Notes (3/15/15)
Prologue
 Yero, J. (2002). Teaching in Mind How Teacher Thinking
Shapes Education. Hamilton, MT: MindFlight Publishing.
 Barry Fishman quote taken from “It’s Not About the
Technology,” Teachers College Record, Date Published:
July 06, 2006 http://www.tcrecord.org
ID Number: 12584
Chapter 1
 Boehmig, S. P. (2006) Pittsburgh’s South Side. Arcadia
Publishing. Charleston, SC.
 Henry Chadwick is also credited with first devising
this statistic, which caught on as a measure 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 winloss record was
considered sufficient in determining their
effectiveness.
 Albert, J., Bennett, J. (2001) Curve Ball Baseball,
Statistics, and the Role of Chance in the Game.
Copernicus Books. NY. p. 2.
 “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
selfpaced 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
 TEMAC Programmed Learning Materials. (1962)
Encyclopedia Britannica Press. Chicago IL.
Chapter 2
 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 firstyear 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.”
Chapter 3
 Pelky, J. (2007) Entrepreneurial Capitalism and
Innovation: A History of Computer Communications
19681988. Chapter 1 Data Communications: Emergence
19561968 Modems and Multiplexers. http://www.historyofcomputercommunications.info/Book/1/1.7EuphoricMarketsVentureCapital6768.html#_ftnref73
Chapter 5
 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: http://en.wikipedia.org/wiki/Mary_P._Dolciani
 Madison Math was a curriculum developed by Robert
Davis at Syracuse University piloted at 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 19661972. His twitter handle is: @themathman. See
blog entry. http://climeconnections.blogspot.com/2010/08/madisonprojectbobdavisandmathman.html
 Links for Pick’s Theorem: http://en.wikipedia.org/wiki/Pick%27s_theorem.
Henri Picciotto’s blog. http://blog.mathedpage.org/2014/01/provingpicksformula.html
 http://www.amazon.com/MathematicalSnapshotsDoverRecreationalMath/dp/0486409147
 Clipped from my blog entry (Dynamic Math Classroom #60
Nov 26, 2012.) http://dynamicmathclassroom.blogspot.com/2012/11/athrowbacktonewmathdaysoflate.html
 Harold Jacobs. (1972) Mathematics: A Human Endeavor. I
used edition 1. http://www.valorebooks.com/textbooks/mathematicsahumanendeavoratextbookforthosewhothinktheydontlikethesubjectharoldrjacobshardcover/9780716704393#default=buy&utm_source=Froogle&utm_medium=referral&utm_campaign=Froogle&date=07/14/14
(Available for $.01)
 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 eighthgrade 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 eighthgrade 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 wellwritten 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
 Maeroff, G. (1975) Junior High is not Easy to Handle.
Lakeland Ledger. Lakeland, FL.
 http://news.google.com/newspapers?nid=1346&dat=19751214&id=mkdNAAAAIBAJ&sjid=4foDAAAAIBAJ&pg=6818,3677755
 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/thebooks/.
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.
 The openclassroom 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
 Cursor Magazine CURSOR  Programs for PET Computers
was the name of an early computerbased "magazine" that
was distributed on cassette from 1978 and into the early
1980s.
Chapter 7
 http://www.penguin.com/book/whywedowhatwedobyedwardldeci/9780140255263?strSrchSql=deci/Why_We_Do_What_We_Do_Edward_L._Deci
 http://theagenda.tvo.org/blog/agendablogs/guestpostwhykhanacademynotanswer
 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
 My Scratch program. http://scratch.mit.edu/projects/10517644/
 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, 171185. New York:
Academic Press, 1982.
Chapter 8
 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
 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
 Toni Stone’s obituary: http://www.edc.org/newsroom/articles/antonia_stone_19302002
 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.” Compute! Magazine Issue 003.March, April,
1980. https://archive.org/stream/198003computemagazine/Compute_Issue_003_1980_Mar_Apr_djvu.txt
 Papert , S. (1980) Mindstorms: Children, Computers,
and Powerful Ideas. Basic Books. NY. http://www.amazon.com/MindstormsChildrenComputersPowerfulIdeas/dp/0465046746
 Ibid. p. viii
 Tammet, D. (2013) Thinking In Numbers: On Life, Love,
Meaning, and Math. Little Brown & C. (p. 136) http://www.amazon.com/ThinkingInNumbersLifeMeaning/dp/0316187372
 Charischak, I. (1988). Creating Dynamic Stories with
LogoWriter. Dynamic Classroom Press. White Plains, NY.
 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
 Newsletter “Scenes from a Dynamic Classroom –
featuring LogoWriter and LEGO TC Logo.” (19891990)
Current version is the blog titled “Math 2.0: Scenes
from a Dynamic Math Classroom” http://dynamicmathclassroom.blogspot.com
Chapter 9
 http://www.onetohio.org/library/Documents/Dr%20Madeline%20Hunter%20Article1.pdf
 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.
 http://climeconnections.blogspot.com/2013/04/empoweringclassroomandbeyond.html
 Steinberg, L. (1996) Beyond the Classroom. Simon &
Schuster. NY. Steinberg discusses this “lack of
engagement” problem throughout the book. http://www.amazon.com/BeyondClassroomSchoolReformParents/dp/0684835754
 Gardner, H. (1991) The Unschooled Mind. BasicBooks. p.
150.
 Papert, S. (2000) What’s the big idea? Toward a
pedagogy of idea power. IBM SYSTEMS JOURNAL. Vol 39, Nos
3 & 4.
 http://dynamicmathclassroom.blogspot.com/2013/06/thefamousjinxpuzzle.html
 Family Fractions activity in Elizabeth http://www.ciese.org/math/elizabeth/family.html
Chapter 10
 NCTM. (2000) Principles and Standards for School
Mathematics. p. 2425
 Guiding Principles for Mathematics Curriculum and
Assessment. http://bit.ly/1CiOrZd
 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/
 Source: http://climeconnections.blogspot.com/2009/07/whatismath20.html
describes a webinar titled “Where is Math 2.0?”
 As of August 2, 2012 Key Curriculum was acquired by
McGraw Hill. See http://blogs.edweek.org/edweek/marketplacek12/2012/08/mcgrawhill_acquires_math_technology_co_key_curriculum.html
 http://en.wikipedia.org/wiki/VisiCalc
 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.
 Devlin, K. Blog entry. What is algebra? http://profkeithdevlin.org/2011/11/20/whatisalgebra/
 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.
 Leron, U. (1985). Logo today: Vision and reality. The
Computing Teacher, 12,2632. 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.
 In Mindstorms Papert gave his first formal definition
of a microworld 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)
 Steve Hargadon’s article http://www.stevehargadon.com/2008/03/web20isfutureofeducation.html
 Solomon, G. (2007) web 2.0 – new tools, new schools.
ISTE. p. 2
 Dan Myer’s blog. http://blog.mrmeyer.com
 http://www.livingmath.net
 http://www.longtail.com/the_long_tail/faq/
Chapter 11
 David Thornburg (2013) From the Campfire to the
Holodeck: Creating Engaging and Powerful 21st Century
Learning Environments. JosseyBass. http://www.amazon.com/CampfireHolodeckCreatingEngagingEnvironments/dp/1118633938/ref=sr_1_1?s=books&ie=UTF8&qid=1401806515&sr=11&keywords=holodeck
 Roger Schank, Teaching Minds: How Cognitive Science
Can Save our Schools, Chapter 8. pgs 8990.
 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.
 See http://mathforum.org/library/drmath/view/74057.html
for a proof that the midpoint between two fractions is
the average of the numerators divided by the average of
the denominators.
 Graphing Equations and Green Globs. http://greenglobs.net
 Gewirtz, C. (2011) Curriculum Definition Raises Red
Flags. Education Week. http://www.edweek.org/ew/articles/2011/03/23/26curriculum.h30.html
Chapter 12
 Zoombinis  http://www.iwitts.org/provenpractices/retentionsubtopics/womenandmath/327zoombinisandtheartofmathematicalplay
 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
 From the song lyrics “Gee, Officer Krupke” in West
Side Story.
 Here’s 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.
 “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/BreakthroughLeadershipDigitalAgeSchooling/dp/1452255490
 Xerox, 1970. The Weird Number. The Fractionville
activity I wrote about in Chapter 9 was inspired by this
video. https://www.youtube.com/watch?v=pSO66sL9SmY
 Read more about the Hippasus story in Brian Clegg’s “A
dangerous Ratio” http://nrich.maths.org/2671
 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/weirdnumber.html
 http://stockmarketgame.org
 http://www.ciese.org/math/elizabeth/Stocks6thgrade.html
 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. http://dmcpress.org/articles/SpiritEratArticle.ic.pdf
 http://www.amazon.com/TheLibrarianWhoMeasuredEarth/dp/0316515264
 According to Carl Sagan’s book “Cosmos” Eratosthenes
hired a surveyor to pace the distance from Syne to
Alexandria approximately 800 kms.
 http://ciese.org/curriculum/noonday
Chapter 13
 Papert, S. (1980) Mindstorms. Basic Books. p. viii
 Barry Fishman quote taken from “It’s Not About the
Technology,” Teachers College Record, Date Published:
July 06, 2006 http://www.tcrecord.org
ID Number: 12584
