Christina's Article Reviews, 2007


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Keywords: Probability, Games, Algebra
Ref: Christina1
Author(s): Colgan, Mark D.
Year of publication : 2006
Title: March Math Madness: The Mathematics of the NCAA Basketball Tournament
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 11(7), p. 334-342
Reviewer: Christina
Date of Review: February 12, 2007

This article focused on the mathematics behind the NCAA men’s basketball tournament which carries out for three weeks in March. Some tournament background is as follows: 64 teams split into 4 regions throughout the country are seeded 1 through 16 based on their regular season performance. The Rating Percentage Index (RPI) measures a team’s strength of schedule and it’s performances against that schedule and is used to determine which teams are invited and how to seed them in the big tournament. The RPI is equal to ¼(WP)+½(OWP)+¼(OOWP) is which WP stands for winning percentage, OWP= opponents winning percentage and OOWP= a teams opponent’s, opponent’s winning percentage. From there more weight is attached to road wins than home wins because of the difficulty. Through this RPI the teams that have the greatest value will be seeded higher than their opponents. The article then goes into comparing the probabilities of higher seeds beating lower seeds throughout the brackets and rounds. A probability is calculated by taking the number of ways that the success can happen and divide it by the total number of possibilities. For example, if we take the final four teams in the bracket in which each team has the same likely hood of winning, each team then has a ¼ chance of winning. The article compares the expected value and the multiplication principle as well. There are many things that can be predicted mathematically when looking at the NCAA tournament, but most people just like to watch the television instead and pray for their team to win!

I thought this was a great article because it showed the mathematics within a very popular sport. This was very interesting to see how they calculate the probabilities of NCAA teams getting into and being seeding in the tournament. I also love knowing this information to help guide myself to choose the right teams when predicting the outcomes of these games. I think everyone show know these things.

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Keywords: Teaching Strategies
Ref: Christina3
Author(s): Reinhart, Steven C.
Year of publication : 2000
Title: Never Say Anything a Kid Can Say!
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 5, No. 8, pgs478-483; April 2000
Reviewer: Christina
Date of Review: March 7, 2007

This article has given me a little taste of how teaching might actually turn out to be. Reading about the situations and decisions that Reinhart had to make about his whole teaching philosophy was very interesting. However, his experiences were also a bit scary. Knowing that I am going into the teaching field soon I might come upon these same kinds of dilemmas and learning how to handle them professionally, as Reinhart did, is going to be another tough assignment to teaching. Reinhart suggests important techniques to enable students to pay attention participate in activities and answer their very own questions. He suggests in order to improve on questioning skills one needs to create a plan, share with students reasons for asking questions, teach for success, and to be nonjudgmental about a response or comment.

This article was full of great ideas that have never once crossed my mind. For example when asking students a question, if a student is struggling to respond, Reinhart suggests quickly moving onto another student. This technique is rather surprising to me because I feel like you should give that student a chance to respond, not just move away from them. Also, I guess Reinhart¡¦s suggestion of never saying anything a kid can say is also something that I never thought about, but will take with me in the future.

By and large this article was a success in providing me with knowledge to apply in my future classrooms. I thought that this has been the most interesting piece of work I have read in a long time and I recommend it to all teachers, not just the cool math ones ļ.

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Keywords: Number and Operation, Teaching Strategies
Ref: Christina4
Author(s): Cramer, Kathleen; Wyberg, Terry
Year of publication :
Title: When Getting the Right Answer is Not Always Enough: Connecting How Students Order Fractions and Estimate Sums and Differences
Journal or Publisher: The Learning of Mathematics
Volume, Issue, Pages: pgs 205-219
Reviewer: Christina
Date of Review: March 7, 2007

Wow, learning how to do fractions the way that this article suggests would have been a whole lot easier for me when I was growing up. The suggestions Wyberg and Cramer manipulate throughout the article are great strategies to help students learn how to work with fractions. This article has given me some great tips in teaching fractions to my future students. The article also focuses on assessing to understand students’ thinking in order to highlight it to help them make future connections with stuff that they learn.

One topic that really stood out to me was the strategy that students can use to order fraction pairs is by constructing mental images. I agree that mental images are essential in understanding fractions and the ways in which they work. I imagine pies and pieces of them, but the article also suggests thinking of lines and sections of them. Getting students to think about fractions in this way will make it easier to relate to them on paper and in number form.

The article goes through the different strategies to solving fractions within three students. I thought this was interesting to look at and examine.

Overall I thought the article was a nice concrete piece of information that was easy to look at and understand. I liked the examples of real student work, I thought it carried out well for the article. The most important suggestion, however, is recognizing students' thinking behind the answers that they give. Figuring out the way in which your students think, will be a key part of the way you teach the lessons.

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Keywords: Algebra
Ref: Christina5
Author(s): Zordak, Samuel E.
Year of publication : 2000-2007
Title: Barbie Bungee
Journal or Publisher: The National Council of Teachers of Mathematics
Volume, Issue, Pages:
Reviewer: Christina
Date of Review: March 17, 2007

I thought his game/lesson is one that I will try and use in my future lessons. I think that there are many ways I could manipulate this game in order to accommodate for all likes of action figures, not just Barbie’s. I could have teenage mutant ninja turtles, GI Joes, Hello Kitty's, Power Rangers, and many more variables to work with and compare. This would make the game more interesting for all of my students. Basically the game can work with anything to make it interesting for anyone. Students get a Barbie doll and a package of rubber bands. They then collect data on comparing the amount of binders used to hold Barbie so when she bungee jumped she would be safe (not hit the floor). Students can go about their own ways using their own mathematical skills.

This game is full of opportunities for students to practice their data collecting and organizing skills. Along with equations, graphs and charts. Barbie Bungee provides a lesson in logical reasoning with given questions at the beginning of the lesson to start them thinking in the right direction.

Again, I think this is an excellent game/lesson that will be very interesting and new for students. I think that is what everyday needs to be, something new. Bored would not be a word anymore if we could always do this. The only thing I would be concerned with would be the behavior of my students. This game could easily get out of hand or inappropriate with many action figures and rubber bands. However, if I make this a point ahead of time, I feel as students will behave better knowing that if they do not, they are done.

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Keywords: Teaching Strategies, Probability, Statistics
Ref: Christina7
Author(s): Kuhl, Opal
Year of publication : 1982
Title: Sports Card Math
Journal or Publisher: Mathematics for the Middle Grades (5-9)
Volume, Issue, Pages: 16, ppgs(162-165)
Reviewer: Christina
Date of Review: April 4, 2007

Sports card math is a great chapter focusing on using baseball cards to teach a mathematics lesson. 20 baseball cards are selected and laminated to prepare for handling by students. When selecting these cards, try to pick teams that are likely to be in the playoffs or that students find interesting, the popular teams. Along with preparing baseball cards, we need to be sure to create a handout to explain all abbreviations and formulas related to the cards themselves. For example, Opal suggests computing earned run average and batting average, along with caluclating the number of single hits (minus the doubles, triples and homers). For this activity we can use calculators, create a variety of graphs while learning interesting facts about athletes.

Opal Kuhl uses a variety of difficulty levels when preparing the questions about a previously selected 20 (or so) baseball cards. The range of difficulty will keep all students busy solving problems they are interested in which will keep their attention on their task. After reviewing this particular activity, I think it will be very efficient to use in my future teaching. However, I might also choose to add a statistical approach and focus on body mass verses batting average for example. Overall, there are many good approaches to using baseball cards. I also like how the cards are "real" and might be easier for the students to understand what they are calculating and looking at.

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Keywords: Select one..., Keyword 2, Optional..., Keyword 3, Optional...
Ref: Christina8
Author(s): Carpenter, Thomas; Franke, Megan Loef; Levi, Linda
Year of publication : 2003
Title: Thinking Mathematically. Chapter 2: Equality
Journal or Publisher: Heinemann Books
Volume, Issue, Pages: pages 8-24
Reviewer: Christina
Date of Review: April 11, 2007

This article goes through the multiple ways students may represent and interpret mathematical problems. They dicuss students' conceptions of the equal sign and consider potential sources for their misconceptions relating to the problems. I thought it was amazing to look at the problem that students have regaurding the equal sign, thinking that it is a command to carryout the calculation. Instead of actually looking at all of the numbers, students were jumping right to a conclusion with only looking at the first half of the problem before the equal sign. The article continues looking at students another responses pertaining to the question and goes through the possible misconceptions. Very interesting. I especially like the interpretation that students are misconcepting the problem based on symbols rather than failure. I think if you were to sit down with the child and remind them about the other side and the extra number, that the percentage of right answers would go up.

I also recommend reading this article to understand the significance of true/false questions. I will definitely be using these in future teaching because it makes the students explain what they are doing and why they are doing it without even knowing. When you answer a question true or false, you usually have an answer of why you answered it the way that you did. This will be good questions for discussion with students.

I recommend this article for anyone who is intrigued by the way their students concept mathematical problems. It will not only inform you about the many different misconceptions that students have, but it will also teach you how to get around them.

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Keywords: Teaching Strategies
Ref: Christina9
Author(s): Usiskin, Zalman
Year of publication : 1985
Title: Conceptions of School Algebra and Uses of Variables
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Christina
Date of Review: April 23, 2007

This article made me really think about mathematics and the way in which people teach certain subjects. This article is the study of algebra and how it is associated with understanding variables and their operations. Conceptions of variables change over time and school algebra is quite different from school to school.

Usiskin does a great job reflecting on algebra as the study of relationships amoung quantities. He takes a look at the way in which functions arrive quite quickly when variables are arguments or parameters. The conceptions lead to notions of independent variables which causes functions to arrive. It is very interesting to know that the different uses of variables creates different conceptions of algebra. I recommend this article for all to read. It holds a better understanding to algebra and provides reason for the functions of roles and important issues.

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Keywords: Teaching Strategies
Ref: Christina10
Author(s):
Year of publication :
Title: Lesson Two: Multiplying Matrices
Journal or Publisher: Core Plus 2: Unit One: Matrix Models
Volume, Issue, Pages:
Reviewer: Christina
Date of Review: April 26, 2007

This article was an excellent review of multiplying matrices. It takes the matrix operations the students just learned and applies them to real world situations. This creates a chance for students to understand why they learn matricies. The lesson starts off by using three different brands of shoes and continues with examples from party planning, little league, houses, and making toys. I really like the way in which a variety of examples where all laid out for the students to tackle. Steps to take and hints were given along with the problems.

Checkpoints were my favorite part of the lesson. These are places for students to stop and reflect on the material that they know. If they cannot answer the questions or have the abilities to perform the duties at the checkpoint, the students know they need to go back to the beginning of the chapter. If they do know, they proceed on to the next checkpoint. I like these checkpoints because they are spots where students are able to evaluate themselves without a teacher and when the teacher has 40 other students to check on, it makes it easier for both parties.

I recommend this lesson for all mathematics teachers who want a solid lesson on mutiplying matrices. Interesting problems that engage students are throughout the lesson.

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Keywords: Teaching Strategies, Activities
Ref: Christina11
Author(s): Johnson, David R.
Year of publication : 1986
Title: Making Minutes Count Even More: A Sequel to Every Minute Counts
Journal or Publisher: Dale Seymour Puplications
Volume, Issue, Pages:
Reviewer: Christina
Date of Review: May 2, 2007

Wow, this book is amazing! I want to first start off by recommending this book to all teachers of all levels. It is an inspiring and interesting book that sucks you in as a reader!

The book, "Making Minutes Count Even More" gives many helpful hints and suggestions through many examples and discussions put on throughout the book. The author does a wonderful job of fully explaining what he does in certain situations that occur during a class setting. He teaches ways in which you can make your lesson work effectively and talks about good and bad communication with parents and students. He comments on communication being an "art" and it is something that you will master over time. The book gives advice in what to do if lessons run too short, run too long, or if they do not flow at all. My favorite part our the minutes at the beginning of class that he commments on because these are the most essential in starting the period. He suggests ways to start class and suggests ways to never start class. They are great.

The book is full of useful information for all teachers. I think you can always learn more as a teacher, so that is why I am recommending the book to all. I will definitely be referring back to this book in the near future. It is going to help me get started on a rewarding career.

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