Being Successful In Math

July 19, 2013

Dear Student,

Math is not scary.  Math is not worthless or to be hated.  Math is everywhere and in everything.  There isn’t a single item or action that doesn’t include math in some way.   Math will never let you down.  It remains consistent in all cultures and all situations.  If you had 2 pencils in one hand and two in the other, if (or when) they discover life on Mars, when you hand all your pencils to the Martian, the Martian will still have 4 pencils.  (2+2=4)  It never changes.  The concepts you learn this semester will stay with you today and appear many times in your lifetime.  Understanding math will open doors to success in the future.

While learning math, I want you to consider math as a foreign language.  A language with its own symbols and lexicon.  Pay attention to your vocabulary as many words that you understand as one thing mean something completely different in a math context.  View math symbols as vocabulary as well.  Every symbol has its own set of vocabulary that can be acted on and manipulated.  This is essential to learning math as much as nouns and verbs are essential to learning English.

To support the learning of the language of math, you will encounter much reading and writing during this semester.  Like an English class, you will be exposed to nouns and verbs as they appear in a math context.  You will be forming sentences through formulas and computations. You may even encounter math themed books and journals.  When you encounter these examples of literacy, like in English, make sure you pay attention to form and vocabulary.  But literacy does not stop in the math classroom.  The reading and writing in the math class is universal.  It will help you in other non-math subjects.  Reading and writing skills used in other non-math courses will enhance your math.  Therefor, read and write as much as you can.  Check out books from the library.  Read newspapers.  Read webpages.  Read bumper stickers and license plates and infer the meaning the owner is trying to make.  Write posts to blogs.  Write letters to parents and friends.  Write letters to the editors of newspapers or your congressman.  Do everything you can to read and write for literacy is truly important to success in the future.

Yours in mathematic literacy,

Mr. Gerringer

10 Strategies for Teaching Literacy in Math

The following strategies are a list of 10 great ways teach literacy in today's math classroom.  They aren't in any particular order.

1.  Occasional Paper 
Definition:  An Occasional Paper is an essay or story written by the student as a reflection of things they experience in their lives as it occurs.  It is read aloud to the classroom.  It is graded for completion but not handed in.
Use:  The OP is used as an effective means of having the student practice reading, writing, speaking and listening.  The paper is written with no deadline in mind and as such doesn't hold the time pressure of a normal assigned paper.  Because it is a reflection of something occurring, the subject can be anything.  As such, because it engages the student completely, the student should be very excited to follow the OP process.  Bill Martin ("A Writing Assignment/A Way of Life") argues that the OP is "one of the most successful and powerful ways of improving student writing." (Martin, p. 52)  In a math class where traditional writing is rare, I can see adding the spin of math to the OP mix.  "Write your OP but try to include some aspect of Mathematics."  This item can help struggling readers by giving them the opportunity to read and write their own words.
Covers:  Struggling readers, assessment, reading comprehension, and critical reading/literacy.

Word Splash

2.  Word Splash
Definition: A Word Splash is a collection of key words or terms jumbled together written or projected to the board.
Use:  Word Splashes are used when vocabulary is being introduced.  It builds on the students pre-knowledge to introduce vocabulary that will be encountered in the upcoming lesson.  Students discuss the words, try to relate them to other words, and predict how they will be used in the upcoming lesson.  This strategy gets the key words out in front of the classroom for all students to read and consider as they are going through the lesson.  It is an excellent way to build pre-knowledge before the lesson and build appropriate vocabulary and comprehension.  This is a strategy I plan to use in my math classrooms prior to any new topic being introduced.  This item primarily helps build reading comprehension as it allows the student to see the term first and discuss its meaning.  Then, after reading the chapter, the student will have more pre-knowledge to add to the comprehension.
Covers:  Struggling readers, reading comprehension and critical reading/literacy.

Frayer Model

3.  Frayer Model
Definition:  The Frayer Model is a type of concept map used for building vocabulary.
Use:  This strategy is used when introducing a new word or phrase.  It provides a visual representation for the student to build vocabulary as well as promotes critical thinking as the student works to fill out the model.  The model builds on the student's pre-knowledge as they build connections with what they know and will learn.  As the students work through the areas of the chart (Definition, Characteristics, Examples and non-Examples) they see attributes of the word as well as define what the word is or is not.  In a math classroom this model can be used to introduce new vocabulary at the start of each lesson.  By defining the word before the lesson it becomes part of the pre-knowledge so it helps in the comprehension of the new topic.
Covers: Struggling readers, assessment, and reading comprehension.


4.  KNWS 

KNWS Chart

Definition: A KNWS chart is a student generated list of things they know and want to know about a math problem.
Use: The chart is a tool that allows a student to go beyond a math problem and identify the critical aspects of the problem. A KNWS chart is used immediately after reading a word problem and filled out completely before attempting the problem. It relies on a students pre-knowledge to summarize the key aspects of the problem. Specifically for use when presented a word problem, it can be used for any other type of math problem. I, however, would strictly use it for word problems in my classroom.  By allowing a student to not only focus on the topic but also what is required to achieve understanding it enhances critical reading/literacy.
Covers: Struggling readers, assessment, reading comprehension and critical reading/literacy.


5.  Providing Diverse Culture Role Models
Definition:  When presenting examples or problems, make sure they include students of diversity involved in the topic.
Use:  In order to engage diverse cultures, students need to see their culture doing the math or engaged in math problems.  For example, using a word problem where the main actor is of mexican decent.  Learning about a female mathematician is another example.  Or maybe showing a picture of a student of indian culture solving a math problem.  Showing examples of students' culture in math allows them to identify with the example and potentially feel more comfortable learning the topic. This is another strategy I will work on deploying in my classroom.  When your examples and figures typically include no culture whatsoever, it will be a bit tough, however in word problems and discovering authors of theories diverse cultures can clearly be seen.
Covers:  Engaging diverse cultures.


6.  Schools of the 21st Century Model.
Definition:  The School of the 21st Century is a community centered school model originally developed by a Yale professor.
Use:  While not really a strategy you can implement in a classroom, it models some ideas that can be.  It exists to provide a full service school from training for parents and teachers to healthcare including dental services.  It attempts to provide children of diverse cultures and needs the basic care that otherwise they would not have access to.  In addition they strive to provide the support structure required as well including educating the parents and working with the community to provide services to the families.  So while not directly influencing literacy, this program gets all the basic needs of a student met.  With the basic needs met, classroom learning (including literacy) will be enhanced.  I can't help but see the benefit this brings to diverse cultures and struggling readers.  Unfortunately I don't have the resources to duplicate this effort in the classroom.  However, after reading Tony Danza's I'd like to Apologize to Every Teacher I Ever Had, I can follow Mr. Danza's and the Schools of the 21st Century model lead and have a "Sandwich Club".  Opening my doors during lunch for anyone to come by, share a half of a sandwich and just chat.  This time would include reading opportunities for struggling readers and perhaps even diverse cultures as alienated kids would be welcome too.
Covers:  Struggling readers, reading comprehension, engaging diverse cultures, and critical reading/literacy.


7. GIST Activity
Definition:  The "gist" of a topic is the main or important concept of the topic.  The GIST Activity is allowing the student to write the gist of the topic in 20 words or less.
Use:  This activity would be great to execute after the student encounters a new topic to check to see if they understand the topic.  Sticking to 20 words or less allows the student to define their thoughts in a concise manner.  It also gives the teacher the opportunity to judge how well the lesson was learned.  This activity can be graded for participation and can be read to the class.  Because of the concise nature of the exercise, students will not only be presented an opportunity for reading and writing but also to critical thinking.  I would like to use this activity in my classroom after I introduce a topic, not only as a tool for assessment but also to judge how well I presented the topic.
Covers:  Struggling readers and critical reading/literacy.


8.  Anticipation Guide
Definition:  An Anticipation Guide is a list of true/false or agree/disagree questions or statements about the upcoming lesson.  The students are asked to check true or false based on their "anticipation" as to what will happen.
Use:  An Anticipation Guide is started before a lesson to induce excitement and prior-understanding about the subject. The teacher lists a few statements geared to introduce the key concepts of the lesson or topic.  Some statements should to be valid and some invalid.  The students are then asked to mark if they "anticipate" the statement to be true or false.  The lesson is then introduced to its entirety and the student then revisits the guide to record what they are thinking after the learning.  A verbal or written reflection time can be included. Assessment can include a participation grade.  This process primarily prompts critical reading/literacy and reading comprehension as they focus on the statement and anticipate the outcome.  This is, to a lessor extent, a good time to monitor the struggling readers.  It provides a good opportunity for reading practice as well as comprehension.  I plan on using the Anticipation Guide in my classroom as I introduce new topics in mathematics.  Word problems are the obvious examples but also questions like "Moving this triangle side causes area to increase by 1/2."
Covers:  Struggling readers, assessment, reading comprehension, and critical reading/literacy.


9.  VVWA
Definition:  VVWA (Verbal Visual Word Association) is another visual organizer like the Frayer Model described above.  The student is asked to reflect and write aspects about a topic:  Vocabulary, picture, definition and how the word relates to the student.
Use:  It creates a visual representation of a topic as well as allowing the student to relate directly to the word or topic being discussed.  This is an excellent tool to use in a math class especially one dealing with geometry.  An example would be he shape of "octagon".  The student would write "octagon" in the word section.  Then they would draw an 8 sided shape in the visual section.  The proper definition would be written in the definition box followed by a brief statement or sketch how they may encounter the octagon.   The student learns the term and makes it "personal" by interacting with the term completely.  I can see this tool would be a great help to visual learners as they try to learn topics.  It also asks the student to think critically as they try to find relationships between the concept and their personal life.  Since this is a personal reflection, assessment should probably be for participation only.  However, it can also be assessment for completion.  It can be reviewed for identifying struggling readers/writers as writing the definition and personal association can identify potential deficits.  I will definitely be using this tool in a geometry classroom.
Covers:  Struggling readers, assessment, and critical reading/literacy.


10.  Math Journal
Definition:  A Math Journal is a personal journal designed for the student to document their thoughts/feelings as they encounter mathematic concepts.
Use:  A student would be asked, as they complete a topic, to record their progress, thought processes, problem solving technique, things that frustrate, etc.  This gives them a document that allows them to go back and self-assess their thought process during the session.  It assists in developing and enhancing the thought processes associated with math.  It allows them to dig deeper into a concept as they interpret their feelings about the topic.  It also improves communication and writing.  So for the student this brief tool becomes a self reflective learning tool.  For the teacher it becomes an opportunity to review how a topic was received, the level of student understanding as well as determining if more time needs to be allotted to the subject.  Of course, a comment like "This teacher stinks." is always possible and indicates that I, as a teacher, am not enticing the classroom enough.  For assessment, a Math Journal can be graded for participation. Because of the literacy implications this journal can be used to diagnose those with writing deficits.  If the journal is read in public (not recommended due to the personal nature) then it can be used to diagnose reading deficits as well.  I like the implications of this tool alot.  I plan on assigning a Math Journal in my classroom.  I also plan on leaving comments in their journals.  It shows I'm really reading and care about their education.
Covers:  Struggling readers and assessment.

10 Resources for Teaching Math

The following resources are a list of 10 great tools to help teach math in today's schools. They aren't in any particular order but have been reviewed for appropriateness.

1.  Khan Academy
Bibliography:  Various. "Kahnacademy.org." Kahnacademy.org. Kahn Academy, n.d. Web.
Summary:  Kahn Academy is a non-profit educational website. Its goal is providing free education to the world through short interactive videos, tracking resources, and support structures.
Use:  Khan Academy is an excellent resource for teachers.  The videos on the site are short, concise and thorough about a specific lesson.  They are suitable to view in the classroom as well as at home.  For a student seeking tutoring, they can set up an account that keeps track of the lessons they have watched.  For classrooms a teacher can set up a "coach" relationship that compiles all the students lessons.  All of this functionality is available on the website free-of-charge.

2.  Flatland: A Romance of Many Dimensions
Bibliography:  Abbott, Edwin Abbott. Flatland: A Romance of Many Dimensions. New York: Barnes & Noble, 1963. Print.

Summary:  Originally written as a social satire to parody the social hierarchy of Victorian Europe, it is celebrated as an excellent discussion on dimensions and the geometric shapes that live in those dimensions.  The story is told by a humble square that lives in the two-dimensional Flatland.  His desire is to travel to the one-dimensional Lineland and three-dimensional Spaceland.  Along the way he meets other geometric characters and encounters rules based on the various dimensions.

Use:  Flatland is an excellent candidate for bringing literacy into the classroom.  It is an great discussion on geometry and dimensions.  The student can read the book and answer various questions of both the literary and mathematical nature.  The student can be asked to present a themed paper to the classroom.  Adding this book to the lesson plan allows a student to practice reading, writing, speaking, listening as well as math.

3.  Making Math Accessible to English Language Learners: Practical Tips and Suggestions Grades 9-12
Bibliography:  R4 Educated Solutions. Making Math Accessible to English Language Learners: Practical Tips and Suggestions, Grades 9-12. Bloomington, IN: Solution Tree, 2010. Print.

Summary:  This book provides strategies and helpful tips designed to help teach math to those learning English as a second language.  It also includes five case studies helpful to the teacher in raising awareness of some of the issues facing the students.
Use:  This resource is specifically for the teacher to enhance teaching skills when it comes to teaching math to kids who don't speak English primarily.  This book is part of a whole series covering all age groups and provides some very valuable tips and suggestions.  I can see using this book as a basis for lesson planning in a classroom.  And since most of the suggestions are applicable to all types of students, it can be applied to a classroom without ESL learners.

4.  Marvelous Math:  A Book of Poems
Bibliography:  Hopkins, Lee Bennett., and Karen Barbour. Marvelous Math: A Book of Poems. New York: Simon & Schuster for Young Readers, 1997. Print.

Summary:  A collection of poems about how math appears in our every day life.

Use:  Part of my philosophy is Math is Everywhere.  Math is significant and important because it plays so many roles in our lives.  This book proves my belief through poetry which will appeal to a younger audience.  This book would be a good one to have in an in-class library.  It is possible that I can use this book in my classroom to help motivate math learners or even help struggling readers by providing them a fun practice reading.

5.  Math Curse
Bibliography:  Scieszka, Jon, and Lane Smith. Math Curse. New York, NY: Viking, 1995. Print.

Summary:  A multi award winning activity book about dealing with numbers in every day activities.

Use:  Following through on my philosophy of Math is Everywhere, this book goes through a day where everything goes wrong (the Math Curse) and ties it in with Math.  Because of the colors, activities and pictures this book would be a great one to have in an in-class library.   It can serve as an attractive book to give struggling readers additional material to practice reading in a math context.

6. Sir Cumference series

Bibliography:   Neuschwander, Cindy, and Wayne Geehan. Sir Cumference ... Watertown, MA: Charlesbridge, 1997. Print.

Summary:  This book series follows a knight, Sir Cumference, through a series of mis-adventures all in a math context.
Use:  This book series serves as another excellent candidate for an in-class library.  The series consists of 6 books (at the time of this post) and has fun characters and stories to really entice new and struggling readers.  I can see where this book would give more material to help struggling readers practice reading in my classroom.

7.  Schoolhouse Rock
Bibliography:  Schoolhouse Rock. N.d. television.
Summary:  A little dated, this video series appeared on t.v. 1973-1984 as a video short.  Set to a catchy tune, various school lessons are acted out by animated characters.  It turned into such a phenomena that it is almost guaranteed there is at least one of the many shorts that you know.
Use:  These videos are so catchy, so wonderfully cute and so delightfully done that they belong in everyone's classroom.  Specifically in my classroom I can see the math lessons being shown at least once per year.  Classics such as "My Hero Zero", "Three is a magic number" and " Figure 8" teach specific lessons in a catch tune that will help students remember the lesson.  The shorts can be integrated in during your planning and shown as part of instruction.  I can see it existing in every in-classroom library.

8.  Pythagoras and the Ratios:  A Math Adventure
Bibliography:  Ellis, Julie, and Phyllis Hornung Peacock. Pythagoras and the Ratios: A Math Adventure. Watertown, MA: Charlesbridge, 2010. Print.

Summary:  As a sequel to What's Your Angle, Pythagoras:  A Math Adventure this adventure book follows young Pythagoras (the Greek Mathematician) as he explores ratio and proportions.

Use:  This book introduces students to ratios and proportions as well as the Green Mathematician Pythagoras.  Another excellent book for the in-class library, this book can be used to help struggling readers understand the theory behind ratios and proportions.   It can see me including it into the planning of a unit or lesson.

9.  RapidTables.com
Bibliography:  "Online Scientific and Engineering Resource." Online Reference & Tools. N.p., n.d. Web. 02 July 2013.

Summary:  An online reference for tables, formulas, and charts for math and science subjects.

Use:  I came across this site when I was brushing up on my factorial skills.  It is a good specialized site that provides detailed information on specific topics.  For example, look at the factorial entry.  It provides a definition, a formula list, a factorial table, and even C (a computer programming language) functions that does factorial calculations.  Information for electrical voltage is even more complete.  What I will use this site for in my math classroom is a reproduction of the graphics and presentations.  For example, in a discussion of derivatives I may have a handout that includes the graphic:

10.  Good Will Hunting
Bibliography:  Good Will Hunting. Perf. Matt Damon and Robin Williams. Miramax Films, 1997. DVD.
Summary:  "Will Hunting, a janitor at MIT, has a gift for mathematics but needs help from a psychologist to find direction in his life." (IMDB.com)
Use:  This movie is #146 out of 250 of the most popular movies on IMDB as rated by the users.  It won  2 Oscars with 18 other awards and 37 nominations.  It holds its own as being a very good movie.  So, for entertainment, it is a recommendation.  But for a math student anticipating more advanced math in the future, this movie is a must.  There are several (albeit controversial in a math context) examples of high level math being shown in the movie.  A little taste of high college math.  I could see this movie being a good "blow off steam" movie.  Maybe the last few days of school where all the papers have been graded, all the exams taken, this movie would serve as a time filler and future math motivator.

Occasional Paper

The morning temperature was a sunny 84 degrees Fahrenheit. Perfect day for a bike ride. As I jump on the 1300 cubic centimeter Honda motorcycle the motor springs to life. 24 miles shows on the trip meter. At 41 miles per gallon and a 3 gallon tank, I should have roughly 100 miles left on that tank of 10 percent ethanol gasoline. Plenty enough fuel for a trip to Pilot Mountain and back, a 53 mile trip.

I pull to a stop at the top of the street, perpendicular to the road that will take me to the highway. I take a second to feel the refreshing 3 mile per hour winds. It is going to be a wonderful ride. The smell of the circular shaped bushes fill the air. The giant isosceles triangle shaped pine trees blur in my peripheral. The path of the bike is not altered by the slow pitch of the road that drops approximately 1/2 inches per foot (or approximately 4%). In fact its hardly noticeable even though it does its job to divert water when its raining.

I pass by a local Mc Donald’s where the sign reads 2 for $3 chicken biscuits but decide to continue riding as I’m already many pounds too heavy. Today there will be one less from the billions served. That’s a shame since the Mc Donald’s “chef” probably worked hard to get the perfect ratio of ingredients to create the tasty biscuits.

I pass by the Wachovia building where on a normal business day bankers look at spreadsheets and models trying to determine where to invest large amounts of money. Customer Service Reps field calls from customers where measurements of talk time and speed of answer are measured for performance.

I pass by the ball field where years and years of playing has proven the physics behind a wooden cylinder coming in contact with a spherical object. An action that brings joy to some and disappointment to others. Where a demonstration of torque and foot pounds combine to send earthly balls to the stars. And pounds of air pressure launch tee-shirts into the crowd where liters of beer flow like water.

And as I point my bike down the highway, I smile to myself and think, “This is going to be a great ride.” And I was right. The sun smiled down and warmed me while the cool breeze kept me from getting too hot. Even though it was a very relaxing trip, my mind was whirling with all the instances of math that I encountered along the way.

From the geometric shape of the trees and bushes in nature to the man who designed the roads beside them. From the electronics contained in the street lights and stop lights to the ratios of ingredients in a Mc Donald’s chicken biscuit. Math is truly everywhere. I don’t believe it is possible to find an object, job, or activity that hasn’t been touched by math in some way. Isn’t it refreshing to think, in a world of variability and change, there is one constant in the universe? This thought, the thought of mathematic’s enduring nature, fills me with euphoria every time I encounter it.

About Me...

Jenn and Phil at the Beach

Who is Phil Gerringer?

I was born the son of a share-cropper and we had to walk to school...4 miles...up hill...both ways...barefoot...

No, none of that is true.  Funny, (at least to me) but not true.  I've spent the last 20+ years as a computer programming consultant, and, after the economy went south, decided it was time for my "retirement job".  I've always loved teaching, working with kids, and math so I figured I'd pursue teaching.  My short term goal is to obtain a lateral-entry teaching position at a high school teaching math.  My long term goal includes finishing my MAT and, after 20+ years of teaching, retire.

I currently live in Winston Salem with my 2nd wife (everyone needs an ex - it builds character) and 4 dogs.  My kids (20 yr. old son and 18 yr. old daughter) both graduated high school and have left the nest.  My son is out in the world searching for his pot of gold and my daughter is off to ECU to continue her studies.  I work at Baptist as a Nursing Assistant Fri, Sat, and Sun from 6:30pm - 700am.  The NA job is fun but I wouldn't recommend the hours.  I've been doing 12 hour nights for 3 years and my body hates me for it.  Right now, my hobbies are school, sleep and work.  My wife and I ride motorcycles and we squeese in time now and then but it isn't as much as we would like.

An Idea...Literacy in Math

My thoughts on Literacy are quite clear.  As I've alluded in a previous post, It is my opinion that literacy is like a key that opens all future doors to success.  And the younger a student is exposed to reading and writing the better.  Even if literacy is being learned in the later grades it still isn't impossible.  Those students just need to work harder and be provided more opportunities.  

I've been struggling with how to include reading and writing opportunities in my chosen profession of math teacher.  But I have an idea...

In my Introduction to the Foundations of Geometry class at UNCG I was assigned a presentation.  We were charged with reading a technical document about a math concept and create a presentation about it.  The PowerPoint presentation is below.

This project easily brought literacy into the math classroom.  Ironically, I did my project on a document about math in literature.  I can see how this assignment can be altered to provide a good opportunity in the classroom.  Find a list of age appropriate math papers or books.  Working in groups or individually, have the students choose one and read it.  Create a presentation on the item and present the topic to the classroom.  This project would provide opportunities for reading, writing, speaking and listening thus providing an excellent chance to practice literacy in a math classroom.

Literacy in the Gerringer House

Of Literacy:
Literacy is the ability to read and write.  Its not quite as simple as that but the definition is the basis of what literacy is.  Being literate is important to every child as it provides building blocks for future learning.  It is the key that opens the doors to success in the future.  In the Gerringer household we have always stressed reading and writing to our children.  And it must have been a lesson learned as we now have some veracious readers ready to devour what the world has to offer.


Of Reading:
In our house reading has been a very welcome activity.  As infants each of my children had subscriptions to the book of the month club. My wife belongs to a book club where she reads a selected book and then meets with friends once a month to talk about what they thought about the book.  I spend most of my hours at school and work but that doesn't keep me from books.  I subscribe to Audible and am currently listening to book 8 of Robert Jordan's Wheel of Time books.  We have subscriptions to many magazines that give us countless hours of reading.  The Gerringer's love for reading is obvious.

We are always on the lookout for good books either for us or the kids.  We keep an eye on the NY Times Best Sellers list.  I even listen to the Sword & Laser podcast to get reviews and interviews from the latest science fiction writers.

It's needless to say we are a reading family.

Of Writing:
Unfortunately since the world has gone electronic, our writing has been reduced to 140 characters on Twitter or short feeling blurbs on Facebook.  Even our thank you, birthday and holiday cards have dwindled down to birthday cards to immediate family only.  I do occasionally write to my blog, but on the whole, writing in the Gerringer family is starting to be less and less.

One activity that hasn't changed the pace of writing is in Education.  I'm, of course, still in school and write frequently.  My daughter is headed off to ECU to start her college career where she will be writing frequently.    My wife writes many notes during the day at her work as an Occupational Therapist.  So, writing has not completely disappeared in our lives, it's just reduced in the house.