Annotated Bibliography

            Many students today are not motivated by mathematical concepts, so it is the teacher’s job to find different ways of motivation.  Reading is not the first thing that comes to mind when in a math class, but using texts that provide different ways of looking at concepts can be very interesting.  Five texts that would enrich a high school or middle school math class would be:  Mathletics, The Greedy Triangle, Do the Math:  Secrets, Lies, and Algebra, http://www.khanacademy.org/, and http://www.coolmath.com/.   These books and websites are all texts that would help motivate students to ask questions and look differently at why they are learning about certain skills.  Students who are in middle school math through Calculus can benefit from these texts, but I would use them each in a specific unit in order to gain their interests.  The books relate statistics to sports, geometry to everyday objects, and algebra to everyday life.  The websites enrich students understanding by provided examples and possibly an alternative way of working out a problem by showing condensed notes or videos. 

Tradebooks:

Winston, Wayne.  (2009).  Mathletics.  Princeton, NJ:  Princeton University Press.
ISBN:  978-0691139135

Flesch-Kincaid readability estimate:  11.4
Amazon Link:  http://www.amazon.com/Mathletics-Gamblers-Enthusiasts-Mathematics-Basketball/dp/069113913X/ref=sr_1_1?ie=UTF8&qid=1316562312&sr=8-1

           Mathletics is an interesting book when it comes to relating sports to math.  It helps answer the question that many students have:  when will I ever use this?  Students who are interested in sports would find this book useful because it contains chapters on baseball, basketball, and football.  Some concepts in statistics are very confusing such as finding the probability of multiple events.  Therefore, I would use this book on a probability unit concentrating on one chapter at a time, such as the chapter on making decisions in a football game.  The book discusses different situations when a coach must make a decision like whether or not to go for a first down during the fourth down when the ball is at the 30 yard line.  Mathletics discusses the probability of these events and explains the mathematics behind them.  A student who likes football might be very interested to find out the exact chance that his/her team might make the next field goal.  Along with football, there are chapters on baseball and basketball which discuss the statistics in managing players and teams.  It contains up to date names which can easily be recognized by a sports fan. 

            I would not assign this entire book to be read at once because it is at a higher reading level than the average student reads.  Those that are taking Statistics would most likely be in eleventh or twelfth grade, but their reading level could be lower.  Therefore assigning one chapter at a time would be more beneficial to prevent frustration.  During a unit on probability I would introduce the concept and assign a chapter such as “Football States and Values” in order for students to see how the concept can relate to football.  During this same unit, there might be a lesson on expected values.  This same chapter introduces the concept by talking through an example about gaining yards in football.  After students have read a chapter, I would have them write about another situation where using the concept of probability can be useful.  The student could choose sports or any other topic.

Burns, Marilyn  (2008).  The Greedy Triangle.  New York, New York:  Scholastic Inc.

ISBN:  978-0545042208

Lexile Reading Estimate:  AD580L which is approximately on the fifth grade level

Amazon Link:  http://www.amazon.com/Greedy-Triangle-Scholastic-Bookshelf/dp/0545042208/ref=sr_1_1?s=books&ie=UTF8&qid=1316562486&sr=1-1

            The Greedy Triangle is a silly book about a triangle that can be many different objects such as a bridge support, instrument, or sail on a sailboat.  The triangle becomes bored with his life and gets greedy for more sides.  After adding one side, the book gives examples of where we might find quadrilaterals.  Throughout the book, the original triangle becomes greedier for more and more sides.  He transforms to a pentagon, hexagon, heptagon, octagon, and many more.  After the triangle gets too many sides, he can no longer stand straight because he is almost a circle! 

            The Greedy Triangle could be used in a middle school math unit on geometry, or a high school geometry course to introduce the many different kinds of polygons.  The average reader in these classes should have no problem reading the entire book at once, therefore I would begin by having students read this book and make a chart of the properties that they notice about each different shape.  After discussing the properties students could work on a hands-on activity where they make their own shapes or find shapes out in nature. 

Lichtman, Wendy  (2008).  Do The Math:  Secrets, Lies, and Algebra.  New York, New York:  HarperCollins.

ISBN:  978-0061229572

Lexile Readability estimate:  1050L  which is approximately on the 7-9 grade level

http://www.amazon.com/Do-Math-Secrets-Lies-Algebra/dp/0061229571/ref=sr_1_1?s=digital-text&ie=UTF8&qid=1316963259&sr=1-1

             Do the Math is a fictional narrative about a girl, Tess, who loves math.  She is in middle school and relates her life to many different algebraic concepts.  First, Tess uses the greater than and less than symbols to compare herself to peers in her class.  For example, she says that Richard > Tess, but later on she says that Richard is < Tess because she catches him cheating on a test by stealing a copy of it.  She uses symbols in her notebook such as a Venn Diagram to compare herself to friends, and exponents to describe her one friend who exaggerates everything.  One day, Tess finds out that her mother’s friend committed suicide, but her mother thinks that it might have been murder.  As Tess investigates, she relates her exploration to different concepts such as tangents, parallel lines, and extraneous solutions.  By the end of the book, Tess helps her teacher discover who cheated on the exam and finds out that there was a police investigation on the murder and it did turn out to be a suicide.

            This book would be a great motivator for an Algebra I class.  Algebra I students should already have multiple exposures to the inequality symbols, so the beginning chapter would not be frustrating for middle school students.  As the book continues, more and more concepts are introduced which can create some interesting questions about mathematical topics. The author explains these clearly by relating them to a middle school student.  I would have students start reading this book during a unit on inequalities and continue from there.  The chapters are fairly short, so I would assign one chapter every two days allowing students time to read.  From the reading, students might have questions on certain topics which would allow for discussion and predictions about other units.  For example, I could refer back to the book during a unit on exponents or the quadratic equation. 

Websites:

http://www.khanacademy.org/

Khan Academy videos are great videos to use for further instruction on many math concepts from Algebra I through calculus. There are videos to instruct these concepts and to provide practice problems in order to gain mastery.  Because of the visual nature of the videos, students are able to see concepts in multiple ways and have multiple exposures outside of the classroom.  In the students' spare time they may use any of these videos to help them prepare for exams and test their knowledge on the classroom objectives.  The readability for this site would probably be fairly low (sixth or seventh grade) because it is easy to navigate and contains many videos.

Along with using these websites at home, they may be helpful in class while instructing a lesson. For example, during a unit on slope, I would show the video in class.  It might raise interest on the topic and students can have access to the video at any time.  After the video I would assign students to test themselves on the website.  There is a hint button under practice, but students’ progress is set back when they use this.  Therefore, students will learn to refer back to the video or notes in class in order to help them.  The website has thousands of videos, so I would use this site often which will help students become familiar with it.

http://www.coolmath.com/

Cool math is a great website that is very colorful and eye catching.  There are so many links on the page which might be somewhat confusing, but the words are big and easy to read.  The site also contains many graphics which is appealing to students in lower levels.  I would estimate this site to be on a fourth or fifth grade level.  There are lessons and practice on subjects that range from pre-algebra to pre-calculus.  There is also a math dictionary to help students with terms that they may not understand. 

I would use this site in an Algebra I class during a unit on writing a solving equations.  There is a great lemonade stand game which would be a motivator to the students when introducing the concept.  I would let students play the game, and then discuss an example on how to write an equation for the profit of selling lemonade.  After being introduced to this site students can then use it to enrich or supplement any unit by reviewing a concept or practicing the skill.

Reading Next Online Activity

“Reading Next” describes the low literacy levels achieved in America’s schools.  The author makes a great point in that school systems have concentrated primarily in word recognition at the early levels, but not in comprehension; which is the most difficult part for students in their later school career.  McKenna said in Chapter three of “Teaching Through Text,” that educators need to know and understand their students’ reading abilities in order to prepare reading materials.  The authors of “Reading Next” expand on this idea and suggest that teachers need to provide the aid and instruction for the in class materials as well as support for independent learning after graduation.  Another recommendation supplied by Biancarosa and Snow is to have diverse texts.  These texts should contain a variety of topics at many different skill levels.  This recommendation aligns closely with the Commission on Adolescent Literacy’s (CAL) suggestion that “adolescents deserve access to a wide variety of reading material that they can and want to read.”  In short, the fifteen recommendations provided by “Reading Next” summarize a great deal of suggestions given by a variety of secondary educational professionals in order to improve reading comprehension in all grades.  

As a future mathematics educator, I am not only responsible to teach math concepts and applications, I am also responsible for exposing students to another type of literacy.  Students in any single math class could be on a wide range of reading levels; therefore, anytime there is a reading activity I must provide a variety of texts.  Even in word problems, students should have access to many different types in order to improve their comprehension and understanding of the different situations.  Students who are at lower reading levels should be paired with those who are at a higher level so that all students are able to learn and enjoy reading about math.  The interaction between students can have a positive effect on the enjoyment of different topics because one student may be able to relate better to a text and share his/her experiences with another student.

            It is very important for mathematics’ students to be able to understand what they read and monitor their own reading progress.  I will aid in this process by providing reading guides and pointing out important vocabulary; but in a math textbook, it is very important that students are able to read and follow along with examples.  Also, when it comes to word problems, summarizing is very important.  During my internship, the mathematics department concentrates on a process called “SOLVE” where the S stands for summarize.  Students are asked to summarize a word problem and describe what is being asked.  I will definitely incorporate this into my classroom for any word problem.

Websites for student use

The High School Assessment (HSA) for Algebra requires the use of a calculator, but many students do not own graphing calculators.  Schools do provide them for use in class, but it would be very helpful if students could get the practice using them at home.  The website, http://www.mathworksheetsgo.com/tools/free-online-graphing-calculator.php is a great way for students to practice typing in equations and graphing them.  This site could be very useful for special education students who require the use of a calculator.  They would be able to use it outside of the classroom on their homework.  It would also be very useful for any student who does not want to spend nearly $100.00 on a calculator.

The free graphing calculator has a tab where students can type in equations, look at the graph, see a table of x and y values, and find the intersection of two functions.  Although the website it set up a little bit different than a typical TI-83 or TI-84, the buttons are similar and students would get used to the terminology used on a calculator.  After looking at a few different graphing calculator websites, this one seemed to be the easiest to use.  I would definitely refer students to this website when giving them a homework assignment that they would greatly benefit from using a calculator.

Another great website for students in Algebra or Geometry is http://www.mathwarehouse.com.  There is a column that has many different areas of study that students can click on, including complex numbers, distance formula, FOIL, and many others.  However, my favorite part of the site is on the right side that has interactive math examples.  These are very interesting because students are able to see how angles, side lengths, slopes, and many more measurements change as they move the points.  

I would use this site by letting students move the points around on the interactive examples and have them come up with a possible theorem or principle related to how the measurements are changing and adding up.  It would be a great introduction to many different topics.  I would also use the site as a reference for any student needing extra help on a certain topic.

STEM Literacy

What is 100K in 10, and how does the government plan to implement it?

100K in 10 is the movement to acquire 100,000 new and excellent teachers in STEM subjects over the next ten years.  President Obama's administration wishes to train and retain excellent STEM teachers by partnering with organizations to help reach the 100,000 excellent teacher goal.  It is very important to reach this goal so America  is able to live up to the high economic and scientific standard set by other countries.  The programs through 100Kin10 are getting reviewed in order to obtain the highest level of training and education.

Some say that the idea of training 100,000 new STEM teachers in the next 10 years in unreachable.  According to an article by Josh Deehas, "The percentage of all students earning Bachelor of Engineering degrees has actually fallen from nearly 10 per cent of the total in the mid-1980s to 5.4 per cent in 2009-10. Computer engineering hit peaks of 4.3 per cent of the totals in 1984 and 2004, but has fallen again to 2.4 per cent in 2009-10. It’s a similar story in other STEM fields too, like biology. The lack of students choosing STEM careers eventually leads to a lack of teachers in the STEM fields.  Without the necessary training, teachers are unable to bring accurate and reliable knowledge and experience to the classroom. 

http://100kin10.org/page/general-faqs
http://oncampus.macleans.ca/education/2011/11/07/students-are-fleeing-stem-degrees/
http://www.physorg.com/news/2011-02-obama-math-science.html
http://www.educationsector.org/publications/high-schools-failing-prepare-many-college-bound-students-science-careers

Websites for student use

SOS Mathematics is a website that students can use at the secondary level.  Subjects included are:  Algebra, Trigonometry,  Calculus, Differential Equations, and Matrix Algebra.  The site even includes external links for help on other subjects from the elementary grades, as well as extra help and practice on other math websites.

This site would be used if a student needs extra help on any of the above topics, or to extend the student's knowledge.  There are many easy to read notes with examples on each subject.  For example, the Algebra link contains categories from fractions through solving logarithmic and exponential functions.  At the end of each lesson, the student can view other similar examples or test themselves by doing a problem and later viewing the solution.

Along with the lessons, there is a link on the homepage where students can post a question on a forum.  The forums are sorted by subject making it easy to navigate.  The creators of the website monitor the forums so they are free of unwanted material.  Overall, the site is laid out nicely and eye appealing.  The only negative that I could find would be when in navigating the different subjects, there is no simple way to click back to the homepage.

At a recent NCTM conference, I attended a seminar on Hot Math.  The seminar was about a website for students wanting to remediate their math skills.   Although there is a fee to join the site, there are some great games that are included for free at http://hotmath.com/games.html.  The games are:  Catch the Fly, Number Cop, Algebra vs. the Cockroaches, and Factortris.

Catch the Fly is a great game to play for any student in middle school math or algebra who needs more practice on plotting points on the Cartesian plane.  There is a frog on top of the plane and the student must type in the ordered pair at which the fly has landed.  If he/she is correct, the frog will eat the fly.

Number Cop is a fast paced game where students must pick numbers by their divisibility.  For example, students can choose multiples of 3, or prime numbers.  The cop car then starts and students control which lane the car goes into.  The goal is to go in whichever lane has a number that is in the set that they are looking for.  This game will create very fast thinkers!

Algebra vs. the Cockroaches is a game where students must find the equation of a line according to where cockroaches are walking.  The students have fun by choosing what will eliminate the cockroaches when they correctly input the equation; they can choose a rocket, laser gun, sprayer, or shoe making it very fun and entertaining for kids.

Finally, there is the game Factortris.  This game is similar to Tetris.  The student is given an area and must choose a rectangle with that area.  The shape is then dropped and the student must make a line of boxes to eliminate them.  Students would love this, and it works on their factoring skills at the same time!

STEM Literacy

How can teachers prepare students for careers in STEM?

In order for teachers to prepare students for careers in STEM, they must first be prepared to teach the integrated subjects.  Many elementary school teachers today are not trained in one specific subject; they are generalists.  In order to be sure that schools are equipped with the most prepared teachers, all science and math teachers should have some training in those fields.  There was research done to compare Chinese and American elementary school math teachers.  American teachers are more focused on the procedures than on the underlying concepts and applications.  Only about 13% of American students end up taking Calculus in high school, whereas almost every Chinese student takes it.  Much of the reason is how students are taught; they are drilled with facts and processes, not with problem solving strategies.

While teachers are getting prepared for these math and science heavy subjects, they need to emphasize problem solving in the classroom. The core subjects of math and science are already incorporated into the curriculum, but technology and engineering must be made aware of early on.  Teachers need to use lessons that contain creativity and innovation.  Instead of separating all of the STEM subjects, teachers should allow for integration of one subject to another.  There has to be more focus on hands on practical experiences rather than just learning facts and processes in order to create original and imaginative technological thinkers for the future.  There are many ways teachers can find to have their students design, model, and test a hypothesis, as long is it is age relevant.  When teachers are excited and able to motivate their students about STEM, students will become eager to learn and master those subjects.

http://libertylyceum.org/articles/mathteaching.shtml

http://www.iteaconnect.org/Publications/TandC/Sep09.pdf

http://www.usinnovation.org/state/pdf_stem/STEMEdMaryland2010.pdf

Websites for student use

Figure this is website that gives many unique challenges for students to work on and think about.  Many of the challenges require more critical thinking and problem solving skills rather than just math computation.  Also, the challenges relate to real life, such as one where there are two cookies with chocolate on top.  The student must figure out which cookie would be better to eat if he is a chocolate lover.  The odd shaped cookies make it difficult to find the exact area, so they my think about a good estimation.  There are many ways to figure the answer out, which really promotes the higher level thinking that the state is looking for.

There are many ways that I might use this website.  For example, it would be  a great warm-up/motivational activity to get students thinking.  The problems are classified by subject area, so when there is a unit on patterns, I would choose a pattern question.  Another way that students might use the site is for a problem of the week.  I would give them the website and have them choose a question to work out and explain how they got there answer.  The students could even work on the problems together with their families.

Paul's online math notes is a great website for getting notes and cheat sheets for the Subjects of Algebra through Calculus.  The site is geared more toward a college level course, but it will help students transition from their upper level high school math to college.  His "cheat sheets" rules in different math categories that are  organized so they are easy to read.  I especially love the trigonometry sheet because it is a quick way to see all of the important rules in trigonometry in about two sheets.  There are also class notes and examples for the different subjects if a student wanted a more in depth look at a specific area.


I would recommend this site to the students if they needed to look at another type of explanation or see more examples.  I would also recommend printing out the cheat sheets so they can refer to them quickly.  There is also a place to look at common errors in math.  My favorite would have to be the section about errors that students make when determining what a number divided by 0 would be.  This is undefined, and there is a proof that 2=1.  This proof would be a great motivator in having students determine why it is invalid (because he eventually divides by 0).  I have used this site when I took calculus and differential equations and I highly recommend it for student use.