Keywords: Technology, Issues, Tests
Ref: Pete1
Author(s): Podlesni, James
Date: 1999
Title: A New Breed of Calculators: Do They Change the Way We Teach?
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 92, 2, pp. 88-89
Reviewer: Pete
Date of Review: February 12, 2001
As the title suggests, this article focused on how new calculator technology has affected teaching mathematics. The author had three main points. First, by giving students access to one button solutions we are no longer teaching them to analyze, to structure their thoughts, and to evaluate problems critically. Since they need only punch a button to find the answer, they no longer need to understand the process behind the solution. Second, he discusses how these high-powered calculators affect standardized tests. Should students be allowed to use them? Third, Podlesni discusses how education is being controlled by technology companies interested in profit and not necessarily in effective education.
This article is a wonderful read for any
teacher. It suggests that calculators are wonderful at removing the
unnecessary tediousness of some tasks. Yet we must be careful that
it is not taken to the point of voiding the necessity of the thought
process behind the math. My only critique of the article would be that
it only paints a portrait of the problem while doing little to suggest
a solution. That is not to say that I have the solution. But this issue
is not going to simply disappear. If anything, Podlesni suggests that it
has only begun.
Keywords: Teaching Strategies, Research,
Ref: Pete2
Author(s): Silver, Jennifer Williams
Date: 1999
Title: A Survey on the Use of Writing-to-Learn in Mathematics Classes
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 92 (5), pp.388-389
Reviewer: Pete
Date of Review: February 19, 2001
The article centered around the issue of whether or not writing-to-learn (WTL)
techniques are helpful in the teaching of mathematics. Historically, math
has been taught in an expository manner, also called "reception" learning,
where much of what the students learn is merely memorizing procedures. Some
early mathematicians thought that writing could greatly help students grasp
the reasoning and meaning behind mathematics. Jerome Bruner said that there
is no better way to learn mathematics than "to catch its complexities in the
constraining structure of words. &1tP> The article revealed results of 117
teachers that had been surveyed. The survey focused on how common an
emphasis on writing was for today's math teachers. The most telling result
was that the majority of the teachers are either unfamiliar with the use of
writing exercises or rarely use them. Only 39% of the women and 29% of
the men regularly assigned writing assignments. Also, it was much more
likely for teachers under the age of forty to use discovery learning
techniques and WTL. Actually, the use of WTL had a high connection
with teachers devoted to discovery learning. Furthermore, teachers
who reported their students as above average were more likely to use
WTL techniques. The results in support of WTL go on and on. &1tP> It
isn't hard to see that this study promotes WTL. Writing will help
students understand more fully. Yet this survey shows that many
teachers are ignorant of this idea or rarely use it. Perhaps
that is because most teachers today learned in reception and
memorization based classes. To improve on this will not be
easy. Teachers in training must be taught about discovery learning
and WTL. Also, these ideas should be shared among teachers as
helpful things rather than a waste of time. This signifies a
significant change in the understanding of mathematics and
the way it is taught. The resolution of this will not come
quickly or easily yet it will be worth every minute we wait.
Keywords: Algebra, Equity, Issues
Ref: Pete3
Author(s): Lesser, Lawrence M
Date: 2000
Title: Reunion of Broken Parts:
Experiencing Diversity in Algebra
Journal or Publisher: Mathematics
Teacher
Volume, Issue, Pages: 93 (1), pp.
62-66
Reviewer: Pete
Date of Review: February 25th, 2001
I really enjoyed this article. Its main focus was on how to diversify the teaching of algebra. However, there is no reason to limit the ideas of this article to algebra alone. Lesser feels that algebra serves as a gateway course to higher education, especially for minority students. Thus, something must be done to attract these students; he feels there are three ways to do this. First, diversify the curriculum with the history behind it. Be sure to make a note of the founders of the mathematics, especially if they are not white, upper class, males. Second, use multiple presentations to reach every student. Use graphical, tabular, and analytical approaches. Also, utilize graphing calculators, computers, and spreadsheets to help reach every student. Lastly, diversify through the object concept of function. Students need to realize that a function is not an object; rather, it is a process.
This article has some marvelous
practical ideas to help diversify mathematics.
As a student, I have struggled with finding a way
to help improve the situation. In my mind, this
is one of the most difficult tasks teachers
face.
Thinking of my
education, I realize that my classes were lacking when it came to
teaching
to a diversified classroom of students. Yet with classes becoming more
diverse every day, this problem needs attention. Lesser is right on
when
she stresses the importance of this in algebra because of its history as
a
class for weeding out weaker math students. So, what is a math teacher
to
do? Well, read this article for starters. It is a great basis to begin
chipping away at this issue.
Keywords: Assessment, Algebra, Teaching
Strategies
Ref: Pete4
Author(s): Murphy, Tricia
Date: 1999
Title: Changing Assessment
Practices in an Algebra Class, or "Will This Be
on the Test?"
Journal or Publisher: Mathematics
Teacher
Volume, Issue, Pages: 92 (3),
pp.247-249
Reviewer: Pete
Date of Review: February 25th, 2001
This article addresses assessment. The author, Murphy, really struggled with using an assessment strategy that avoids testing on regurgitation of formulas and problem-solving skills for isolated scenarios. She has begun asking question such as How many questions asked students to formulate or investigate? Murphy firmly believes, as I do, that what we assess communicates what we value. If we test on drill-and-practice type problems, then that is what the students will care about. Murphy hates it when her students ask, Will this be on the test? It suggests that students have found that they only need to learn how to do it and they will pass and even do well in school. However, we want students to go deeper than that. We want them to describe and investigate the why of mathematics.
So, Mrs. Murphy began altering
her assessment. First, she used quizzes at the
beginning of every class testing not skills but
rather the concept.
An
example of a question is, "A student claims that the equation (the
square
root of negative "x" equals 3) has no solution, since the square root of
a
negative number does not exist. Why is this argument wrong? Give
examples
to support your answer." This is just one example. In addition, she
has
her students write an assignment, once every two weeks, involving
investigating, formulating, and explaining themselves. Also, her tests
have
strayed away from objective questions and began including question
involving
synthesizing and applying their knowledge to new ideas. It is
interesting
that she notes that her students resisted this form of assessment
initially.
Of course they did, it is harder, but it is better.
Keywords: Research, Equity, Issues
Ref: Pete5
Author(s): Jackson, Carol D; Leffingwell, R. Jon
Date: 1999
Title: The Role of Instructors in Creating Math Anxiety in Students from Kindergarten through College
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 92 (7), pp. 583-591
Reviewer: Pete
Date of Review: February 28th, 2001
What an eye opening article?! I never gave math anxiety much credit before I read this. It surveyed 157 students who had graduated college and asked them if they had ever been experienced any challenging, stressful moments in their math classes. Of all the students surveyed, only seven percent had only positive experiences in their math history. That alone says a lot. The majority of students are experiencing math anxiety. The survey tells both when the majority of students encounter it and what teaching characteristics trigger it. The results indicated three major times that students reported math anxiety. The first was third or fourth grade. The major problem here was topics like fractions, timed tests, tables, and formulas. The second group was ninth through eleventh grades. At this age, it wasn't so much about the topic as it was about the form of the class. The last level was entry-level freshman college courses.
Three poor qualities of teaching were reported at all three
levels. The first was hostile or embarrassing instructor
behavior. Examples of this are forcing students to work out
something on the board in front of the class when they are scared
to death and have no clue what to do. Second, gender bias is
very significant. In some cases, teachers were reported to have
told students that girls don't need mathematics. Of course, it
Lastly, instructors were seen as uncaring and insensitive; they
would appear frustrated and angry when students didn't understand
or show anger when students asked for clarification. The article
boils all these behaviors down into two categories, overt and
covert. Overt are things teachers say and do while covert things
are the subtle things students pick up on. Overall, this article
revealed much about the cause and occurrences of math anxiety.
All teachers should read this article if they have doubts about
the impact of math anxiety on students.
Keywords: Activities, Planning,
Ref: Pete6
Author(s): Coughlin Jr., Robert S.
Date: 1999
Title: Graphing Vertical and Horizontal Lines
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 92 (3), pp.222-223
Reviewer: Pete
Date of Review: March 4, 2001
Coughlin writes a fabulous practical lesson in this article. As an algebra teacher, he realizes that students often have trouble associating the equations of vertical and horizontal lines with their respective graphs. So, he came up with a lesson to enable students to better grasp this concept. The basic outline of the lesson is simple. On Graph paper, have students draw any figure they want to. The only guideline is that only vertical and horizontal lines can be used. Next, the students will describe their pictures with the equations of the lines that form the shape. One thing to note is to have the students include the interval of the line.
This is a very simple article yet it
has good insight into this lesson. I think one key to this
article is that the teacher realized that the students were
struggling in the first place. Many teachers would simply say
y=2 is horizontal and x=4 is vertical and leave it at that for
the students to struggle with. Teachers need to learn to read
their students for understanding. Also, why wait until students
are confused to use more constructive lessons and discovery
learning? I think that these types of lessons are great the
first time through, not just for clarification and reinforcement.
Keywords: History, Planning,
Ref: Pete7
Author(s): Kelley, Loretta
Date: 2000
Title: A Mathematical History Tour
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 93 (1) pp.14-17
Reviewer: Pete
Date of Review: March 4, 2001
Teaching mathematics could benefit greatly from teaching the history of math as well as the facts and findings of that history. This article suggests three reasons for bringing the history of mathematics into the classroom. First, it would put math into its historical context. Introducing students to biographies of mathematicians introduces students to the stories of these people and also gives them a context of name, place, or anecdote to remember material by. Sounds obvious, right? Yet this practice is nearly nonexistent in today’s classrooms. Second, this article suggests that we also connect math with how it has interacted with culture. This connects closely to popular question, “When will I ever use this in real life?” In response to these questions, you could raise the stories of mathematicians creating the calendar, making astrological predictions, building bridges, designing medical techniques, etc. This will also help give the students both motivation and context to learn.
Third, and finally, teachers should realize that history lays out
the general order for teaching. For instance, we teach integers
before complex numbers since that is the route that humans took
when they learned very slowly over the years. In addition to
planning, looking at history like this will help us understand
when students do not grasp a concept quickly. After all, it took
humanity thousands of years to get where we are today. In
general, I think bringing history into the classroom will bring
some variety and life to the teaching of math. These three
suggestions are just some of the ways that history can benefit
mathematics.
Keywords: Connections, Research,
Ref: Pete8
Author(s): Knuth, Eric J.
Date: 2000
Title: Understanding Connections between Equations and Graphs
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 93 (1), pp.48-53
Reviewer: Pete
Date of Review: March 11, 2001
This article did research on students' understanding of graphs and equations. The study was given to 284 upper level math students. The study consisted of questions that encouraged graphical approaches to solve them. Yet the findings show overwhelmingly that the majority of students revert to algebraic techniques to solve the problem while viewing the given graphs as useless or unhelpful. Instead of recognizing that every point on the graph is a solution, students used the equation to "plug and chug" until they found a solution. After solving the question, students were asked to think of an alternative way to solve the same question. Many students said flat-out that there wasn't another way while other gave answers that did not make sense mathematically. Few realized that the question could be solved graphically.
What does this mean? It speaks strongly about
the way equations and graphs are being taught. In many classes,
students are taught the y = mx +b form of equations and told to
convert to this form whenever solving these types of problems.
The study shows exactly that. Student would commonly convert the
equation into this form out of standard form claiming that it was
the only way to solve the problem. This suggests a fundamental
misunderstanding about equations and graphs in general. Students
need to be taught to solve these questions both graphically and
algebraically. Teachers should encourage the use of graphing
calculators to develop this idea. Also, supporting other forms
than the traditional y-intercept form for equations will help fix
this misunderstanding.
Keywords: Teaching Strategies, Activities,
Ref: Pete9
Author(s): Countryman, Joan
Date: 2000
Title: Journal Writing in the Mathematics Classroom: A Beginner's Approach
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 93 (2), pp.132-135
Reviewer: Pete
Date of Review: March 14, 2001
The article summarized the experimentation a few teachers had bringing weekly journaling into the classroom. They all agreed that writing would be beneficial for both the teachers and the students. Along the way they learned some very helpful points. First, ten minutes is a good length of time in class for the students to write them. Also, try doing it only once a week. Any more than that becomes too much work for both the students and the teacher. Second, tell the students why they are journaling and how it will be assessed. This will probably be a new idea for most students, so laying it all out before them is a good idea. Third, ask two kinds of questions, mathematical prompts and affective prompts. The mathematical prompts can ask the students to describe specific math concepts that the class is covering while affective questions are more general like the statement, "Describe what a `fair' test is and tell how you prepare for math tests and quizzes."
Countryman learned that
bringing writing into the math class isn’t simple. It is a trial
and error thing. Also, expectations and procedures for
journaling will be different for each class. As teachers, we
need to adapt it to elicit a productive and helpful journals from
students who are excited to explain themselves with sentences
instead of with tests and quizzes (although these things do not
have to be opposites, they have been historically).
Keywords: Activities, Teaching Strategies,
Ref: Pete10
Author(s): Szydlik, Jennifer Earles
Date: 2000
Title: Activities That Help Students Discover Permutations and Combinations
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 93 (2), pp. 93-99
Reviewer: Pete
Date of Review: March 28, 2001
This article covers Mrs. Szydlik’s approach to teaching permutations and combinations. Good examples of student discourse and teacher discourse are built into this lesson. She suggests that the students work in groups on worksheets to think creatively about different types of counting problems. The first one deals with ordering people for photographs and another one works with picking committees from groups of people. The kids learn the significance order and many notational and specific properties that arise when counting like this.
This lesson
had many strengths. First, it was stretched out over at least
three class periods. It will take time for students to learn
this and struggle with it. But the extra time is worth the end
results; the students will grasp the concept better. Second, the
teacher is not supposed to help the students too much. If they
are struggling with something, let them. They will learn it
better that way. Another strength of the lesson is that it
involves discussing the ideas of all the groups as an entire
class. This promotes critical thinking skills when comparing,
contrasting, and criticizing methods. And it also lets the
students fit more pieces of the puzzle together on their own;
they take ownership of it that way and are more motivated to
learn.
Keywords: Problem Solving, Activities, Teaching Strategies
Ref: Pete11
Author(s): Miller, Catherine M.
Date: 2000
Title: Student-Researched Problem-Solving Strategies
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 93 (2), pp. 136 - 138
Reviewer: Pete
Date of Review: March 28, 2001
I really enjoyed this article. The author, Catherine Miller, was sick of teaching problem solving skills in the traditional style, by telling the students the major approaches and then having them attack various problems. So, she brainstormed an approach in which the students research how people solve problems. Each students takes a list of problems, selects three people to work on the problems, and then observes the various methods they use as they solve these problems. She also had them record the effects the attitudes of the people had on how well they solved the problem. Then the class gathered and shared their findings. Of course, they find things like finding patterns, drawing pictures, guess and check, and so on.
I love this idea. It
really makes learning fun. It involves family members and
friends and lets the students learn on their own. In addition.
incorporating attitude into the research helps students realize
that positive attitudes and cooperation really do help solve
problems and keeps the situation fun. How much more fun is this
approach than simply telling them how to do it? The "boring"
style doesn't seem worthwhile after reading this article.
Keywords: Activities, Teaching Strategies,
Ref: Pete12
Author(s): Iovinelli, Robert C.
Date: 2000
Title: Chaotic Behavior in the Classroom
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 93 (2), pp.148 - 152
Reviewer: Pete
Date of Review: April 2, 2001
What is chaos theory? Most people would say that it describes how things eventually tend towards disorder and confusion rather than order. These people would be wrong. In this article, Iovinelli introduces a simple lesson on chaos theory. Through it, students will learn that its true meaning is that a system is very dependent on initial conditions. If the initial value it altered ever so slightly, the end result will be vastly different. For instance, the initial population estimates for a species of animals determine the end population for the animal. If that initial value is altered slightly, the population will resolve at a very different number.
Iovinelli introduces this
to students by having them analyze graphs with graphing
calculators. Students primarily look at the equation
y = ax*(1- x). Through group work and various trials, students
will see that the value of a in this equation greatly effects the
end behavior of the graph. This lesson is simple yet it helps
students understand this concept while also giving them good
practice on modeling situations, such as weather or population
growth, with equations and graphs.
Keywords: Trigonometry, Activities, Geometry
Ref: Pete13
Author(s): Eggleton, Patrick J.
Date: 1999
Title: Experiencing Radians
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 92 (6), pp. 468 - 471
Reviewer: Pete
Date of Review: April 9th, 2001
Ask any student what a radian is and you will probably get a mumbled response about angles and conversions. The truth is many students do not truly grasp the concept of a radian as an angle measure. They will commonly think of it just as some other way to symbolize an angle without knowledge of where it comes from. This article provides a lesson to help fix teach radians to students. It is simple in design. Students use a plate and a piece of adding machine tape to explore circumference, diameter, radius, and radians. Through marking off lengths on the adding tape based on the length of the plate’s radius lets the students see where the idea of radians comes from.
This article
reveals a common practice in the teaching of math, simply telling
the students the end results and equations without letting them
discover it and take ownership of their learning. This leads to
a shallower education. That is why when you ask many students,
even adults, to define a radian they have no clue. This trend
needs to be reversed.
Keywords: Probability, Statistics, Research
Ref: Pete14
Author(s): Bisbee, Gregory D.
Date: 1999
Title: Studying Proportions Using The Capture-Recapture Method
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 92 (3), pp. 215 - 218
Reviewer: Pete
Date of Review: April 18th, 2001
How can probability ever come into play in real life? Well, this article gives a great practical research idea that students can do to understand this topic more fully. It is fairly simple in nature. Simply give the students a population too large to count. For example, let the population be the total number of grasshoppers in the school’s baseball field. Then have use the capture-recapture method. Catch a certain number of these grasshoppers, mark them, and release them back into the population. Then, when you take a random sample from the entire population, the proportion of marked grasshoppers in the sample can be used to estimate the total number of grasshoppers (the population and sample ratios should be equal).
This has got
to be fun for students. You can make it easier and quicker by
using bags of candy or buckets of golf balls. The point is that
with this method students really see how the power of probability
and proportions can be useful in practical ways. Maybe you could
have students brainstorm new, creative ways that proportions and
probability can help us describe and learn about things in the
real world. I bet they could come up with some great ideas. One
other plus of this lesson is that it also has the importance of
percent deviation built into it. In cases where the actual
population is known, students will realize that the actual
population and their estimations may differ. This allows for
discussion and understanding of why we need to have something
called percent deviation and what its significance is.
Keywords: Algebra, Arithmetic,
Ref: Pete15
Author(s): McConnell, Michael; Bhattacharya, Dip N.
Date: 1999
Title: Using the Elegance of Arithmetic to Enhance the Power of Algebra
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 92 (6), pp.492-495
Reviewer: Pete
Date of Review: April 7th, 2001
Sometimes the teaching of algebra becomes too abstract. In this article, McConnell and Bhattacharya stress the importance of combination of arithmetic and logic provide great supplements to the teaching of algebra. It is most easily understood through an example. We have 380 oranges; every boy gets four and every girl gets five. There are a total of eighty-five students. How many boys are there? How many girls? Of course, a system of two equations and two unknowns can be put together leading to a solution. But often times solving the problem this way leaves the students wondering where the answer really comes from. Sure they found an answer by manipulating symbols, but it simply appeared after we fooled around with equations.
The authors
suggest that using simple arithmetic and logic greatly increases
the students understanding of both the solution and of the
algebra. Instead of setting up equations, approach it this way.
Give every student four oranges. This accounts for 340 oranges.
The remaining oranges are given to the girls since they get one
extra orange. That means there are forty girls and forty-five
boys. The beauty of this is that the algebra is still embedded
within this new approach. The first step can be seen as
simplifying the system of two equations, but now it has been cast
in an understandable context. Then, the students substitute and
find the number of boys. The students now understand the algebra
much better. This is a great idea for teaching algebra. When
students are first introduced to algebra, it can seem very
abstract. Teaching it this way, however, brings algebra back
into an understandable form for many students.
Keywords: Algebra, Discrete, Teaching Strategies
Ref: Pete16
Author(s): Forringer, Richard S.
Date: 2000
Title: (A + B + C)^3
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 93 (1), pp.6 - 8
Reviewer: Pete
Date of Review: April 19th, 2001
Discrete mathematics can be used to teach many algebraic concepts. This article attempts to teach the expansion of terms to the second, third, and eventually fourth power. The main approach taken is to show the students that these expansions are really just adding up little, discrete “chunks” that make up the total sum. The activity proposed entails students trying to make a cube out of cardboard cubes and rectangular prisms labeled with side lengths A, B, C, etc. Obviously, this comes after squaring terms. Begin with expanding a two-termed quantity and then move to three terms. Once the cube has been formed, students can write down the cubes that make up the sum of the entire cube.
Advantages of this activity are that students really
understand the discrete aspect of expanding polynomials. By
adding together smaller chunks that make up the whole, students
understand more fully the nature of expansions as efficient ways
of adding up many small pieces. Another advantage is that
students will have incentive for learning how to expand
polynomials. They will have found a tentative hypothesis with
the activity; they will want to see if the mathematics arrive at
the same conclusion that they did. When it does (hopefully it
does), they will have earned a sense of accomplishment and
satisfaction. One possible disadvantage is that it may take a
long time to piece together twenty-seven prisms to form the final
cube. This may frustrate students. Also, having small, easily-
thrown objects in the hands of students is always a risk. But
that just makes teaching more fun.
Keywords: History, Problem Solving,
Ref: Pete17
Author(s): Kahan, Jeremy
Date: 1999
Title: Ten Lessons from the Proof of Fermat's Last Theorem
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 92 (6), pp. 530 - 531
Reviewer: Pete
Date of Review: April 17th, 2001
What comes to students minds when they think of proofs? They are
boring, hard, and no fun probably would be mentioned. This
article lists ten things that we can learn about proofs from
Pierre de Fermat and his proposition that has no natural
solutions for natural numbers a, b, and c when n is greater than
two. The first and perhaps most important point is that
mathematical thinking takes time as well as intellectual courage
and skills. Yes, proof writing is hard. But it is even hard for
the best of the best. It took hundreds of years for Fermat’s
proposition to be proved. The second point is that much of proof
work is an individual process; many mathematicians work alone on
their propositions. This should be encouraging to students when
they feel alone and are struggling Also, the person who
eventually proved the proposition, Wiles, needed help from
others. This is the third thing we can learn about reasoning and
proofs; it is a group effort. Wiles received help from two
Japanese mathematicians. Without their aid, the proof may not
have come together as quickly as it did. The next seven points
get more specific about proof-writing. They show that we can
learn much by looking at how the best mathematicians handle this
very thing. Even for them it was a arduous, difficult process.
Students should know this as they approach reasoning and proof in
high school.
Keywords: Statistics, Activities,
Ref: Pete18
Author(s): Pandolfni Jr., Thomas J.; Alfano, Joseph L.
Date: 1999
Title: Statistics and the Academy Awards
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 92 (3), pp. 219 - 221
Reviewer: Pete
Date of Review: April 19th, 2001
One of the best ways to teach is to make the activities fun and interesting. This article would have sparked my interest as a student. The main idea is to bring data of the academy awards. Specifically, this article brought data regarding films that won best picture. Some of the data were number of nominations the movie received, how many they actually won, did it win or get nominated for best director, etc. From this basis of information, students can begin exploring relationships such as, “What proportion of the awards that a film is nominated for do they actually win?” Many of these fun questions can be created. Students can also make graphs, box plots, and pie charts from this data.
I really like this activity. One
problem I see is that it may be difficult to find such detailed
information like this for such an activity. Perhaps the Internet
would have something along these lines. The data is so very
thorough, but it needs to be for this activity to be successful.
Teachers may have ideas similar to this, but they may be hard to
use for reasons like this. On the upside, this lesson makes math
relevant and fun to students’ lives. Everyone watches movies and
has a few favorites. Surely everyone would enjoy the setting of
this lesson and thus be more motivated to learn. Teaching
motivated students is much easier than doing the opposite. Also,
this activity lends itself to cooperative group work and leaves
room for the students to search after the information and
statistics that they find most interesting.
Keywords: Research, Issues,
Ref: Pete22
Author(s): Watanabe, Tad
Date: 2000
Title: Japanese High School Entrance Examinations
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: 93 (1), pp. 30 - 35
Reviewer: Pete
Date of Review: May 6th, 2001
Japanese and American schools teach mathematics differently. This article takes a look at the entrance examinations that Japanese students take in order to make it into high school. These entrance exams cover five major topics, one of them being mathematics. The article included a sample of a typical math test. There were only seven questions, which says a lot in itself. A similar American test would probably have many more questions than seven. Of these seven questions, only one involves simple computational skills. The other six all require application of given information to a problem in search of a solution. On average, students answer sixty to seventy percent of the questions correctly. Furthermore, better high schools tend to take students with higher scores ranging from eighty-five to ninety percent.
At the close of this article the author is
very careful to note that international comparisons must be made
with an understanding of the society which is being analyzed.
This is very true; just because Japanese students perform better
than Americans on international tests and comparisons does not
necessarily mean that Americans should ditch all of their
teaching styles for that of the Japanese. Granted, the tests
show there is room for improvement. And perhaps this improvement
could come from borrowing concepts from the Japanese. They
definitely teach differently than we do and much could be learned
through interaction between both countries.
Keywords: Issues, Connections,
Ref: Pete20
Author(s): Smith III, John P.
Date: 1999
Title: Preparing Students for Modern Work: Lessons from Automobile Manufacturing
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: 92 (3), pp. 254 - 258
Reviewer: Pete
Date of Review: May 2nd, 2001
This article emphasizes the connection math has with the working class world, specifically in automobile manufacturing. The main point is that an average worker in an assembly line or automotive factory must know many mathematical concepts and rules to perform their job well. For instance, measurements and calculations can take a very important role when manufacturing parts. Furthermore, these measurements usually need to be compared to standards. Another point raised is in regard to machining. When making machine parts or tools, a high level of two and three- dimensional spatial and geometric knowledge is necessary. For instance, when programming a computer to make certain drills at exact places on a sheet requires an understanding of the coordinate system.
The author feels that the separation
between school math and the math of work should be reduced. Many
people probably do not understand the prevalence of math in the
world of work. They always ask is school, “Why do I need to know
this?” And this article gives a great reason. Math is not
simply for those going on to college. It is a skill inherent in
much of the working world. This should be made clear to students
in school. It may provide motivation and purpose to a subject
than many students used to find meaningless.
Keywords: Problem Solving, Connections,
Ref: Pete19
Author(s): Magnus, Teresa D.
Date: 2000
Title: Will the Best Candidate Win?
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: 93 (1) pp.18 - 28
Reviewer: Pete
Date of Review: May 8th, 2001
What decides an election? Most everyone will answer that winning the popular vote earns the victory in elections. Most people probably assume that this method for deciding the winner is the only way, or perhaps the best way, to decide an election. This article focuses on the various ways elections can be decided. The four methods given attention are the hare system, the Borda count, sequential pair wise voting, and plurality voting. The article provides a four-page worksheet for the students to follow. It introduces them to the four methods and has them compare and contrast them.
Representation is a major focus
of this lesson. Students learn that different models can be used
to describe the same topic. They also should learn how to move
back and forth between these representations. This satisfies one
of the standards. Perhaps holding a class discussion to
determine which method is the most favorable would be
advantageous. This lesson also encourages creative thinking
since students hopefully learn that math is not a strict rigid
science of right and wrong approaches to problems. There are
many ways to approach problems, some more useful than others.
Also, this lesson lends itself to taking a class survey about
something and then analyzing the class’s data. That would give
the students more ownership and motivation. This lesson idea is
fabulous.
Keywords: Planning, Connections, Teaching Strategies
Ref: Pete21
Author(s): Schloemer, Cathy G.
Date: 2000
Title: I Found Sinusoids in my Gas Bill
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: 93 (1), pp. 10 - 12
Reviewer: Pete
Date of Review: May 8th, 2001
Students often struggle with finding practical purposes for
learning mathematics. The typical problem of train A leaving the
station in New York at 6pm at a speed of 70 miles per hour does
not cut it. Students need more. The author of this article
realizes that. She has found one idea for connecting the
mathematical concept of sine and cosine waves to a practical
application, a gas bill. Her bill fluctuates up and down with
seasons; it can be fit quite nicely to a trigonometric curve.
Bringing the gas bill data to class and letting the students
attempt to fit it to a function could be a great lesson. This
tests the higher levels on bloom’s taxonomy. For instance,
analyzing the data and then connecting it to their knowledge of
trig functions requires higher order thinking skills. That is a
definite plus of this lesson. In addition, students are
encouraged to extend these connections to other areas outside of
school. They learn that math extends beyond the classroom; its
concepts and structure pervade much of society. Helping students
realize this may motivate them in the math class and get them
excited about learning math rather than bored.