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. 

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.

Readability

I chose to do a readability calculation on the Tennessee Bridge Math book since that is the book that I kind of, sort of, use in class. I was a bit shocked to see the average readability of the three passages  I chose was only a 6.4. It makes a bit of sense considering the course is a remedial course, but still 6 is a bit low. The first two passages I quoted were only a 5 while the third was a 7.6. I am very curious to see just exactly how readability is calculated. I used the Flesch Method for calculating it by copy and pasting text into Microsoft Word. I would also like to see if the different methods calculate readability differently.

Web Resource: CoolMath.com

The website CoolMath.com is a great resource for teachers, students, and even parents. The site addresses many different levels ranging from prealgebra through calculus. The site was designed for just about anyone. The sites claims to be designed for "math geeks," students just looking to get through a class, and even those that claim to hate math. the creator, Karen, created the site looking to help anybody that seeks help in the math world. It seems that the majority of funding stems from donations and also ad space. There are ads on the sides of just about every page, but there are no pop up ads and the ads take up very little space. Most importantly, the ads do not take away from the functionality of the site. There is a clear link to the donations or ad space information if anyone is interesting in supporting the site.
Upon entering the site, it is quite clear that it is meant to be edgy. There is neon colored font on a black background. This layout and design does not hinder the navigation of the site; as a matter of fact, it seems to enhance it. Everything is clearly labeled and takes you directly where it says it will take you.
At the top of the home page, you will notice tabs that will take you to a spin off of the CoolMath site that take you to special sites for teachers, students, parents, finance, etc. The site seems to be best utilized as a source to help solidify your understanding of a concept (from a student's perspective). It does not necessarily teach a concept, rather than let you explore it. This is mostly done through completely interactive games. However, using the teacher resources, there is access to many lesson plans, activity templates, and many other things that can be used as a teacher in the classroom. The amount of resources for both the teacher and the student is astounding. There are suggestions, examples, and templates for lessons and other resources such as eportfoios or web quests. One of the only drawbacks of using this site is that each student will need access to the internet and a computer in order to use the site properly.
Overall, this seems to be a great resource for anyone experiencing any sort of math from any perspective. The site is very user friendly and easily navigated. I was personally impressed with the amount of resources acquired since its creation in 1997. Check it out!

Developing Lanuage

Hart and Risely

This article focuses mainly on the development of language of children from different economic environments. In particular, it focuses on the experience of words during early childhood. There is a large gap of the number of words children are exposed to by the age of four. Children coming from upper socioeconomic status have experienced up to thirty million more words by the age of four then children living in a welfare family.  It also states that the gap seems to grow as the children get older. This is a good reminder to educators that there a lot of factors that affect a child’s life before schooling even begins and that many of these factors are out of our control. It is important to remember as an educator, that every student is different.  I would have liked to see a little more results regarding the middle classes. It also seems that this study was a bit skewed due to the fact that they were only able to gather info from families that were willing to cooperate. There are many factors that could alter a child’s language development regardless of socioeconomic status.

Since my focus is mathematics, I found myself often wondering just how this study would affect mathematics language development. Most words used in mathematics have a good chance of never being experienced until introduced in a classroom, regardless of socioeconomic status. I am curious to see just how much early childhood language development affects the ability to learn mathematics vocabulary in school.