Keywords: Communications, History,
Teaching Strategies
Ref: Andy1
Author(s): Mendez, Edith
Date: 2001
Title: A History of Mathematical Dialogue in
Textbooks and Classrooms
Journal or Publisher:
Mathematics Teacher
Volume, Issue, Pages: Vol. 94,
No. 3, pg 170-173
Reviewer: Andy
Date of Review:
Feb. 15
This article tells the history of how dialogue evolved throughout history. The author lists four periods of time and states how the students and teachers communicated. The first period of time that is described is in ancient sources such as Plato and Euclid. In Plato’s Meno It described how students can be led to find a specific answer. This is done without giving the student any opportunity for reasoning or justifying. This type of method will never teach the student to think outside of the box. Next, the author states that the only way we can know of communication in these ancient times is through textbooks. Two of these known textbooks are A Chinese text, Chou-pei Suan-ching and Euclid’s Elements.
The next time period looked upon was the Medieval and Renaissance times. For most of this time dialogue was done by lecturing. Most of the textbooks were written in dialogue between scholar and master. An educational reformer named Comenius helped to create conversation by having the students repeat what the master just had said. He also proposed that teachers divide classes up into smaller groups that could go over what was just learned.
Dialogue in the early American schools was mostly just memorization. Typically the way that conversations went at this time was that the teacher gave the problem, and then the student would either figure out the problem or try to get help which he would not always get. This was unfortunate because the teacher then had direct control over everything that the student would learn. No independent thinking would then be encouraged.
The nineteenth century brought about a turn in the educational process. This was where students were encouraged to develop there own methods of solving the problems. Teachers began to find multiple ways of teaching depending on the topic. The methods of learning as we experienced in high school had evolved. Classrooms now encouraged independent thinking. By far the best way to learn is by using multiple methods. No student learns the same way or at the same rate. Keeping the classroom free and open to new ideas encourages is a great way to encourage learning.
Keywords: Statistics
Ref: Andy2
Author(s): White, Wes
Date: 2001
Title: Connecting Independence and the Chi-Square Statistic
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 94, No. 2, pg 134-136
Reviewer: Andy
Date of Review: 2-18-04
This article is sort of a step by step process of using the Chi-Square statistic to find out how far the sample data strayed from the expected values. It was written by Wes White, a high school AP statistics teacher. White wrote this article as if he was laying down a lesson plan for someone to follow. He started off by giving an over view of the goodness-of-fit test. The teacher used the example of rolling dice to see if it is fair or not. This was done in a way that seemed that he would just be lecturing on the process and that the students would be taking notes of this at this time.
Next white would dive a little deeper into the subject. He found that since the students previously knew of independence he could now make the connection between the Chi-Square and independence. Mr. White now modeled his example after the basketball team. This would be a good practice for making connections in a classroom especially if you have some students from the team in class. This process was explained step-by-step along with class participation. Mr. White had the students do the computations for him to get some feedback. The article told how he made use of question in his lesson. This helped to make sure that the students knew what they were computing and not just going through the motions. He had the class vote on whether they were convinced of their answer or not. And again at the end they voted again to see how their views changed.
Mr. White finished up by summarizing how his presentation to the class has evolved. The two parts of the presentation are linked very well. He does a good job of breaking down the idea on the first day so it is easier for the students to understand and then expanding on the idea the second day while still keeping the connections.
Keywords: Teaching Strategies......
Ref: Andy3
Author(s): Alejandre, Suzanne
Date: 2004
Title: Understanding Algebraic Factoring
Journal or Publisher: Math Forum
Volume, Issue, Pages: http://mathforum.org/alejandre/algfac.html
Reviewer: Andy
Date of Review: 2-23-04
This lesson starts out by giving the key terms and their definitions. The words are broken down to their root words to help to understand the words. This gives a good overview to what the students are going to be learning. It might also give some refresher to spark some ideas of what the students have learned in the past. The purpose of this lesson is to show the geometric basis of algebraic factoring. This lesson objective is stated by the author which is then followed by the materials for the demonstration.
The lesson plan that is given is very detailed in the process that is needed for presentation. The lesson gives ways to explain to various types of learners. A student that learns more form visual and special relations would be able to follow in this lesson because of the way that the lesson is being explained. The lesson is based on using shapes to represent the equation that you are finding. After the diagram is shown then the teacher goes into depth about how this is represented numerically.
There are three different procedures that follow all of this background. I am not sure if this all could be done in one period. This lesson might have t o be split up into two days. Then the question is where you split up the lesson. Either way I think that this is a very well thought out lesion plan.
Keywords: Standards......
Ref: Andy4
Author(s): Wiske, Martha; Levinson, Cynthia
Date: 1993
Title: How Teachers Are Implementing The NCTM Standards http://www.ascd.org/publications/ed_lead/199305/wiske.html
Journal or Publisher: Educational Leadership
Volume, Issue, Pages: Vol. 50, Num. 8, pg 8-12
Reviewer: Andy
Date of Review: 2-25-04
This article gives examples of how the National Council of Teachers of Mathematics standards are a good curriculum to establish. Examples were given about how this method of teaching helps to create a positive learning atmosphere in the classroom. That is makes the students and teachers enjoy mathematics more.
A list of obstacles was given that explained the hindrances to switching to the NCTM standards approach. The following were all listed: incompatible texts and materials, inaccessible technology, inappropriate assessments, inadequate professional development, incompatible educational paradigm, and lack of time. According to the teachers polled these changes would have to be made to create an effective classroom.
The article sited schools in Montana, Kentucky, and Pittsburg where innovative teachers are implementing the types of standards brought on by the NCTM. Using different and multiple texts was a topic that was explored. Also, the use of collaboration that would link schools, universities, and business people together with the students was said to be helpful in development.
The article summed up what can be learned from these teachers in these five ways: Provide direction with discretion, Align texts, tests, technology, and teacher development, Provide sustained support for professional development, Support collegial networks, and Attend to the details of school culture and structure.
Keywords: Teaching Strategies, Problem Solving
>Ref: Andy5
Author(s): Martinez, Joseph
Date: 2001
Title: Thinking and Writing Mathematically: "Achilles and the Tortoise" as an Algebraic Word Problem
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 94, No. 4, Pg. 248-251
Reviewer: Andy
Date of Review: 3-1-04
This article gave a very good representation of integrating word problems into your lessons. It explains the importance of having students learn word problems. How it creates a thought-provoking problem and has the students thinking critically about their problem.
The problem of focus is the adaptation of Zeno's paradox, Achilles and the Tortoise." I liked this because as I was reading and not thinking about it mathematically I was thinking year the tortoise will never get passed by Achilles. This makes you stop and think about what you are really doing. Also how to interpret what the information in the word problem actually means. Like how it is a race so Achilles would not wait for the tortoise to finish its distance before going again.
I also liked the way that the teacher presented the lesson. How he split it up into two parts. The students would think about it theoretically and then find the actual mathematic solutions to it. The lesson was also supplemented with other "activities" that enriched the understanding of the lesson. A clip from "IQ" was shown stating the paradox and. The students also made a real life representation of "Achilles and the tortoise" to further the understanding.
I would really like to include this lesson into my own classroom. These are the types of class activities that make students enjoy the classroom. It shows that learning especially word problems can be fun.
Keywords: Technology
>Ref: Andy6
Author(s): Gordon Calvert, Lynn M.
Date: 1999
Title: A Dependence on Technology and Algorithms or a Lack of Number Sense?
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: v6 i1 p6
Reviewer: Andy
Date of Review: 3-3-04
This article talks about how students become so dependant on technology especially calculators to some simple math problems. It gives the example of the frustration that happens when a student pulls out their calculator to add -9+4. The way the author looks at this though is that it is not the calculators fault for the dependence. It is rather a lack of knowledge and creativity that causes the students to not be able to figure out a simple way to answer a problem.
The author gives a real life example of how at the cash register, when given change to make a simpler amount some people do not know how to give that correct amount. Flexibility is the key that the author is trying to get across. Students need to know many ways to compute 4 x 6. That taking 4+4x5 is the same thing along with 2 times 4x3. She states that with this knowledge base the students will not be as calculator dependent. The author also states that it is not a short term process. It takes time and experience to learn this number-sense. She closes repeating the importance of flexibility in the student's methods of solving problems.
Keywords: Geometry
>Ref: Andy7
Author(s): Soto-Johnson,hortensia; Bechthold, Dawn
Date: 2004
Title: Tessellating the Sphere with Regular Polygons
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 97, No. 3, Pg 165-167
Reviewer: Andy
Date of Review: 3-9-04
This is a great article especially for those that have taken geometry during J-term. The article shows how to create tessellations in the spherical plane. The authors' first review with you the basics of what tessellations are. They then describe why there are only three shapes that will tessellate in the Euclidean plane. Next, it goes through the steps that are needed to find the number of figures that can tessellate a sphere. From this it is deduced that figures with sides 3, 4, 5, 6, 8, 12, and 20 can be created. They also gave very good visuals in this article. The visuals show steps that are used to create the tessellating patterns on a sphere.
The proof of how to find the number of faces in of the figures in Euclidean Geometry would be something that could be done in a high school classroom. I do not think that the proof for Spherical could be done in the classroom without the student having more math classes under their belt.
I really enjoyed the article. Spherical geometry really sparked my interest during Geometry. I really liked using the spherical models to visualize the properties in this geometry, especially, the property that shows that three right angles form a triangle. This would be a great lesson to show that there are other geometries and create a deeper understanding of Euclidean Geometry in the students.
Keywords: Number and Operation, ...
Ref: Andy8
Author(s): du
Sautoy, Marcus
Date: 2003
Title: Beckham
in his prime number
Journal or Publisher: Plus
Magazine http://plus.maths.org/issue26/features/sautoy/index.html
Volume, Issue, Pages: September, Issue 26
Reviewer: Andy
Date of Review: 3-14-04
This article, Beckham in his Prime Number, was a very funny and interesting history of the view of prime numbers. The article starts out with a question of why David Beckham, a famous European soccer player, changed his number to 23. The author points out that his number is a prime number and then proceeds to point out how profound of a choice it is.
Then the article goes on to tell of some interesting facts about prime numbers. How the Chinese found that odd numbers were more masculine and that primes were even more so. They also gave a reason of survival. The cicadas he described hid in the ground for seventeen years. Scientists believe that this helps to keep predators that cycle through the years also away from them more often. Random fact are placed throughout the article such as how the Ancient Greeks proved that there are infinite primes and that they have recorded a prime with more than four million digits. There are also practical issues discussed such as how buying things on the internet uses two prime numbers to encrypt your information so it does not get intercepted by the wrong people.
This would be a good article for high school students to read to give an interesting perspective on prime numbers.
Keywords: Representations, Activities...
Ref: Andy9
Author(s): Cramer, Kathleen
Date: January 2001
Title: Using Models to Build an Understanding of Functions
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Volume 6, Issue 5, Page 310
Reviewer: Andy
Date of Review: 4-14-04
This article shows examples of how to use modeling to create an understanding of functions. It explains that it is important for students to make connections with physical representations to gain the most out of the teachings. The article stresses that it is important fr the teacher to make sure that the models build on each other to ensure that the students understanding is growing.
The next part of the article shows some examples of classroom activities that can be used to show this modeling. It also shows how they are building upon each other. After all the little experiments the data is all collected and summarized to find out if any connections can be made.
This article states that the students will gain a deep understanding by exploring multiple ways of approaching problems.
Keywords: Technology, Games, Planning
Ref: Andy10
Author(s): Strinmoen, Chris; Ring, Jon
Date: 2004
Title: Building Homes of Our Own - An Innovative Building Game
Journal or Publisher: Media Options, Inc.
Volume, Issue, Pages: Computer CD-ROM
Reviewer: Andy
Date of Review: 5-4-04
This was the last session that I went to of the conference. The two that presented the information were both fairly new teachers. At first I was skeptical about the software that they were using, especially because they were taking a whole week for this activity. The software was integrated into a math classroom very well by the teachers though. They had a packet of information that the students would have to fill out. The students would have to approach the problem in very different ways to get to be able to sell their house. There is a lot of planning that goes on, so the game is not as simple as it seemed.
The developers of the game also provide the teacher with a guide that explains the connections with the game to the NCTM standards. This is nice to see the connections. Their presentation was a little dry. They only went through the tutorial of the game and explained some parts as they went. It would have been nice to see some examples of whet there students produced.
This is a program that I was being implemented in some way in my classroom. I
might not spend a week on it like they did, but I would be nice to use it in
some form.
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Keywords: Connections, Teaching Strategies, Geometry
Ref: Andy11
Author(s): Russell, Alan
Date: 2004
Title: Pick's Theorem: What a Lemon!
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 97, Issue 5, Page 352
Reviewer: Andy
Date of Review: 5-17-04
This article talks about the versatility of lemons and how that is similar to the versatility of Pick's Theorem. How with a lemon you can use different parts to make two very different things. Using Pick's Theorem you can vary its use in math.
The way that Pick's Theorem is used in the classroom is through geoboards. How to find the area of an irregular object is a project that is used with the geoboards and Pick's Theorem. The article is broken down into three parts, the simple idea, listening, and connections. Each one of those was another way to use Pick's Theorem to get some type of information across to the students. Just like how each part of the lemon can be used for some different purpose.
He also stresses how listening to his students helps him to tailor his lesson in new ways. He goes on to say that this helps him show that, "Ideas can expand to show the richness of mathematics."
Keywords: Teaching Strategies, Geometry, Technology
Ref: Andy12
Author(s): Edwards, Michael
Date: 2004
Title: Fostering Mathematical Inquiry with Explorations of Facial
Symmetry
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 97, Issue 4, Page 234
Reviewer: Andy
Date of Review: 5-17-04
This is a good article for those that are interested in integrating computer imagery into the classroom. In part of this article you learn how to use photo software to find symmetry lines. This idea was based on an article that the teacher found in Newsweek about symmetry and facial beauty.
The teacher split the activity into two tiered assignments, one with photo processing software and scanned photos, the other with interactive geometry tools and student built models. The computer uses basic software to create an introduction to facial symmetry. You look at a scanned face to see if it is symmetrical down the center. The other activity is setting up an algorithm. This algorithm is set up to see how close to symmetric the faces are. It uses angle measures to calculate the proportion. Numbers close to one are considered to be the most symmetric. After the initial algorithm the students can try and come up with one of their own then has a greater accuracy of symmetry.
This is an activity that I can see myself adapting to fit in my geometry classroom. I do not know if it will be a tiered activity but I will definitely use the algorithm aspect in some way.
Keywords: Algebra, Geometry...
Ref: Andy12
Author(s): Jones. Michael A. and Cohen, Stanley F.
Date: 2004
Title: Fairness: How to Achieve It and How to Optimize in a Fair-
Division Procedure
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 97, Issue 3, Page 170
Reviewer: Andy
Date of Review: 5-17-04
I found this article not to be that great if you would follow it exactly as they have it laid out, but some of the ideas are really interesting. The idea all stemmed from Donald and Ivanna Trump's divorce. Like the author said divorce is not a good topic for a school lesson so the information was set up to contest winnings between two people. The lesson then follows to show how you can mathematically find out the correct and fair way to split up the winnings.
Some terms that were described are: envy free, pareto efficiency, and equitability. These are all explained and used to establish a set of fair rules to split up the winnings fairly. I had a problem with the last part of this article. They were splitting up a video game system and I thought there could have been a better example. You can not really split up a video game system into 22/50th. This just confused me a little and I thought that money or a set of books would have been a better example. If adapted right this could be a good activity.
Keywords:
Ref: Andy14
Author(s): Arlton, Stanley
Date: 2004
Title: Fascinating Mathematical Relations
Journal or Publisher:
Volume, Issue, Pages: MCTM Conference
Reviewer: Andy
Date of Review: 5-19-04
This was my favorite of all the workshops that I went to. I really enjoyed this speaker. He had so much energy and passion towards math. There was a fire in this man to get everyone excited about math.
His methods maybe were a little old school. He did not use a text book in the traditional way. What he did use was very detailed math books that he handwrote himself. I couldn't believe these things. They were so amazingly done. The questions were very thought provoking and always had some type of practical use to them. Well maybe everything except the wheel of numbers divisible by 23.
I would have enjoyed having Mr. Arlton as my mathematics teacher in high school. He definitely would have sparked an interest in me and my classmates. He only spoke for an hour and I left wanting to hear more. He is a great example of the passion that teachers should have towards teaching and learning.
Keywords: Measurement, Connections, Statistics
Ref: Andy15
Author(s): Attila, Tamar Lisa
Date: 2004
Title: using School Lunch to Study Proportion
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9, NO. 1 17-21
Reviewer: Andy
Date of Review: 5-20-04
This is a great activity to incorporate into the your lessons. There are so many things that are good about this activity. For one this activity on the nutritional value of their school lunches has so many important connections to the real world. It is very important that people watch what they are eating so that they can stay healthy and this activity creates awareness in the students.
The activity also pulls in information and ideas from other sources to complete the activity. The teacher incorporated research from using the Internet to find sources for the Recommended Dietary Allowance. The teacher had the students interpret their information through charts and graphs. This is a very good way to make sure of the students learning. They also had to summarize their findings, which show an understanding of what was learned.
I also like how the teacher had the students do a follow p to see if they could
make improvements in their eating habits and then what the charts and graphs
would look like. That is a good way to reinforce the healthy eating habits that
are needed in life.
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Keywords: Measurement, Connections, Statistics
Ref: Andy15
Author(s): Attila, Tamar Lisa
Date: 2003
Title: using School Lunch to Study Proportion
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9, NO. 1 17-21
Reviewer: Andy
Date of Review: 5-20-04
This is a great activity to incorporate into the your lessons. There are so many things that are good about this activity. For one this activity on the nutritional value of their school lunches has so many important connections to the real world. It is very important that people watch what they are eating so that they can stay healthy and this activity creates awareness in the students.
The activity also pulls in information and ideas from other sources to complete the activity. The teacher incorporated research from using the Internet to find sources for the Recommended Dietary Allowance. The teacher had the students interpret their information through charts and graphs. This is a very good way to make sure of the students learning. They also had to summarize their findings, which show an understanding of what was learned.
I also like how the teacher had the students do a follow p to see if they could
make improvements in their eating habits and then what the charts and graphs
would look like. That is a good way to reinforce the healthy eating habits that
are needed in life.
Return to Index
Keywords: Statistics, Connections, Activities
Ref: Andy16
Author(s): Goldsby, Dianne
Date: 2003
Title: "Lollipop" Statistics
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9, NO. 1 12-15
Reviewer: Andy
Date of Review: 5-20-04
This article on, "Lollipop Statistics" is a great way to get students interested in statistics. They say that music is the universal language so using the lyrics to the song "Lollipop" is a great way to hopefully try to draw in all of the students. I found this to be a very clever activity.
The level of this is suited for early middle school. It deals only with basic properties of statistics such as, counting, tallying, and graphing. That does not deter this from being a good lesson though. It gets the students thinking about statistics and also interested in statistics. I could see this as an activity that I would have at the beginning of the year to get the students to know that statistics is not all just confined to numbers.
A big factor in understanding statistics is having data and information that you
are interested in. then you will have some inspiration to figure out what the
data is trying to say. I think that the teacher has found that with this lesson
because the students seemed to really be engaged in the activity.
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Keywords: Problem Solving, Algebra, Measurement
Ref: Andy17
Author(s): Engel, Bill; Schmidt, Diane
Date: 2004
Title: How Big is a 16-Penny Nail?
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9, NO. 8 422-426
Reviewer: Andy
Date of Review: 5-20-04
This is a very interesting article because I did not know what the true meaning of what a Penny-Nail was. I thought that the setup as very interesting and provided the students with at background that would interest them too.
I thought that the way that they set up the investigation was very effective. How there were two sets of nails, smaller ones and larger ones, that were both used to predict the length of a 16-Penny nail. This makes the students use a lot of very important thinking strategies. The students took the problem and approached in some really good ways. They used their problem solving skills to decide if what they were doing was working or if it should be abandoned. In the end they found out that neither group was right so that they needed to find out something else that was the reason that they were called penny nails.
The only problem I have with this is that it does not give any clear explanation
of the term penny. I do like how they used outside sources to try and figure
out what the meaning was behind it. Some students might get discouraged with
not being able to have the reason while other will use that as a springboard to
find out why.
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Keywords: Number and Operation, Connections...
Ref: Andy18
Author(s): Jamski, William
Date: 2004
Title: The Arithmetick of Lewis and Clark and the Corps of
Discovery
Journal or Publisher: Mathematics
Volume, Issue, Pages: VOL.9, NO. 9 pg. 471-474
Reviewer: Andy
Date of Review: 5-20-04
I did not think that this article was as helpful as the other that I have been reading. I figured that there would be a lot of connections integrated with the history of the Lewis and Clark adventure with mathematics. They author did make some connections but I feel that they were really unrelated and would be hard to integrate into a single lesson.
It seemed as if the math in the lesson was being pulled from everywhere. There are no specific lessons to apply this to, be it geometry or algebra. There are some good math questions in this article, though. Question four on the amount of error there would be in one degree of measurement was a really interesting.
If connections could have been made to today this lesson would have been more
effective if for example after the student found out what the price was per acre
back then and then found out what the price was today they could make some
connections about inflation. They could see how the value of lad has changed
over time. I think that this could be made into a stronger lesson if you could
tie this to one specific type of lesson.
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Keywords: Geometry, Activities...
Ref: Andy19
Author(s): Morris, Barbara
Date: 2004
Title: the Beauty of Geometry
Journal or Publisher: Mathematics
Volume, Issue, Pages: VOL.9, NO. 7 pg. 358-361
Reviewer: Andy
Date of Review: 5-20-04
This is a great activity for use in a geometry course. The connections with art and geometry are very present in this activity. That might be the reason that I like this article so much. In this activity the students use geometric figures to create stained glass windows. This can be seen in the art of Frank Lloyd Wright who also used only geometric figures in his architecture.
This article goes into great lengths to explain how this activity fits into the curriculum and fits with the standard set by the NCTM. The teacher get the students really involve in the assessment process by having the students look and evaluate each others work.
I know this is something that I would like to incorporate into my classroom.
There are so many possibilities with this in the classroom. The students also
get to have beautiful physical proof of their accomplishment and understanding
of geometry. This is also a great way to make the students that are not usually
interested in math have more interest.
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Keywords: Algebra, Activities, Planning
Ref: Andy20
Author(s): Gupta, Neil
Date: 2004
Title: Algebra 1's Speed Trap
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: VOL.97, NO. 1 pg. 14-16
Reviewer: Andy
Date of Review: 5-20-04
This is a good activity that get students out of the classroom and has them learning math at the same time. It also teaches them about safety and being aware of the speed limit. This is an activity that requires a lot of planning. This planning determines how successful the activity is going to be. So the students should know that they should put an emphasis on there preparation.
Most of the math in this activity is done in the preparation. The students had to come up with quick ways to deliver the speeds and for converting the times. For this they needed to use their algebra skill and dealt with ratios. A conversion table was made to speed up the process.
I think that this would be a good activity to get students motivated. It is a good way to promote communication and cooperation between the students. Teamwork skills are developed through this, which is a very important element to learn. With planning and cooperation from the police and schools this could be a good activity to incorporate into the classroom.