Keywords: Conjecturing, Technology, Reasoning
Ref: Colvin1
Author(s): NA
Date: 1993
Title: Topics in Mathematics in a Fractal Class -
http://www.ncsa.uiuc.edu/Edu/Fractal/Ftopic.html
Journal or Publisher: University of Illinois Board of
Trustees National Center for Supercomputing Applications, Education
Group
Volume, Issue, Pages:
Reviewer: Colvin
Date of Review: July 16, 2000
It can often be difficult to find creative ways to teach students basic skills in ways they can understand. It can also be difficult to instill in students a drive to use what they already know to solve new problems. This article talks about how fractals can be used to give students a greater understanding of the coordinate system, negative numbers, scientific notation, simple arithmetic, multiplication, and the distributive law.
The article is good at showing how all these ideas relate to fractals, but
doesn't do as good of a job explaining how the relations might be
presented in a real-life classroom. I would imagine that a variety of
discovery based activities would be most effective yet these are left for
the teacher to design themselves.
Keywords: Technology, Standards, Problem Solving
Ref: Colvin2
Author(s): Eiser, Leslie
Date: March 19993
Title: Math for a reason
Journal or Publisher: Technology & Learning
Volume, Issue, Pages: v13 n6 p52(5)
Reviewer: Colvin
Date of Review: July 20, 2000
The NTCM standards emphasize the importance of a classroom in which "the students and the teacher talk the language of math; work in groups to solve open-ended, real-world problems; use calculators, manipulatives, and computers intelligently; and verify their answers together, using mathematical reasoning rather than an answer key." It can be rather difficult (especially for teachers that are new to these concepts) to find good materials to use in the classroom.
This article reviews several different math products that are
standard based and emphasize real-world situations. All of the
products sound rather good and vary from computer software to
video programs. Most of the products are designed for elementary
grades but several of these include grade 6. This article could
be a good starting point for teachers interested in finding
standard based technology products that also help teach real-world
math and problem-solving at middle school levels.
Keywords: Issues, Connections, Curriculum
Ref: Colvin3
Author(s): Ford, Patrick
Date: Sept 12, 1994
Title: What they did on their summer vacations.
Journal or Publisher: The Business Journal Serving Greater
Sacramento
Volume, Issue, Pages: v11 n24 pS4(2)
Reviewer: Colvin
Date of Review: July 22, 2000
Have you ever wondered how you are going to relate your teaching to real-world situations? Do you know what you are going to say when students asks why they have to do a certain task? If so, this article could help.
Ford explains how an program like Industry Initiatives for Science and Math Education may help prepare teachers to relate their teaching to the real-world. More explicitly, IISME teaches teachers about the real-world. IISME provides opportunities for teachers to actually work for corporations during the summers. Teachers are trained into the company and are then asked to complete an eight-week project.
The logistics of the program sounded a bit complicated (one summer, because of insufficient funds, only six teachers found placements) but the idea could be used for any teacher no matter what programs are available. The program stresses the fact that teachers are sheltered. Most leave college and go directly to work as an educator. However, the world of an educator varies quite drastically from the worlds of other professions.
Teachers need real world experiences if they are expected to teach
real-world applications. So, before you jump into the education
field, consider trying a more "real-world" occupation for a while.
And if you can't wait to get into the education field, consider
finding summer employment or some sort of internship at a local
"real-world" company. You and your students will benefit greatly.
Keywords: Technology, Connections, Teaching Strategies
Ref: Colvin4
Author(s): Stapleton, Lisa
Date: June 1990
Title: Visualizing math: computer graphics transforms the
face of traditional math education.
Journal or Publisher: Computer Graphics World
Volume, Issue, Pages: v13 n6 p58(5).
Reviewer: Colvin
Date of Review: July 24, 2000
This article praises the worth of computers to help teach complicated math concepts to students. Many teachers and administrators would probably agree that computer programs are helpful teaching aids but would also probably complain that the programs are typically too expensive for low-budget schools. However, this article describes several math computer programs that sell for a remarkably low price.
Math software can be extremely helpful because it helps students overcome many typical hurdles that can be encountered. Computers are much more impersonal. This may be viewed as a negative aspect but students more frequently prefer this approach when first learning a concept. Most students feel uncomfortable having someone watch them struggle through a concept.
Computers also allow students to work at their own speed. If a few do not understand a concept the whole class doesn't necessarily have to stop and wait for a concept to be explained.
Also, computers help students visualize math concepts. Many students
find it difficult to transfer what they see symbolically to what
they can understand visually. Computers help students understand
how changing a variable changes the outcome. Computers can be used
to teach students how to think and predict. It makes them active
learners. This is something I think all teachers can appreciate.
Keywords: Issues, Assessment,
Ref: Colvin5
Author(s): Norman, Colin
Date: July, 1988.
Title: Math education: a mixed picture.
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Colvin
Date of Review:
This is a short article talking about a study in the public schools of Montgomery County, Maryland. The school system is fairly high budget and yet there seemed to be troubles regarding blacks, Hispanics, and females in mathematics. The study stated that racial and ethnic differences started to be evident as early as first or second grade. Gender differences usually only showed up in the last few years of high school.
The study also attempted to discover why differences in performance occurred. The study found that parental influence has the greatest influence on student's performance with the next largest influence being encouragement by teachers. So, with this in mind, it is clear why it is important to keep parents involved in the school and its' programs. If parents feel like they have some say as to how the school is run, they will more likely have a positive attitude and influence on their kids.
The study also looked at SAT scores of students and found that boys and
girls performed equally well on two standardized tests but males scored
better than females on the SAT. This may indicate a problem with the way
the SAT is set up and is also a good reminder that standardized tests may
not be the best indicator of how much a student knows.
Keywords: Technology, Issues, Standards
Ref: Colvin6
Author(s): McCarthy, Robert
Date: Sept 1992
Title: Hands-on math & science
Journal or Publisher: Electronic Learning
Volume, Issue, Pages: v12 n1 pS8(6)
Reviewer: Colvin
Date of Review: July 30, 2000
This is another article proclaiming the importance and value of computers in the mathematics classroom. Described in this article is the Alabama School of Fine Arts and their use of Apple computers especially in the math and science classrooms. The philosophy of the school is that hands-on learning should come first and that theory comes second.
The program in place at this school is based primarily on the NCTM reports on how students learn better by doing math when it has a purposeful context. They believe that the new standards in place help students do math instead of just sitting and listening about math. At ASFA, students do an experiment first, analyze it and then go into the classroom to learn about the theory.
Computers help the students learn math through a discovery-based experimental approach. Otherwise, students would have to constantly redraw a geometrical shape or re-plot a new graph after a variable had been changed. Computers help students focus on what happens when something is changed rather than on how to change it.
One concern with using computers so heavily in the classrooms is that students will no longer be able to re-plot a graph or re-do an equation using different variables without the help of a computer. I suppose it all depends on what you think is inevitably important. If you feel that the most important thing is for students to be able to write out equations or graph by hand, then computers are not what you want to use in the classroom. If you want students to understand the theory behind the math then maybe computers will help you achieve that goal.
At ASFA, students cover an introduction to mathematical thinking and also courses covering plane geometry, analytic geometry, and non-Euclidean geometries in their first year. Their second year, they cover algebra and trigonometry. The third year covers calculus and the fourth year coves linear analysis, number theory, and logic. In each of these classes, the relationships to science will be explored.
This really sounds like quite a wonderful program - one I would like to be involved in. Budget is a bit of a problem for the school but they do receive funding from primarily private but also some public sectors. Another possible problem for schools adopting this philosophy in teaching is to find teachers who share the same beliefs. Considering that many of these concepts are relatively new, it may be difficult to find teachers who are believers in the new system.
Besides the possible hurdles, I believe that the system of using
computers and promoting hands-on learning is extremely valuable and
effective. I think it helps students learn and remember more and
also have a greater interest in what they are learning. It also helps
them transfer their learning to other subjects. I don't think any
teacher would argue that these aren't desirable outcomes from teaching!
Keywords: Standards, Geometry, Statistics
Ref: Colvin7
Author(s): Hoffman, Kenneth M.; Steen, Lynn Arthur
Date: Nov-Dec 1989
Title: Making math education effective.
Journal or Publisher: Technology Review
Volume, Issue, Pages: v92 n8 p22(2)
Reviewer: Colvin
Date of Review: July 30, 2000
This article focuses on how math education needs to be refocused for students at younger grade levels. Hoffman and Steen argue that children who are taught geometry and statistics and an early age will be more suited to understand more complex math when they are older than those students who primarily focus only on arithmetic at early ages.
They explain that the learning gained in mastering basic geometry and statistic skills at early ages can be applied toward learning about elementary fractals and about plotting data and understanding more formal statistics. Hoffman and Steen also point out that early learning of geometry and statistics can carry over to life out of school. They claim that students who are have learned a greater variety of math skills by doing a more hands-on rather than a pure number-crunching approach.
The new NCTM standards also stress the importance of more kinds
of math at an early age. In fact, the standards stress more
varied math than Hoffman and Steen do. I really agree with the
new standards. I feel that students who have been introduced in
elementary concepts in many different math subjects will be more
prepared to tackle advanced subjects at an earlier age and then
go on to more advanced topics than were previously covered in the
typical high school curriculum.
Keywords: Issues, Assessment, Teaching Strategies
Ref: Colvin8
Author(s): Leo, John
Date: May 26, 1997
Title: That so-called Pythagoras. (the multicultural
dumbing-down of math education)
Journal or Publisher: U.S. News & World Report
Volume, Issue, Pages: v122 n20 p14(1).
Reviewer: Colvin
Date of Review: July 30, 2000
In this article, John Leo strongly argues against the new math being implemented in the schools. He argues that the correct answers are no longer important and that math is now more concerned with real-life than it is with actual math.
He sites an example of an Algebra book with doesn't actually have an equation until page 165 and that the first solution for a linear equation is found on page 218 by guessing and checking. He also claims that the whole book is basically lecturing about ethnic and environmental issues instead of math problems.
What I feel that Leo forgets is that anything (no matter how good) can be misused. What I think he has forgotten to do is to see the potential for correct use of the new math education system. He fails to see that some of the things the new math is trying to do could actually improve how students perform.
Leo also sites an example of Palo Alto, California where students standardized math scores dropped from the 86th percentile to the 58th when they implemented the new math curriculum. However, this may just prove that standardized tests don't always test how much a student may know.
Another argument Leo makes is that math is concentrating too much
on ethnic issues. He seems to be making a joke about how math
educators have been focusing lately on how to make those students
of ethnic backgrounds do better in math. He seems to think that
there is no difference from a black or Hispanic student than from
a white student. Has he not looked at test scores of the average
black or Hispanic student compared to the average white student?
There definitely seems to be a problem with making math
accessible to ethnic students. Unless of course he's going to
argue that ethnic students must just be less intelligent than the
average white student.
Keywords: Standards, Connections, Reasoning
Ref: Colvin9
Author(s): Waite-Stupiansky, Sandra; Stupiansky, Nicholas
G.
Date: Nov-Dec 1998
Title: Mathematics ... a Web of connections (teaching math
to grades K-12)
Journal or Publisher: Instructor (1990)
Volume, Issue, Pages: v108 i4 p76.
Reviewer: Colvin
Date of Review: August 1, 2000
This brief article discusses the importance of making "mathematical connections," one of the four process NCTM standards. While this article mainly discusses elementary classrooms, the concepts presented can easily be applied to any grade level.
The article discusses the several different connections that should be made to help students enjoy math, and understand it better. Five different basic connections were discussed. The first connection is between math and real life. We have all talked about why this is important and about ways in which to implement this in the classroom.
The next connection discussed was that between math and other subjects. This implies that collaboration between teachers is very important. Relating each subject to each other helps students feel that their classes have relevance and also helps prevent them from feeling overwhelmed. If subjects relate to one another, students don't feel like they're having to learn so many things at a time.
Connections within math are very important. Students should understand how all the operations are connected. For a basic example, they should understand that addition and subtraction are opposites and that multiplication and division are reverse operations. I believe these connections are usually discussed in classrooms already.
Another important connection is between procedural and conceptual knowledge. This means that students should not only know how to apply a formula but why they work. Students who feel they do not understand why a formula works have to memorize it without understanding it. Students who understand why formulas work have an easier time remembering them and also knowing when to use them.
The last connection is between concepts and physical materials. It helps for students to actually be able to see and manipulate materials. Computers can aid in this as well as the many manipulative kits that are becoming more popular. Anything to aid students in 'seeing' math can be extremely helpful.
All of these connections are important. They help students
understand math better and also help make teaching math more
enjoyable. By teaching and discussing connections in math, we
help students make their own discoveries and become more active
learners.
Keywords: Issues, Assessment, Standards
Ref: Colvin10
Author(s): Dunne, Diane Weaver
Date: 2000
Title: Cautions Issued About High-Stakes Tests
Journal or Publisher: Education World
Volume, Issue, Pages:
http://www.education-world.com/a_issues/issues110.shtml
Reviewer: Colvin
Date of Review: August 2, 2000
With the recent concern in the news about the math standards test, I felt this was a rather appropriate article. The American Educational Research Association has recently issues several guidelines about high-stakes testing.
One of the guidelines does warn against issuing tests which determine whether or not a student will graduate or move on to the next grade level. The AERA states that such tests are only appropriate if there is sufficient opportunity for students to retake the tests with time between taking them in order to improve.
The AERA also warn against tests which determine the fate of a school system or the fate of a teachers' salary. They point out that tests are not always an accurate depiction of how much knowledge the students have or of how well the teachers have been doing.
They also warn against the dangers of teaching for the tests
rather than for real learning. I think this is a good article and
is definitely worth looking over. There is a lot of controversy
about testing - especially high-stake testing - and I think much
is warranted. I fear the school system in which tests scores
(instead of student curiosity, reasoning, problem solving, etc.)
are the ultimate goal. The AERA does not condemn all high-stakes
testing but just wishes to set up several guidelines to help
insure that high-stakes testing is effective and not abused or
misused. Perhaps the testing associated with the grad standards
are among those that should be re-evaluated.
Keywords: Issues, Teaching Strategies,
Ref: Colvin11
Author(s): The Christian Science Publishing Society.
Date: August 10, 1999
Title: In teaching math, few benefits in small
classes.(USA)
Journal or Publisher: The Christian Science Monitor.
Volume, Issue, Pages: p9
Reviewer: Colvin
Date of Review: August 2, 2000
This is a brief article about class size in relation to performance in math. The claim is that students in smaller classes show little or no improvement than students in larger classes.
The study also claims that students in Australia, Flemish Belgium, and France performed better in larger classes. Students in Canada, Germany, Iceland, South Korea, and Singapore performed at relatively the same levels, whether in small or large classes. In the US, there was evidence that eighth-grade math students did slightly better in smaller classes.
My one concern with this study is that it does not mention how teaching strategies were dealt with. Perhaps students in smaller classes need a different classroom set-up and teaching style. Perhaps the only reason students in other countries did better in larger classrooms is because the larger classrooms were more familiar and that teachers in the smaller classrooms had a harder time figuring out how to manage the different class size.
In short, the study described in this article is not enough to
convince me that smaller classes are not better than larger classes.
I think teaching style needs to be examined more closely as well as
many other factors that did not seem to be included in the study.
Keywords: Standards, Issues,
Ref: Colvin12
Author(s): The Christian Science Publishing Company
Date: May 23, 2000.
Title: In math education, who decides what works best? THE
MATH MELTDOWN.
Journal or Publisher: The Christian Science Monitor
Volume, Issue, Pages: p14.
Reviewer: Colvin
Date of Review: August 6, 2000
What is the ultimate goal of math education? Do we wish to teach students to be mathematicians or to be citizens who understand how the world of mathematics relates to their world and their jobs. This article addresses this question and the question of who decides what math teaching method works best.
In Palo Alto California, there is a debate between the mathematicians of the town and the math teachers. The mathematicians argue that the current math standards don't make math challenging enough. The math educators argue that just because the mathematicians understand math does not mean they understand how to teach it. Perhaps both have good points to make. How do we decide what is best?
Perhaps there needs to be some sort of balance. The new new math standards from NCTM promote hands-on math - math that emphasizes real-life problems, in groups. There are certainly possible problems with this system. For instance, group work sometimes enables some students to be lazy and let others work for them. In any system, there are certainly going to be possible problems. Scissors can kill but they don't have to.
What I think is that the new math standards are good things but
that they need to be balanced with some "old style" math teaching
as well. After all, there are several different learning styles
and some students are going to learn better with the old system.
I believe teachers now have to find a way to incorporate
traditional mixed with new. Perhaps both mathematicians and math
educators can have their way - it will just mean a lot more work
for math educators.
Keywords: Teaching Strategies, Issues, Standards
Ref: Colvin13
Author(s): Forbes, Inc.
Date: Jan 24, 2000.
Title: On My Mind: Math Myopia.
Journal or Publisher: Forbes.
Volume, Issue, Pages: p36.
Reviewer: Colvin
Date of Review: August 6, 2000
This is a good article discussing how important computation is
but also about how important real-life application is to math
education. The author explains how rote memorization has been
overused in math classrooms but also admits that real-life
applications, story problems, etc. can be overused. What is
suggested in this article is that the new new math and
traditional math be combined and used in cooperation to create an
effective math educational system. I suggest everyone read this
article - it's brief and explains much.
Keywords: Manipulatives, Geometry, Teaching Strategies
Ref: Colvin14
Author(s): Sheeler, Jim
Date: April 25, 1994.
Title: Boulder, Colo., Company Creates a Tool to Help Make
Teaching Math Easier.
Journal or Publisher: Knight-Rider/Tribune Business News.
Volume, Issue, Pages: p04250164.
Reviewer: Colvin
Date of Review: August 6, 2000.
This is an article reviewing a math product. The Zometool is a set a plastic pieces which can be used to represent items as simplistic as a triangle to complex model spatial structures representing hyperspaces of up to 31 dimensions. The set consists of different colored and shaped sticks which plug into the core of the system - a white plastic ball that has 62 sides, all different shapes.
For quite a while The Zometool was used only at high tech labs.
Companies such as NASA, MIT and Bell Labs all have a set. But
lately, the educational value of Zometool is being realized. The
product is now being sold in toy stores and being used in
classes. Classroom materials are being developed and it is easy
to see how having a set to build almost any geometric shape is
something to be valued. You can even purchase a Teacher's Bundle
which includes detailed lesson plans. What a great way to get
students "doing" geometry.
Keywords: Issues, ,
Ref: Colvin15
Author(s): Rivard, Jerry
Date: May 1992.
Title: The engineers' obligation.
Journal or Publisher: Automotive Industries.
Volume, Issue, Pages: v172 n5 p53(1).
Reviewer: Colvin
Date of Review: August 7, 2000.
In this article, Jerry Rivard is basically trying to encourage the engineers to get involved in the educational system - particularly in the areas of math and science. He claims that not enough students are pursuing science, math and engineering due to several factors. Among those factors are the typical - fear of the subjects' supposed difficulty, lack of motivation, etc. Another factor, claims Rivard, is that there are not many capable math and science teachers and that these teachers do not do well at making math and science appealing to their students.
To combat this, Rivard encourages those of the industrial community to take the initiative to change the education process. He suggests to become involved in the Society of Automotive Engineers, which has developed two programs designed to provide educational materials and personal support to teachers in primarily elementary classrooms. The goal is to get younger students interested in science and math by making it more fun and interesting.
While I agree in SAE's efforts at promoting math and science
education I don't agree totally with their end goal. They seem
to believe that the only importance of math and science education
is to train a population to work in engineering type jobs that in
SAE's mind, keep America functioning. It is true that
engineering jobs are important to the functioning of our society
but I feel that it is also important for people to develop
mathematical and scientific thinking skills which will help
improve all people, whether they end up working in an engineering
field or become an artist. The critical thinking and problem
solving skills learned in math and science are useful for people
in any field.
Keywords: Assessment, Issues,
Ref: Colvin16
Author(s): Bracey, Gerald W.
Date: Feb 2000.
Title: Research - Trying to Understand Teaching Math for
Understanding.
Journal or Publisher: Phi Delta Kappan.
Volume, Issue, Pages: v81 i6 p473.
Reviewer: Colvin
Date of Review: August 7, 2000
This article is a book review of two books, "The Teaching Gap" and "Knowing and Teaching Elementary Mathematics." The review discusses the research method used in each book and how it presented American math education in relation to math education in other countries. The first book analyzes TIMSS videotapes of various middle school teachers from America, Germany and Japan. The second book analyzes elementary school teachers' (from America and China) responses to various instructional problems.
The review discusses how there is much dishonest data presentation and how other test results were sometimes ignored. The books also discusses the differences between teachers from America, Germany, and Japan. According to the study, American teachers present more definitions during math lessons, but hardly ever present mathematical proofs. American teachers are also less likely to take the time to develop a concept. Instead, they state an topic or concept and move on.
Teachers from Japan and Germany were more likely to encourage students to look at math as "a set of relationships between concepts, facts, and procedures." American teachers think of math as "a set of procedures, and they want their students to become skilled in using these procedures." The article also discussed how Japanese family life and cram schools could affect test results and account for some of the difference in math performance.
The article also includes a sub-article talking about some surprising results of a study of elementary math classrooms. You really should take a look at these - some are rather frightening! One sixth-grade classroom was presented with the problem 8 + 4 = _ + 5. All students in the class filled the blank with 12.
While this review was a bit confusing at times, I really think it
deserves to be read. At least it brings up some important issues
about testing and factors that are sometimes failed to be
included in the results of studies. If nothing else, certainly
take a look at the sub-article, "Equals Doesn't Add Up."
Keywords: Assessment, Issues,
Ref: Colvin17
Author(s): Schmidt, William H.; McKnight, Curtis C.
Date: Dec 4, 1998.
Title: What Can We Really Learn from TIMSS?
Journal or Publisher: Science.
Volume, Issue, Pages: v282 i5395 p1830(1).
Reviewer: Colvin
Date of Review: August 7, 2000.
This article discusses the TIMSS results. According to the results, the United States is not doing well in math and science performance. The test noted that while the US did fairly well at the third and fourth grade levels, the seventh and eighth grade levels showed a decrease in performance compared to other countries.
A possible reason for the decline could possibly be the repetitive nature of American classes and the fact that they cover several topics throughout a year and in return can't spend much time on each. US schools teach concepts like algebra, geometry, physics, and chemistry much later than do schools in other countries. This could also account for the decline from 3rd/4th to 7th/8th grade classes - we don't get any improvement because we're not teaching a whole lot of new information.
This article also helped argue some criticisms that have been
made of the TIMSS results. Overall, I think this article is a
good one. It helps make some sense of the TIMSS results and also
helps explain some of what America needs to do to improve math
and science achievement. I highly agree with the findings about
the repetitive nature of classes and of how too many topics are
crammed into a year. The TIMSS results give us a lot of
information on why we need to work even harder.
Keywords: Issues, Teaching Strategies,
Ref: Colvin18
Author(s): Vergano, Dan
Date: Nov 30, 1996.
Title: Science and math education: no easy answer.
Journal or Publisher: Science News.
Volume, Issue, Pages: v150 n22 p341(1).
Reviewer: Colvin
Date of Review: August 10, 2000.
This article is about a study that compared US students in math and science to those from other countries. The result showed that US students and those from better scoring countries spent about the same amount of time watching TV and that US students spent more time in school. The test also showed that US students do more homework that those in many other countries. The problem is that the quality of US education is not as good as that in other countries.
The study explains that US classrooms cover more topics and can therefore not go into as much detail as those classrooms that cover fewer topics. Another problem with US classrooms is that they spend about 96 percent of their time doing routine problems while Japanese math classes spent only 40 percent. Japanese classrooms concentrate more on applying learning from previous lessons and on gaining a deeper understanding of math.
I'm not really surprised by the results of this study. Obviously
quality wins out over quantity. Also, I've always believed that
too much time is spent on routine problems in math classes. I
have always preferred classes that pose problems and give some
tools to solve those problems. It is then the students' job to
use those tools correctly to solve those problems. Students
really can teach themselves and they will learn more if they
discover something for themselves. Teachers are certainly needed
to guide the students in their explorations but should not give
out answers if students have not yet exhausted their options.
Keywords: Activities, Problem Solving, Reasoning
Ref: Colvin19
Author(s): Burns, Marilyn.
Date: Jan-Feb 1998.
Title: Hands-on prediction problems.
Journal or Publisher: Instructor (1990).
Volume, Issue, Pages: v107 n5 p86(2).
Reviewer: Colvin
Date of Review: August 10, 2000.
This is an article describing a problem-solving activity for finding the halfway mark of a cup. The cup was the type that is wider at the top than at the bottom. Students were paired up and given measuring spoons, dried beans or rice and a 1-cup measuring cup. Students were then encouraged to come up with a procedure for finding the halfway mark on their glass. The students then shared their ideas with the rest of the class and all the ideas were then discussed.
This activity was designed for grades 4-6 but the ideas and theories behind it could be applied to any grade level. What I felt was important about the activity is that it made students think for themselves about an answer. They had to ponder things for a while. This seems to always make students more interested in the instruction that is then given to them to explain the solution of the problem. They also remember these lessons better because they have something to relate it to.
The author also explains how the activity could be varied a bit
by providing many different types of containers for the students
to estimate halfway marks for. Whatever activity you decide to
do in your classes, make sure it promotes thinking and also
provides an opportunity for discussion and sharing of ideas.
Learning to express your ideas is just as important as having
ideas.
Keywords: Issues, Teaching Strategies,
Ref: Colvin20
Author(s): Selvin, Paul.
Date: Nov 13, 1992.
Title: Math education: multiplying the meager numbers.
(Special Section: Minorities in Science)
Journal or Publisher: Science.
Volume, Issue, Pages: v258 n5085 p1200(2).
Reviewer: Colvin
Date of Review: August 10, 2000.
This is a very good article explaining many programs designed to help minorities from grade levels from kindergarten to graduate school. Selvin states that the key to minority success is cooperative learning, connecting mathematics to daily life, and starting young.
One program works at making math more cool. It emphasizes that math is for everyone and that not being able to do math is as unacceptable as not being able to read. Another program focuses on getting minorities to take algebra in middle school. The program starts out by focusing on real-life experiences and then building math abstractions out of those experiences. One example is a lesson in which students start out by building drums and then move onto ideas about circumference, areas, and ratios.
Teamwork was also cited as another big factor for helping minorities succeed in math. In Chicago's College Preparatory Mathematics Program, students learn through cooperation. "The goal is for students to help each other and 'take responsibility for each other's learning.'" Students in this program even starting coming to math when they were cutting other classes!
All of these programs sounded excellent and seem worth implementing even in classes without minorities. These programs can easily be started anywhere. They don't need a huge re-vamp of the system to work. The theories behind them can be applied at a more basic class-to-class level. However, if these theories were adopted system wide, I think all would profit from them.