Thursday, March 24, 2016

Top Eight Tool Kit





1) Hyper Space: Michio Kaku.

           This book is a wonderful example of how math and science can have beautiful applications. Michio Kaku explains time travel, alternate dimension and travel through interstellar space. He explains these topics without the over use of technical jargon and he uses analogies accessible to the average person. Mathematicians don't just sit around and think about solving math problems: they also think about what awesome applications the math they work on can have. This book will allow students the opportunity to learn that the topics that would interest them also interest mathematicians as well. This book also will allow students to learn that most math majors don't work in pure math. Mathematicians are people too and they want to work on interesting projects just like everyone else does. 

           This book also gives a very brief introduction to the history of mathematics. This history of mathematics is not taught to students until there junior year in undergrad. Providing students with an easy introduction can help prepare them for their training. This book and others like it can provide some amount of scaffolding for interesting topics in mathematics and the history of mathematics. This book is meant for the non math fluent reader so it is accessible to most readers. 

           Hyperspace also offers a broad overview of cosmology. Michio Kaku goes into detail about scientist best theories on what the universe was like before the Big Bang, why there was a Big Bang and how our universe will end. Most people do not have access to these theories without going to grad school for astrophysics but Michio Kaku and other writers like him explain these theories before we get to grad school so we can know we are interested in them before we decide math has no interest for us. 

 Kaku, Michio. Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the 

            Tenth Dimension. New York: Oxford UP, 1994. Print.                          


2)  The Man Who Knew Infinity: Robert Kanigel

            This book is about a  self taught mathematician who grew up in India during the late eighteen hundreds and turn of the century named Srinivasa Ramanujan. This mathematician was a devoutly religious Hindu and believed that a specific Hindu deity acted as a muse and gave him his mathematical theorems. Ramanujan developed a mathematical style that was extremely original and unorthodox but also very prolific: he discovered 3900 theorems during  his short life. This work would give young math students the opportunity to learn about a man who thought of math as a form of creativity. He believed math was a form of spiritual enlightenment.  In India, he flunked out of every subject except math, but single handedly discovered mathematics so advanced that we are still finding applications for his math almost a one hundred years later. 

             While it is true mathematicians work hard on the memorization component of their work, this book will allow students to see a mathematician who saw himself as a creative artist. When Ramanujan was admitted into Cambridge and they tried to show him some mathematics he didn't know he would become inspired by what they were telling him and create new theorems based on what they were telling him. Literally watching him most have been like watching Mozart improvise at the piano on a given theme. 

             Ramanujan often would create mathematics impulsively. Inspiration would hit him at odd times and he would spend hours working out the details in his math notebooks. He filled his notebooks with thousands of theorems. He once discovered 100 new theorems in one day. Even when he was death bed he the ideas were coming to him and he was still jotting them down. 
               
              We are used to thinking of math as a subject we do to get a good grade. This book would give students an example of a man who did math because it was an art form for him. No one ever told ramanujan math wasn't fun so it became a spiritual quest for him. 


Kanigel, Robert. The Man Who Knew Infinity: A Life of the Genius, Ramanujan. New York: C. 

           Scribner's, 1991. Print.            

3)    Women in Mathematics


           This book contains biographies of 6 of histories most influential female mathematicians. This book will allow students to see that not only can great mathematicians be women but they can lead interesting lives outside of mathematics. Many women believe that women are not as good at math as men are and this is really a myth. Most scholars who ascribe to that theory believe the effect of testosterone on the developing fetus gives men an advantage at the more advanced concepts so this effect shouldn't the k-12 grades. The differences in performance and in career choice for men and women are complicated, but there is a large social component influencing young girls feelings toward math. This book does not provide proof that males and females are equal in math ability but it can be a god start in convincing some girls. Some people like examples better than theory. Those people will respond to the claim that females and can do math with the same level of expertise as males with the question name a great female mathematician. After a student reads this book they could name 6.

           This book also gives some detail how historically men believed they were better than woman at math and how slowly woman are closing the achievement gap. For example it is believed by some researchers that woman are better at algebra and men are better at calculus. This belief existed in the 1800's when women were not given the opportunity to study math in college and could only earn their respect by doing the long difficult and tedious calculations that we now use computer programs to do. Male mathematicians took advantage of female mathematicians that wanted to build a reputation by making them do the repetitive and boring parts of their job and then said it suited women better.



Osen, Lynn. Women in Mathematics. Cambridge, Massachusetts. Mit Press. 1974. Print.



4)    Math Games for Middle School: Challenges and Skill-Builders for Students at Every Level

              This book would allow students to enjoy recreational mathematics. Math games typically only require basic arithmetic but high amounts of practice builds fluency and all people are more likely to engage in activities that they enjoy. No one wants to do math homework for half an hour every day but playing a math game 15 minutes , twice a day is an easy objective to meet. Success in these games would build confidence. The type of studying most likely to achieve results are repeated short intervals and not long cramming sessions. Practicing 15 minutes every day is more likely to have have positive results than practicing 2 hours in one day once a week. The game allows for repetition which will build speed and ease. Math games also allow students to actually enjoy math and not just see math as a way to get a good grade. We educators have to foster the love of learning in our students. 

                This book is specifically designed for middle grade students. The book is part of a series with books for every grade level. Therefore the book contains techniques that the students will actually do in class and is directly useful to their education. These types of books would make good supplemental material for any school text book. This is an easy non threatening way to introduce some of the jargon specific to mathematics to the student. If the student uses these books as introduction to the material there ability to relearn the math in class will be greatly enhanced. 


Salvadori, Mario. Wright, Joseph. Math Games for Middles School: Challenges and Skill-builders at 



             Students at Every Level. Chicago Review Press 1998. Print.


5)     A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form


This book is an important addition to the list because students must understand that if they decide to either major in math or a math intesive field that it is possible to enjoy math. The author makes the analogy between math and art. He believes that math is more like art than most of us realize. If art where taught the way we teach math no one would think that art is a method of self expression. The author makes the claim that math can be just as creative an expression of individuality as art. In math class we are drilled on technique and there is no room for creative self expression or discovery. All creative fields rely on route practice but the point of practicing musical scales or dance routines is to do something creative with them. Once we know the techniques of math we can begin to attempt problems that we do not know how to solve. These problems will require us to think creatively. 

The author says that when we are at our most creative we must not be afraid to fail. A math class is the exact opposite of a creative environment. Students are only concerned with the right answer and therfor not interested in taking the kind of risks that creativity requires. It is important that students learn to arrive at correct computations and to do it quickly but we as a society have forgotten that there is another side to math; the side that looks for patterns symmetry elegance and even beauty. Mathematics are used to make computer graphics increase the beauty of computer graphics to create the shimmering effects of the mandelbrot set. 

Lockhart, Paul. A mathematicians lament: How Schools Cheat Us Out of Our Most Fascinating and Imaginative             
             Art Form. Belleview Literary Press. 1, April 2009. Print.



6)    The Cartoon Guide to Statistics

Statistics is an intimidating field of math. Students are required to master many difficult concepts and to understand many mathematical techniques requiring two or three dozen steps. Also, the students that are asked to learn these techniques are not math majors or in math intensive fields so they are thrust into the world of learning a lot of math very quickly. This is a very stressful situation. The Cartoon Guide to Statistics is an easy low stress introduction to statistics and a wonderful primer for the topic before taking the class. So many college majors require statistics class that it is a good idea for any high school student aspiring to go to college to read this book. Since I believe that all students with normal IQ should go to college almost every high school students should read this book before they go to college. 

When and if it is appropriate I would incorporate some of the text in this book into some of my class work for the students. It can be difficult to teach material that is not required by the state but if the class has a section of work from statistics I would allow them to use parts of this book. Either I would print hand outs or scan the needed pages and email the pages to them. Not all students have regular access to email so I might provide the text in more than one way. I would use this work to alleviate some of their math and statistics anxiety. 

Gonick, Larry. The Cartoon Guide to Statistics. Harper Perennial. 1993. Print.






7)      Math Fables Too: Making Science Count 


This book is the easiest of the texts on this list. This work is also intended for the youngest on audience on the list at about 1st grade. This book uses children's stories to teach math and to give examples of the usefulness of basic arithmetic. These stories require students to count and learn the basics of addition subtraction in order to follow the plot. I included this book on the list because I wanted to be prepared to provide some supplemental reading for students of any age in the Kindergarten - twelfth grade system. 

If I included this work for students in middle grade maths I would have them read the stories and create their own stories and share them with each other. In our modern times we don't even need to wait for a publisher to recognize the merit of the students creative work but we can publish it ourselves on a Blogster. This would give students the opportunity to think critically about when does a scenario require a specific math skill. Reading and rereading their classmates stories would allow students to become experts at solving simple word problems. This book would serve as great practice for students who have problems knowing when to do a specific technique while working on word problems.     


Tang, Gregg. Math Fables Scholastic Press (September 1, 2007)


8)    Fear Of Math: How to Get Over It and Get on With Your Life! 


Math anxiety is a documented phenomenon that impedes math success for students. Math anxiety is completely learned and it is possible to unlearn it. It is generally harder to unlearn a behavior than to learn a behavior. To be specific we do no unlearn behaviors we only learn to more nuance to a behavior when under different circumstances, in a different context, or in response to different environmental cues. Millions of Americans have some amount of Math Anxiety. Fear is an emotion we learn to associate with specific situations from our environment. It is true that humans are predisposed to develop certain fears with more than others and that is why certain phobias are more common than others. However, math anxiety can come from a variety of sources. Social Shame and embarrassment is one of the key factors that allow for the possibility of math anxiety. No one likes to be ridiculed and we are made to do a task that we feel we are not good at in front of everyone it is easy to fell that our fears will be realized. 

I would allow my students to read short excerpts from this book and tell them it is my intention to create a safe place where the students do not need to feel intimidated and can learn without the added stress of ridicule. However, once I tell this to my students I must show this to them as well. My students and I will then spend the school year improving their math abilities increasing the sense of self efficacy and alleviating their math anxiety.

Wednesday, January 27, 2016

Occasional Paper,

 The readings of this class have given me a lot to think about. I have only worked as a tutor and in after school programs. the students in those settings are always performing math at different grade levels. Of course I suspected a student or two might be a year or so behind their grade level. I didn't think that most of a class could be 2 or 3 years behind their grade level. One wonders how these children are promoted to the next grade. Its my job to get them to pass an end of grade test. I could privately tutor them on my own time.  FOR FREE. I could teach to the test. unacceptable. If a child is 3 years behind their grade level and with my help they become one year behind their grade then they have moved 2 years academically in one years time. That would be a great achievement but it wouldn't be good enough for my teacher report card to earn me some of that merit pay. perhaps I am just stressed out. everything looks like doom and gloom when your stressed out enough.

Speaking of stress.
         
It should be said, out loud, that students have stressful lives. For example, financial aid sent my refund check, of considerable amount of money, to the wrong address and I know the guy. He seems nice to me but my neighbors suspect him of being a crook and a scam artist. Why oh why did he get my refund check? My mother suspects my 12 year old niece of having a 20 year old boyfriend. I have a pre cancerous growth and will have surgery on my throat in a few weeks. I had to drop my undergrad class because of my surgery will leave me to drained to do grad school and undergrad. Despite the fact that I dropped it after three weeks I am not getting any of my money back, because its all a scam I unfortunately paid for undergrad class out of pocket. I have been selected for jury duty ( which I am planning on ignoring). I have a performance in a few months where I have to play piano music of more difficulty than anything I have ever played. Playing piano makes me nervous enough to vomit but it is how I pay the bills. Well I do enjoy it after it is done so it is not all a horror story. But wish me well on my endeavors.  I was even chased by a dog on my way to school today January 27 2016.

I am extremely impressed with the breadth and depth of insight in the assigned readings and in the scholarly education literature in general. It makes me wonder. Why is the education system in such a hot mess of a bad situation. Researchers working in education actually have a firm grasp on the psychology of learning. The problems that occur in a classroom are understood and discussed at length and there is a ton of literature devoted to all of the problems individually.

Just because researchers know what the problems are doesn't mean people in the education system are using their findings. After all do politicians sound as if they read political science articles. If they did they would never get elected. I mean, only graduate students understand those things. The education system probably has a history of people in positions of power jockeying for more power, political back stabbing etc. Correct me if I'm wrong but doesn't the teachers union make very large campaign contributions to the democratic party.

As stated I am just in some weird mood because the speed of the dog that chased me was far greater than mine and I don't know how I didn't get eaten alive and it bothers me. I have heard of many fantastic teachers achieving amazing results with wonderful children so obviously despite all of its short comings the American Education System is still a place where good happens intermittently.

After reflecting on it I went to 5 elementary schools, 3 middle schools, 4 high schools and every teacher I remembered seemed to know their content area extremely well. I suppose the data reflects that observation. Most teachers know their material well enough to be a good teacher. My worst teachers were impatient or completely disengaged. I had a teacher who used to constantly leave in the middle of class and go to McDonald's.

Well, these occasional papers are more fun than I thought.
         





Wednesday, January 20, 2016

Literacy Autobiography.

        Told in five memories

Memory 1

When I was 4 my mother read a dozen Dr. Seuss books to me. These are my earliest memories related to reading. While I currently don't remember all of the books, my mother told me that I had all of the books memorized and that I used that memorization process to learn to read before I enrolled in kindergarten. As an aside I only discovered Dr. Seuss whimsical masterpiece Fox in Sox a few years ago and I did find a natural affinity for its alliteration, rhyme schemes, and various literary techniques.

As a young child I enjoyed these works so much that I would recite them while watching television or playing with toys. An odd but fascinating detail is that I remember Green Eggs and Ham as one of the books from my mother read to me before I was 5, and when I  recently tried to  memorize that work I achieved that goal without effort in less than five minutes. It took me half an hour to memorize William Blake's poem the "Chimney Sweeper". It is true that alliteration, rhyme, and repetition eases memorization, it is also true that the chimney sweeper is a much shorter work and is filled with lots of evocative imagery and metaphor which also aids in the memorization process.

I even remember reciting the Cat In The Hat in kindergarten from memory. When I began reading in class I already learned to read for fun. Most people who tell me they do not read for enjoyment also tell me there dominant memories of reading is reading page after page of some school assignment that they didn't want to read. Once they are done reading for the assignment they, don't want to read another word! Its seems simple when it is said plainly, but if we want students to read more then they should be encouraged to read material they find interesting. Society wouldn't function if we refused to read any texts we didn't find interesting in the first 5 seconds, but wouldn't society be a more interesting place to live if most people spent a little more time reading.

Memory 2

When I was 13 I read the biography of Bruce Lee. My step father has five black belts: so I always loved martial arts and Bruce Lee was a family favorite. What I learned from that book was not martial arts but Bruce Lee's philosophy. Bruce lee practiced martial arts during the 50's, 60's, and early 70's. At that time people did not like to mix different martial arts because they believed what ever martial they were practicing was the best one. Bruce lee was one of the first great martial artists to supplement his training by learning dozens of different styles. This meant that he could adapt to more variety of situations than anyone else he encountered and he became of the greatest martial artists of his time. All martial arts have strengths and weaknesses and Bruce lee would learn one style after the other and he as a fighter would work on his weaknesses until he was a well rounded world class expert.

To quickly go threw some details from the book. Bruce Lee practiced a style called Wing Chun and it gave him phenomenal hand speed and coordination, but when scientist measure the force of the punches thrown by Wing Chun practitioners they are almost twice as strong as an untrained 300 pound NFL player, but not as strong a lot of other styles, So he practiced boxing to sharpen his coordination even more and to add more power to his punches. Wing Chun also doesn't do any grappling, throwing, slamming, or joint locks so when fighting a wrestler or grappler, Wing Chun proponents are often man handled. Bruce lee studied Greco-Roman Wrestling, Catch Wrestling, Jui Jitsu, Judo, and Aikido to make himself a world class grappler.

This was important to me at the time because I was a musician and I didn't want to be hampered by thinking any one style of music was complete or better than the other. I wanted to be as well rounded in music as Bruce Lee was in martial arts. So I practiced jazz and classical and I dabbled in other genres. I am not pursuing music anymore but when I was pursuing my undergrad in psychology I remember thinking this would be really useful for teachers. While I think of myself as a math teacher I am more than happy to supplement my curriculum with relevant finding is psychology sociology anthropology etc. little did I know that a lot of people had beaten me to the punch. 

This approach does mean I will have to constantly challenge myself to work on my weaknesses. If I want to be as good as a math teacher as Bruce Lee was a Martial artist, then I have no choice.

Memory 3

When I was a senior in high school I read a book titled the Color of Water. This book was assigned by an English teacher and I associated school reading as skimming material to prepare me for tests. This book was the first time I experienced reading an assignment that I enjoyed. The book consists of two biographies. James McBride's autobiography and his biography of his mother. the chapters alternate between the two stories. I was assigned to read the book over the course of three weeks and read it three times in three weeks instead.

The most surprising thing about detail about the book is that James barely knew his mothers history before he interviewed her from the book. His mothers history was so painful that she didn't bother to ever talk about it. This woman raised 12 children in the 60's and 70's in the ghettos of Manhattan and all of her children went to college two of whom became medical doctors. It was shocking to me that you could know a person for 30 years and not know them well at all. James Mcbride constantly remarked on his surprise of his mothers story. The courage of a woman to allow herself to be excommunicated  from her Jewish family and to go into poverty to marry a black man, or the courage of a woman to tell the social workers she didn't need put her children in foster care she knew what she was doing. Raising 12 Children seems counter intuitive because I do not believe most people man or woman could raise 12 children by themselves and do half as good a job as James' mom. The courage to face racist and violent police officers in the 60's to protect her kids. The Courage to face drug dealers pimps and violent criminals to protect her teenage children. I feel like I could do those things but I know I could be wrong, And I am a 300 pound muscle bound, martial arts enthusiast freak of nature power lifter and she was a 100 pound old lady.

 Before I read this book I mostly read for fun. This was the first time I read anything and was emotionally affected by it. while it is great to read for your own enjoyment sometimes it is good to be challenged to do an activity outside of your comfort zone.  To quote a great mind " we must allow for the unexpected discovery   ( Commander Tuvak Star Trek Voyager). I discovered that I could be inspired by what I read. I was 18 at the time which is young by most standards, but at the time I remember thinking I should have known this already. His mother must have been intelligent courageous, creative, tenacious but also caring compassionate. All of her children felt loved and cherished. etc. I cant come up with enough positive adjectives to do her justice.

Memory 4

During my undergrad, I was once accused of cheating on a paper: I didn't cheat. The assignment was to pick a short story and write an analysis on it. The first paper was on Edgar Allen Poe's the "Fall of the House of Usher" but after I was accused of cheating he said do the assignment over so I choose  Tolstoy's "How Much Land Does a Man Need?". To prepare for a third story I read Dostoevsky's the Grand Inquisitor. This story affected me so much I make it a tradition to reread it every year around the time of my birthday.

The short story the Grand Inquisitor is a chapter from a 1000 page grand novel titled The Brothers Karamazov. The Grand Inquisitor is a story written by one of the major characters of the book and he is recounting the story to one of his brothers whom is also another major character of the book. The two characters often talk about the story as one character is telling the story to the other.

Story begins in heaven and Mary mother of Jesus is pleading with god to forgive the sinners burning in the lake of fire for forgiveness. God says how can I forgive them when my son has holes in his hands and feet from the barbarous technique of crucifixion. She begs all saints martyrs and angels to join her cause and god finally gives the souls the Easter weekend off every year and gives them those few days of respite from the lake of fire.

 Immediately I could tell that this story was about the meaning of suffering and an examination of our historical psychological and sociological responses to it. The previous chapter of the book is used to allow the character telling the story of the grand inquisitor to preface the story with many shorter stories of suffering innocent children. Most of those stories about children are based on true stories. This book made me think about suffering about the colossal amount of it in the world. It is easy to ignore suffering because it is so uncomfortable, but much easier to tolerate it if it is put into an aesthetically pleasing format. Perhaps this is why it is easier to watch a mournful melancholy film, but harder to learn about the true story the film is based on.This gives the reader the emotional distance necessary to process the material.

After the introduction the story takes place in Spain during the Spanish Inquisition and Jesus returns to earth and starts performing miracles. The church arrests him and tell him he will be burned alive in the morning. When the Grand Inquisitor hears that Jesus is going to be burned at the stake he rushes to Jesus cell and interrogates him. The bulk of the story is the Grand Inquisitor's attempt to goad a response out of Jesus by critiquing his first attempt to save mankind through redemption. He calls Jesus's crusade an utter failing. Just a few centuries after Jesus was crucified Christians were crucifying pagans in the same barbarous manner. He goes on to say during this christian age it is your religion that is the main perpetrator of violence. After admitting to working for Satan and thinking Jesus should have accepted Satan's offer during his temptations the grand inquisitor says Jesus acts as if he doesn't understand humans. he says humans are not strong enough to embrace salvation and rarely wise enough to even understand it. You don't save people by offering salvation but you save people by alleviating the suffering of the world.

However, somehow this turned into the Grand Inquisitor burning hundreds of heretics at the stake everyday. If anyone has failed it is the Grand Inquisitor.... I wouldn't call the Spanish Inquisition a success.

When I read it I thought I should do something to alleviate suffering and one of the many things I thought I could do was to teach. As a math teacher I would help students get into good colleges and improve their socio-economic status, and one of my fantasies is that one of my students will go on to do important work on important 21st century problems.

Memory 5

Three years ago I realized that Wikipedia had an article on every comic book, film, novel and manga I had ever half read watched or read so I took two weeks out of my life to devout 5 hours a day to reading only this kind of material. I became an encyclopedia of comic book lore and as an aside both of my brothers tend to know more than me in this area. This made me realize that we live in a world with more access to information than anytime in human history, and our access to information is growing at an exponential rate.

Because we have more access to information than ever before it is more important to be able to read than at any other time in human history. I believe this is true even with the amount of videos on the internet ready for consumption. It's also more important to be able to think critically about the content a text. The internet is filled with quack conspiracy theories and we all have to learn how to navigate through an age of over saturation of data.

When you read the history of comic books you realize that 70 years of comics means that there is a lot of conflicting stories out there. This means that you have to double and triple check your facts and try to confirm you information through independent sources. If  your second source received all of its information from the first source then you don't have two sources. That's why in science you want another researcher to duplicate the results of an experiment independent of the first researcher.

Wikipedia only works because there are thousands of people writing articles. It was Wikipedia that made me think about how many people literate people it takes for our society to function. Large products are produced by at least hundreds of people and sometimes more. Novels are on average written by one person but the publishing company hires teams of editors to proof read the novel. The publishing company also hires teams of advertisers, pubic relations, and marketing folks to create an interest in the book. The writer is usually influenced by at least a dozen or so authors who are also influenced by a dozen or so authors.
This means that all of us readers and writers are all influenced by each other, no one is an island to themselves and no one writes in a vacuum.