Keywords: Activities, Measurement, Connections
Ref: Furst1
Author(s): Rose, Mary C.
Date: 2000
Title: Millenium Mastery
Journal or Publisher: Instructor
Volume, Issue, Pages: January/February p.14
Reviewer: Furst
Date of Review: 3/8/00
This brief article gives a good suggestion on how to have kids
understand exactly how long the millenium is by creating time lines of
their lives using an inch to represent each year they've been alive. Then
they can create timelines of the millenium using the same measurement as
they did for their own. That timeline will span the classroom multiple
times. By incorporating visual aspects to time measurement, students are
better able to understand just how long a millenium is. A creative
activity that allows important events dates in history to be learned.
Keywords: Geometry, Connections,
Ref: Furst2
Author(s): Hansen, Vagn Lundsgaard
Date: 1999
Title: From Figure to Form
Journal or Publisher: Math Horizons
Volume, Issue, Pages: November p.8-11
Reviewer: Furst
Date of Review: 3/11/00
This article talked about how math pops up in our everyday lives. It
is unlike most discussions of math being all around us because it didn't
focus on math in nature. It actually only talked about math in nature
during the last paragraph. Rather, the focus was on how shapes and
figures are all around us. A neat example was brought up about drinking
out of a cone-shaped glass. It discussed how tilting the glass will make
the liquid rest in the shape of an ellipse, and if you were to pour that
in your mouth, you would be swallowing a hyperbola. It also talked a lot
about tiles, and different patterns and shapes that can be created with
them. These are neat ways of seeing shapes in ordinary situations. I
think it would be a fun activity to have students find instances where
shapes just pop up, and have a show and tell type of activity to discuss
how math is always present in our lives, and in the objects around us.
Keywords: Problem Solving, ,
Ref: Furst3
Author(s): Gannon, Gerald E., Martelli, Mario U.
Date: 2000
Title: The Prisoner Problem-A Generalization
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol.93 No.3 192-193
Reviewer: Furst
Date of Review: 3/13/00
This article gives an idea of an example to use in helping students
solve problems, and then make generalizations based on their results. The
prisoner problem is good because it forces students to fully think through
all possibilities in order to solve it. This is also a good problem for
showing the value of making tables. It shows how to add to the problem by
introducing more prisoners to make the problem more complex. The authors
stress that this is a problem within reach of most students, and is not so
over-used that students are tired of seeing it. The ultimate goal is to
use this problem so that students will recognize the importance of the
final step of problem solving-considering possible generalizations.
Keywords: Algebra, ,
Ref: Furst4
Author(s): Winter, Mary Jean, and Carlson, Ronald J.
Date: 2000
Title: Liquid Assets: Increasing Students' Mathematical
Capital
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: volume 93, number 3 172-179
Reviewer: Furst
Date of Review: 3/15/00
This article offers an idea on how to have students participate in an
activity that allows them to collect data, plot it, and interpret it.
Students measure the level of water in a glass after sipping water. By
doing this multiple times, they have the information needed to create a
graph. The students should then determine the equation for the line that
best fits their data. Technology can be incorporated for more advanced
students by having them do a linear regression to find the best
approximation of the plotted points. This is a good way of introducing
dependent and independent variables. Also, by posing hypothetical
questions that would slightly alter the experiment, and therefore the
data, you can check to see if your students have a good understanding of
what is going on. I really liked the ideas presented here, and the fact
that there are worksheets that can help for classroom work.
Keywords: Algebra, Problem Solving,
Ref: Furst5
Author(s): Demby, Agnieszka
Date: 1997
Title: Algebraic Procedure Used by 13-To-15 Year Olds
Journal or Publisher: Educational Studies in Mathematics
Volume, Issue, Pages: v33 n1 p.45-70
Reviewer: Furst
Date of Review: 3-17-00
I really enjoyed this article. The information it provided will be most helpful if I end up teaching algebra. The article talked about a study done on 7th and 8th graders who were given two tests. The results of the tests showed that the students who did better on the test usually utilized many more methods of solving the problems of simplifying terms than those students who did much more poorly on the tests.
More traditional methods of teaching algebra tend to focus on finding the answer, and give little explanation if any as to why to utilize specific methods of solving. By not explaining the reasoning behind the processes, students won't have a good understanding of what exactly they are doing. Many textbooks give formulas without any arguments as to how or why they work. The message is that teachers need to focus on what it is they are trying to get the students to learn, and then they need to teach them the what's and why's of what they are learning.
It surprised me to find that
when many of the students were asked whether or not they would get the
same answer if they plugged in a number into the given expression, and the
simplified form that they themselves had generated, they didn't know how
to respond! It doesn't make sense to teach them how to simplify if they
don't understanding of what is going on. I really liked the ideas
presented here, and the fact that there are worksheets that can
help for classroom work.
Keywords: Statistics, Activities,
Ref: Furst6
Author(s): Nally, Michael, Sommers, Paul, M.
Date: 1998
Title: Striking Back: The Baseball Fan Boycott of 1995
Journal or Publisher: Journal of Recreational Mathematics
Volume, Issue, Pages: v29 n3 pp.184-188
Reviewer: Furst
Date of Review: 3/23/00
This article gives some basic statistics on fan attendance at
games after the big strike of 95. The article itself isn't all
that informative, or helpful for teaching, but it raises ideas
that can be helpful such as the need for students to be able to
interpret data. If students are presented with data on baseball,
they will more likely have interest in using that information as
compared to them getting a bunch of numbers and statistics that
have no meaning to them. It seems to me that students should be
able to pick the types of areas they have interest in investigating
with regards to a unit on statistics. Questions could be asked at
a more intuitive level by having students make conjectures as to
why they think the data is as it is. Lots and lots can be done
with statistics, and finding a creative way to teach it will make
a world of difference.
Keywords: Issues, ,
Ref: Furst7
Author(s): Leo, John
Date: 1997
Title: That So-Called Pythagoras
Journal or Publisher: U.S. News and World Report
Volume, Issue, Pages: v122 n20 p.14
Reviewer: Furst
Date of Review: 3/30/00
This article basically bashes the whole "new math" approach, and trying to bring multiculturalism into the math classroom. He raises a good point that students should be guided by teachers and that the basic skills should be learned by them. Students should not be passive participants in their education. He did discuss a specific textbook that had me wondering who would publish something like that. He talked of it posing more environmental type questions than math related questions. Being an algebra textbook, he was also surprised to find that linear equations weren't introduced until a quarter of the way into the book. And to top it off, they only solved it using a guess and check method.
I disagree that we should just throw all
of our current methods out the window, but it seems to me that things
do need to change, and we are doing a lot about that right now. I also
disagree with his idea that, "unless we plan on using Yoruba calculators,
or start balancing our checkbooks the ancient Navajo way, it's probably
safe to ignore the whole (multicultural) thing." Different things
can be done.
Keywords: Assessment, Research,
Ref: Furst8
Author(s): Schmidt, William, H., McKnight, Curtis, C.
Date: 1998
Title: What Can We Really Learn From TIMSS?
Journal or Publisher: Science
Volume, Issue, Pages: v282 p1830
Reviewer: Furst
Date of Review: 3/30/00
This article talks a lot about what we saw in the C-SPAN video, and
what
we talked about after listening to the radio show about TIMSS. The
authors
contend that the TIMSS is legitimate, and that we need to re-evaluate our
focus
within curriculums. Their major suggestion is focusing on less topics.
Compared
to other TIMSS countries, we cover many many more topics, and don't focus
on the
areas of physics, chemistry, algebra or geometry enough in the early years
of education.
I think we are moving in the right direction with the way math education
is currently
headed. I agree that if we teach something, we should make sure that it
is understood
before moving on to something new just for the sake of teaching as much as
we can.
Keywords: Games, Technology,
Ref: Furst9
Author(s): Gross, Neil
Date: 1997
Title: No Math Until Homework's Done
Journal or Publisher: Business Week
Volume, Issue, Pages: Dec. 8 p.126
Reviewer: Furst
Date of Review: 3/30/00
This article talks about all of the new software programs available
about math. It discusses how kids can really get attached to them
and like them the same if not more than their Sony playstations.
He claims that the programs can hold kids' attention, and let them
learn some math at the same time. Keeping their attention can be half
the battle sometime, so a tool like this seems even more important than
ever. The author suggests trying software out before purchasing it, if
at all possible. It also suggests having kids do their homework before
being allowed to use the programs. Let them think that its just for
fun, and the tough stuff must come first. I've tried a couple of these
out, and I have to admit that they are pretty fun, and I bet pretty
effective.
Keywords: Teaching Strategies, ,
Ref: Furst10
Author(s): Burns, Marilyn
Date: 1998
Title: Can I balance arithmetic instruction with real-life
math?
Journal or Publisher: Instructor
Volume, Issue, Pages: v107 n7 p55-58
Reviewer: Furst
Date of Review: 3/30/00
This brief article talks about how parents and teachers may differ
on the importance of how to teach the basics. Some argue for the
traditional paper and pencil excercises, while others find value
in class activities, and some prefer to focus on problem solving.
This article lists seven basics about the goals of arithmetic instruction,
and offers classroom strategies to fit each basic goal. Her strategies
focus on involving students as much as possible to make them aware
of how prevalent arithmetic is in their everyday lives. I liked
her tip that memorization, while important, should never preceed
understanding.
How true indeed! The ideas she has are similar to ideas discussed
about cgi. Discussion appears to be more prevalent in today's math
classroom, and rightly should be. Children should learn to feel
comfortable
discussing ideas with their classmates, and learning from one another.
Keywords: Tests, ,
Ref: Furst11
Author(s): Lord, Mary
Date: 2000
Title: High-stakes testing: It's backlash time
Journal or Publisher: U.S. News and World Report
Volume, Issue, Pages: April 3, 2000 p.54
Reviewer: Furst
Date of Review: 4/5/00
This article is bringing up the issue of standardized tests, and mostly arguing that they just aren't cutting it. One point made was that teachers are starting to "teach-to-the-test". Material regularly covered that won't be appearing on the standardized tests is being eliminated from the curriculum. This makes me very sad.
As a person who is very aware that standardized tests and I just don't mix, I'm fearful that these such tests are being used to determine if students meet the proficiency level to continue on to the next grade. I realize that the material covered on the exam may be knowledge that is imperative for students at that age, but one multiple-choice test shouldn't be the only determinant. Many of the parents and educators in the article agree.
I'm by no means saying that assesments shouldn't be made, I merely think
that it
is a very good idea to seriously look into reforming the means by which we
assess
students. When you take into account the sheer anxiety that tests cause
some students,
and the fact that a child's life is sometimes being based on a single
test, I wonder how
it was that educators came to feel that this sort of assessment was valid.
Keywords: Teaching Strategies, Connections,
Ref: Furst12
Author(s): Allen, Melissa
Date: 2000
Title: Head of the class
Journal or Publisher: Isthmus Newspaper
Volume, Issue, Pages: n3 p.23
Reviewer: Furst
Date of Review: 4/9/00
This is an article about cooperative preschools in Madison, Wisconsin. It raises the issue that these such schools are often less expensive than other preschool options, yet tend to be used by middle, and upper- class families. These schools work by having parents in the classroom all the time, in addition to the teacher. Parents come anywhere from 2-12 times a year. Having such a program allows students a connection between the schools and family. Students don't have to feel like going to school means leaving their family, and they can see it as the family growing to accept the schools.
This program sounds wonderful to me. When children are at the preschool
age, they love to be around their parents. Their behavior probably
improves,
and their motivation to do well with their parents near by more than
likely
increases. Young children need guidance, and the more they can get from
their
parents, the better. Especially if it is in conjunction with school. I
really
like the community-based education they are providing in these schools.
Keywords: Issues, ,
Ref: Furst13
Author(s): Peterson, Sandra
Date: 2000
Title: Licensure:the key to student success
Journal or Publisher: Minnesota Educator
Volume, Issue, Pages: v2 n15 p2
Reviewer: Furst
Date of Review: 4/9/00
This article discussed the need of having teachers licensed in the specific areas that they are teaching. It talked about how Minnesota is in the vanguard of the country, but with the impending rate of teachers due to retire in the next decade, they will be in short supply of properly licensed teachers.
Studies have shown that students being taught by properly licensed teachers do better in school. Also, the most important components of teacher quality are preparation and licensure.
Due to the lack of teachers in areas such as math, ideas have been tossed out to make teaching more appealing. Some of those include: stronger mentoring programs for new teachers, loan forgiveness programs in areas that have shortages, and salaries that properly reflect the importance and value of teaching.
I am shocked that teachers sometimes are teaching in areas that they
don't
even have a minor in. How can we possibly find them qualified enough?
It seems though that with the shortages, we are being forced to deal
with
what we have, and to make the most of it. Having someone that is a
certified
teacher sounds better to me than having someone with no teacher
training.
It just seems sad to me that students suffer for this. The incentives
mentioned about seem good, and should be explored further.
Keywords: Issues, ,
Ref: Furst14
Author(s): Codell, Esme Raji
Date: 2000
Title: Diary of a Rookie Teacher
Journal or Publisher: Reader's Digest
Volume, Issue, Pages: May, p117-121
Reviewer: Furst
Date of Review: 4/26/00
This is an inspiring little article about the first day of class for an elementary school teacher. She talks about how her confidence made that one of the greatest days of her life. She also talks about the need to build trust with your students, and that will make a huge difference in how things run in your classroom.
One of the parts of her article that really struck me was when she talked about the secret lives that her students led. One of her students was late to class everyday that week, so she pulled her aside one day to see what was going on. She was told that they were staying in a shelter that week, and the girl had to take her little brother to his school and then ride the train to get to school herself. She told that student that she was happy that she was making it to school everyday. This wasn't the only case she found out about. A parent approached her and asked her to take her children in for a night while she tried to get a restraining order on the man of the house who had shot her in the arm. Scared, she accepted the request realizing how much that put her job at risk.
This teacher had words of wisdom that she got from her mentor that really
struck me. She
says that the difference between a beginning teacher and an experienced
one is that the
new teacher asks, "How am I doing?", and an experienced teacher asks, "How
are the children doing?"
I hope to adopt that mentality early on in my teaching.
Keywords: Technology, ,
Ref: Furst15
Author(s): Montoya, Perry, and Graber, Vicki
Date: 1999
Title: Tools for Mathematical Understanding in Middle
School
Journal or Publisher: Mathematics Education Dialogues
Volume, Issue, Pages: May/June, p.12
Reviewer: Furst
Date of Review: 4/17/00
This article talks about the benefit of calculator usage at the middle school level. They claim that the teachers in their district are trained on specific calculators, and then provided a classroom set. Thus, the teachers are capable of properly using the calculators, and determining when it is appropriate to use or not use them. The authors support their claims by showing that through further training and support, teachers have used calculators effectively.
I thought it was good that the authors at least recognize that there is the possiblity of calculators having a detrimental effect on the education of students. However, they support their usage as tools to help promote mathematical thinking, and to assist in the organization of data. They also claim that calculators give students the capability of manipulating numbers so as not to get bogged down in the nitty-gritty and lose sight of the actual solving of the problem.
I agree with the authors. In this age of technology, it is silly to
think
that we should not allow calculators in the classroom when they are
readily
available in "real world" situations. I do agree though that with more
training, teachers will be better able to know how to use them effectively
without allowing their students to use them as a crutch.
Keywords: Inquiry, Statistics,
Ref: Furst16
Author(s): Shah, Allie
Date: 2000
Title: Charter-school scores add momentum to movement
Journal or Publisher: The Star Tribune
Volume, Issue, Pages: Thursday, April 27 p.A23
Reviewer: Furst
Date of Review: 4/27/00
This was an interesting article about the math results in area charter schools. The improvement on the basic-skills tests in math have improved drastically in some of these schools. Some feel those results are based on the fact that these types of schools often have well-organized staffs with clear missions, making it easy to improve results quickly. The fact that charter schools often have small classes is another reason for the dramatic increase in scores.
One of the teachers at a math and science magnet school said that they key to the improvement recently seen is the integrated math approach that they have been taking. He said, "Math has to mean something." He is exactly right. The discussions we've had on the use of curricula like Core-Plus lead me to believe that an integrated, concept approach is definitely the way to go in math education.
There were some schools where the math scores dropped. The main thought
behind
this is that they are only now beginning to implement the use of new
curricula, and
therefore need a little time before the scores will go up. I agree with
that rationale,
and think that we are really onto something with the changes we are
currently seeing in math eduation.
Keywords: Reasoning, Problem Solving,
Ref: Furst17
Author(s): Schilling, Mark
Date: 2000
Title: Three Estimation Challenges
Journal or Publisher: Math Horizons
Volume, Issue, Pages: April p.22-24
Reviewer: Furst
Date of Review: 4/28/00
This article raises some topics that could be useful for a unit on estimation or problem solving. There are three examples explored: a penny loss problem, class size, and drug use.
Each example raises issues that make the problem that seems pretty straight forward, not quite as simple as it seems. The problems that they are posing here tend to have basic ideas at hand, but more complex mathematics involved. So while these topics might seem appropriate for middle schoolers, they would most likely need to be explored by more advanced, upper-level math students.
This seems like a neat way to make the "older kids" feel like math can
be fun again. It seems to me that once we get past most basic math,
teachers don't put any effort into trying to keep it fun and
interesting.
I think more of that needs to be done, and these ideas are great for
that.
Keywords: Algebra, Research,
Ref: Furst18
Author(s): McQueen, Anjetta
Date: 2000
Title: Algebra textbooks don't help students, researchers
warn
Journal or Publisher: The Wisconsin State Journal
Volume, Issue, Pages: April 27 p.8A
Reviewer: Furst
Date of Review: 4/29/00
This article talked about how our nation's selection of algebra textbooks is simply no good. Of the 12 books they researched, only 7 were even deemed okay. The other 5 were doubted to have any potential for student learning. I was not excited to see that of those 5, the top 3 algebra books used in this country were included.
It seems that many schools tend to choose their textbooks from the biggest, best well-known publishers. School districts simply don't have the time, or the money to put into properly analyzing the resources that are out there. Algebra is no longer encouraged for the college-bound students only. We're looking to have everyone with a knowledge of algebra since it is a part of so many daily activites such as balancing a check book, or figuring out mileage problems. Don't we owe it to our students to teach them with a book that will actually be helpful?
I'm not sure if the Michigan Connected Math Series has any books on
algebra, but it seems
to me that we need to develop some high quality algebra books with our
current intentions
in math education at heart. If students don't understand what variables
stand for, or how
numbers relate to one another after they take algebra, then they haven't
learned algebra.
I hope that with all of the changes going on right now we will soon see
some algebra textbooks
worth using.
Keywords: Algebra, Connections,
Ref: Furst19
Author(s): Koirala, Hari P., Goodwin, Phillip M.
Date: 2000
Title: Teaching Algebra in the Middle Grades Using
Mathmagic
Journal or Publisher: Mathematics Teaching in the Middle
School
Volume, Issue, Pages: v5 n8 p. 562-566
Reviewer: Furst
Date of Review: 5/3/00
This article reminded me a lot of my first micro teaching lesson. It offers the idea of incorporating algebra into a fifth or sixth grade classroom by making algebra appear to be magic. The article gives multiple examples of ways to trick the students into thinking the teacher is performing magic when all they are really doing is algebra.
It was brought up throughout the article that students get very motivated when this technique is used. One of the main reasons for this is because they can use the same problems and examples from class at home with their family or with their friends. Many observations were made on these students after they had these mathmagic lessons, and they were seen doing it with their friends in the cafeteria during lunch. I think it is a goal of many teachers to have this kind of interest and enthusiasm present in students, and this seems like the perfect way of doing that. Many of the students enjoy seeing the teacher perform the "magic", and then want to learn how to do it themselves.
After the magic problems were done, the class tried to analyze the underlying mathematical concepts. Through thorough discussions, students were able to see how magic wasn't even a factor in the solving of the problems. Students were able to understand concepts like variables and expression. By incorporating charts to help "solve" the problems, students were able to very clearly represent the situations they were working on.
If incorporating algebra into my middle school classroom is an option,
I definitely plan on using the mathmagic approach. I think that if this
idea is used, telling the students the name of the unit, and not even
hinting
at the word algebra will make it even more beneficial for the students.
I think that students would really like doing activites like these, and
would be impressed with their abilities even more if they found out
afterwards
that they were doing algebra.
Keywords: Activities, ,
Ref: Furst20
Author(s): Bird, Elliott
Date: 2000
Title: Counting Attribute Blocks: Constructing Meaning for
the Multiplication Principle
Journal or Publisher: Mathematics Teaching in the Middle
School
Volume, Issue, Pages: v5 n9 p.568-573
Reviewer: Furst
Date of Review: 5/3/00
This was a neat article on how to use a fun activity to get your students to understand the fundamental counting principle. This teacher used four different shapes, two different sizes and four different colors. He placed some of them on the board, and then had the remaining ones in a box. He then asked the class what the remaining shapes were. When a correct shape was guessed, it was placed on the board with the rest of them. If students stopped guessing, the box would be shaken again to indicate that there were still some that needed to be guessed. Students were also asked to estimate how many objects there were total before the activity was complete, and students were encouraged to switch their guesses at any point.
I thought it was good that the teacher encouraged the students to change their minds. It's important to recognize the difference between a guess and a more educated selection. This way, students don't need to feel bad if they guessed wrong the first time.
I really liked this activity because it allows students to make the connection of the multiplication principle. Students were asked to explain their guesses. Many offer that with 2, 3 and 4 differences, you just have to multiply them. Many students don't understand the reasoning behind the multiplication principle even though they understand that it works. They are able to see the relationships of the 3 numbers by having those viual aids. By incorporating number sentences, students get a much better grasp of what is going on. The use of tree diagrams would also be very helpful for this goal. I think that students would increase the problem solving skills of many students; the method of guessing would also move from pure guessing to much more educated guesses. Activites like these will make teaching the concepts much easier, and will allow the students to really have an understanding of them.