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Topic: History
Replies: 14   Last Post: Sep 2, 2000 3:10 PM

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David Slavit

Posts: 26
Registered: 12/6/04
Re: History
Posted: Sep 1, 2000 11:37 AM
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One *suggestion* I would make would be to accompany your history of math
discussion in tandem with a history of mathematics education, particularly
during the last century. Here are some notes I use to do this in my
methods course:

Throndike - Harvard psychologist, S-R bond forming through drill
Dewey - Chicago, social perspective, learning by doing, used materials

Incidentalists - "math as a "tool" subject", math should be taught
incidentally to doing something else (like building a box). Meaning and
structure were not stressed.

1930's and 1940's
Henry Van Engen speaks of learning the meanings in numbers as best source
for learning - not just facts or activities. I.e., the numbers themselves
contain meaning through the relationships between them via the mathematical
Wm. Brownell - "Meaning Theory of arithmetic" - meaning would come from the
math itself, activities provide only the context through which to learn
Meaning can be found in: Concepts - equations, ratio, etc.
Operations - +, -, x, /
Principles - Commutavity, Associativity
Base # system and place value
Like Dewey, Brownell also made use of materials.

Behaviorism is still the dominant psychological perspective, and drill and
practice continues to be dominant in math classrooms

Cognitive psychology is "born" and behaviorism begins to decline throughout
the 1960's. With this came the realization that there is something worth
considering besides what we can say - the mind became a legitimate thing to
study and consider, even thought it could not be directly observed.

Sputnik in 1957. Caused Congress to spend lots of money, which led to the
"New Math" movement in the 1960's. For the first time this allowed the
curriculum to be organized by mathematicians, not psychologists. They
chose sets and functions as the unifying themes. This was somewhat
successful at the H.S. level, but failed at the elementary level:
Problems were too advanced (3+_=10 - is algebra, and is written
Too much rigor - number vs. numeral
Very little attention to facilitating children's connection between
symbols and ideas
This approach also fit in well with Gagne's ideas of readiness - we should
identify all of the necessary prerequisites to a math concept or skill, and
then make sure students learn them before moving on

"Back-to-basics" movement. Emphasized drill and computation. "Our
children need to learn to compute"
The 70's also saw the beginning of Constructivism. This grew out of
theories of:
Bruner - 1960's, enactive-iconic-symbolic
Piaget - 1950's-70's, looked at qualitative tasks and conservation,
theorized that children's development psychologically influences their
learning, 3 kinds of knowledge - physical knowledge, social or conventional
knowledge, logico-mathematical knowledge
Vygotsky - Soviet from the 1920's and 30's, English translation in the
1970's, factored in the role of language and social behaviors into learning
"scientific principles"

Everybody Counts
A Nation at Risk
NCTM Standards (1989) - defined math as P.S., communication, reasoning,
connections. Based on research and constructivist philosophy.
Goal: Allow students to construct their own knowledge and understanding
via appropriate mathematical experiences that allow them to communicate and
reflect on their ideas and procedures.

Reform based on Standards unfolds, despite political turmoil it shows promise
Emphasis on middle school curriculum
State-wide, standards-based assessments have strong influence on
instruction both positively and negatively

>One of my teaching assignments for this year will be to teach math
>history to a group of primarily pre-service grades 4-9 mathematics
>teachers. I'm excited about this but am asking for some input concerning
>content for the course, textbook, resources, ways to make this material
>relevant to these students given math background and future ambitions to
>teach math in the middle grades. These students will have a background
>in our standard el. ed. math courses, algebra/trig, introductory
>statistics, finite math, and at least two quarters of calculus.
>Please send any ideas or positive suggestions via private e-mail to
> Thanks in advance for your help.
>Tena Roepke
>Ohio Northern University

David Slavit
Washington State University, Vancouver
College of Education, EHD 231
14204 NE Salmon Creek Avenue
Vancouver, WA 98686-9600
Office: 360-546-9653
Fax: 360-546-9040

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