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Q: Teaching the math teachers: All about methods. ( Answered 4 out of 5 stars,   1 Comment )
Subject: Teaching the math teachers: All about methods.
Category: Reference, Education and News > Teaching and Research
Asked by: oswaldhjoogink-ga
List Price: $50.00
Posted: 10 Aug 2002 08:40 PDT
Expires: 09 Sep 2002 08:40 PDT
Question ID: 52971
How to teach mathematics? What is known about the teaching methods for
math teachers to use? Which methods are known? What are the results of
methods used? How to Develop math teaching methods?
Subject: Re: Teaching the math teachers: All about methods.
Answered By: till-ga on 10 Aug 2002 10:03 PDT
Rated:4 out of 5 stars
Teaching mathematics in a way that will be found be interesting for
pupils is an important goal in modern education. I went to school in
the seventies in Germany and all my math teachers used the old
fashioned frontal lecturing: teacher speaks and writes things on
blackboard, pupils write it down and donŽt understand anything. Or
almost nothing.
Later at University I discovered how interesting mathematics can be.
And how many – endless as a matter of fact – applications there are.
Your question is very complex so I doubt if a comprehensive answer can
be given. I tried to filter some highlights for you. Google search
returns 125,000 documents under “ teaching methods mathematics
comparison”. So I had to select things that seem interesting for you.
I hope I took the biscuit.

Interesting facts for mathematical methods at York University
“ Teaching Methods
Methods of Study
Lectures and Books
Lectures form the central feature of most mathematics modules, and the
Department regards attendance at these lectures as essential. For
reasons which are somewhat mysterious, most mathematics students find
that their understanding of the subject is considerably assisted by
regularly attending lectures; indeed, for many people even a bad
lecture course is easier to follow than a mathematics textbook.
Explanations can be given for this: there is an advantage in hearing
something said at the same time as it is written down; a lecturer can
underline points of importance more effectively than is easily done in
a book; and it is often easier to convey the reasons for a particular
sequence of mathematical manipulations in a lecture than on the
printed page. Two other points which are often forgotten are that
lectures do give a good indication of a reasonable rate at which to
assimilate new material (and similarly help to encourage regular
study), and that a lecture can sometimes give a useful bird's eye view
of a subject and in the process provide a detailed syllabus. Some
lectures convey a real enthusiasm for the subject, but this is by no
means true of all lectures, which may be as well, as such a lecture is
not necessarily the best way of learning new material, as opposed to
acquiring the desire to learn. In mathematics, unlike many other
subjects, a difficulty or misunderstanding arising during a lecture is
often best dealt with by asking a question immediately; the chances
are that many other students present have the same difficulty.
It is quite difficult to learn how to take lecture notes, and rather
hard to explain the art to those who have not yet acquired it, but
this should come with time. However, it is desirable to be selective -
it is not necessary to take notes when the lecturer says "Good
morning". On the other hand, some things which are said but not
written on the blackboard are worth making a note of. For most
students it is a waste of time to make a fair copy of lecture notes.
Anyone who can learn to write reasonably legibly at speed can
generally find something better to do with his or her time. But it is
desirable to find the time within a few days of a lecture to look
through the notes, correct any misprints, make sure they make sense,
and make any necessary additions.
The use of mathematics books differs significantly from the use of
other academic books. Mathematics students are not expected to read
large numbers of books - indeed, a really good knowledge of the
contents of, say, ten books is quite enough to get a First by the end
of the second year. But mathematics books can be very hard to read. It
can take half an hour to see how one line follows from the line above.
Often it is easier to take on trust a statement the proof of which is
difficult to follow, read on, and then return to the difficult point
again. But of course it is inadvisable to read on taking too many
things on trust. Lecturers generally give advice as to which books to
use, but in cases where several alternative texts are suggested it is
worth thinking carefully which text to use (the cheapest is not always
the best) - the preface can give some idea of the level, and so can
dipping into the book and flipping through its pages. Other students
may give advice as to which books they have found helpful, but it is
perhaps worth bearing in mind that someone trying to sell a book will
not necessarily give an objective appraisal of its merits. It can help
to look at more than one book on a particular course, but quite often
the difficulties arising from the fact that different authors tend to
use different notations can mean that it is confusing to use more than
a couple of books in connection with the same course. It should be
remembered that it is not usual to begin a mathematics book at the
beginning and go on until you reach the end (or even, necessary, to
stop then), and that the utility of a mathematical book can be greatly
increased by proper use of its index.
One of the great difficulties in understanding mathematics is that by
the time a student is able to explain what he or she doesn't
understand, then he or she is four-fifths of the way to a full
understanding. However, any difficulties which do arise with parts of
lectures or books should be raised in an appropriate seminar or
tutorial, or with one's supervisor.
Exercises, Seminars and Tutorials
It is impossible to understand mathematics at undergraduate level
without doing a large number of exercises. For this reason, most
lecturers provide a weekly sheet of exercises. Some of these are
designated as coursework, which is marked and returned. These marks
should give you a reasonable indication of your progress on the
module. As an additional incentive to tackling exercises, ten percent
of the final assessment for each module is based on coursework marks.
Typically, in a nine week lecture course your best five or six pieces
of coursework are used for this purpose, whereas in a six week course
your best three or four pieces are used.
Attempting the coursework exercises should however be regarded as a
minimum ambition, and it is well worth while to try as many additional
exercises as possible. One can gain a great deal by talking about
problems with fellow students, provided that all participants do
genuinely try to participate rather than simply copy the answers from
the genius who lives down the hall. It is useful to learn to be able
to write out solutions as the ideas arise rather than to produce
random jottings on scraps of paper and then to spend time preparing a
beautiful copperplate copy to hand in. However you approach the
challenge of solving mathematical exercises, you will usually have the
opportunity to compare your solutions with those of the lecturer,
which are made available via the university library or the internet,
although of course not before the corresponding coursework has been
handed in.
In Mathematics at York, a tutorial is a meeting with your personal
supervisor and up to two fellow students, which takes place weekly
throughout the first term of the first year. The primary purpose of
tutorials is to discuss mathematics in an informal setting, although
notions of people sitting in armchairs sipping sherry are somewhat
misleading. There are no hard and fast rules about how a tutorial
meeting is conducted, since this depends largely on the individuals
involved. However, discussions are often sparked by questions about
the current batch of lectures. The informal atmosphere of tutorials
also helps new students to settle into the Department, and make the
necessary adjustments to university life.
After the first term, tutorials are superseded by seminars, and these
run until the end of the second year. Seminars differ from tutorials
in several respects. The number of students involved in a typical
seminar is between ten and twelve, in addition to which there is the
seminar leader, who is either a member of staff or a postgraduate
student. Each lecture course has its own seminars, meeting fortnightly
in the Autumn and Spring terms, and weekly in the Summer term, and
each student on the course is allocated a particular seminar group to
The primary purpose of seminars is to provide a congenial environment
in which to discuss aspects of the associated lecture course; for,
even though interaction between lecturer and audience is encouraged,
genuine discussion in a lecture theatre of up to 150 people is rarely
possible. Topics discussed in seminars vary from the unpicking of
lecture notes, through worked examples and exercises, to new material
suggested but not covered by the lectures. In addition, seminars
provide an ideal opportunity for many students to take an active and
constructive role, by presenting some of their own work to the rest of
the group, using either the blackboard or an overhead projector. Such
presentations are valued by many students as a means of developing
their communication skills, and can legitimately be mentioned as such
when it comes to preparing your curriculum vitae for a prospective
employer. (Some guidelines for putting together a maths talk are given
in the next section, Talking about Mathematics). Although seminar
leaders will regularly encourage participation in this way, nobody is
ever coerced to do so against their will, and so you should never
allow yourself to feel intimidated from attending a seminar. Indeed,
the Department regards seminars as an essential component of the
degree programme, and monitors seminar attendance quite closely. If
for some reason you are unable to attend a scheduled seminar, then you
should notify the seminar leader before they notify you! (e-mail is an
effective way of doing this).
In the case of most third and fourth year modules there are no
seminars, because of the reduced class size. Instead, all students
taking the module meet once a week for an examples class in which
exercises and problems are worked through in detail.
It is often possible to learn more from other students than from
members of staff, if only because things are not quite so blindingly
obvious to them, and so it is a good idea to discuss difficulties with
fellow students from time to time. Supervisors are also prepared to
try and help with mathematical (as well as non-mathematical) problems,
and it can be consoling to discover that their knowledge of some areas
of mathematics is not much more extensive than that of their students.
Talking about Mathematics
Speaking in public is a daunting and nerve-jangling prospect for most
of us, no matter how experienced. Nerves may be beyond our control,
but every other aspect of the job is amenable to reason, and like all
other skills can be developed and improved with practice. The
essential point to bear in mind is that the object of the exercise is
to communicate a piece of mathematics in a comprehensible, even
enjoyable way.
1. What do I want to say? To be clear-minded about this will increase
your confidence, and also help to calm the nerves. One of our biggest
fears is that we will "blank out" when the big moment arrives. At the
very least take time to write out the mathematics you are going to
present, and make sure you have your 'script' to hand, even if you end
up surprising yourself and impressing everyone else by not using it!
2. How do I want to say it? Mathematics uses a very concise language,
and just regurgitating a string of formulas will probably not go down
too well with your audience. Indeed the essential detail of a
mathematical argument is best conveyed in written form, which usually
means on the blackboard. Nevertheless, you will have to supply a
spoken commentary. Again, think about this in advance. You may want to
annotate your notes to remind you of helpful remarks. For example, if
you want to write down the inequality,
n3/3 > n3/3 - n2/2 + n/6 
your commentary might be "because the square of any non-zero integer
is always greater than one third of that integer", which, after a
suitable pause (never underestimate the power of a pause!), should
convince even should convince even the most sceptical members of your
audience! And remember to speak up, particularly if you are naturally
3. How will I use the 'props'? We have already mentioned the
blackboard, which most mathematicians will find to be the ideal prop
in presenting their work. The big advantage of blackboards over more
sophisticated gadgets (like overhead projectors, with prepared
transparencies) is that the necessity of writing on them encourages
the gradual unfolding of complicated mathematical arguments, at a pace
which gives everyone a fair chance to register what's going on, aided
and abetted by your verbal pearls of wisdom. This is the ideal; but in
practice the following glitches tend to creep in, and detract from the
overall effect.
1. It takes time to get used to writing on a blackboard. To be visible
from the back of the room you will probably need to write larger than
you think, and with more pressure on the chalk.
2. Unless you break it in half first, a new piece of chalk will tend
to 'screech', causing extreme discomfort to everyone present.
3. Getting the pace right can be difficult. If you're desperate to get
the whole thing over and done with, the temptation will be to rush,
and your writing will degenerate to scrawl. On the other hand, if
writing on the blackboard slows you down too much, an element of
tedium will creep in (yawning in the audience will alert you to this).
4. Writing and speaking simultaneously can be a strange experience.
The biggest temptation is to address your entire presentation to the
blackboard! When writing, rather than facing the blackboard try to
stand 'side on', and in a position which allows people to see what
you're writing as you write it. Also, take the occasional opportunity
to turn and speak directly to your audience. This can be scary, but
will seem a lot easier if you focus on an individual in the room and
imagine you are speaking to him/her. However, remember to change your
point of focus regularly, otherwise you are in danger of turning your
public presentation into a private conversation.
4. How did I do? Your first presentation might turn out to be a
brilliant tour de force. If so, congratulations! However, the chances
are that this will not be the case. (and certainly nobody expects it
to be). It's useful to get some feedback, so why not have a quiet word
with the seminar leader just after the seminar to find out how it came
across, and maybe pick up a few suggestions, for the next time! “
Teaching Methods of mathematics at York
( )

A Very interesting scientific research report containing  e.g. “ the
results of a statistical analysis of the relationship between
technology and academic achievement in mathematics”
Does it Compute? The Relationship Between Educational Technology and
Student Achievement in Mathematics
Alternative Title: ETS Policy Information Report
Author: Wenglinsky, Harold
Description: This research report, written by Harold Wenglinsky is one
in a series published by the Education Testing Service (ETS), Policy
Information Centre (Princeton, New Jersey). The report presents the
results of an ETS study into the effectiveness of educational
technology in schools throughout the USA. The report is organised into
four chapters: the first introduces the debate on technology's
effectiveness; the second contains descriptive information about
access to and use of educational technology by school children; the
third presents the results of a statistical analysis of the
relationship between technology and academic achievement in
mathematics; the fourth concludes the research by suggesting
implications of the study's findings for policymakers and
practitioners working in this field. The report is available as a .pdf
file. Users will require Adobe Acrobat reader software to view it.
'Education Testing Service (ETS)', educational technology, educational
theory, academic achievement, mathematics education
Subject Section(s): Sociology of Education Education Educational
Theory Teaching Methods
Resource Type: Articles/Papers/Reports (individual)
Copyright: 1998 Educational Testing Service
Admin Name: Policy Information Center
Admin Email:
Language: en 
SOSIG Record Details
This is a pdf  document which youŽll have to download. It will load
rather slow as it is a big document but I’m sure youŽll find it

A kind of (huge !) portal website is found at WetEd:
“Mathematics education has long been an area of considerable strength
at WestEd. The involvement of about 20 different projects provides
educators with curriculum that supports standards, innovative teaching
methods, professional development to enhance practice, tools to assess
whether students are learning what they are being taught, as well as
comprehensive evaluation services to gauge the impact of math programs
at the school or district level. “
YouŽll find detailed project descriptions and resources there about :

24ź Game Demonstration Project 
Beyond Description of the Problems 
California Mathematics Implementation Study 
California Schools Implementation Network (CSIN) 
Cognitive, Sociolinguistic, and Psychometric Perspectives in Science
and Mathematics Assessment for English Language Learners
Cultural Validity in Assessment 
Evaluation of California's Standards-Based Accountability System 
Evaluation of Interactive Multi-Media Exercises (IMMEX) 
Evaluation: Mathematics and Science Teacher Education Project (MASTEP)
Gender Equity in Math and Science (GEMS) Online Learning 
Inside the Classroom 
International Middle Grades Mathematics and Science Teacher Induction
K-12 Alliance 
Leadership Curriculum for Mathematics Professional Development 
Learning from Assessment (LfA) 
Mathematics Case Methods Project: Cases for Teachers 
Mathematics Case Methods Project: Materials for Students 
Mathematics Renaissance Leadership Alliance (MRLA) 
Mid-Atlantic Center for Mathematics Teaching and Learning (MAC-MTL) 
MMAP/Pathways Curriculum Support Center 
Nevada High School Proficiency Exam 
Parents Rediscovering and Interacting with Mathematics and Engaging
Schools (PRIMES)
Professional Development Cases 
Professional Development in Mathematics Through Videocases 
Regional Alliance for Mathematics and Science Education 
Supporting National Board Certification: Materials Development 
Synergy in Reform 
Teacher Education Materials Project (TE-MAT) 
Video Interactives for Teacher Analysis and Learning (VITAL) 
WestEd Eisenhower Regional Consortium (WERC)

Which resources feature Mathematics?

Beyond Description of the Problems: Directions for Research on
Diversity and Equity Issues in K-12 Mathematics and Science Education
Bold Ventures Volume 1: Patterns Among U.S. Innovations in Science and
Mathematics Education
Bold Ventures Volume 3: Case Studies of U.S. Innovations in
Mathematics Education
Connecting Mathematics and Science to Workplace Contexts 
Culturally Responsive Mathematics & Science Education for Native
Designing Professional Development for Teachers of Science and
Dilemmas in Professional Development 
Effective Assessments: Making Use of Local Context 
Enhancing Mathematics Teaching Through Case Discussions 
Enhancing Program Quality in Science and Mathematics 
Examining the Examinations: An International Comparison of Science and
Mathematics Examinations for College-Bound Students
Facilitating Systemic Change in Science and Mathematics Education 
Final Report on the Evaluation of the National Science Foundation's
Instructional Materials Development Program
Inspired by Standards: Math Teachers in Their Classrooms 
Learning from Assessment: Tools for Examining Assessment through
Mathematics Implementation Study: Final Report, June 2000 
A Mathematics Source Book for Elementary and Middle School Teachers 
Mathematics Teaching Cases: Fractions, Decimals, Ratios, and Percents
Mathematics Teaching Cases: Fractions, Decimals, Ratios, and Percents:
Facilitator's Discussion Guide
More Swimming, Less Sinking: Perspectives on Teacher Induction in the
U.S. and Abroad
PASS Science Assessment 
Pathways to Algebra and Geometry 
R&D Alert Winter 2000 
Mathematical Sciences and Their Application Throughout the Curriculum:
Final Report
Thinking Practices in Mathematics and Science 
WestEd Eisenhower Regional Consortium Web Site 
WestEd Resource Catalog 2002"
( )
As you can see an enormous amount of projects and resource listings.
Many “funny” or playful methods.  YouŽll find detailed descriptions
(and of course many links) of websites available videos and book on
the subject.

Why not combine Literature and Math in learning ?:
“Discovering Math in Literature 
You can pull math concepts out of many interesting books. Use our
suggestions below to help you find real-world application of math
skills and broaden the educational value of reading in your classroom.
Pattern Recognition and Sequences
The ability to perceive and predict visual and numerical patterns is
fundamental to later success with number abstractions. Your students
may begin by "finding the one that's different" in a linear series of
Rechenka's decorated eggs, Angus's jack-o-lanterns, or Strega Nona's
customers. Then, you may ask them to reproduce given patterns, such as
the stars on Strega Amelia's gown or the markings of one of the
Millions of Cats on blank objects or character shapes. This prepares
your students to identify, predict, and extend missing elements of a
repeated pattern of objects or characters encountered in this thematic
Number Sense and Numeration
"A picture is worth a thousand words," and the illustrations in these
picture books offer a wealth of visual representations that will lead
your students to count, manipulate, and group real world objects on a
variety of skill levels. They may count the number of eggs in
Rechenka's basket and the eggs in a carton at the supermarket. They
can actually see what happens when they add one more pumpkin to nine
pumpkins. Rudimentary concepts of place value will be developed as
your students organize the Millions of Cats on the faraway hill in
groupings of ones, tens, hundreds, and thousands, preparing them for
later use of rounding procedures and operating with larger numbers.
Mathematics in Motion
Some students may learn best when they can "feel" mathematical rhythms
and "move" to the calculated beat. Taking a cue from Tanya's dance
teacher, who clapped out the beat of her barre exercises, you can
engage your students in rhythmic clapping, marching, jumping, ball
bouncing and, yes, even dancing to any number of beats fast and slow,
classical and contemporary. Like Tanya, they might enjoy the different
rhythms and moods of Tchaikovsky's Nutcracker ballet; or like
Babushka, they might count out and move to the beat of a Russian folk
dance; or like Strega Nona, they might clap and twirl to an
enthusiastic tarantella. If your students come from a variety of
cultural backgrounds, you can invite them to bring in music from their
home cultures to share and discuss rhythmic similarities and
differences with their classmates. Bravo, to all!

Puzzles and Games
Imagine the delight of your students as they assist some of their
favorite stories and characters jump from their pages into homemade
games of various sorts. A Millions of Cats game can be played on a
board of squares upon which color-coded cats of ones, tens, hundreds,
and thousands place value are randomly scattered. Upon the throw of
dice, players move along the squares collecting the colored cats where
they land. The first player to reach a predetermined number is the
winner. Card games are a sure way to reinforce number facts. The
Wolf's Stew game is played like "Double War" with two decks of cards,
all worth face value (picture cards are worth ten). All cards are
dealt face down in two piles for each of two players. At his turn,
each player turns over the top cards on each pile, and totals them by
adding, subtracting, multiplying or dividing. Tallies from each turn
are recorded, and the first player to reach the number one hundred
exactly keeps all the cards from that round. The player who reaches
one hundred most often and collects the most cards wins the game.
Guessing games, matching puzzles, crossword puzzles – there's so much
fun to be found in the pages of a book!
What's Cooking?
Cooking inspired by story provides a natural integration of literature
and math. The steps involved in following a recipe lend themselves to
counting whole numbers and fractional parts, measuring, estimating,
and weighing, in addition to dealing with concepts of volume,
temperature, and time. It seems only fitting to have your students
celebrate Halloween and their reading of Pumpkin Light with
ceremonially baked pumpkin pie, divided into fractional parts and
eaten by the bakers themselves. The Wolf's Stew offers a number of
culinary treats (pancakes, doughnuts, cake, and cookies) to be tested
and tasted in your classroom; and a reading of Rechenka's Eggs can be
tastefully topped off with some of Babushka's Easter bread. There are
many child-friendly cookbooks that provide recipes for these and other
treats. Bon Appetit!

Hands-On Geometry
Did you notice that the roof on the chicken's house in The Wolf's Stew
is a triangle? Or that the moon in Pumpkin Light is a circle? Your
students will love searching out basic geometric shapes "hidden" in a
variety of places and positions in these picture book illustrations
and in their own world. Once familiar with the properties of these
forms, it's an easy jump to creating their own drawings and collages,
folding paper cutouts, or using mirrors to investigate lines of
symmetry, and constructing models of plane and solid figures out of
clay, fabric, and imaginatively used household/classroom materials.

Graphics You Can Count On
Your students will discover that the collection, organization, and
display of data gleaned from these stories is easy and fun to do with
the aid of graphic figures. The ways in which Strega Nona and Strega
Amelia, or Calabria and Moskova are "the same but different" can be
visually enhanced through overlapping Circle Venn diagrams. Favorite
food or music? Funniest Strega Nona remedy? In-class surveys offer a
fun way of extending and personalizing your students' literary
experiences. Collected information, once sorted and tallied, can be
displayed and interpreted on picture or bar graphs.

Story Problems
If Rechenka laid two eggs a day for three weeks, how many eggs would
Babushka have? If the old man started home with one thousand cats, and
an equal number of cats stayed on each of the five hills he traveled,
how many cats stayed on each hill? Your students will find story
problems featuring these familiar tales and characters fun and much
less intimidating than those word problems lacking a well known
context. You, as teacher, will find the stories and characters in this
thematic unit an infinite resource for creating story problems
targeting specific analytical/computational strategies and skills.”
Discovering Math in Literature

How can learning disabilities be solved ?:
“ Planning Pyramid for Multilevel Mathematics Instruction
Many elementary students with learning disabilities experience
difficulties in basic mathematics computation skills and/or in problem
solving (Peters et al., 1987). These difficulties frequently inhibit
full participation in classroom mathematics instruction. Some
intensive, direct instruction of students with special needs in
learning mathematics (either individually or in small groups) may be
necessary. However, with close attention to the scope and sequence of
instructional content, to teaching strategies (e.g., Howell & Bamhart,
1992; Montague, 1992), and to the design of practice activities (e.g.,
Camine, 1989) the level of participation and success of students can
be greatly enhanced.
What is the adaptation? 
The Pyramid approach provides an excellent framework for mathematics
instruction. Many teachers have told us that most of their mathematics
instruction is whole class. Students with learning disabilities as
well as other students with challenges in learning computational and
problems-solving skills were frequently lost and trapped in a downward
spiral. The Pyramid can help teachers think about attending to
differentiated student needs while thinking about the needs of the
class as a whole. In using the Planning Pyramid for mathematics
instruction, the following questions need to be considered:
5. What is the skill or concept to be taught? 
6. What are the prerequisites for this skill or concept? 
7. What does it take for students to master this skill or concept? 
8. What are extensions and applications of the skill or concept?
What does it look like in practice? 
Mr. Miller teaches third grade students in a large, urban elementary
school. He uses the Planning Pyramid for preparing for whole-class
lessons in mathematics. As Mr. Miller puts it,
With the right adaptations, I can get all my students to the top of
the Pyramid! I still work with small groups of students to help them
develop their computational skills. Some of my students have not
become automatic in using basic facts or in basic operations; they
need extra help. But they also like to feel part of the class; I don't
want to separate them too much. That's why I use the Planning
Pyramid--it makes me think about adaptations and how they can provide
support for students who need that little boost.
Mr. Miller used the Planning Pyramid to develop a unit on money He
used manipulatives, calculators, and cooperative learning groups to
provide support for students who needed it. For two students, he
needed to provide an oral, rather than a written, examination. As Mr.
Miller told us, "All in all, planning for individual differences
doesn't take much more time. It's worth the effort when I see students
succeeding and feeling part of what we're doing in class."
Mr. Miller's Unit Plan--Money 
Grade: 2 
What SOME students will learn: 
 Write and solve money word problems. 
 Give correct change (act out and on paper). 
 Given a certain amount of money, pick two things that are
What MOST students will learn: 
 Add and subtract using pennies, dimes, and nickels. 
 Using price tags, pay for items with coins. 
 Read and write different money values. 
 Match coins with certain prices. 
 Show money equivalents between dimes, nickels, pennies, and
What ALL students will learn: 
 Use terms penny, nickel, dime, quarter, cost, price, buy,
sell, and money.
 Act out the process of "buying" and "selling" goods. 
 Recognize and name the penny, nickel, dime, and quarter. 
 Recognize the cent symbol. 
 Read pricetags. 
 Plastic money for manipulation. 
 Pricetags. 
 Items to buy and sell. 
 Real coins for identification. 
 Create a store in the classroom. 
 Play store. 
 Combine a hands-on manipulative approach with an audio/visual
approach to create an atmosphere where all students can learn.
 Create a learning center with price tags for independent
 Use homogeneous and heterogeneous cooperative learning groups
to enhance learning for everyone.
 Use peer tutoring for help with manipulations. 
 Observational rubrics. 
 Problems of the day. 
 A final test. 

Planning Pyramid for Multilevel Mathematics Instruction
( )

Another scientific research on the results of teaching methods is
found at the Kassel Project:
“ The main aim of this project is to carry out research into the
teaching and learning of Mathematics in different countries, and
ultimately to make recommendations about good practice in helping
pupils achieve their mathematical potential.
The project has grown out of collaborative work between the Center for
Innovation in Mathematics Teaching (CIMT) at the School of Education,
University of Exeter in England, and the Mathematics Education Group
at Kassel University in Germany. Our initial interest was centered on
finding appropriate ways to use applications in the teaching of
Mathematics, but this has now widened to encompass all major strands
of Mathematics teaching in secondary schools.
As well as achieving our main aim, we hope that this project will
provide relevant data for
 the comparison of progress in a variety of mathematical
 the comparison of mathematics curricula in participating
 the comparison and correlation of the ability to solve
problems in context and apply mathematical concepts to real
situations, with mathematical attainment;
 the evaluation of the effectiveness of different approaches
to teaching mathematics;
 the use of calculators, computers and other resources; 
 the evaluation of self-based schemes of work compared with
traditional teacher-led methods;
 effect of setting/streaming; 
 the comparison of 'expectations' at all levels of ability in
different countries;
 recommendations for a mathematics curriculum for the 21st
This research is based on a longitudinal study of representative
samples of pupils in participating countries. It is the first
extensive comparative study in Mathematics, based on monitoring the
progress of individual pupils.”
The Kassel Project
( )
The 3 years progress report is at:
( )

A comparison of teaching methods in an international context:
“ University of Southampton Center for Research in Mathematics
A version of this paper appeared in Mathematics Teaching, 159, June
Some Lessons in Mathematics: a comparison of mathematics teaching in
Japan and America
Keith Jones, The University of Southampton, UK
Interest in the results of international surveys of education often
focuses solely on the relative achievement of the countries taking
part. Usually this is not good news as far as the performance of
English pupils in mathematics is concerned. As David Reynolds and
Shaun Farrell confirm in their comprehensive review of international
surveys over the past thirty years, "performance in mathematics in
England is relatively poor overall" and furthermore, they claim, it
has "deteriorated relative to other countries" over that period of
time [1, page 52]. From their report it is possible to identify a
range of factors that are characteristic of English mathematics
teaching, compared with other countries”
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A study of Stanford University :
A comparison of IMP1 and Algebra 1 at Greendale School
Again a pdf – so i canŽt copy anything here.

Search strategy used:
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oswaldhjoogink-ga rated this answer:4 out of 5 stars
no other comment than 'A good job!!!'

Subject: Re: Teaching the math teachers: All about methods.
From: till-ga on 10 Aug 2002 10:06 PDT
IŽm sorry about the "" signs appearing in the text. There is
no preview function available and i forgot that some signs may not be
used here in the formatting.


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