Text Set Collection #1 Pythagorean Theorem

Books:

Hidden Harmonies: The Lives and Times of the Pythagorean Theorem 

Author: Robert & Ellen Kaplan

Grade: 10+

This book takes a look at the development and role of the Pythagorean Theorem over time. From its discovery, to its uses today, this book views history in relation to the theorem. There are a few proofs that may require a little more than the average knowledge of mathematics but the history is easy to follow for just about anyone. 

The Pythagorean Theorem: The Story of Its Power and Beauty

Author:   Alfred S. Posamentier 

Grade: 8+

In this book, a math educator tries his hand at clearing up misconceptions about the theorem. He also makes it clear to the reader as to the importance of the theorem throughout history. He addresses why this theorem has fascinated many people throughout history. 

Whats Your Angle Pythagoras? A Math Adventure

Author: Julie Ellis

Grade: 3+

In this illustrated book, Pythagoras is a young man who's curiosity  leads him to discover and important formula that he can use to solve right triangles. We follow him through his journey of discovery and application. 

The Pythagorean Theorem: Crown Jewel of Mathematics

Author: John C. Sparks

Grade: 5+

This book is an introduction the Pythagorean Theorem and its applications throughout mathematics. It takes a brief look at the history of the theorem and its development over time. This book also addresses spinoffs from the theorem including games, past times, and trigonometry. 

APPS:

Khan Academy

Grades 3+ 

This app is a version of the online Khan academy. The Khan academy is a great place to find just about any math concept you can think of. The app has the academy divided into subjects. When clicking the math then geometry section, you can find an entire section on the Pythagorean Theorem and its applications. 

Websites:

Pythagoras Theorem

http://www.mathsisfun.com/pythagoras.html

Grades: 6+

This site is a somewhat interactive look at the Pythagorean Theorem. A very brief history leads to a mathematical and visual proof of the theorem. Also as you advance down the page, Everything from the definition to applications is shown to the site visitor. 

Pythagorean Theorem

http://www.purplemath.com/modules/pythagthm.htm

Grade: 

This site is a little less creative but is very straight to the point when addressing the theorem. It begins with a statement of the theorem and its definition and then walks you through step by step solutions using the Pythagorean Theorem. 

Pythagorean Theorem

http://www.cut-the-knot.org/pythagoras/

Grade: 10+

This site takes a deeper look at many of the proofs of the Pythagorean Theorem proven since its existence.

Pythagorean Theorem Calculator

http://www.algebra.com/calculators/geometry/pythagorean.mpl

Grade: 7+

This site gives a summary as to what and how to use the Pythagorean Theorem. It also provides an input calculator that allows you to quickly calculate and side of a right triangle if you know the other two. 

Practice with the Pythagorean Theorem

http://www.regentsprep.org/regents/math/algebra/at1/pracpyth.htm

This site is an interactive "quiz" dealing with the theorem. Questions are posed in real world scenarios and all have to do with the theorem. The questions are multiple choice. 

Articles:

Surprising Uses of the Pythagorean Theorem

Better Explained
Grades: 11+
This article is a very interesting read. It introduces multiple ways to use the Pythagorean Theorem for things other than a right triangle. Almost any shape lends itself to the use of the theorem

Revisiting the Pythagorean Theorem
Clay Davenport & Keith Woolner
Baseball Prospectus
Grades: 8+
In this article, the two authors put an interesting spin on the Pythagorean Theorem. They make small tweeks and manipulations to the theorem to show how it can be used for calculating a handful of baseball statistics. Great read for a  baseball fan.

All Hail the Hypotenuse
Alan Hirshfeld
The Wall Street Journal
In this section of the Wall Street Journal, Hirshfeld takes a look at the Pythagorean theorem and its uses over time. He recognizes specific examples of using the theorem on certain things from throughout history. He also gives a brief explanation as to why and how it was used.

Jason Garrett Wants the Cowboys to Know the Pythagorean Theorem
Michael David Smith
NBCSPORTS.com
http://profootballtalk.nbcsports.com/2013/07/24/jason-garrett-wants-the-cowboys-to-know-the-pythagorean-theorem/
Grades:Any
In this article, Jason Garrett, the coach of the Dallas Cowboys, is quoted stating the importance of being intelligent football players. He specifically would like his players to know the Pythagorean Theorem becasue of its importance on the football field.

James Garfield was the Only President to Prove a Math Theorem
Esther Inglis-Arkell
i09.com
http://io9.com/james-garfield-was-the-only-u-s-president-to-prove-a-m-1037750658
Arkell takes a look at President Garfield's interest in mathematics. In particular she shares and discusses his very own proof  of the Pythagorean Theorem. 

Reflection #8 Bromley

Bromley's article this week was a very interesting read. He addressed the actual English language and some interesting facts about it. One of the most shocking things I found was that English's most used words consist of about 70% of words with multiple meanings. That is surprisingly high. It was also interesting that the English language is such a large, extensive language. I have heard for a while now that English is the hardest language to learn. I always assumed it was because of the goofy and confusing grammar rules. I never even considered how much words with multiple meanings would play into it. As a matter of fact, the grammar rules of English are actually supposedly some of the easier ones to learn.

This article points out that words are easier to learn when associated with something else. This is a great way to learn vocabulary in math because almost every word can have  some sort of visual representation of that word. 

Reflection 7

In Tierney and Readace's chapter, the reader is introduced to 7 different strategies for increasing students' vocabulary. These 7 strategies were  possible sentences, list-group-label, contextual redefinition, feature analysis, world map, vocabulary self-collection, and Levin's keyword method. The authors do a good job providing descriptions of the strategies and also the purpose of the strategies. Unfortunately, I do not believe that all 7 strategies could be 100 % successful in a maths classroom.
This chapter points out a recently popular idea that most students will struggle with reading and comprehending if there are words that they are unfamiliar with. This makes a lot of sense. I believe a big problem is that the students may not be able to use context clues to determine the meaning of a word and most will definitely not take the time to look the word up. Therefore, if they do not give up immediately, they will continue to read with very little understanding. therefore it is the teachers job to take time to identify any words they believe may give the students problems. Take time to define these words or ask students to provide definitions before they read. This is a great pre-reading activity. This also can help with the implementation of the new common core standards that pertain to vocabulary.

Reflection #6

In chapter 11 of D and Z's text, they address why many students often struggle when reading texts. I really enjoy that they focused on maths. It is rare that reading in maths is addressed, especially readers that struggle. They point out that many students often struggle because are unable to visualize what they are reading. Also, sometimes they lack certain prior knowledge to help them understand certain words and contexts in the text they are reading. I believe that visualizing problems, especially word problems, can really increase understanding of what is being asked. Another plus is the fact that an opportunity to connect it to the real world presents itself. One way I believe can help students understand and visualize is having them draw a picture of what is happening in a word problem. This allows them to not only see what is being asked, but also creates a visual reference to guide them all the way through the problem.

Reflection #5 BBR Ch. 6

This chapter was a great reminder of strategies to help improve a student's reading comprehension.The majority of these strategies have been introduced to me before but I must say that the refresher course was much needed. Sometimes it is easy to forget the importance of both pre and post reading questioning.
Surprisingly, I think many of these can be used in mathematics even though most would not see reading activities lending themselves to mathematics. One particular strategy I liked was the quick writes strategy. With common core recently being implemented, there will be much more more writing and defending of answers, even in maths. Quick writes can allow ample opportunities for students to practice this before being formally evaluated for it on the CCSS testing. It is important for students to be able to defend and explain their answers. Not only will this give us a better insight into their thought processes, but being able to articulate your thoughts can increase the likelihood of recognizing where an error occurred.

D & Z Chapters 3&4

Recently we have been discussing the readability and effectiveness of text. I must say that I never took it much into consideration before. In this weeks chapters. D and Z brought up some great points. I personally related to Chapter 3 when D and Z discuss the poor design of textbooks. Textbooks are meant to be an aid in education and unfortunately sometimes something as simple as the design and layout of the text can hinder the users education. Math texts are very unique when it comes to content and design. I have seen and used many different types/publishers of texts and the differences are usually quite obvious. It seems to me that most texts are written to use for 100% of the concept introduction and teaching of that content. I have come across books that I do believe can be used just about every day and can be very beneficial to students but this is not the case with the majority of texts.
I am teaching a Bridge math course, which is a fairly new type of course. Therefore, the books are relatively recently written. Because of this, I believe that the text was rushed to publication and there was not enough time or planning spent in creating the text. I do not actually use the book in my class. I use it mostly as a guide for me to determine which concepts should be taught in what sequence. The students don't seem to mind not having a text. I believe the Tennessee Bridge Math book is one of the most poorly written texts I have read. It covers a wide variety of topics but does not provide many well detailed examples. It is definitely a representation of the ever popular education phrase "a mile wide and an inch deep."
I dont think that all texts are bad and that teachers should disregard their help, but I am gaining much more confidence in my ability to find the usefulness of a text.

Reflection #3

This weeks reading from Daniels and Zemelman was a nice change of pace. Mathematics does not often get recognized when speaking about text books. I really enjoyed that chapter 6 provided many ways to help both teachers and students interpret math texts. This chapter points out that often times, math texts are the most difficult to read and follow. I have a feeling that this just intensifies student's frustrations with mathematics. The typical layout of math texts is very different from what students are used to when they imagine a text book. As do most people, students get very uncomfortable when dealing with unfamiliarity. I believe students often struggle reading math texts because of this lack of comfort. When reading math texts, students will often get stuck in the middle of reading and immediately get frustrated. If they do not give up, then their frustration clouds the rest of the reading. This really bothers me because I believe math texts can be very easy to read if given a far chance. Most math texts give a step-by-step instruction when introducing a concept and/or formula. Also, many times there are side notes that elaborate even more on the step-by-step instruction. I think that teachers can give students directions and suggestions on how to read through math texts at the beginning of the year to help rid some of the future frustration.