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| Idea Bank for Approaches to Math Instruction
(Share your ideas, too!)
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 return to the Idea Bank index |
(including math resource books and links sprinkled through the discussions) |
| Best practices in math
> I am part of a task force to study best practices in math, nationally
My best practices include allowing the students to find out
what makes sense and then explain and defend their own
thinking. For example, this year we put a number of fraction
addition equations on the board. They had to figure out which
ones were reasonable and, using any method (manipulatives,
numbers, explanations), justify their thinking. I feel it is
very important to ask students to explain their thinking. I
use a strategy called "think, pair, share" a lot whereby they
initially think about what they did or what they believe to be
true about a problem and then get in a pair and share with one
another. They are expected to challenge what does not make
sense in their partners' thinking.
I expect them to be open to learning from one another and tell
them that very clearly. They start out with what they know and
then, in fourth grade, should be able to clearly explain what
they learned as a result of listening and watching others'
ideas about a mathematical subject (including mine). I expect
them to use mathematical language. What I came to realize is
that many times math class resembles the scientific process.
You start out with a hypothesis, look at the evidence and then
draw a conclusion.
My role as teacher is to help them make connections, seek out
what makes sense, and be part of what is available to them to
learn with. I also present problems a lot and consider it my
responsiblity to think, based on the immediate assessment of
what goes on day to day, what is the next right step for my
class. I keep the standards structured into my annual plan but
also plan my daily and short term lessons to meet the needs of
the students. Where are they weak? What understandings need
to go to a deeper level? What calculations need work? What
does this lesson tie into?
Ramos, 5/24/00 on teachers.net math board |
| improving math instruction
> I teach grade 4 and have concentrated heavily on revising my
Today as an example:
We did Daily Math Review---a mixture of many math skills I
hand out every morning and we go over it at the beginning of
math time.
Then we did a mad minute for multiplication: 0,1,2.
Then we did a textbook lesson on rounding. I did a diagram of
a roller coaster, and showed how getting to the middle (5)
sends you flying down to the next side. We practiced some
exercises whole class, then I let groups read and solve some
word problems involving rounding.
We went over the answers, then I assigned homework.
So, to answer your question, I do many things in the space of a day.
Karen/PA, 9/25/00 on teachers.net math board
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Kelley,
Dee, 9/27/00 on teachers.net math board
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| When will we ever use this?
> Thankfully, for the first time, I am going to be given the
regarding "... But I'm NOT going to be..."
Well, I think 2 strong ideas come to mind when kids bring
this up. But it would take a little work on your behalf.
1. Kids usually think concretely and want examples they can
relate to (that's why they said "I won't use this," as if they
know exactly what they will do forever). I would find some
pretty easy but important examples of famous people who
started doing something different in their life and
completely changed careers. This will stick in their minds
that what they think they may want to do as a career or
profession might not always be what they end up doing. We
change as we grow.
2. I would investigate and talk about how math is used in
fields that they probably don't even know is used. There is
also a book called When Are We Ever Gonna Have To Use This?
by Hal Saunders (Dale Seymour Publications, currently out of stock.) It isn't the
best book, but it does chart all the areas of math from like
grades 3-12 and how they are used in different fields. Comes
with a chart and is fascinating enough so that they will not
ever WANT to ask the question again. Mission accomplished :-)
Posted by "me," 7/30/00 on teachers.net math board
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I hear this all too frequently - in the middle school years
more than in the high school. My stock answer is that if they
are asking WHERE this skill is used, I can tell them that. But
if they want to know if THEY are ever going to use this, that I
can't answer. No one knows where they will end up. Careers
change. Interests change. But learning the early material
paves the way for later interests. If they decide to become an
engineer (instead of a writer) in college, they will at least
have the basic, prerequisite material needed to change majors.
They are too young to make irreversible decisions. I tell them
that they need to learn everything they can, so that they can
make a better choice later.
I also remind them that solving problems in math makes it
easier to make non-math decisions in life in a more logical
fashion. I use the example that they are driving down a major
local road. Suddenly, there is an accident a short distance
ahead of them. Should they wait it out and creep past it? Is
it better to get off of that main road and take a parallel
road? Is there a way to exit, and go back to a different cross
street? These types of decisions are made everyday - and
lightning quick. We don't realize all of the processes we go
through to think this through - we just do it. The ability to
process all of the parameters quickly comes from being a good
problem-solver in math. The neural pathways are set up by
doing something over and over (like riding a bicycle) until
they become second nature, with no conscious thought.
Hope this helps.
BTW, worse than this is when one of your honor students comes
to you and tells you that his father told him that one of the
math logic puzzles you assigned for homework (from the
textbook) was useless - because he will never have to do
puzzles in his life. This actually happened to me. And it was
so sad.
DSF/NJ (Donna), 7/31/00 on teachers.net math board
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When will we ever use this?
> I have a difficult bunch of geometry kids this year. I am getting
Depending on the ages of the students, I remind them that they
really can't know at this time what they will need to know and
use later in life. I can show them WHERE these things are
used, but a guarantee that any individual in the class will use
them???? not possible. Also what is wrong with a well-rounded
education? Education for education's sake?
I also like to explain the theory of why we never forget how to
ride a bike (although it probably doesn't hold as much truth
for many of today's kids). I learned in college psychology,
that every time you learn a new skill, a "path" is cut into
your brain tissue that connects the different neurons needed to
perform this skill. Since most children ride their bikes
excessively, that "channel" gets cut deeply into the brain.
When they get the first car, and stop riding the bike, the
brain slowly starts to fill in that channel. But because it is
SO deep, it never fully fills in. So, when in our forties we
decide to exercise and pull out the old bike, we wobble for a
few minutes until the brain finds that old channel and slices
through the new tissue quickly and "it all comes back to us."
The more you do something, the more you own it.
Why deductive reasoning? We are setting up those neural
pathways in the brain that allow us to make coherent, logical,
NON-MATHEMATICAL decisions later in life. We practice the math
problems so that we can be cool under pressure later in life.
When driving on a busy road and there is an accident suddenly
in front of us, we quickly consider our options - do I wait it
out until I can go around or turn off here and take a parallel
road? Do I get off and go back an exit to find an alternate?
Decisions such as these are made everyday in our lives - and
need to be made quickly. People who are good problem solvers
can quickly sort out the options and make the most reasonable
choice. Does it always work? No, but it increases your odds.
BTW, no matter what line in the grocery checkout I choose, it
will be the one that comes to a grinding halt. One of Murphy's
laws. Math doesn't help me there.
DSF/NJ (Donna), 9/23/00 on teachers.net math board |
| Math Philosophy?
There appear to be two camps in math (like reading -
phonics vs. whole language): hands-on, math writing vs.
paper pencil skill and drill. I've tried both. Here is
what I'm thinking:
Last year we departmentalized. We had
a lot of really low math kids. Fifth grade math has always
been a toughie. State test scores always drop big time
from 4th to 5th. The thing is, for the first time ever in
our district (it's not too commonplace other places
either), we had 100% of our kids pass the state test. Go
Figure! It was like a miracle. So I pick the brain of the
math teacher. What did you do?
She used the math textbook
(Harcourt), the overhead, math workbooks (are you seeing
pencil paper skill & drill here) and that's it! Now,
granted, the kids complained about math all year. It was
too hard, there was too much homework, etc., etc., etc....
Occasionally she threw in a hands-on activity for fun. So
what's up with this Marilyn Burns (who I follow faithfully)?
So, I'm thinking balance. Pencil, paper, skill and drill
because you don't throw out the baby with the bath water.
Hands-on to make it fun, bust the boredom and to reach the
Tk kids. And writing for the Language Arts folks like
myself. (After reading about math writing I was mad that I
never got to write about math in school - figured that's why
I shut down).
Just thinking...What do yall think?
Mae in Texas, 7/25/00 on teachers.net math board
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Mae, I wished we worked together
I'm a high school math teacher and I totally agree with your philosophy. I think
there is more to math than drill, although it does have its
place. Nothing aggravates me more than when we're doing a
really involved application and they can do the hard parts
but get stuck in the quadratic formula, something they should
know.
Also, I think making math meaningful and interesting
is key. Students should know how powerful and important and
beautiful this subject truly is. When we spend 3 weeks on
factoring, its no wonder kids hate math. Writing,
manipulatives, technology, hands on activities are all things
I love to use.
My kids rave that they've never had a class
like mine because we do so much. But, you know what I think
really makes the difference? The fact that I have a
tremendous amount of enthusiasm and I really love math. I
see other teachers do activities but the kids don't have the
same response. My kids get a kick out of me because I get so
into it and am so interested in what I do. Again, I guess
it's the teacher that makes the difference, not the gimmicks.
Kathy, 7/25/00 on teachers.net math board
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Math is my toughest subject. I'm not mathematically inclined.
Fifth grade math scares, high school math would send me into
orbit! You sound like a wonderful math teacher. I wish I had
a teacher like you! I shut down in 4th grade after division.
It really didn't help when the teacher yelled at me and let me
know how stupid I was! So now I teach 4th grade. At the end
of the year, I always ask students what they learned, and math
is always on top of the list! Go figure!
An older, wiser teacher once told me that bad math students make great math
teachers because they understand the kid that doesn't get it.
I hold onto that. I also don't leave a kid in the dust. I'm
determined that we will all get it together or die trying.
Fractions drive me nuts! They are hard for me to explain.
I've been known to cry after a day's battle with fractions!
I like math writing because that is something I can understand.
I figure there are students who need math writing the way I
do. I like hands-on because it makes math fun. I'm not sure
it really develops the concept (it might just be me though),
but it takes out some of the fear of math.
The one thing I have found to be effective is working on the overhead. It's
like a magic trick I can't explain. It works though! I have
to use a good textbook with a good sequence to keep myself
focused. That is why I liked it when I used Saxon.
Now that I have been teaching awhile, I feel much smarter in math. It
occurs to me that kids who are having trouble in math need to
teach the concept to someone else. That responsibility sheds a
whole new light right through the frustration block.
Mae in Texas, 7/26/00 on teachers.net math board
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super article that addresses this very subject
A super article that addresses this very subject is from the AFT
American Educator magazine. Click the link for a .pdf file of the original article.
"Basic Skills Versus Conceptual Understanding," by H. Wu.
Harbinger, 7/26/00 on teachers.net math board
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Harbinger, I read the article and learned from it. I have 21 years
of experience and find myself becoming more and more like
those "old" teachers I used to hate when I first taught. You know
the type, the ones who teach memorization and use workbook pages.
I came from a gifted classroom which was very much conceptually
based to a small first grade using ABeka materials. I can't
believe how much better my kids are at math using the traditional
method. Sure we play games and explore tangrams and geoboards but
the basics come first. Now I'm the teacher down the hall who won't
change with the times. Aghhhh!
Pam/1/GA, 8/03/00 on teachers.net math board |
| Math Research
> However, there doesn't seem to be as much shared about MATH
You raise a very interesting point. I went to the site of
the National Council of Teachers of Mathematics
( www.nctm.org ) to see what research they might share, and
their featured link was to a report issued at the end of
September by the Glenn Commission. NCTM highly endorses this
report and its recommendations. It is called:
Before It's Too Late: A Report to the Nation from The
National Commission on Mathematics and Science Teaching for
the 21st Century .
In reading the Executive Summary, I notice that it has a lot
to say about teacher education and nothing to say about at-
home support. It does follow logically that if students are
being encouraged to do at-home reading each day, and parents
are encouraged to read aloud to young children etc.,
comparable attention should be placed on at-home math, too.
(See more below on Family Math.)
The NCTM site also provides links to its
numerous journals, some of which focus on mathematics
research. Reading the online summaries of some of the
research from the Journal for Research in Mathematics
Education, it appears to me that these articles are written
more for the population of math researchers rather than for
teachers who would like research overviews without all the
technicalities of specific studies. A better bet might
be "Teaching Children Mathematics." I quote from the NCTM
site:
"Teaching Children Mathematics is an official journal of the
National Council of Teachers of Mathematics. It is a forum
for the exchange of ideas and a source of activities and
pedagogical strategies for mathematics education pre-K - 6. It
presents new developments in curriculum, instruction,
learning, and teacher education; interprets the results of
research; and in general provides information on any aspect
of the broad spectrum of mathematics education appropriate
for preservice and in-service teachers."
NCTM produces other journals for middle school and high
school math teachers. A subscription to the NCTM journal of
your choice is included with your membership in NCTM, and I
strongly encourage anyone interested in mathematics education
to join the NCTM! Go to their site for info.
Over the years, I have gotten a lot of use out of the
outstanding book,
There is another book by the same lead author (Jean Kerr Stenmark) and others, Family Math for Young Children: Comparing.
Wendy P. of Math Cats, 10/23/00 on teachers.net math board |
| great N.C. site for math instructional strategy
Strategies for Instruction in Mathematics K-5
This is a superb site with very readable, do-able math lessons
and games--a lot that will help you with the drill and repetition
that they will need, in a fun way. Scroll down to your grade level
and the year is divided into 4 quarters plus a section of
blackline masters.
Darcy, 11/02/00 on teachers.net primary elementary board
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If you have trouble getting to that great N.C. math
instruction site, just type in
Click on instructional resources.
Good luck! It is worth the trouble to get there!
Cindy, 7/21/00 on teachers.net primary elementary board |
| Teacher-trainer looking for good math methods books...
> Do you have any ideas on interesting and thorough methodology books?
I purchased the book, Activity Math: Using Manipulatives in the Classroom, Grades 4 - 6 by Bloomer and Carlson. It has all the units by chapter that you
would teach to this grade level. It focuses on introducing
the concept at a concrete level with manipulatives--some which
can be xeroxed at the back of the book in the resources
section. It's an excellent book.
[Also available: Activity Math: Using Manipulatives in the Classroom, Grades K - 3 ]
Jody, 9/15/00 on teachers.net math board
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I have taught the math for elementary teachers course for almost 20 years
and have used a variety of texts. My favorite is Musser, Burger, and
Peterson. It has a wonderful problem solving chapter to start the book,
and then continues the theme throughout. It is readable and challenging in
the best ways; it provides good historical contexts as well as talking
about open questions. It makes a real effort to share some of the
excitement of mathematics while it works to ensure a strong understanding
of the foundations of arithmetic. It does not talk down to the
students. It is now in the 6th edition.
Lee Sanders, Miami University Hamilton, 11/12/03 on MathTalk discussion list
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You might also want to examine "A Problem-Solving Approach to
Mathematics for Elementary School Teachers," 8th Edition, by Rick
Billstein, Shlomo Libeskind, and Johnny Lott, ISBN 0321156803, July
2003. Some good supporting materials are available. It will push your
community college students, but their efforts will be rewarded. [If the
8th edition is not available for sale in the USA, you can get the 7th
edition from Addison Wesley Longman, ISBN 020134730X, 2001.]
Ron Ward, Western Washington University, Bellingham, WA, 11/12/03 on MathTalk discussion list
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I am a novice. I am teaching a course for elementary teachers using
Helping Children Learn Mathematics (seventh edicition) by Reys,
Lindquist, Lambdin, Smith and Suydam. I find all of the Math Links for
each chapter very rich. Here is the Student Companion website:
> http://jws-edcv.wiley.com/college/bcs/redesign/student/0,,_0471151637_BKS_1598____,00.html
Since math is not the strength of the non-traditional students that I
teach, I am using mostly hands-on activities to involve the students in
the beauty of the connections they need to see in mathematics. The
students I teach need to walk into their first teaching experience
without fear of tackling math. This text gives many, many references
through electronic links and connections to elementary literature. I am
enjoying the opportunity to share mathematics with future teachers.
Linda Hall, Fairleigh Dickinson University, 11/12/03 on MathTalk discussion list
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I'm not a college teacher, but I have used the
John Van de Walle book, Teaching Elementary and Middle
School Mathematics for professional development.
Teachers have responded in a positive manner to this
text. It is a standards based text that helps
teachers understand math and give suggestions how to
help students in their classroom.
Craig Morgan, Haddon Township, NJ, 11/13/03 on MathTalk discussion list
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Although I am a big fan of the Van de Walle text, and have used it for many years in all editions in my METHODS classes for K-8 teachers, I thought the initial question concerned possible texts for math CONTENT classes. I would question its appropriateness for those, unless you are really attempting some kind of integrated content/methods class and, perhaps, supplementing or augmenting the content portion from some other resources. Also, since the initial question had to do with community college students, I think it would be better for them to focus on mathematical concepts and procedures -- getting a good content foundation -- and save math pedagogy for their university work.
Ron Ward/ Western Washington University/ Bellingham, WA, 11/14/03 on MathTalk discussion list
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At The University of Texas at Austin, we have switched to
Bassarear, Tom (2001), Mathematics for Elementary School Teachers,
Second Edition. Houghton Mifflin Company, Boston, MA. Text and
explorations manual
in all of our mathematics content courses for elementary education
majors. The students seem to find the text readable and the
explorations manual has many good activities.
When I supplement, I have found myself using a preliminary copy of
Masingila and Lester published by Prentice Hall.
Good luck!
Jennifer, U. Texas at Austin, 11/14/03 on MathTal discussion list |
| Mathophobic teacher in need of help
> I am hoping all you wonderfully skilled math teachers can
> Does anyone have any ideas for me or a book I can read to
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A book that I highly recommend is About Teaching Mathematics by Marilyn Burns.... an excellent book that has
almost become a "bible" to me in teaching math. She is a
great advocate of helping children to use methods and
strategies that "make sense" to them in solving
problems. She also has a large number of math lessons in the
book that are generally in the primary-middle school
spectrum.
In addition, check out her web site, www.mathsolutions.com, for her one-week workshops in the
summer, which I found very helpful. Good luck!
Debbie B, 9/12/00 on teachers.net math board
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Check out the Marcy Cook books ... all hands on and a lot of fun!!
Jam, 10/06/00 on teachers.net math board
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I especially recommend Math Starters! 5- to 10-Minute
Activities That Make Kids Think, Grades 6 - 12
Gisele, 9/12/00 on teachers.net math board |
| Mountain Math
> What exactly is mountain math? Who prints/publishes this
Hi Mrs. B.,
By now you probably have found the Mountain Math/ Language
website... but just in case here is the link below.
I have used Mountain Math in my class for 5 years and I do
like it. Make no mistake: it is a bulletin board not a
complete curriculum. It is a review program that can
supplement whatever program you are currently using. MM/L is
not a total program, and the authors are quick to tell you
that. It is to help in reviewing and aid in the retention of
previously taught concepts.
I enjoy using it because it provides great vocabulary
development for my kids in the Math/Language area. It also
provides a kind of "spiraling" (for a better word) curriculum
review. Each grade level kit comes with a list of objectives
and all of the bulletin board pieces on very colorful card
stock kind of paper. All you have to do is cut it apart and
put it up. You can use all or as much as you want. I find
with younger kids it can be used as a morning calendar
activity. However, in the older grades it could be used as a
type of Daily Oral______(language/math) activity. Or even
centers, if you prefer. Even if you haven't taught a specific
concept yet or the kids have not had enough practice to gain
mastery on a concept, just the fact that you have the board
up leads them to ask questions or gives you the opportunity
to share the "language" of the particular concept that you
will, in the future, teach to them. For all it is
worth, it is a great way to have daily review of learned
concepts, without a worksheet--although the upper grade
level kits, I understand, have such things!
Laura, 6/02/00 on teachers.net math board |
| Liping Ma
I am reading Liping Ma's book, Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States
, and am greatly interested in
discussing what she is saying with other elementary math
teachers. I especially would like to talk about using her
understandings and insights with our Standards to make some
professional development for our school. Any ideas out
there about how to bring the two together?
Ramos, 5/22/00 on teachers.net math board
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I've been reading her book, too, and think its really
interesting and insightful. I think she's correct when she
says that Chinese teachers have a deeper understanding of
mathematics than most American teachers. Case in point:
there was a message posted on t-net from a kindergarten
teacher who asked how to figure out what a child's grade would
be if he missed 7 words out of 27. The thing that struck me
was that although I'm sure the teacher is a kind, caring
person and is probably very good with young children, anyone
with a college degree (let alone a teaching certificate)
should know how to figure percentages. I've run into teachers
who can't add fractions or perform basic calculations without
a calculator, so when Liping Ma says American teachers need to
have a better understanding of mathematics, I can believe it.
SGE, 5/23/00 on teachers.net math board
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I'm glad to hear someone else is finding her book to ring true.
What impresses me is the connectedness of the way they see
things and the thorough understanding. I was hooked in the first
chapter on division with regrouping when the connection was made
between composing a 10 in addition when there are too many ones
and decomposing a ten in subtraction when there are not enough
ones to subtract. I have been practicing this concept on my
seven year old daughter, who I realize from reading the book,
has a procedural not a conceptual understanding of much of
addition and subtraction as she is about to graduate first
grade. I also support completely the social nature of learning
math, the talking, discussing, and challenging that needs to go
on instead of the endless math work.
Ramos, 5/23/00 on teachers.net math board
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Hi, I don't know if people are still reading this,
but I found it important to have the same skills (that
Ma describes for teaching elementary math) for teaching college mathematics. The same skill of diagnosing a student's subtle misunderstanding, and
explaining the nature of subtle differences in math
operations (as in the multiplication / neglecting
place and zeroes example) is relevant at all levels of
mathematics, and probably other disciplines.
I cast "the ability to diagnose misunderstanding" as
one of the teacher's most important skills.
What emphasis is placed on this skill in teacher training
and education programs? How do you test it?
Owen Ozier, 10/13/00 on teachers.net math board
[The Liping Ma book has also gotten rave reviews from readers at amazon.com. - W. Petti of Math Cats]
|
| Multiage Math 1-2
> I am looking for ideas to successfully teach first and second
I suggest using Kathy Richardson's series, Developing Number Concepts.
It is an excellent program for a multiage classrooms, because it is very hands-
on, and allows for students of varying ability levels.
Younger students work with the same materials as the older
students, but because of their various levels of
understanding, they work in different ways.
Developing Number Concepts, Book 1: Counting, Comparing, and Pattern
Kris, Japan, 8/04/00 on teachers.net math board
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| Math-a-pedia
> Does anyone know where I can get the book Math-a-pedia?
It is at amazon.com:
Math-A-Pedia: Primary
(Author is David Brummett.)
Lauri/ms math, 9/05/00 on teachers.net math board
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| Singapore Math
> Is anyone using the Singapore Math textbooks? If so,
> Tell me more about them, since I know you are interested in
Ramos, you can order the Singapore Math textbooks (as well as
the science program used in Singapore) at www.singaporemath.com. I've been using the math textbooks for two years now and, if you'll excuse an excess of parental pride, my son has scored
in the 99 percentile on the Iowa Test of Basic Skills these past
two years (1st and 2nd grade), which was well above the school
average. The math textbooks are terrific and present each topic
in a logical, sequential way, without jumping around from topic
to topic like so many of our American math programs do. They
emphasize strong basic computational skills, as well as
conceptual skills. As you can guess, I'm totally sold on them
and next year, my son's whole school will be using Singapore
math.
The Singapore math website also offers enrichment materials in
English, science, and math, as well as two math software
programs. You can also order a copy of the math section of the
leaving certificate exam taken by 6th grade children in
Singapore. The leaving certificate exam was a real eye-opener
for me because it demands math skills that far exceed the skills
of most of our 6th grade students.
SGE (Suzanna), 5/24/00, on teachers.net math board
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| Open-ended questions?
> I am looking for a resource that can help me write open-
Kimberly, 6/02/00 |
| Good Math Review Games
There are some really great websites to investigate at
http://www.geocities.com/Athens/Academy/6617/math.html
jk, 9/02/00 on teachers.net math board |
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| © copyright 2000 - Wendy Petti of Math Cats. All Rights Reserved. |
