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:
1900-1920 Throndike - Harvard psychologist, S-R bond forming through drill Dewey - Chicago, social perspective, learning by doing, used materials
1920's 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 operations. Wm. Brownell - "Meaning Theory of arithmetic" - meaning would come from the math itself, activities provide only the context through which to learn math. 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.
1950's Behaviorism is still the dominant psychological perspective, and drill and practice continues to be dominant in math classrooms
1955 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.
1960's 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 horizontally) 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
1970's "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"
1980's 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.
1990's 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 >email@example.com. 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 firstname.lastname@example.org