Keywords: Teaching Strategies, ,
Ref: Gabe1
Author(s): Fiore, Greg
Date: 1999
Title: Math-Abused Students: Are We Prepared to Teach Them?
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 5, May 1999, pages 403-405
Reviewer: Gabe
Date of Review: February 13, 2001
I found this article to be very interesting. It talks about those students who are sufferers of math
anxiety. The article also gives suggestions on how to overcome these problems. It seemed to point out that
those who suffer from math anxiety usually have had some terrible experience with math. This traumatic
experience has lead to a difficulty in learning and even understanding math.
The article also gave one idea on how to combat this phenomenon. The suggestion was to have
students write a small paper about math. They are to answer some questions and explain their relationship
with math itself. Surprisingly, when students are given a chance to explain themselves they open up and
then are able to be helped. The article said many more women then men wrote about feelings and
experiences, I would think that this supports the existence of the old stereotypes, such as females in
language and English, males in math and science.
Keywords: Teaching Strategies, Connections,
Ref: Gabe2
Author(s): Krussel, Libby
Date: May 1998
Title: Teaching the Language of Mathematics
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Volume 91, No. 5, 436-441
Reviewer: Gabe
Date of Review: March 1, 2001
This article discussed the idea of learning math as one would learn a language. There was a small section debating whether, math should be learned implicitly, through experience, or explicitly, through books and school. Another section debated whether math could even be comparable to a language at all. I don't think this important so I will not discuss it further but I do believe math is similar to a language. It has its own characters and definitions. If one looks at math as a pseudo-language it would only make sense to learn in both implicit and explicit experiences. It is important to learn the definitions before some concepts and other times it is better to put definitions to concepts already experienced.
Assuming the best way to teach math would be like a language, it would then be important for
students to have structure to their learning. Writing is a key concept that is not often used in math. The
article pointed out that with calculators and computers students don’t need to write anymore, so why not
make them write out how they came up with the answer. I think that if a teacher can incorporate writing
into math, the concepts will solidify more quickly in students because they are able to apply their own
metaphors and ideas to these concepts. Students would also have a chance to express themselves pulling
them into the class. Math history is important as well. By showing dead-ends and difficulties encountered
along the way, students might realize that math is more than just “math”. It is constantly moving and
fluid. Math illiteracy is still widely accepted. Clearly the author feels that this view needs to change. I
would agree with her. I think this can be done by making math more than numbers and theorems. By
incorporating writing and expression math can come alive and students can start to relate, this is when
students will probably start to learn and understand a little more.
Keywords: Assessment, Teaching Strategies,
Ref: Gabe3
Author(s): Odafe, Victor U.
Date: March 1998
Title: Students Generating Test Items: A Teaching and Assessment Strategy
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Volume 91, No. 3, 198-202
Reviewer: Gabe
Date of Review: March 1, 2001
This article addressed the idea of students generating test questions and gave ideas on how to implement this idea with out great difficulty. This concept received great praise because almost all students enjoy taking part in designing and creating tests. Many students said that they studied harder as well because they knew that classmates would put difficult questions on the tests. Also they thought they learned more by creating tests because they had to learn the material to create the questions that might meet the teachers expectations.
Questions were formulated in groups and done according to a guideline. This way content would
not be at risk. I think this is a good idea because it makes students feel like part of the class. It also makes
the teacher more of a teacher than an authority figure. Furthermore, a teacher can assess the understanding
of students by simply walking around and listening to conversations. The formation of small groups also
leads to a fellowship in the classroom. Those having trouble with questions can be helped by those who
understand. Since students will create the questions, it also alleviates some of the stresses on a teacher.
Instead of creating and constructing the test the teacher can just put the test items together. Lastly, I think
that this concept might only work well in some content areas, such as algebra, probability and statistic
related material.
Keywords: Standards, Assessment,
Ref: Gabe4
Author(s): Benson, Christine; Long, Vena M.
Date: September 1998
Title: Re: Alignment
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Volume 91, No. 6, 504-507
Reviewer: Gabe
Date of Review: March 1, 2001
This article addressed the standards and specifically assessment that is designed to meet the standards. The big question was curriculum alignment. Alignment occurs when the homework, assessment, curriculum and instruction all communicate the same expectations to students. In the past, traditional methods of teaching were thought to be aligned with the standards but this is not the case. No higher level thinking was needed to complete these tests or homework assignments. Furthermore, the tests were the majority of the grade, newer assessment data was rarely, if ever used. Currently, teachers that often do different assessment are frustrated with themselves and society, because they often don't feel confident using alternative assessments in final grades. The message the article was getting at was that we put too much of our emphasis on the final product. Little emphasis is put on the actual learning and thinking processes done before the test. Often tests are traditional in nature because students can do well on them. Newer tests incorporating higher order thinking are difficult, to make and to take.
I think that many of these ideas are good. I am for higher level thinking, but how
does one break the mold. How does one push into the new strategies without losing
students? New assessments are out there such as the performance tasks, rubric scoring
and portfolio assessment, but we have to be willing to change focus to these instead of
the old way. Tests can also be written better, but it takes more effort and more time.
Fill in the blank questions only ask recall questions. Multiple choice doesn't really
elicit higher order thinking. Essay questions or questions with one right answer but many
ways to get there would elicit higher order thinking because they push the envelope.
Students need to think out of their box to be pushed. These tests also are longer and more
difficult to grade. It means more work for teachers but I think that students can learn
much more, better.
Keywords: Teaching Strategies, Curriculum,
Ref: Gabe5
Author(s): Wohlhuter, Kay A.
Date: October 1998
Title: Geometry Classroom Pictures: What's Developing?
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Volume 91, No. 7, 606-609
Reviewer: Gabe
Date of Review: March 1, 2001
This article took a look at five teachers and their role in the geometry classroom. One of the five had a 55 minute class, three others were on the block schedule, and one was a combination. The five classrooms were very different in the approach that was take. Some were lecture based, some were discussion based and others were group investigations and hands on. The classroom that was 55 minutes long was generally based on the lecture method. I would think that this seems logical because management would be necessary in order for anything to be accomplished and possibly learned in class. The three block scheduled classes had more hands-on, investigation and constructivist learning. However, the time constraint wasn’t the real determining factor in teaching strategies. It was the teachers’ preference and what they felt comfortable with, that most influenced how they taught geometry. Three of the five teachers attended many professional development gatherings because they wanted to learn new ideas or new ways to teach something. One of the teachers said that she wanted to focus on a student-centered classroom instead of a teacher centered one. This changed her classroom from lecture based to a hands-on, constructivist, investigation based classroom. Professional development is then an important tool for teachers to get help in the reform process.
The Standards are also mentioned. The emphasis on these was the ease at which
the new strategies can align with the standards. Higher order thinking is increased in
many of these classrooms, especially when teaching is moved away from the lecture and
two column proof method. The focus on thinking between lecture based and hands-on
based learning changes from deductive thinking to inductive thinking, where students
form thoughts and processes themselves through experimentation.
Keywords: Activities, History,
Ref: Gabe6
Author(s): Ryden, Robert;
Date: 1999
Title: Astronomical Math
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 9, December 1999, pages 786-792
Reviewer: Gabe
Date of Review: May 7, 2001
This article I found extremely interesting. It discussed all of the math involved
behind some of the great astronomy discoveries. The neat thing about this article is that
students can understand and follow the math involved in these calculations. A historical
view point can be brought into the classroom. Big problems were solved using some
basic math and trigonometry and little or no technology. The circumference of the earth
was calculated in the 3rd Century BC. The 16th Century brought Copernicus to the
forefront of modern sciences with his heliocentric theory of the solar system and his
distances between the earth, the sun and other planets. His numbers are surprisingly
accurate, and even more amazing when we realize they were done 500 years ago. Kepler
is also a name that many recognize. His three laws also were theorized back in the
1600's. He published his findings in 1609. Newton also came along revolutionizing the
field of physics. How is the math involved easy enough for students to understand?
Many of these discoveries were done with some simple assumptions and basic
trigonometry.
A neat activity that students can do is finding distances through triangulation, or
through another process called Parallax. Students can measure the distance between two
objects, by making a simple small angle measuring device and using some trigonometry.
Their answers can be checked simply by measuring. It can be surprisingly accurate. I
not only think this article is great for the math behind it, but its historical content and
physics applications is tremendous as well.
Keywords: Management, Teaching Strategies,
Ref: Gabe7
Author(s): Murdock, Tamera B.
Date: 1999
Title: Discouraging Cheating in Your Classroom
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 7, October 1999, pages 587-590
Reviewer: Gabe
Date of Review: May 7, 2001
Cheating is a rising problem and from discussions with a friend it is difficult to
prove dishonesty, and difficult to constantly monitor behavior. So what does one do to
discourage cheating in their classroom? The article gave many possible solutions to the
problem which will be helpful, but also gave some reasons for the increased frequency of
cheating, both over grade levels and from decade to decade.
So what are some of the main reasons students cheat? The most prevalent reason
given by many students is when a classroom is perceived to be performance based and
fewer cheat in a setting where tasks and goals are emphasized. I guess it is one thing to
have it be task oriented but if it isn't emphasized to students many may not view it the
same. Other reasons given are fear of failure and also if the students think that the
teacher is incompetent, or appears to not care about the students' learning. One of the
other reasons for cheating I found very interesting. The article states that students are
more likely to cheat on a test, which contains material that was not emphasized in the
course or is not seen as valuable. This is interesting to me because we are taught to not
"teach to the test". If we aren't teaching to the test there is bound to be material not
emphasized in class, found on the test. Similarly, problems which don't look like
"standard" problems, may also "encourage" cheating. Some of the solutions given are
well thought out but might be difficult to introduce in a lower level math setting (K-8).
Of the three solutions mentioned in the article the one that stuck out most was
including questions that aren't just number answers, but have the students write down
their reasoning also. If students cheat and try to disguise their reasoning, "they usually
omit important items and copy verbatim the less important parts." This would clue us
into who was cheating and furthermore who is having difficulty with the concepts.
Keywords: Number Theory, Games,
Ref: Gabe8
Author(s): Shi, Yixun
Date: 1999
Title: A Mathematical Study of the Game "Twenty-Four Points"
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 9, December 1999, pages 828-832
Reviewer: Gabe
Date of Review: May 7, 2001
In this article a child’s game is put to use in the classroom. The game is 24
points. It is played by drawing numbers from the set {1-10}, with replacement. Four
numbers are drawn and the object is to get a total of 24 by using the four basic functions
and following some simple rules. The game can be played at all levels and is quite
interesting. However, at the high school levels, the game can be looked at as a
mathematical situation and students can investigate some of the questions they have or
may develop along the way. Such questions are: Why the number 24 and not 23 or 25?
Are there combinations of numbers that don’t have an answer of 24? Some basic and
more advanced math is used to investigate these questions. Some algebra can be used to
determine what variables to use. Problem solving skills are also incorporated, as well as
data analysis and probability.
This game is a veritable gold mine. It can cover many of the concepts designated
in the standards if used properly. I can envision using this game throughout an entire
semester or year of classes. It can be introduced in a class period towards the beginning
of the term. Later during other chapters when new skills are learned the dust can be
blown off and questions can be made, problem solving skills can be used and students
can develop their own interest and love for mathematics.
Keywords: Algebra, Activities,
Ref: Gabe9
Author(s): Edwards, Thomas G.; Chelst, Kenneth R.
Date: 1999
Title: Promote Systems of Linear Inequalities with Real-World Problems
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 2, February 1999, pages 118-123
Reviewer: Gabe
Date of Review: May 7, 2001
This article dealt with finding optimal solutions for two variable inequalities. It
began with some history on linear models and operations research but moved into their
application into the classroom. The first problem mentioned was building tables and
chairs using Legos?. Given so many pieces of stock, what amount of each product will
optimize profits? Students can easily make all of the possible solutions and then figure
out the according profits. Later, the idea of “decision variables” can be made and
inequalities can be set up. The Legos? are a concrete example to the concepts behind the
problems. Left over pieces means a loss of profits. The final example was similar to the
Legos? problem except it is a bit more difficult. Some calculations and conversions are
needed to set up the inequalities, though once done the problem is quite simple. Lastly
the article introduces the corner principle. This is where the optimal solution lies.
I think this article is a good example of how to incorporate things students know
into their learning in the classroom. I have always loved Legos? and know I would have
been interested in their use in my classrooms as a student. Likewise, I think that building
chairs and tables out of them, can be a good tool to help solidify the ideas behind finding
an optimal solution involving two or possibly even three variables.
Keywords: Geometry, Problem Solving,
Ref: Gabe10
Author(s): Bonsangue, Martin Vern; Gannon, Gerald E.; Buchman, Ed; Gross, Nathan;
Date: 1999
Title: In Search of Perfect Triangles
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 1, January 1999, pages 56-61
Reviewer: Gabe
Date of Review: May 7, 2001
This Article has to be the one article so far that has caught my attention and
created the most curiosity. I also think that the content of this article will generate the
same enthusiasm in a classroom setting.
It begins from a recent investigation, where the authors were looking for
rectangles with the same numerical perimeter as the area, and sides having natural
number values. They found 2 cases in the 2-D space, 10 in 3-D space and 108 in 4-D
space when dealing with hyper-volume equals volume. This was interesting so someone
proposed to try and find “Perfect Triangles.”
This problem was more difficult than expected. They began by searching for
special cases, right, isosceles and equilateral triangles. Through the use of algebra and
some basic proof techniques, the authors were able to get two perfect triangles, both right
triangles. The authors were fairly sure that they had both of the perfect triangles but
because of a peculiarity, decided to look at the scalene case anyway. What was peculiar
about the two perfect triangles, they both had an inscribe circle of radius 2. Upon further
investigation, three more triangles were found for a total of five. Technology was the key
to finding the last three. A computer program made the solution quite simple.
This article could be used as a great example to problem solving. It also
incorporates basic proofs and algebra. It would be a great way to bring together many
mathematical concepts in on problem. The best part is that the solution is given so if a
teacher has difficulty explaining something they can always refer back to the problem.
The article also gives a basic program that can be used to solve the Perfect Triangles
problem.
Keywords: Probability, ,
Ref: Gabe11
Author(s): Bisbee, Gregory D; Conway, David M.
Date: 1999
Title: Studying Proportions Using the Capture-Recapture Method
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 3, March 1999, pages 215-216
Reviewer: Gabe
Date of Review: May 24, 2001
Proportions are widely used in mathematics and in other applications as well.
One of a more common use of proportions is to determine population sizes of animals in
their natural habitat. In this fashion, animals are captured and tagged, then they are
released. After some time later a population of animals is captured again. Proportions
can then be used if some of the recaptured animals have been previously tagged. The
activity to go along with this involves mandm bugs. I was confused at first until I
realized they were M&M bugs.
This is a great activity for students to participate in data collection. Furthermore,
I think a good discussion of possible flaws of this method could be brought up. This
discussion would help students learn about data collection first hand and also understand
some of the work that must go on to determine, whether or not the data accurately reflects
the population. Other mathematical concepts besides data collection can be incorporated
in the activity as well. Probability is the most obvious, as questions can be easily
formulated to fit a similar activity. I think one of the most promising aspects of this
activity is fostering students' enthusiasm towards itself, and encouraging them to think
about proportions and data collection.
Keywords: Discrete, ,
Ref: Gabe12
Author(s): Szetela, Walter;
Date: 1999
Title: Triangular Numbers in Problem Solving
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 9, December 1999, pages 820-824
Reviewer: Gabe
Date of Review: May 24, 2001
Triangular Numbers are one of many sequences of numbers that aid in problem
solving. They are easy to understand and the recursive formula is quite obvious but not
many know that they are a widely used sequence in problem solving. Sometimes the
relationship is not so obvious as the triangular numbers are in "disguise" but none the less
they are they sequence behind the solution.
Specifically this article closely resembles what is done in a discrete mathematics
classroom. Many problems are poised and either through solving the problem or
transforming the problem into an easier more comprehensible question, patterns are
formed. These patterns usually correspond to a known sequence. Further investigation
can then be done on the sequence itself. The sequence is just a means by which to solve
the problem but it also presents more questions.
Connections can also be made between very "different" questions. Solutions arise
that are quite similar and students are then able to see the relationships between the two
questions. Conjectures can also be made when patterns are formed and often they are
easily tested.
This is a good article because it shows one aspect of utilizing the triangular
numbers. They are a common sequence and students can be shown or experiment with
objects and see why they are named the triangular numbers. The article also mentioned
some problem ideas that could be used in a classroom.
Keywords: Games, ,
Ref: Gabe13
Author(s): Larson Quinn, Anne; Koca, Robert M. Jr; Weening, Frederick;
Date: 1999
Title: Developing Mathematical Reasoning Using Attribute Games
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 9, December 1999, pages 768-775
Reviewer: Gabe
Date of Review: May 24, 2001
The concept of Sets is often difficult for students to understand. It is abstract and
can be the cause of frustration. Mathematical Reasoning dealing with sets is often more
difficult then understanding sets. This article was written to give ideas on how to ease
frustration when students are learning sets.
I was actually surprised by the approach the article used. It was simply based off
of a set game. One I was actually looking at buying and similar to games I have seen on-
line. The game consists of 81 cards each having a combination of 4 attributes. Sets are
made with three cards and are made either when all attributes are different or the same.
This game is a great concrete example of sets. Certain cases using the cards can also be
set up. Questions about these situations are great ways to elicit higher-level thinking.
Broader questions can be asked as students become more comfortable with the cards.
These questions might otherwise be too difficult to answer without the aid of the set
cards. This game with an easy to understand objective, is a great tool for exploring a
difficult topic in mathematics. Ultimately, a higher level of mathematical reasoning is
achieved due to the thinking students did, by trying to answer questions about certain
game cases.
Keywords: Problem Solving, Teaching Strategies,
Ref: Gabe14
Author(s): Erickson, Dianne K;
Date: 1999
Title: A Problem-Based Approach to Mathematics Instruction
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 6, September 1999, pages 516-520
Reviewer: Gabe
Date of Review: May 24, 2001
In many classrooms students aren't thinking at high levels. This is due to "the
way the teacher approaches mathematics instruction". As one of the goals of education is
to teach students to think critically, a classroom with this situation would be falling short
of our expectations. Furthermore research supports a classroom where students are
constructing the knowledge themselves because they tend to understand more. Thus it
seems appropriate to have a classroom that is taught through a problem-based approach.
What exactly does this mean? It simply means that students try to solve problems. There
is one key point that needs to be emphasized; the problems don't have a known procedure
or algorithm to find the answer. The focus is on the procedure or algorithms developed
by the students, rather than the answer.
The article supports this type of classroom because, once implemented, this
approach is valuable. It also points out items a teacher must remember if they are
planning to implement such a strategy. Time and Organization in planning are two main
points the article makes. The activity or problem must be allowed sufficient time so
students are able to develop their thinking. Organization during that time is also
necessary. Students need to be guided along so that they are able to make conjectures
and given an opportunity to listen to others ideas as well.
Even though there is a possibility of high level thinking to be done, and large
amounts of learning as well, there can be some problems. The biggest problem, I think
would be keeping students motivated to try and solve the problem. Frustration builds
with an activity like this and one does not want to turn a student off to mathematics. This
is a difficult thing to do as "students must be allowed to struggle". However, through
good teacher question and appropriate guidance for an activity such as this can help
students along in their problem solving strategies.
Keywords: Teaching Strategies, ,
Ref: Gabe15
Author(s): Duke, Johnny I;
Date: 1999
Title: Service Learning: Taking Mathematics into the Real World
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 9, December 1999, pages 794-796
Reviewer: Gabe
Date of Review: May 24, 2001
Learning in the classroom is supposed to be preparation for the real world but
many classrooms follow curriculum and teaching styles that deal with book problems.
"The indictment from the Mathematical Sciences Education Board of the National
Research Council [states], 'students who progress through this curriculum develop a kind
of mathematical myopia in which the goal is to solve artificial word problems rather than
realistic word problems.'" Many classrooms have followed this path but this article
suggests just a few ideas on how to get the learning back into the real world. One such
idea was preparing taxes for the elderly.
Ideas such as these are valuable because it promotes a mathematics world bigger
than the classroom. It also gives students a chance to do something productive in their
community, hopefully making the students feel good about what they are doing in math
class. Almost 88 percent of students done in an anonymous survey said they learned
something positive through an experience such as this. Lincoln High School in
Philadelphia has put a large emphasis on service learning. Students in this school helped
to design city parks and as a result they have a Two million dollar horticulture program,
built from private donations.
I think that service learning can be a very valuable educational tool if it is utilized.
I also think that many students would jump at a chance to participate in such programs.
This enthusiasm brought by students would help to alleviate occurrences of Math Anxiety
and help many to see the importance of mathematics.
Keywords: Teaching Strategies, Communication, Research
Ref: Gabe16
Author(s): Jackson, Carol D; Leffingwell, R. Jon;
Date: 1999
Title: The Role of Instructors in Creating Math Anxiety in Students from Kindergarten Tthrough College
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 7, October 1999, pages 583-586
Reviewer: Gabe
Date of Review: May 24, 2001
Math anxiety is a large problem for those who fear to take a math class or those
who refuse to participate in any math activity. It is usually developed by some bad
experience with mathematics at a young age. This article investigated the instructor
behavior that lead to math anxiety in students. The study found that most bad
experiences in math occur in three clusters; grades 3 and 4, grades 9-11 and the first year
in college. 42 percent of those questioned, had bad experiences in the first two clusters.
That means that at least 42 percent of those graduating from high school could suffer
from some degree of math anxiety. This is astounding to me. I was only one of the 7
percent that said they had a good mathematics experience growing up.
Why would so many people suffer from math anxiety? Most of the occurrences
were due to instructor actions. Many cases were due to gender bias and many more were
due to instructor insensitivity. More were also a result from embarrassing the student in
front of their peers. This article points out that these situations are most often
inadvertent. Regardless, it is still damaging to students. This article should raise the
awareness of teachers and their actions so that many more sufferers from math anxiety
can be avoided.
Keywords: Statistics, Activities,
Ref: Gabe17
Author(s): Alfano, Joseph L; Pandolfini, Thomas J. Jr;
Date: 1999
Title: Statistics and The Academy Awards
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 3, March 1999, pages 219-221
Reviewer: Gabe
Date of Review: May 24, 2001
Statistics can be a uneventful and intimidating subject area in mathematics.
Similarly, many people avoid statistics because they don't think it pertains to anything
interesting. This article takes something 1.5 Billion people watch every year and makes
it an interesting subject matter to study in a statistics course. Together, the Best Picture
winners, along with nominations and wins for other categories, is a great set of data that
gives rise to many possible questions pertaining to statistics and probability. Many other
concepts such as Venn Diagrams, and statistical plots can also be generated to explore
other aspects of the data.
Although short, this article contains a rich, and more importantly, interesting data
set, from which many questions can be asked. The data set also allows students to
investigate their own questions relating to statistics. The article suggests finding data for
the Emmies and Grammies as well.
Keywords: Research, Teaching Strategies,
Ref: Gabe18
Author(s): Richardson, Joan;
Date: 2001
Title: Lesson Study: Japanese Method Has Benefits for All Teachers
Journal or Publisher: Results published by The National Staff Development Council
Volume, Issue, Pages: December/January 2001 pages 1,6
Reviewer: Gabe
Date of Review: May 24, 2001
Lesson Study is a Japanese method of continually improving a lesson through a
team effort of teachers. A lesson is taught and observed and refined as many times as
needed to make the lesson as effective as possible. This article mentioned one school that
tried to develop a lesson study program with the aid of some teachers from the
Greenwich Japanese School. This school is a Japanese school in Connecticut, set up and
funded by the Japanese government for children of Japanese nationals working in the
United States.
The lesson study itself went through major refinements. It also took 15-18 hours
to complete for the different groups. Also another interesting point was mentioned about
observing. When we videotape in the classroom we videotape the teacher. We should
videotape the students because they are whom we are concerned about. We should be
able to see what they are doing in a classroom. I do think that videotaping myself is also
helpful but it is a good idea to tape the students as well.
So could something like this eventually make it in most U.S. schools? The article
thinks it won't because of the large amount of time needed to develop such lessons. I
would have to agree because extra time is something teachers don't have too much of.
However, I do think it might be developed in small pockets across the U.S. It won't be
widespread but I foresee some use of lesson study as it is a stable concept in the rapidly
changing field of education.
Keywords: Curriculum, Geometry,
Ref: Gabe19
Author(s): Geddes, Dorothy;
Date: 1992
Title: Curriculum and Evaluation Standards for School Mathematics: Geometry in the Middle Grades
Journal or Publisher: NCTM: National Council of Teachers of Mathematics
Volume, Issue, Pages:
Reviewer: Gabe
Date of Review: May 24, 2001
This book is helpful to me for understanding what geometry concepts are covered
at the middle grades. It gives many activities and ideas for activities to do with students.
One additional thing I like is that it discusses some things that are currently in use such as
tangrams or pentominoes and explains how they are useful to students. It also mentions
things currently in use that are effective at helping students learn.
In general many of the geometry concepts covered in the middle grades can be
done through manipulatives and various activities. Ultimately, one of the goals of this
book is to help teachers develop curriculum or activities above the curriculum that help
students understand "the essential role of geometry and reasoning in our society". The
book also presents different approaches to current standard practices. The goal of these
new ideas and activities is to develop students' thinking beyond the basic levels. Higher
level thinking is encouraged by all researchers, thus it needs to be made a staple in the
classroom, especially at the middle school level where students are capable of
understanding and learning much more than we think. It is also important at this level
because the mathematical concepts learned here, are the foundations of many of the
concepts expanded on in high school and college.
Keywords: Games, ,
Ref: Gabe20
Author(s): Konhauser Math Tournament
Date:
Title:
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Gabe
Date of Review: May 24, 2001