So What?

Towers, J., Martin, L. C., & Heater, B. (2013). Teaching and learning mathematics in the

collective. The Journal of Mathematical Behavior, 32(3), 424-433.

Purpose of article (What was studied/discussed): 
"In this paper we analyze and explore teaching and learning in the context of a high school mathematics classroom that was deliberately structured as highly interactive and inquiry-oriented.” The article explores teaching and learning in highly interactive classrooms, which is something not all teachers and students are used to, especially in mathematical classrooms. The article also focuses on the role of the teacher in inquiry-oriented classrooms, which again dramatically differs from the original role of the teacher because they now act as a facilitator, rather than a lecturer. Finally, the article discusses the idea of positioning the work as a way of being with mathematics, in hopes that math will actually mean something to the students rather than just something else they have to learn. Overall, the authors claimed, “We attempt to show how this classroom of mathematics learners operated as a collective and focus in particular on the role of the teacher in establishing, sustaining, and becoming part of such a collective.”

Important terms: Enactivism; Group learning; Group cognition

Results:
The authors focused on the idea of enactivism because it is in the interaction between the learner and environment that learning happens, not because of the learning environment (including the teacher) or the learning him/herself. The study then was based on the nature of collective mathematical understanding, which evolves from interaction and woven ideas. Data was collected in two high school classrooms (taught by the same teacher) in a single high school in a Canadian city.  "Our analysis reveals significant insights into the ways in which a collective might be orchestrated in the high-school setting."  The authors then clustered their findings into two groups: "(1) those that address the (teaching) structures necessary for initiating and sustaining such a collective, and (2) those that reveal the kind of relationship with mathematics that is fostered in this environment."

So What?

Should students primarily be in or out of their seats while learning?
The authors primarily focus on the set up of the classroom and were analyzed throughout the study. "Most days, the students are offered a problem and encouraged to get out of their desks to work on the many whiteboards.  Considerable numbers of whiteboard pens are made available to them and they jostle for position, some students writing on the board, others offering suggestions about what to write or draw.  Students often add to one another's drawings, or erase all or parts of a drawing someone else has created."  Personally, I love the idea of having students out of their seats and presenting their work to the rest of the class because this fosters higher-order thinking, questioning, and good discussion.  Do you think this classroom environment is effective or would it simply cause chaos and disturbance for other students?

Is the planning worth the product?

As a new teacher, I am certainly aware of how demanding this job is because we have to constantly be prepared, in ways that are primarily beneficial for our students. Do we have time to really design a plan of which fosters group work and collaboration or should we just stick to the basics to save time? “Planning for teaching and learning in this kind of space requires a preparation that goes well beyond the textbook and teachers’ guide. Sharon plans for teaching in a flexible manner, starting with the curriculum guide to ‘locate’ herself for the unit, drawing on a range of resources or creating her own problems and activities, and always reflecting on the previous lesson to determine where to begin the next.” I know that this type of classroom is more meaningful and engaging, but is all the planning worth the final outcomes?

Do you agree with the idea that “what is not prohibited is permitted”?
What can we interpret about a way of being with mathematics in a classroom like the one the authors described? “Students move freely around the room once the task is initiated.  There are natural limits but there is no densely woven, blocking, and stifling system of rules.” The authors stress on the idea that mathematical problem solving should not be something students need to struggle with on their own, but rather make it a public process and discuss with others. This type of interaction certainly calls for such freedom of movement around the classroom. In this type of classroom students are encouraged to look at other classmates’ work, by analyzing, questioning and challenging other students’ solutions. Do you agree with this idea of learning or do you consider it cheating? 

Text Set Collection #2

Topic: Trigonometric Functions

Books:

"Trigonometry For Dummies"

Grade: 9-12

Trigonometry For Dummies is a friendly guide for students who fear trig by explaining the basic concepts , offering lots of easy-to-grasp example problems, while adding a humorous tone throughout the entire book. I also chose this book as a resource because it successfully explains the "why" of trigonometry by using real-world examples that highlight the value of trigonometry in a variety of careers.




"The Humongous Book of Trigonometry Problems"

Grade: 9-12

The author created this book to offer, not only a collection of problems, but also notes in the margins, adding missing steps and simplifying concepts and solutions. I thoroughly enjoyed this aspect of the book because students will now have the opportunity to attempt the problems with the security of no longer being left to wonder where a particular answer came form.



"Trigonometry Demystified"

Grade: 9-12

The ongoing problem with mathematics is that students are never offered an explanation of where the concepts came from but this book unravels many topics' fundamental concepts and theories at the student's own pace.  This book eases students into trig and offers them detailed examples make it easy to understand the material, and end-of-chapter assessments to help reinforce key ideas.



"Trigonometry Success In 20 Minutes a Day"

Grade: 9-12

"Trigonometry Success in 20 Minutes a Day helps students quickly and painlessly acquire practical skills in trigonometry through a series of simple, 20-step lesson plans."  The authors of this book thoroughly explain to their readers all of the basic concepts of trigonometry and offer them hundreds of practice problems for students to attempt on their own to master the material.


Websites:

http://www.regentsprep.org/regents/math/algtrig/ATT1/trigsix.htm

Grade: 9-12

"The goal of this nonprofit site is to help high school students meet the New York State Regents requirements in English, Mathematics, Science, and Social Studies." The website offers students wonderful lessons, resources, and practice problems regarding the six trigonometric functions to help them master the key concepts of trigonometry.

http://www.clarku.edu/~djoyce/trig/functions.html

Grade: high school/college

Clark University's website offers students a "Dave's Short Trig Course," which simply brakes down the trigonometric functions by using key vocabulary, interactive videos, and in-depth explanations regarding the history of trigonometry.



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

Grade: 9-12

"Purplemath contains practical trig lessons demonstrating useful techniques and pointing out common errors.  Lessons are written with the struggling student in mind."  I chose this website as a resource for trigonometric functions because it contains helpful trigonometry lessons, quizzes, worksheets, and free online tutoring to help students gain self-confidence.
Purplemath created a wonderful webpage for students to reference while graphing trigonometric functions, which includes examples with amplitude, vertical shift, and phase shift.





http://www.mathopenref.com/trigfunctions.html

Grade: 9-12

The Math Open Reference Project is a free interactive math textbook on the web, initially covering high-school geometry. These interactive tools and animations, provides an engaging way to learn and explore the subject because teachers will now have new ways to teach, and provide students with a new way to learn that is fun and engaging.

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

Grade: 10-12

Paul's Online Math Notes is a free website that includes math tutorials and notes pertaining to Algebra, all the way through Calculus III.  I chose this website as a resource because I frequently use it to answer any questions I have. Paul's online notes provide students with simple explanations clarified a different way.  These notes are very well organized, allowing students to quickly see the connections between different topics by simply scrolling through his notes. 




https://www.khanacademy.org/math/trigonometry/basic-trigonometry

Grade: 9-12

Khan Academy is an organization with the goal of changing education for the better by providing a free world-class education for anyone, anywhere, anytime. Khan Academy's materials and resources are available to everyone (teachers, students, parents) completely free of charge.  The Trigonometry page provides students with many YouTube videos that they can watch, as well as interactive notes for them to reference.  These videos reinvent education and allows the opportunity for more instruction for the students.



http://www.sparknotes.com/math/

Grade: 9-12

SparkNotes is known for containing "today's most popular study guides."  I chose SparkNotes as a resource because it offers study guides and discussion forums for many mathematical subject.  I was thrilled to find out that this site offers detailed, educational study guides for mathematics because I believe that so many students already use SparkNotes to improve their understanding of other topics. The website is extremely easy to understand and navigate, allowing any student to study and practice at home on their own!



http://www.mathsisfun.com/algebra/trigonometry.html

Grade: K-12

I absolutely love Math Is Fun and frequently use it on my own time for my own benefit! It is an excellent resource for students of all ages, teachers, and even parents because is mathematically beneficial and easy to navigate.  On this website trigonometry is easily explained for all to understand and offers multiple puzzles, games, quizzes, and interactive worksheets.



http://www.sosmath.com/trig/Trig2/trig2/trig2.html

Grade: high school/college

S.O.S. MATH is a free online resource of math review material for students, ranging from Algebra to Differential Equations. It's a wonderful resource for high school students, because it offers help with homework and quickly refreshes their prior-knowledge of many key concepts. S.O.S. Math is filled with more than 2,500 pages of mathematical resources and easy to understand explanations, including an in-depth analysis of trigonometry.



http://www.coolmath.com/reference/triangles-trigonmetry.html

Grade: K-12

Cool Math is a fun and interactive website for those who are confused, bored, hate math, or simply can't get enough of it!  Wether students just want to play games to enhance their understanding or read about a concept that they can't seem to master, this site offers every type of student an opportunity to explore and find a love for mathematics.  I absolutely love this website and often reference to it while teaching.



http://www.mathtutor.ac.uk/trigonometry

Grade: 7-12

Math Tutor was created by a group of teachers, mathematicians and new media producers from the Universities of Leeds, Lougborough and Coventry to create a mathematics tutorial site regarding seven different math topics, including trigonometry.  This site offers interactive videos for students to watch, text for them to read, a diagnostic test for students to complete, and many exercises for them to really master trigonometry at their own pace.

Reflection #11

Sinatra: Teaching Learners to Think, Read, and Write More Effectively in Content Subjects

"The method of teaching learners to think, read, and write more effectively described in this article is a teaching-learning construct that incorporates text structure, concept or cognitive mapping, and a shift in teaching style that helps learners achieve the reading-writing connection in content subjects."  The article then goes onto discuss how schools can implement a plan like the Teaching-Learning Construct.  Teachers initially have to model to their students what they are expecting from them, especially whole-class instruction to explain and organize the content information of the current topic.  Once students have completed a few model mapping lessons, the teacher can move to "guided practice," in which students are practicing the strategy with the help and guidance of the teacher.  Finally, once students have had to opportunity to work together they can then complete these mapping strategies on their own by incorporating higher-level thinking and planning.

I believe it is extremely important for teachers to remember how valuable a picture or visual representation can be for students' academic success.  "Because concept maps portray model plans of text structure, students formulate mental plans of comprehending and composing as they read and write."  Through implementing this type of strategy in the classroom, teachers are capitalizing on the "big idea" and allowing students to discover it on their own, which gives the material much more meaning.  This style of teaching can certainly be applied to by content area because it is extremely important in mathematics for teachers to understand that this different teaching style, "involves moving from a didactic, direct-instruction teaching style to one that is more indirect and calls for student participation." Giving students the opportunity to really explore a topic by completing hands-on and authentic activities, they are able to gain a deep understanding of the concepts and ideas. Mathematics teachers could definitely use a classification map in geometry because the main topic is classified or categorized into different subclasses and/or by relationships of different examples (i.e. triangles).

Web Resource Review #2

Math is Fun -- Math Resources

Math is Fun is an excellent resource for students of all ages, teachers, and even parents. This site is regularly updated on a daily basis and has been helping students learn for nearly thirteen and a half years now.  On this website math is explained through an easy language for all to understand and offers multiple puzzles, games, quizzes, worksheets and even a forum. The homepage is extremely easy to navigate (shown to the right), and allows one to quickly pick the area of mathematics they want to investigate.  Also on the homepage, students have the opportunity to view Math Tools and Math Links, which brings them either to a page full of online technological math tools and/or calculators, or another page full of different mathematical links anyone can access.  Once a student clicks on one of the links, they are brought to another page, which usually has an introduction, links to the basis of that subject, as well as links for almost every other idea pertaining to that topic.  I really love how friendly the website is because a lot of students fear math due to the mathematical language, but this site's language is respectful to all students.  The examples are extremely beneficial and the activity index allows students to "learn best by doing," which is always helpful!

As stated above, this website is also a wonderful resource for teachers because the authors of Math is Fun created a link on the homepage titled, Teacher's Page, where teachers can find plenty of manipulatives, puzzles, quizzes, and worksheets.  As a first year teacher, I know how wonderful and useful these types of resources are because it is hard to always find the time to create our own materials.  The site is free for all users and is constantly asking for suggestions from their users because they try to cover the material for all ages and are willing to modify the site in anyway possible.  

Reflection #9

CCSS Implementation Becomes a Flashpoint for State and Federal Action

This week's readings primarily focus on the Common Core State Standards, as well as why and how administrators are implementing the standards within their state.  "The Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them."  The reasoning behind these standards is to provide students with a higher and more challenging education, which will prepare them for college and careers.  The consistency among the standards is also a a key aspect of the CCSS because the educators, students, administrators, and parents all have the ability to know when and what the students should be learning.  Unfortunately this change is a very big change for students and teachers.  "The balance is very difficult as the change to the new standards is a significant change in curriculum. Not only do teachers need to re-orient much of their instruction, students must be re-oriented to this new change as well."  This is one of the major issues that I have seen at my placement school and in my own classroom because teachers don't seem to have enough resources, while students are unaware of what the new standards are asking them to do.

With this said, I still believe that the Common Core State Standards are going to make a positive impact in our school systems because teachers have to push their students and present them with challenging exercises.  This can definitely be applied in my content area because a big part of CCSS is for teachers to have their students justify and explain everything. Although this can become annoying for students, the final product is worth it.  I recently did a task called, "The Missing Coefficient," which forced my students to use the Remainder Theorem and to think abstractly.  Although they were struggling at first, once we shared ideas and talked it out all of my students were able to come up with an answer and justify it.  I have to say it was a lot of fun to watch them figure it out and I could tell that many even enjoyed the challenge!  CCSS is definitely a change but teachers should embrace the positive aspects of it and see if it works in their classroom!

Text Set Collection #1

Topic: Exponential and Logarithmic Functions

Books:

Schaum's Outline of PreCalculus

Grades: 11-12


Fred Safier (author)
McGraw-Hill; 1 edition (October 1, 1997) (publisher)

This book was created to help students study the concepts and ideas of pre-calculus without the overwhelming and unnecessary detail.  Students can get a complete overview of the subject, as well as plenty of practice exercises to test their knowledge and skill.  I chose this text because I really like the idea of giving students the opportunity to analyze and review the material through a different approach because sometimes students have a hard time understanding it with just the teacher's explanation.


Dr. Math Explains Algebra

Grades: 9-12

Dr. Math Explains Algebra is a book that sets a clear introduction of algebra for students, especially those who just got out of pre-algebra and believe things are going to get harder in algebra class.  Dr. Math is a popular online resource, has also created books to help students with their trickiest algebra problems. This book is filled with practice problems, clear explanations and helpful hints.  Students will find "the answers to dozens of real questions from students who needed help understanding the basic math concepts in a typical algebra class."  I absolutely love this aspect of the book because by using real students' problems, other students are more likely to find meaning in this type of resource and can easily connect to these common miscommunications.




Algebra I Essentials For Dummies

Grades: 9-12

Mary Jane Sterling (author)

Algebra I Essentials For Dummies was created to help students review and/or reference critical concepts of algebra that they need to fully understand before moving on to more challenging concepts and ideas.  This book focuses on the critical components of algebra but provides explanations that are clear and easy to understand by most, if not all students.  I chose this book because I think it is a wonderful resource for both students and their parents to reference while studying for tests or completing daily homework assignments.  The layout of this book is easy to follow and clearly states and highlights the imporant information that students really do need to succeed in algebra.





Algebra Survival Guide: A Conversational Guide for the Thoroughly Befuddled

Grades: 9-12

"If you think algebra has to be boring, confusing and unrelated to anything in the real world, think again! Written in a humorous, conversational style, this book gently nudges students toward success in pre-algebra and Algebra I."  I chose this book because I believe that the conversational tone is something that many students would find humorous and meaningful, hopefully allowing them to find an interest in algebra.  This book has a question/answer format, with also many practice problems for the students to complete on their own, with a tutor, or even with their parents.  It also includes lively cartoons created by Santa Fe artist Sally Blakemore, an Emergency Fact Sheet tear-out poster, and even an "Algebra Wilderness" board game, allowing students to actually have fun while learning algebra!




Painless Algebra (Barron's Painless Series)

Grades: 9-12

Lynette Long Ph. D (author)

Painless Algebra was particularly written for those students who find algebra unusually difficult and confusing, or even just plain boring.  This self-teaching guide helps students clear up any confusion and common misconceptions so that their interest in mathematics can become increasingly positive.  This book offers many intriguing and exciting ways that students can use the subject material and actually apply it for a practice use.  Dr. Long also presents the material in a fun and humorous way by always offering fun-learning exercises, including puzzles, games, and challenging "Brain Tickler" problems to solve.  I chose this book because it challenges the students but in a manor that is extremely approachable.


Practical Algebra: A Self-Teaching Guide, Second Edition

Grades: 9-12

Peter H. Selby (author)
Steve Slavin (author)

Practical Algebra: A Self-Teaching Guide is an excellent book for beginning algebra students because it is easy and fun to use.  By using this book as a reference, students quickly become in command of all the basic concepts and ideas of algebra.  This interactive book is filled with practical, real-life examples and practice problems that help students make meaning of the subject.  Selby and Slavin provide their readers with with techniques for solving problems in a wide range of disciplines.  " Step by step, Practical Algebra shows you how to solve algebraic problems in each of these areas, then allows you to tackle similar problems on your own, at your own pace."  Finally, self-tests are offered at the end of the book for students to test their knowledge at the end of each chapter before moving on.


Websites:

https://www.khanacademy.org/math/trigonometry/exponential_and_logarithmic_func

Grades: 8 and up

Salman Khan (author)

Khan Academy is an organization with the goal of changing education for the better by providing a free world-class education for anyone, anywhere, anytime.  Khan Academy's materials and resources are available to everyone (teachers, students, parents) completely free of charge.  The Exponential and Logarithmic Functions page provides students with many YouTube videos that they can watch, as well as interactive notes for them to reference.  I chose this website for a reference because it allows the opportunity for more instruction for the students.  These videos reinvent education.




http://tutorial.math.lamar.edu/Classes/Alg/ExpAndLog.aspx

Grades: 9-college

Paul's Online Math Notes is a free website that includes math tutorials and notes pertaining to Algebra all the way through Calculus III.  I have personally used this website many times to answer any questions I had or simply have an explanation clarified a different way.  These notes are very well organized and students can quickly see the connections between different topics from simply scrolling through his notes. 


http://www.sosmath.com/algebra/logs/log4/log4.html

Grades: 9-12

S.O.S. MATH is a free online resource of math review material for students, ranging from Algebra to Differential Equations.  This website is an excellent resource for high school students, especially while studying because it offers help with homework and quickly refreshes your prior-knowledge memory of many key concepts.  This site is filled with more than 2,500 pages of mathematical resources and easy to understand explanations.




http://www.ixl.com/search?q=exponential+and+logarithmic+function

Grades: All grades

IXL is an excellent resource for students to use at home or in the classroom!  "Practice makes perfect, and IXL makes math practice fun!  IXL motivates students through interactive games and exercises. With more than 2,500 skills spanning pre-school through high school, IXL offers a dynamic and enjoyable environment suitable for any learning style. Students who use IXL are succeeding like never before."  After exploring the website I was beyond pleased with what I found.  Every grade and/or mathematical subject has links that bring the students to an array of  questions, even word problems, that are algorithmically generated, which means that student will never come across the same problem, no matter how long they visit the website to practice.


http://www.sparknotes.com/math/precalc/exponentialandlogarithmicfunctions/

Grades: 9-12

SparkNotes is known for containing "today's most popular study guides."  This website offers study guides and discussion forums for many mathematical subject.  I chose this site because I really liked the way SparkNotes broke down the information, resources and examples of exponential and logarithmic functions.  I was thrilled to find out that this site offers detailed, educational study guides for mathematics because most students are already extremely familiar with SparkNotes!


http://www.brightstorm.com/math/precalculus/exponential-and-logarithmic-functions/logarithmic-functions/

Grades: 9-12

Brightstorm provides students with quick homework help through expert videos lessons and instant answers.  The creators of this website find the best teachers, film them teaching, and build learning solutions around those great teacher videos for students to easily reference.  I really liked this video of logarithmic functions because I think the teacher clearly portrays the meaning and provides many useful examples.  By watching videos online, students are able to pause them whenever they would like, so writing notes and solving problems doesn't become as rushed, as it would be in a normal classroom.


http://library.thinkquest.org/20991/alg2/log.html

Grades: 8-12

This site was created to help the students who struggle in math (may even consider themselves "morons") clarify some of those confusing math concepts that they just cannot understand.  ThinkQuest is an educational foundation that offers tutorials, same problems, and quizzes, as well as message boards (problems already solved) and formula databases (equations) that any students can reference anytime, anywhere.  I really liked how much this website had to offer and how interactive it is with the students.


http://mathforum.org/index.html  

Grades: All grades

This site is one of the largest and most useful math sites found on the Internet. Math Forum is an online resource for "teachers, mathematicians, researchers, students, and parents using the power of the Web to learn math and improve math education."  This site includes practice problems, team problem solving, research, and online mentoring for students.  Math Forum is one of the most comprehensive resource for math education on the Internet.  It provides Problems of the Week, engages students though Math Help and Math Talk, as well as creating a Student Center, which provides resources for all students.




http://www.purplemath.com/index.htm

Grades: 9-12

"Purplemath contains practical algebra lessons demonstrating useful techniques and pointing out common errors. Lessons are written with the struggling student in mind."  I chose this website as a resource because it contains practical algebra lessons in order, quizzes, worksheets, and free online tutoring to help students gain self-confidence in algebra.

Reflection #8

Bromley: Nine things every teacher should know about words and vocabulary instruction

I believe Bromley chose to write this chapter because he wanted to inform teachers that teaching vocabulary well is a key aspect of developing engaged and successful readers. "This article discusses nine things teachers may have forgotten (or have never known) but need to remember about words and word learning to be effective teachers of vocabulary and their content area."  The following are the nine aspects Bromley believes teachers should always remember: English is a huge and unique collection of words, the rules of English are simple and consistent compared to other languages, language proficiency grows from oral competence to written competence, words are learned because of associations that connect the new with the known, seventy percent of the most frequently use words have multiple meanings, meanings of 60% of multisyllabic words can be inferred by analyzing word parts, direct instruction in vocabulary influences comprehension more than any other factor, teaching fewer words well is more effective than teaching several words in a cursory way, and effective teachers display an attitude of excitement and interest in words and language. This chapter brought a lot to my attention regarding words and word learning, as well as what techniques are most beneficial for my students.  "Overuse of dictionary hunting, definition writing, or teacher explanation can turn students off learning new words and does not necessarily result in better comprehension or learning."  As teachers, we have to give a variety of options to our students for learning because we can't expect that they will all understand the words and material by using the same techniques.

"When students store new information by linking it to their existing schema, or network of organized information, there is a better chance the new word will be remembered later." This definitely applies to my content area because mathematics is a subject of building blocks.  Concepts and ideas are always building from each other and if students can recognize these relationships they will definitely have a better understanding of the material. As I math teacher, I definitely believe that we need to engage students' prior knowledge and related experiences before teaching the new material.  If students already know something and can relate the new content to previous ideas they will understand it at a whole other level.  I also loved the idea of creating three-dimensional words because being able to associate a word with something meaningful is always helpful for the students.  Three-dimensional words include a definition, sentence, drawing, and real object to represent the word.  By doing this students are able to put an image to the word and in mathematics this is crucial for complete understanding!

Reflection #7

Tierney & Readance: Chapter 8

1. What was the chapter about?
In this chapter, Tierney and Readance discuss the idea that vocabulary knowledge and reading comprehension go hand-in-hand with each other because "Word knowledge is a requisite for reading comprehension: people who do not know the meanings of words are most probably poor readers."  Although this quote seems a bit out of date, I do strongly believe that students whom are familiar with more vocabulary words are certainly going to have an easier time reading and understanding materials.  As teachers, we are all aware of this and thus need to discover ways to help those students that unfortunately have not gained the same amount of vocabulary knowledge over the years.  Tierney and Readance described seven strategies that teachers can use dying the instructional lesson to promote students' vocabulary development: possible sentences, list-group-label, contextual redefinition, feature analysis, word map, vocabulary self-collection strategy and Levin's keyword method.

2. What does this chapter tell you about teaching students?
This chapter tells us a lot about teaching students because it gives us a great insight into how we can successfully help them become, not only better readers, but improve their reading comprehension as well.  The seven strategies talked about in this article indicate that many students have trouble determining the meaning of unknown words, relating these unknown words to their prior knowledge and using the context to make informed guesses of unknown words.  These strategies are a way for teachers to help students with this confusion.  This chapter also reminded me that many students can excel by simply being opened up to new vocabulary terms, which can be accomplished by using maps to promote independent vocabulary development.  Finally, making the new words and information more visual to our students can also really help improve their reading comprehension level.

3. Can this chapter be applied in your content area?
Yes, this chapter can definitely be applied in my content area because although there is not a ton of reading in mathematics, there is a lot of vocabulary that most students are not familiar with.  Some of these strategies described in the chapter could definitely be successfully implemented in a math classroom.  For example, Feature Analysis is designed to help students improve their vocabulary and categorization skills, understand the similarities and differences in related words, and expand and retain content area vocabulary and concepts.  This is exactly what a math teacher needs to implement in the classroom! This would help my students recognize the relationship among different vocabulary words and see how they some build upon each other, which is the exact realization I wish to see among my students!

Reflection #6

Chapter 11: Help for Struggling Readers

1. What was the chapter about?
This chapter was primarily filled with many suggestions for teachers on how to help their students who are struggling with reading.  Daniels and Zemelman discuss the approaches that Kenya Sadler (a social studies/reading teacher), her students, and the experts all claim are paramount.  Teachers should build supportive relationships, model thoughtful reading, use activities that build engagement with the text, promote self-monitoring, use materials students can successfully read, and provide books and articles on tape.  After reading through all of these different strategies, I definitely believe that teachers can help improve their student's reading level and comprehension by implementing these techniques.

2. What does this chapter tell you about teaching students?
"Show students that you care intensely about their reading, believe they can succeed, and won't accept anything less."  I absolutely loved this quote from the article because I think it is so important for teachers to remember that students, especially ones that are struggling, need this type of encouragement from their teachers and need to be reminded that they do have the skills to succeed.  Teachers have to show their students that they really do care about them and their education!  Also, I think this chapter reminds me about teaching students that just because we are familiar with the information does not mean our students do!  "Another issue is the sheer unfamiliarity of the content for these students.  They lack background knowledge."  We have to remember to choose readings and materials that students can actually relate to and successfully read on their own.  Finally, it is crucial to promote self-monitoring within the classroom because if we don't push this type of responsibility our students will never grow towards being a successful reader.

3. Can this chapter be applied in your content area?
As I was reading about the situation in the freshman physics class, I was immediately able to relate it and apply it back to my content area.  "First and foremost, they aren't accustomed to turning the words they read into mental pictures.  They don't see what's happening in the problem until considerable amount of discussion brings the picture into focus -- exactly the problem that researchers say is characteristic of struggling readers."  Exactly!!  This problem arrises almost every time my students try and complete any type of word problem.  They have such a hard time gathering the information from the problem and putting it into mathematical context and I now understand that this may be due to their reading level and not even math!  My students also have a hard type completely reading the directions before they begin their work, which causes them to really struggle while completing the work.  In these situations, I believe my class should "model thoughtful reading" to assure that everyone understands what the problem and/or directions are actually saying!

Reflection #5

Tovani Chapter 5: "Why Am I Reading This?"

1. What was the chapter about?
In this chapter, Tovani discusses the idea that reading shouldn't be race.  Reading has a much more significant purpose for students, rather than just trying to be the first one to finish. While reading, students should always try to read to gain something by taking away important information of which they may not have encountered otherwise.  The chapter also discusses who is in charge of setting the curriculum for each content area and how teachers should implement that material to fit their students needs.

2. What does this chapter tell you about teaching students?
I believe this chapter told me a lot about teaching students because teachers have to remember to be clear in their reasons for assigning the reading.  I loved when Tovani said, "When readers have a purpose, they tend to remember more of the text," because I think this is something all teachers definitely have to remember when teaching students.  If we give our students a purpose for reading the material, they can better determine what is important and what they should really take away from the material.  It's also crucial for teachers to remember that it's impossible to effectively teach all of the material in the textbook because how can we expect our students to master the information in less time than we the experts did.

3. Can this chapter be applied in your content area?
Yes, this chapter can certainly be applied in my content area, as well as every other content area!  The "instructional focus guide sheet" is an excellent way for any teacher to narrow down his/her purposes for a specific text.  Tovani did an excellent job of showing how this instructional guide sheet could be implemented in every content area.  Any math teacher could definitely use this sheet to help themselves think through what is most essential and how they will get their students to master these ideas.  Finally, it's extremely important that teachers remember to use their conversation voice in a math classroom, which involves a voice that has a conversation with the text, rather than just simply reciting the words.

Reflection #4

Why Textbooks Are Not Enough

1. What was the chapter about?
In Chapter 3, Daniels and Zemelman review the many reasons why textbooks are simply not enough in the classroom.  They discuss the central role of textbooks, the trouble with textbooks and concludes the chapter by offering suggestions for teachers of whom do and do not use textbooks in the classroom.  The main focus of the chapter was definitely about the disturbances textbooks cause in the classroom, for both students and teachers.  Daniels and Zemelman believe they are extremely overused, which I can agree with to some degree, because some teachers may feel that textbooks are their only resource and don't try to push themselves to find more in depth information.  "Textbooks are superficial, exceedingly hard to read, badly designed, authoritarian, are often inaccurate, not written for students and sometimes cost too much."  Daniels and Zemelman suggest that teachers buy only classroom copies of books, rather than one per student, which would bring down the cost. They also noted that teachers and administrators should be very selective towards the books they decide to purchase because a lot actually come with extra material (CDs full of handouts, videos and posters) and teachers should take advantage of that.

2. What does this chapter tell you about teaching students?
This chapter tells me a lot about teaching students because I now understand how much of an impact textbooks can make on a student's education.  Choosing "the right textbook" can make or brake whether or not a student ends up really understanding the material or not.  I believe the biggest idea is that textbooks are simply not written for students.  Some children may actually know the content material but can't understand what the book is trying to say and convey to the readers.  As teachers, it is our responsibility to make sure we choose books that are student friendly and establish any vocabulary barriers because the lesson begins.  This way, our students won't be as anxious about the textbook and can concentrate more on the actual material.

3. Can this chapter be applied in your content area?
Yes, this chapter can definitely be applied in my content area.  Mathematical textbooks are constantly being published, which allows school systems to trade out old ones for new ones, which is something we as teachers really need to watch out for.  Although textbooks are an excellent resource in the math classroom, there are definitely some textbooks that are better than others.  For example, at the school I am teaching at right now all of the teachers love a certain precalculus textbook and even though different levels of this course require different textbooks, every teacher goes back to that one textbook because of how well written it is.  Although all of the precalculus books are filled with examples, the way this one is laid out and written makes it so much easier to understand the material.  As a math teacher, I will definitely want to use a textbook because it is an excellent resource, for myself and the students, and usually flows in an appropriate manor, but I will certainly keep in mind that some textbooks are better than others and try to find the one that suits mine and my students' needs the best!

Reflection #3

Rationale for Adolescent Literacy

1. What was the chapter about?

Overall, this chapter provided a rationale for specific content-area reading strategies.  Many teachers have noticed a decrease in the comprehension reading levels of most American students and tried to figure out why this is.  Bean, Baldwin and Readence believe, "Diverse and complex issues such as social equity, bilingual education, and formulas for funding public schools combine to make universal literacy one of the greatest challenges of the 21st century."  Our world has gone through so many advances, some of which help students learn but others making this process of reading to learn more difficult.  "Learning to read is the main focus of primary school education; reading to learn is its logical extension and must be the responsibility of middle and secondary school teachers."  This chapter primarily focuses on the difference between these two abilities and offers secondary teachers many suggestions on how to successfully teach their students how to read to learn!

2. What does this chapter tell you about teaching students?

I believe the most important thing this chapter reminded me about teaching students was that, "It is not true that students will automatically modify elementary reading reading skills to suit subject-matter reading demands."  Learning to read and reading to learn are most definitely different concepts and even though students gain the ability to learn in elementary schools, teachers have to remember that their students have not been taught how to read to learn and may not truly understand how to read to interpret a textbook.  "Good teachers know how to tailor the message, activate prior knowledge, focus students' attention and monitor comprehension by checking to see if students understand important parts of a text presentation."  It is our job as secondary teachers to teach our students the skills of reading to learn and if we use these four, crucial suggestions in the classroom, our students will gain this ability and many more!

3. Can this chapter be applied in your content area?

Although this chapter didn't focus specifically on strategies for teachers to use in a mathematics classroom, I believe the suggestions the authors gave for good teachers to have are definitely relevant in my content area.  As I am teaching I have to tailor my message by adapting the presentation of my lesson to the needs of all of my students.  I was immediately able to claim which of my students were going to need more help and whom learned better visually than verbally, allowing me to adapt the way I presented the material.  I definitely also try to activate my students' prior knowledge to remind them that what we learned yesterday can help us gain mastery of what we will learn today, which also helps them focus their attention towards the material.  Most importantly  it is so crucial to make sure all of my students are on the same page as I am and really understand the material.  I never want to move on to the next topic until I know everyone has mastered the current topic, which is why I always ask for their feedback and walk around the room to get a glance at their notes and work to look for any mistakes that should be clarified!  All of these techniques will help students read to learn any day!

Web Resource Review #1

Online Math = FUN - ixl.com is an excellent resource for students and teachers to use at home or within the classroom!  "Practice makes perfect, and IXL makes math and language arts practice fun!  IXL motivates students through interactive games and exercises while keeping teachers and parents informed and involved.  With more than 2,500 skills spanning pre-school through high school, IXL offers a dynamic and enjoyable environment suitable for any learning style.  Students who use IXL are succeeding like never before."  After exploring the website for a while I was beyond pleased with what I found.  Every grade and/or mathematical subject has links that bring the students to an array of  questions, even word problems, that are algorithmically generated, which means that I student will never come across the same problem, no matter how long they visit the website to practice.

What's the advantage for teachers?  This website generates a reports and data analysis tools for teachers to use to gain insight into their students' performance on the website.  This student-friendly website also allows children to work on problems at home, even with the help of their families.  Parents have the opportunity to get on IXL with them and explore the mathematical topics that their children are currently studying.  I absolutely love that IXL offers help to students in Pre-K all the way through Algebra II because the more help our students can get in mathematics the better!  It's extremely convenient that teachers can also allow their students to actually use the website in school so they can monitor and quickly identify how their students are doing on certain topics.  IXL is extremely user-friendly and even though they do have an option for parents and teachers to become members, the website still offers over thousands of practice problems for students to solve for free.  Everyone should check it out!