1.Boehmig, S. P. (2006) Pittsburgh’s South
Side. Arcadia Publishing. Charleston, SC.
2.Henry Chadwick is also credited with first
devising this statistic, which caught on as ameasure of
pitching effectiveness after relief pitching came into
vogue in the 1900s. Prior to 1900 – and, in fact, for
many years afterward – pitchers were routinely expected
to pitch a complete game, and their win-loss record was
considered sufficient in determining their
effectiveness.
3.Albert, J., Bennett, J. (2001) Curve Ball
Baseball, Statistics, and the Role of Chance in the
Game. Copernicus Books. NY. p. 2.
4.“Programmed Learning is a learning
methodology […] first proposed by the behaviorist B. F.
Skinner in 1958. According to Skinner, the purpose of
programmed learning is to ‘manage human learning under
controlled conditions.’ Programmed learning has three
elements: (1) it delivers information in small bites,
(2) it is self-paced by the learner, and (3) it provides
immediate feedback, both positive and negative, to the
learner. It was popular in the 1960s and through the
1970s, but pedagogical interest was lost in the early
1980s as it was difficult to implement and its
limitations were not well understood by practitioners.
It was revived in the 1990s in the computerized
Integrated Learning System (ILS) approach, primarily in
the business and managerial context.” Source: http://en.wikipedia.org/wiki/Programmed_learning
5.TEMAC Programmed Learning Materials. (1962)
Encyclopedia Britannica Press. Chicago IL.
Chapter 2
1.I don’t remember the title of
the book. It probably was his “Abstract Algebra” book
that was published in 1959. Dr. Sawyer did write a book
about Linear Algebra in 1972 from which I quote: “The preparation of
this material was undertaken because no published books
seem to meet the needs of the first-year engineers. Some
books were mathematically overweight; in order to prove
every statement made, long chains of propositions were
included, which served only to exhaust and antagonize
the students.”
1.Although
[Mary]
Dolciani is not well known by the general public, she
was influential in developing the basic modern method
used for teaching basic algebra in the United States.
Source: Wikipedia http://en.wikipedia.org/wiki/Mary_P._Dolciani
2.Madison
Math
was a curriculum developed by Robert Davis at Syracuse
University pilotedat Madison Junior High
School in Syracuse where it began in 1957, to explore
how learning of mathematics works, which led to his 1966
book “Discovering
Mathematics: A Text for Teachers.” Don Cohen
(nicknamed the Mathman) worked with Bob and was one of
the Madison Project’s chief advocates and also led the
Saturday Madison math sessions at PS 41 from
1966-1972. His twitter handle is: @themathman. See
blog entry. http://climeconnections.blogspot.com/2010/08/madison-project-bob-davis-and-mathman.html
7.Columbia
Prep
School Newsletter “Authors on the CPS Faculty” by
Barbara Ash, September 10, 1974. Quote from that
article: “This September [1974], Mr. Charischak is
beginning his 4th year as mathematics
instructor for seventh and eighth graders. For Mr.
Charischak the 1974 to 1975 school year also marks the
first official seventh and eighth-grade mathematics
program in sometime. This new program represents a
synthesis of his own ideas as well as techniques
borrowed from the math textbooks with which he has been
especially pleased. Through his work with the Madison
Project for mathematics teachers and his frequent
unfortunate experiences with many texts, Mr. Charischak
has developed the criteria for a successful program for
seventh and eighth-grade math students. His basic ideas
include the following:
·Mathematics
books
for junior high school students must be composed in a
style that can be appreciated by that age group.
·The
process
of learning mathematics, as with other subjects should
be one of discovery.
·The
concepts
and rules of math must relate to reality as much as is
possible. To accomplish these goals, Mr. Charischak
emphasizes the use of visual and manipulative aids,
along with well-written reading material which can be
enjoyed by seventh and eighth graders. He plans to spend
more time compiling his ideas and eventually hopes to
publish his work on the development of a successful
mathematics program for junior high school students.” I
never did publish it.
Chapter 6
1.Maeroff, G. (1975) Junior High is
not Easy to Handle. Lakeland Ledger. Lakeland, FL.
3.The
eight
students who participated in my Codes and Ciphers
activities in 1977 all had above average skills in
everyday math. I wish I’d had some less skilled
students.They
could have revisited skills they’d had in another
context (normal classroom teaching) and might have
been able to overcome the difficulties they’d had with
them. If I were doing the activities today I would
have so many more choices in delivering them.A Google
search leaves me breathless at the possibilities.Here’s a
book I just had to order from the UK. “Secret Breakers
– The Power of Three.” http://hldennis.com/the-books/.
Not because I expect to find a lot of math here, but
because it is advertised as a DaVinci Code for kids.
What a rich source to embed some mathematical
exploration.
4.The
open-classroom
movement originated in the British public elementary
schools after World War II. The movement, known then
as informal education, spread slowly to the United
States. In 1967 a parliamentary commission headed by
Lady Bridget Plowden published a report, “Children and
Their Primary Schools,” that promoted open
education in all British schools. American educators
who visited British schools during the late 1960s had
read the Plowden report and visited classrooms where
informal education dominated teaching and learning.
They viewed informal education–or, as they came to
call it, open classrooms or open education–as an
answer to both the American education system’s critics
and the problems of U.S. society. Source: http://educationnext.org/theopenclassroom
5.Cursor
Magazine
CURSOR -
Programs for PET Computers was the name of
an early computer-based "magazine" that was
distributed on cassette
from 1978 and into the early 1980s.
3.The
original
source for this chart is long since forgotten. You can
see a similar chart here: Smith, S. (2009) Craps … A
Casino Game of Pure Chance. http://herkimershideaway.org/writings/craps.htm
5.Soloway,
E.,
Lochhead, J. and Clement, J. Does Computer Programming
Enhance Problem Solving Ability? Some Positive
Evidence on Algebra Word Problems. In Computer
Literacy, edited by Robert J. Seidel, Ronald E.
Anderson, and Beverly Hunter, 171-185. New York:
Academic Press, 1982.
Chapter
8
1.Antonia
("Toni")
Stone created the Playing to Win Computer Center,
which was the first Community Technology Center (CTC),
at Union Settlement Association's Washington Houses
Community Center in East Harlem in the early 1980's.
Video by S L Productions. http://www.youtube.com/watch?v=1JogbUzJHJs
2.The
Fortune
Society is a nonprofit social service and advocacy
organization, founded in 1967, whose mission is to
support successful reentry from prison and promote
alternatives to incarceration, thus strengthening the
fabric of our communities. Source: http://www.nycservice.org/organizations/index.php?org_id=1847
4.New
York
Area Educators Note: “Computers and software for
classroom use can be tried out by New York area
teachers and school administrators at Teachers
College/Columbia University's new Microcomputer
Resource Center, the first program of its kind in the
Northeast. The Microcomputer Resource Center, which
opened November 1, 1980 is a free service to educators
confronted with the sudden popularity of computers in
elementary and secondary schools. It features three
microcomputers frequently purchased by schools and a
cassette library of educational programs written by
local teachers as well as those published by computer
companies. Among the specially designed materials are
a baseball game that pitches arithmetic problems, a
bowling game that teaches decimals, and a dart game
that is scored by a student's speed in estimating
round numbers. Karen Billings, director of the
Microcomputer Resource Center, explained that it was
organized because computers, already in homes and
business, are coming to the field of education, and
teachers need a place to learn about them. “Many
schools began purchasing microcomputers about two
years ago,” she continued, “when technology reduced
the price and size of computers to $2,000 and less for
a tabletop model.” Although originally acquired for
mathematics classes, the machines are now being used
for all academic subjects; simulated chemistry
experiments and geography drills, for example, are on
cassette in the Center library. A qualified staff
member, who already has taught with computers in his
or her classroom, is on hand at the Microcomputer
Resource Center to introduce the novice to the
equipment. Teachers experienced with computers also
are welcome to experiment with materials and meet with
colleagues interested in improving microcomputer
services in their schools. The Center contains a
growing collection of books and periodicals relating
to computers in education.”
8.Charischak,
I.
(1988). Creating Dynamic Stories with LogoWriter.
Dynamic Classroom Press. White Plains, NY.
9.CLIME
is
currently named “Council for Technology in Mathematics
Education” and has been a affiliate group of NCTM
since 1988. Its current publication is “CLIME
Connections.” http://climeconnections.blogspot.com
10.Newsletter
“Scenes
from a Dynamic Classroom – featuring LogoWriter and
LEGO TC Logo.” (1989-1990) Current version is the blog
titled “Math 2.0: Scenes from a Dynamic Math
Classroom” http://dynamicmathclassroom.blogspot.com
2.CIESE
model
for lesson implementation in a nutshell:
·Step 1: Set the stage.
Engage the students. This is more than just a simple
anticipatory set. It is about engagement.
·Step 2: Do the activity. My
setting the stage was leading up to something. This is
where you do the “something.” (Example will follow
later in the chapter.)
·Step
3: Debrief. Ask the students what they learned today.
It can take 5 minutes. This part is critical.
Otherwise the point of the lesson (activity, etc) may
be lost in the shuffle of the kids moving on to the
next activity or class.
3.An update to the 2000
principles and standards was published in Feb, 2014
called “Principles to Actions – Ensuring Mathematical
Success for All.” In this update the technology
principle became Tools and Technology and included the
use of manipulatives such as Geoboards and Cuienaire
Rods. http://www.nctm.org/PrinciplestoActions/
7.Source: “Focus in High
School Mathematics Technology to Support Reasoning and
Sense Making.” Chapter 5. Simulations as a Path to
Making Sense of Probability, p. 69
9.I took a BASIC program
Popshot from the CURSOR magazine collection in 1980
and turned it into Place Value Popshot which helped my
6th grade students with reviewing their
place values in decimal numbers in a fun way.
10.Leron, U. (1985). Logo
today: Vision and reality. The Computing Teacher,
12,26-32. Uri describes the tension caused by Papert’s
initial insistence of Logo being taught free form
without teachers and curriculum and those that felt
that the teacher’s role in Logo environment was
important as was developing curriculum materials that
would support Paperts notion of powerful ideas. Papert
did eventually concede that when writing “Mindstorms”he didn’t
take into consideration enough the needs of teachers.
11.Papert
(1980)
gave a first formal definition of a microworld in his
book Mindstorns as a: “...subset of reality or a
constructed reality whose structure matches that of a
given cognitive mechanism so as to provide an
environment where the latter can operate effectively.
The concept leads to the project of inventing
microworlds so structured as to allow a human learner
to exercise particular powerful ideas or intellectual
skills. ”(Mindstorms, p. 204)
2.Roger Schank, Teaching Minds: How Cognitive Science
Can Save our Schools, Chapter 8. pgs 89-90.
3.The idea behind Fraction
Darts is an old one. Darts was created in 1973 with
support from National Science Foundation. The authors
were Sharon Dugdale and David Kibbey. Many versions of
the program have appeared since. The version I'm
currently using was written in Flash in 2005 by Jason
Sayres for CIESE.
Ricky Carter and Robert Berkman collaborated
with me on a Logo version of Darts that I used in my
workshop for years. Jason Sayers version is easier to
use and looks spiffier but it’s a closed microworld,
Access to the HTML part of the code allows for some
modification e.g. specific placement and size of the
balloons. Altering it further would require knowledge
of Flash. It would be great if someone wrote an open
source version in Scratch (or equivalent) that allows
for altering the code.
2.Gary Stager. Learning Adventures: A new approach
for transforming real and virtual classroom
environments. A paper written for the ACEC 2008
conference in Perth, Australia. http://stager.org/articles/72_Stager.pdf
3.From the song lyrics “Gee, Officer
Krupke” in West Side Story.
4.Here’
a
typical assessment of math students knowledge of math
in the 4th grade. According to Conceptua
Math in their youtube video (http://www.youtube.com/watch?v=RcINoiD6n_s)
when students hit 4th grade, many begin to
lose confidence in their ability to do math. Like most
vendors Conceptua math has something special that they
believe flattens the fractions barrier for most
students and will prep them properly to pass the
tests. But how well do they do that is still an open
question in my mind.
5.“Given what we
know about learning, how can new technological tools
help promote great teaching and learning?" The good
news and bad news about technology and learning are
one and the same. Schools have not yet begun to
systematically tap learning science through technology
to deepen, accelerate, and nurture learning. The "bad"
here is obvious. So what's the “good” news? It’s that,
since we mostly haven't figured out the right way to
put things together, we're in a position to make
enormous progress by tapping emerging tools and
technologies the right way. Hess, F. Breakthrough
Leadership in the Digital Age: Using Learning Science
to Reboot Schooling, p. xiii. http://www.amazon.com/Breakthrough-Leadership-Digital-Age-Schooling/dp/1452255490
8.A
professor of math education used the Weird Number
video as a motivator for a lesson development
assignment by his students. Here’s what they came up
with. http://edu320.blogspot.com/2006/09/weird-number.html
11.This part is based on an
article I wrote for ISTE (International Society for
Technology in Education) entitled “In the Spirit of
Eratosthenes: Measuring the Circumference of the
Earth” in 1998.
1.
Papert, S. (1980) Mindstorms. Basic Books. p. viii
2.Barry
Fishman
quote taken from “It’s Not About the Technology,” Teachers College Record, Date
Published: July 06, 2006http://www.tcrecord.org
ID Number: 12584, Date Accessed: 7/13/2006 2:27:31 PM