Keywords: Geometry, Activities,
Ref: Cory1
Author(s): Kelly, Paul
Date: 1999
Title: Build a Sierpinski Pyramid
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 5, p. 384-6
Reviewer: Cory
Date of Review: 2/12/01
This is an article that gives a specific example of how to help students visualize fractals as well as give them a hands on activity. Back in 1997, Mr. Kelly and his classes built a 19’ Sierpinski Pyramid that was on display at the NCTM’s 75th annual meeting. The project was done using paper folding techniques to construct many small pyramids, for which a template is given. These small pyramids are then connected at their verticies. A stage 5 pyramid takes 4096 small pyramids to construct!
Mr. Kelly makes many good suggestions that help to make this a learning tool. First of all, students need to know that real fractals are made by starting with the whole pyramid, and then removing area from inside, not starting with small pyramids and building up. Also, it is very helpful to have many classes work on the project, because it can take some time to complete.
I thought that this article gave an excellent way to incorporate difficult ideas into a high school classroom.
Ref: Cory2
Author(s): Jackson, Carol D,; Leffingwell, R. Jon
Date: 1999
Title: The Role of Instructors in Creating Math Anxiety in Students from Kindergarten through College
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 7; pp. 583-6
Reviewer: Cory
Date of Review: 2-19-01
This article speaks about the anxiety that most all students feel at some time or another about math. Research was done to try to find out when and why students start feeling math anxiety. The results showed that there are three main time students have anxiety. The first is in grades 3 and 4, the second is in high school, and the third is in college (especially as freshmen).
A common reason among all three groups was the behavior of the teachers. Many students felt their teachers put too much pressure on them to understand at once hard concepts that seem easy to the teacher. All three also spoke of gender bias among teachers, specifically about females being put down.
The article also gives some great strategies for teachers to help their students with this. Most of it is preventative. Most of the information in this article seems obvious after reading it. Being a self-reflective teacher is not easy, however, and so this article is a good way to check up on yourself to see if you are doing the things necessary to make math class fun (or at least tolerable) for your students.
Keywords: Algebra, Communication,
Ref: Cory3
Author(s): Rerlstein, Ruth
Date: 1996
Title: Family Algebra Night
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 89, No. 1, pp. 28-9
Reviewer: Cory
Date of Review: 2-21-01
This article gives an example of what a school in Virginia has done to help students who have algebra problems. They started a family algebra night, where families of students can come into school with their student for an evening. Parents and students worked together to find out what students can do to be more successful in the math classroom.
Parents benefited by finding out what the teachers expected from the students. Students then benefited because their parents were more able to help them with their work. One teacher would demonstrate the importance of redoing tests and homework by dumping a big bag full of work into the garbage, symbolizing lost opportunity.
Perhaps what I got most out of this article was an exercise that students and parents did together. They were given a typical algebra problem ( Simplify: 11-3(x-5) ), and asked to write out every step, and the write out in complete sentences what they did. I thought that this would be a great first day of Geometry class exercise. Because proofs are a big fear for Geometry students, starting them this way would be a great way for them to start proofs without knowing it. It would also be an algebra review from the previous year, and a chance to make the connection from the year before to the current year.
Keywords: Statistics, Teaching Strategies,
Ref: Cory4
Author(s): Plummer, Robert; Levine, Maita; Rolwing, Raymond H.
Date: 1993
Title: Using the TI-81 to Analyze Sports Data
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 86, No. 8, pp 636-41
Reviewer: Cory
Date of Review: 2-28-01
This article described a way to bring many things together into one lesson. By using a calculator to analyze trends in world record track marks, students can learn about statistics and regression and how to use their calculators to do these things, all in a familiar context which makes it both interesting and fun.
If you look at the regression line formed by plotting the world record times in the mile over the last 100 years, the graph would suggest that someday someone will run the mile in an impossible time. By running regressions on things that the student can visualize, they can better understand what they are finding in their statistic work.
I liked this article as an idea for a class. It is common sense that people learn better when they are interested in what is going on. This article gave a great example on how to find this interest.
Keywords: Geometry, Technology,
Ref: Cory5
Author(s): Brown, Alan R.
Date: 1999
Title: Geometry's Giant Leap
Journal or Publisher: Mathematics Techer
Volume, Issue, Pages: Vol. 92, No. 9, pp. 816-9
Reviewer: Cory
Date of Review: 3-26-01
This article focused on how technology, specifically the TI-92, can help us in the Geometry classroom.
We have long used the calculator for Algebra and Calculus classes, but not as much in Geometry. The TI-92 and Cabri Geometry software allow students to make the constructions they would normally make with compasses and straight edges, and then to change certain characteristics and study the invariants.
I thought this article provided great information about how to keep up to date in Geometry. The examples gave good illustrations of how new technology can be used to benefit learning while still using the good techniques that we have always used.
Keywords: Algebra, ,
Ref: Cory6
Author(s): Brutlag, Dan
Date: 1990
Title: Making Your Own Rules
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 83, No. 8, pp. 608-611
Reviewer: Cory
Date of Review: 11/4/01
This article talks a how to get students to make conjectures in class. Mr. Brutlag gives an example from his math class. He had his students figure out ways to combine and altar the digits in a three-digit number. The students would then have to make a conjecture about the outcome the sequence. Because there are only 1000 three-digit numbers, any sequence that a student creates is guaranteed to repeat sometime. What Mr. Brutlag and his class found out was that any sequence that a student created showed its pattern within twenty repetitions.
As well as the example, this article gives a good idea to help students make conjectures. The class formulated a list of "Number-Operations" and of "Number-Properties" to help students generate ideas when creating sequences.
I think that this article is a GREAT read, especially for people in our class. We're learning about how important it is for students to be doing activities like this, but it is hard to think ways to incorporate it into class. This article gives a great idea and helps generate ideas for other ways to get students to conjecture.
Keywords: Discrete, Games,
Ref: Cory7
Author(s): Quinn, Anne Larson; Koca, Robert M. Jr.; Weening, Frederick
Date: 1999
Title: Developing Mathematical Reasoning Using Attribute Games
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 9, pp. 768-75
Reviewer: Cory
Date of Review: 4/24/01
This article showed how you can apply mathematics to the game Set to have students study patterns, combinatorics, and probability.
Set is played with a deck of 81 cards, each with 4 attributes, shape, count, color, shading. Cards are removed in sets of 3, where each attribute must be either all the same of all different. Students explored questions such as: How many sets are possible? What types of sets are you most likely to find? and What is the average number of sets among 12 cards?
I thought this was a great example of a way to get students thinking mathematically in a place where they usually don't see the connection. The authors gave great examples of how all students, from ninth grade to college sophomores, can benefit from this activity.
Keywords: Discrete, Problem Solving,
Ref: Cory8
Author(s): Grassl, Richard
Date: 1996
Title: Counting Tile Patterns
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 89, No. 1, pp. 8-10
Reviewer: Cory
Date of Review: 4/24/01
Counting Tile Patterns is an example of how the complex mathematical concepts of power series and partial fractions can be used to solve a discrete math problem.
Using two different colered 1"x1" tiles, and three different colored 1"x2" tiles, students are asked to find the total number of ways these can be arranged to make a 1"x10" pattern. To do this, students must first find the recursive pattern using smaller designs, and then use power series and partial fractions to find an explicit formula for a 1"xn" pattern.
We did a problem similar to this in my college discrete math class. I think that power series and partial fractions are very difficult topics for high schoolers. This activity may be most useful as an exercise in finding patterns and recursive formulas at the high school level.
Keywords: Connections, Curriculum,
Ref: Cory9
Author(s): Smith, John P. III
Date: 1999
Title: Preparing Students for Modern Work: Lessons From Automobile Manufacturing
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 3, pp. 254-8
Reviewer: Cory
Date of Review: 4/30/01
This article addresses the question of what we can do with students who are not college bound. It gives examples of the math skills needed of workers on an automobile assembly line.
"Work in automobile manufacturing calls for the mathematics of space, geometry, measurement, statistics, and numerical operations on measured quantities." These are skills that should be necessary for all students anyway. What we need to do for those who are not college bound is present these skills in a context that is relevant to what they may do. This article gives some great examples of how to do this.
I worked for a couple of summers in a factory, and noticed right away how math fit in. It was very important to understand measurements, know comparisons between fractions and decimals, and to do a lot of math mentally. These are some of the things that Mr. Smith talks about in this article. I would highly suggest it to any teacher for reading.
Keywords: Activities, Connections, Probability
Ref: Cory10
Author(s): Haug, Mikel
Date: 1998
Title: Up the Creek with a Paddle
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 6, pp. 456-60
Reviewer: Cory
Date of Review: 5/01/01
This article is an example how one school in Texas incorporated math into an interesting real life situation. It is also a good example of connecting different subject areas into a big project.
The students at this school were asked what the probability of the creek that runs through their town flooding. They had to research the situation, figure out what data needed to be collected, and collect it, use the data to form a conclusion, and report their findings. There was a lot of math in this project. I particularly noticed how it fits in with how the new standards are focused more with data collection and representation.
While this article may not have direct use to most people, I would still recommend it for it’s general ideas. This idea seems like a story we would see in a Core-Plus textbook.
Keywords: Algebra, Technology, Teaching Strategies
Ref: Cory11
Author(s): Friedlander, Alex
Date: 1998
Title: An EXCELlent Bridge to Algebra
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 91, No. 5, pp. 382-3
Reviewer: Cory
Date of Review: 5/7/01
I've come across many articles that talked about using spreadsheets in math, but this is the first one that I've read. I had no idea about where the connection was, and was pleasantly surprised after reading the article.
This article talks about using spreadsheets to introduce algebra. Mr. Friedlander writes that knowledge of spreadsheet use is common enough now that we can go right into using spreadsheets for math and not have to introduce how to use spreadsheets themselves. Spreadsheets provide a natural introduction to functions and variables. Kids introduce variables by clicking on an actual number, creating a perfect connection. The article also talked about how using the "fill down" feature of spreadsheets, students can be introduced to recursive functions.
I think this is a good article to get teachers thinking about the possibilities of using spreadsheets in their classes. It is a great introduction to this because it is short, yet has a couple of concrete ideas for teachers.
Keywords: Algebra, Connections, Issues
Ref: Cory12
Author(s): Nicol, Marsha P.
Date: 1997
Title: How One Physics Teacher Changed His Algebraic Thinking
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 90, No. 2, pp. 86-9
Reviewer: Cory
Date of Review: 5/10/01
This article tells the story of a physics teacher, Mr. Mike Smith, and how his views of mathematics have changed. Mr. Smith is a physics teacher, and in the past has been against using calculators in his classroom. He viewed algebra as "symbol manipulation". However, after some of his colleagues had gotten him to attend a conference on calculators in a physics classroom, he changed his mind totally. He now sees mathematics as telling the "big picture", and that is really shows him what's happening, not just a solution.
This article is very useful to see a great illustration of just what mathematics should be. It also provides a great connection between subjects. In the article an activity involving one of Mr. Smith's labs is described in detail as an example. So this article is a resource not only for classroom ideas, but professional development as well.
Keywords: Connections, Communication,
Ref: Cory13
Author(s): Pugalee, David K.
Date: 1997
Title: Connecting Writing to the Mathematics Curriculum
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 90, No. 4, pp. 308-10
Reviewer: Cory
Date of Review: 5/10/01
Much is said about the importance of students understanding math, not just being able to memorize and apply algorithms. This article talks about one way to accomplish this, through writing.
This article starts out by giving some of the research that supports writing in the math classroom. Mr. Pugalee then gives some good examples of questions he's asked before, and what they have told him. I think that the biggest message here is that writing provides a teacher to see what exactly students are thinking, their "metacognitive development". Often times we can get frustrated with students because they don't understand something we think they should. By having them write down their process, we can see exactly where they go wrong.
I would suggest this article to teachers who are thinking about using writing in their classroom. I think that it does a good job of showing one way where writing in math is useful.
Keywords: Algebra, Connections
Ref: Cory14
Author(s): Bell, Garry
Date: 1997
Title: Showing That a - b = -(b - a)
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 90, No. 5, pp. 394-6
Reviewer: Cory
Date of Review: 5-21-01
This article presented an alternative way to approach teaching why a - b = -(b - a). They argued that just telling students that the negative in front of the right side is really a -1 is not really mathematics.
Their approached involved absolute difference. To do this, you subtract like normal, one column at a time from right to left. The difference like when the top number is smaller than the bottom. When this happens, you subtract backwards, and then subtract the result from its self twice (ie. (b-a) - (b-a) - (b-a)). From this result, students should be able to conclude for themselves the desired result.
I thought that this technique made the problem even more difficult. It is a good way to get students to look at math differently, but I feel would be more useful after they have already learned a - b = -(b - a).
Keywords: Geometry, Activities, Puzzles
Ref: Cory15
Author(s): Miller, Willam A.; Wagner, Linda
Date: 1993
Title: Pythagorean Dissection Puzzles
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 86, No. 4, pp. 302-314
Reviewer: Cory
Date of Review: 5/22/01
This article talks about the Pythagorean Theorem and how it should be taught to students. Most of the time, we are taught a2 + b2 = c2, and never full understand why this is true.
There are ways to teach the concept. By constructing squares off the legs of a right triangle, the smaller two can be cut as so they fit perfectly inside the larger square. This gives students a visual representation of an algebraic formula. This activity conforms to the Geometry standard that students should "discover this relationship through explorations."
I think that this is a great activity for the introduction of the Pythagorean Theorem. This article gives detailed instructions for doing this with you class.
Keywords: Geometry, Games,
Ref: Cory16
Author(s): Ericksen, Donna; Stasiuk, John; Frank, Martha
Date: 1995
Title: Bring Pythagoras To Life
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 99, No. 9, pp. 744-7
Reviewer: Cory
Date of Review: 5/22/01
This article describes a game that can be played to sharpen skills with the Pythagorean Theorem. It "was developed to afford high school students more opportunity for practicing the formula in an engaging way."
The game has a board shaped in (what else) a right triangle. Players move around the board by shaking dice. When they shake, they take the two numbers they get, and compute what the third side of a right triangle would be if they had the lengths of the legs. They then use the integral part of their answer to determine their move. As they move around, they will either land on squares that tell them to do something, like roll again or skip a turn, or a big question mark. If they land on a question mark, they have to pick a card and answer the question. If they get the answer wrong, they have to move back to where they started the turn, otherwise they get to stay. The game is won by the first person make it around the board twice.
I think this game is a good way to sharpen skills in this area. It could be used as a review before a test, the day after the topic was introduced, or later in a course just to brush up.
Keywords: Geometry, Discrete, Connections
Ref: Cory17
Author(s): Boulger, William
Date: 1989
Title: Pythagoras Meets Fibonacci
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: pp. 277-82
Reviewer: Cory
Date of Review: 5/22/01
This article describes the surprising relationship between pythagorean triples and the Fibonacci numbers.
These are two of the biggest ideas in math, but very rarely related. It can be shown that if you take any four consecutive Fib numbers, and take the product of the outer terms and twice the product of the inner terms, you have two legs of a right triangle. What’s more, the third leg will also be a Fib number. The article goes more in depth describing why this works and offering some other connections, such as the pythagorean triples to the golden ratio.
I thought that this was a very interesting article, and great way to integrate a discrete lesson into a geometry class, but the article offered very little to help bring it into a class. He did mention that this connection can spark students interest and encourage them to conduct their own mathematical investigations.
Keywords: Standards, Curriculum, Statistics
Ref: Cory18
Author(s): Burrill, Gail; Burrill, John C.; Coffield, Pamela; et al.
Date: 1992
Title: Data Analysis and Statistics Across the Curriculum
Journal or Publisher: National Council of Teachers of Mathematics
Volume, Issue, Pages:
Reviewer: Cory
Date of Review: 5/22/01
This is a publication of the NCTM. It goes more in depth on specific subject areas than their Principles and Standards.
I really like how this book is presented. There are eight areas that they cover. In most areas, the chapter starts by explaining the meaning of the standard, why it is important and how to use it, and then gives a couple of sample activities that a teacher can use.
I think all teachers should be using these books when they can. Not only do they provide the research and background behind the standards, but also give examples on how to use them.
Keywords: Must Select At Least One, ,
Ref: Cory19
Author(s):
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Title:
Journal or Publisher:
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Reviewer: Cory
Date of Review:
The Konhauser Problemfest