So What?

Adams, Thomasenia Lott (2003). Reading Mathematics: More than Words Can Say. The Reading  

            Teacher, Vol. 56, No. 8, 786-795

Purpose of Article: Adams wants to provide “impetus for teaching children to read mathematics” (p. 787).

What was studied/discussed: Adams discusses reading mathematics in more depth than typically considered. She believes that it should be read as a language and provides examples related to  reading mathematics that can also be applied across other subject areas.

Important Terms: symbols, numerals, words

Results: Adams identifies key characteristics to reading mathematics as a language. First, definitions can be beneficial to students using both formal and informal definitions to learn the meaning of a word. A way to help students develop definitions is asking them to identify examples and non-examples. Another characteristic of mathematics to consider is words with multiple meanings and how these multiple meanings can confuse the child trying to understand maths. Making connections to the student’s prior meaning of the word and the mathematical word can help solidify and strengthen the student’s understanding of the maths terminology. Homonymic words can also present a challenge when reading because students may attach an incorrect meaning to a new term because of its similar sounding partner from everyday language. Students must be provided ample opportunities to read mathematic passages. In order to ensure understanding of the passages, it is important to focus on the key mathematical terms that add complexity to the passage.

So What?

·         At what grade level should teaching reading become the priority? Obviously, teaching students how to read mathematics in this fashion requires a lot of time, planning, and effort from both the students and the teachers. Teachers these days are always pressed for time in a math classroom. These are great ways to strengthen understanding but what sort of compromises need to be made in order to ensure time for the material to be covered and focus on reading? If reading ability is a factor, does it become the math teacher’s responsibility to strengthen reading ability?

·         Where should passages be found in order to provide ample opportunities to read mathematical passages? I have a hard time finding mathematical passages that lend themselves to reading outside the textbook. Even the text has scarce reading passages. I believe that reading the mathematics language often can be great for students. I just am unsure as to where readings can be found. Also, how will you know if a reading is to complex?

·         How much time will it take to break the meanings wrongfully connected to terms? There are many cases that can lead to students connecting wrong meanings to words. I am sure this can be undone, but at what cost? It is not exactly easy to unlearn something. The more you read, the more opportunities you will have for these wrong connections to be made.

Reflection 11Tovani Ch8

I enjoyed reading this chapter. It really got me considering some things That I hadnt previously. This chapter focused on assessment and it purpose in your classroom. Assessment can be a very powerful tool if used correctly. In particular, assessments need to have a purpose. This purpose must be relevant to the students if  you seek the best results possible.
One tool that I may use in the future was the conversation calendar. It seemed like a good way to give students an opportunity to speak their minds without criticism from their peers. Also it allows the teacher to converse in a less formal fashion and build a relationship with the students.

Text Set Collection #2 Fractions

Books:

Grade 6 Fractions

Author: Kumon Publishing

Grade: 6

This book is designed specifically for 6th grade work with fractions. In particular, this book addresses how to add, subtract, multiply, and divide fractions with unlike denominators.

Full House: An Invitation to Fractions

Author: Dayle Ann Dodds

Grade: 1-4

This book tells a story of a character that hosts "Strawberry Inn" and takes in all sorts of visitors. Readers are encouraged to interactively do math while reading the book to predict how portions of food will be divided amongst the guests. 

Fractions Decimals and Percents

Author: David Adler

Grade: 2 and up

In this book, readers take a look at how fair games use fractions, decimals, and percents. The reader will apply real world applications of the concept and use their knowledge to increase their chances of winning at the fair. 

Funny and Fabulous Fraction Stories

Author: Dan Greenberg

Grade: 3-6

Greenberg takes an entertaining approach to practicing fractions. This book is a collection of 30 different funny and entertaining reproducible stories to help motivate students to participate in using fractions. 

Fraction Fun

Author: David. A. Adler

Grade: k and up

This book uses illustrations to help portray fractions visually. Common uses such as money and pizzas help demonstrate how to use fractions. 

Whole-y Cow!: Fractions are Fun

Author: Taryn Souders

Grade: 1-4

Using a clever and funny cow, Souders shows that fractions can be fun. Throughout the story, the goofy cow uses poetry and games to journey through the basic concepts of fractions.

If You Were a Fraction

Author: Trisha Speed Shaskan

Grade:1 and up

This book asks students to consider ways they could be fractions. Using real world applications, readers are able to gain a better perspective as to how fractions can be used 

Websites:

Fractions by Zeebo

http://www.coolmath4kids.com/fractions/

Grade: 2 and up

This link is a menu that navigates you to many different topics involving fractions. Everything from what a fraction is to dividing fractions. Also at the bottom of the page you can find a link to some games involving fractions. 

Fractions!

http://www.mathsisfun.com/fractions-menu.html

Grade: 3-7

This menu leads you to different ages that elaborate on different characteristics of fractions. It begins with a description and definition of fractions and also provides some real world applications. This menu is easily navigated and describes fractions in great detail. 

Visual Fractions

http://www.visualfractions.com/

Grade: 3 and up

This site allows many visual representations of fractions. You are able to create fractions and perform operations on those fractions. It allows you to see, visually, what each operation is doing to the fractions. This is a great site for visual learners. 

Help with Fractions

http://www.helpwithfractions.com/

Grade: 4 and up

This site was created for those that have already been introduced to fractions. It is meant to be an aid and elaborate guide to extending understanding of fractions. It can be helpful for those that struggle with fractions and also those who simply want to increase their understanding. 

Apps:

Fraction Monkeys

http://www.fractionmonkeys.co.uk/

Grade: 4-7

This app is an interactive game involving fractions. This app is designed to solidify understanding of equivalent fractions and ordering fractions. Monkeys are used along with a number line to help visually understand fractions. 

Articles:

New Approaches to Teaching Fractions

by Sue Shellenbarger

The Wall Street Journal

This article addresses a government funded research project. The government is researching new ways to teach fractions. This article explains new approaches discovered and also describes the type of research being done.

History of Fractions

by Liz Pumfrey

NRICH

This short article takes a look at how fractions developed throughout history.Surprisingly, fractions are a relatively new development. There is a brief overview of numbers and how they were used to create fractions. 

Teaching Fractions According to Common Core Standards.

by H. Wu

This article takes a look at how common core will effect fractions in the classroom. It addresses changes that must be made in the classroom in order to incorporate common core standards. There are also suggestions on how to teach and use fractions in relation to the common core expectations. 

BBR Chapter 7

This chapter addressed a crucial topic that pertains to students learning. In chapter 7, BBR discusses strategies to develop student's independent learning abilities. It is important for students to be able to work with others but it is also important for students to be able to learn on their own. In college, students will be required to learn much more material on their own than they are used to. This will aslo be crucial when studying for exams. 

I believe that the PLAE was a great strategy for students to learn to use. PLAE stands for preplan, list, activate, and evaluate. My favorite characteristic about this strategy is the fact that it requires students to address all three parts of reading. They must preplan before they read to get ideas about what they are going to read. Many students do nothing for pre-reading. Then they are also required to use the strategy while they are reading in order to increase the opportunity to comprehend their reading. After reading, the students must reflect and evaluate what they have just read. Being active in all three parts of reading will most likely increase the chance of retaining what was read. 

Reflection #9

The Long article was very interesting. It was nice to get another perspective on the CCSS and it's implementations. I must say that there was one point that really got my attention. I noticed that the CCSS was striving for mostly technology based assessments. This raises some major issues for me. First off, the most obvious thing is that every school and every student must have access to technology. Not every school has a budget to obtain enough technology needed for this. Another issue is electricity itself. Just last week, the power at my school went down school-wide. Lets say hypothetically you were completing one of these tech based assessments when this happened. What do you do? Is it really fair to make students start all over? More than likely, the work would not be saved, and all of it would be lost. Just as easily, the internet could go down. I imagine that the internet would be a crucial component to these tech based assessments. I like that the government had goals in mind when creating these standards, however, I feel that some things dont consider every possible situation. Seems to be a reoccurring theme in education.

Web Resource: AAAmath.com

AAAmath.com is a easily navigated site. At the top of the page, you can search for a topic via grade level. On the left side of the page, you search another why by searching by topics. Unfortunately, the topics only cover material for kindergarten through 8th grade. I believe the site could be used in schools, however, it seems to be more beneficial as a preview of a concept or a review of the concept. 

One thing I enjoy about the site is its organization. After finding your topic, the first thing you will see is a description of the topic. It is not an extensive description but is definitely sufficient. There is also examples provided. After the description, you will find an interactive practice tool that allows you to practice the topic using your examples. These practice tools are helpful because its inputs are labeled. This can help solidify your understanding of why something  is in the place that it is and also what happens at that place. As you get towards the bottom of your topic page, the majority of the topics have an interactive game that you can play as extra practice. 

There is no sign up necessary. There are some ads but all of the ads that I have noticed pertain to some sort of education site. 

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.