)

by Hiroshi Yuki, Tony Gonzalez

Readability - 3.6

The authors write this book as a narrative and it keeps one interested while still doing math.  Most high schoolers should be able to follow the book at least half way through (the book's mathematical concepts get more challenging as the book goes on) but in the end gives some of the mathematical concepts that lead to a proof of Fermat's Last Theorem (which wasn't really his last theorem per-se).

The Moment of Proof: Mathematical Epiphanies

by Donald C. Benson

Readability - 7.6

This book gives some interesting math appetizers that really hook the reader into reading more.  I felt it almost read like a detective novel only the stories are much shorter and have longer explanations.  

Games

http://www.themathlab.com/geometry/mathcourt/howtoplay.htm

Readability - 6.8

This is  an interesting game to help your students get better at proofs.  I like how all the materials are available for your use - eventually.  I don't like how you have to do a bunch of clicking to get those materials together.

http://feromax.com/cgi-bin/ProveIt.pl

Readability - 2.6

This is a site to practice your geometry proofs simply by clicking.  Great for those who have technology and also have horrible handwriting.  This allows students to practice with their focus on the proof, not the writing.

http://calculationnation.nctm.org/Games/
Readability - 7.7

This site contains games that cover all sorts of subject matter in mathematics.  My favorite is "Slam Ball" where, even though you don't actually prove anything, you have to use the knowledge you have gained from proofs to complete the game with the highest score.

9 things about vocabulary

I read the article Nine things every teacher should know about words and vocabulary instruction.  This article covered a collection of suggestions to help you teach vocabulary to your students.  This article really seemed to focus on vocabulary in the sense of actually teaching vocabulary as the primary subject.  It didn't seem to apply much to how I would be teaching vocabulary in a math classroom.  Either way, I found the article interesting because it gives a clear and to-the-point way of looking at vocabulary.  I really liked Table 1 - a simple organizer for common prefixes, roots, and suffixes.  In rereading the article, I found a few things that could work in a math classroom.  Connecting previous knowledge is something that's always being done in a math classroom.  Other items for consideration included things we've already discusses in our class.  Using K-W-L strategies or using context to figure out the meaning of words students are struggling with are a few of the ideas presented in the article.  Overall an interesting article, but hard to contextualize for mathematics.

BBR ch 5 - Strategies!

I read BBR's chapter on reading strategies.  The chapter outlined numerous ways to help students learn vocabulary with the idea that students are also learning reading strategies.  As I was reading I noted a number of reading strategies that could be applied to mathematics, however as the chapter moved on, the strategies seemed to peter out.  They became to complicated to cover within the timeframe of a class, namely my algebra 2 class that is taught in a traditional way.  Then I started thinking about my algebra 1 class and how I would like to be able to split the low flying students and give them more specialized instruction.  It would be great using some of these strategies with these students.  More specifically, I really liked the idea of a personal glossary.  Students can add to it as they need to, and come to me later for help defining words they're struggling with.  Another strategy I liked was the verbal/visual word association diagrams.  I liked how it used a more visual way to create a personal glossary for the words that students are struggling with.  Along with being visual, I like how it tries to build on what students already know - very constructivist!  Further, I like this one best because it let's students quickly refer to their glossary without having to get bogged down with practice sentences.  I forces the student to keep it short, sweet, and to the point.

Struggling readers

The chapter I read (ch 11 from D&Z) went in depth into key strategies for helping struggling readers.  I think it's important because it points out things that I need to keep in mind with my students.  Foremost, I need to keep in mind that by the time a student reaches high school, many have experienced failure after failure at reading Mathematics texts.  It makes it doubly important that if I implement these key strategies, I do it full tilt.  Our classes this semester has beat modeling into the ground, and I already see the importance of building supportive relationships and promoting self monitoring.  I feel these lead to a student learning to teach themselves.  A challenge I've set myself is creating materials students can successfully read.  My mentor teachers still rely heavily on the text and on previous materials they've built, borrowed or stole.  I don't have those resources yet, so many times I'm creating my own materials.The idea of providing books and articles on tape sounds like an amazing idea.  It would be nice if my students could have the option of having theorems read to them so they could complete guided notes.  I have some students with IEP's and I suspect that many of their problems stem for being unable to read mathematical texts well.

Why are we reading this?

"It dawns on me that Lisa is equating fast reading with good reading.  She doesn't see reading as thinking.  She views it as a race. Lisa doesn't understand that good readers adjust their pace when they read."

I really wish someone had explained this to me when I was in high school.  I'm just like Lisa.  I could read most anything quickly and get the gist of what was being said - enough to write that report or make a high grade on my ACT.  All that doesn't mean squat.  I come from a generation where late night commercials claimed they could teach you to speed read.  Teachers timed how many pages we could read in a certain time.  Reading fast was reading well.

That's just not the case anymore.  In a world moving forward technologically speaking, people need to read to comprehend, not necessarily to be fast *and* comprehend.  I read slower than ever, but I ***understand*** what I'm reading, and I ***comprehend*** and am able to internalize what I learn.

This week it is my goal to teach my students this important lesson.