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Mathematics: The History, Theories, and Implications of
Yesterday and Today
by: Tiffany Barnes Cathy Binetti Rachel Ivie
Cathy Uhl
Why take the time to learn the history of mathematics education?
To develop an understanding of the people and events that shaped the foundations of mathematics
To appreciate the importance of public opinion and the value placed on mathematics education throughout history
In the Beginning…
Evidence and documentation of tally marks, number systems, and mathematics date back to the beginning of recorded history.
Babylonians developed a number system based on place-value notation.
The Ancient Greeks
Around 2,000 B.C., the Babylonian basis of mathematics was passed on to the Greeks.
Mathematics divided into two subjects:
1. geometry
2. mathematics (divided into two forms)
a. one taught to middle class for general use.
b. one was number theory for the upper class
Contributions of Greek Mathematicians
Odd and even numbersGeometryAlgebraTrigonometryConcept of continuous numbers
Education in the Roman Empire
similar to Greek system, but had different beliefs in what was to be taught and why
taught children only what was considered necessary and practical
low opinion of mathematicsseveral Greek words were translated into
Latin
Europe: After the Fall of the Roman Empire
decline in educationfirst few centuries were very volatilethe plague devastated Europe in the 13th
century; further decline in education14th century—the concept of rote learning
was established
European Education during the Renaissance Education
major shift in ideaschildren should be taught life skills, not just
those required by their occupationprinting press invented; books more
assessable education in the 17th and 18th centuries
was influenced by the close relationship between church and state.
19th Century Brings Changes to Education
belief of the time—children should start learning mathematics and basic arithmetic as soon as they start school
math now considered the most important subject
some advances in teaching methods, but some still used rote learning
History of Mathematics Education in America
look to the past to learn from mistakes and successes
many new ideas are actually old ideas with a new name
assess present and future needs
The Early Days of American Education
1650s—2 basic tracks of education which were based on the English system:
1) elementary schools for lower economic citizens to learn reading, writing, and religion
2) Latin grammar schools for upper class boys to prepare for Harvard or Yale
Common teaching methods were: copying examples from the blackboard, recitations, skills drills, memorization
1800’s brought advances to American education
Education of the 20th century
1900—funds available for public high schools 1900-1940s—testing as assessment became common;
compulsory-education acts 1950s—Brown vs. the Board of Education; major
educational reforms after the Soviet launch of Sputnik 1960s—Civil Rights Act; Elementary and Secondary
Education Act 1970s—era of “Open Education” and “New Math” 1980s—math education focused on problem-solving;
National Board of Professional Teaching Standards established
1990s—use of manipulatives became common; high-stakes standardized testing
Current Theories and Implications
NCTM supports using manipulatives, open-ended word problems, real-world connections
less skill and drill activitiesfewer worksheetsless “right answer” math approachesmore student self-reflectiontwo instructional approaches outlined that
follow these guidelines and suggestions
Teaching Math Through Problem-Solving
big idea mentalitystudents solve problems by seeking
patterns and order; use own way of thinking
forming patterns and connections to prior knowledge enhances comprehension
metacognition important to problem-solving environment
reflections on thinking and learning
Investigations in Number, Data, and Spaces
built around four major goals:1. offer students meaningful mathematical problems
2. emphasize depth in mathematical thinking
3. guide students in communicating effectively with their teachers about the math content
4. expand the overall number of mathematically literate students
Units are presented through investigations conducted by students.
Strategies and Implications for Special Needs Students
small groups or partners work with manipulatives, math games, visual aids, and technology
adaptations can include increased time on assignments, limited number of problems, peer helpers, and open-ended problems
child-centered classroom with many different activities
technology is essential
Technology and Mathematics
more frequent use of calculators in classrooms access to online or virtual manipulatives offers a variety of real-life situations for student
practice provide motivation for struggling students allow students to self-check and monitor
themselves provides parent resources that reinforce current
strategies used in the classroom
Sample Sites for Integrating Technology
Online calculatorshttp://www.1728.com/
Online manipulativeshttp://www.matti.usu.edu/nlvm/nav/vlibrary.html
Problem Solving siteshttp://www.stfx.ca/special/mathproblems/grade5.html
Math Gameshttp://www.kidscom.com/games/tangram/tangram.html
Internet Activity Huntshttp://www.sbgmath.com/chaps_gr5.html
Parent Tutoringhttp://www.sbgmath.com/study_buddy.html
Obstacles to Integrating Technology
lack of computers and software inadequate teacher training low levels of instructional technology in
curriculum and assessment
Conclusion
Educators should continue to strive to improve instruction and to enhance students’ comprehension of mathematics.
Research results enable educators to make well-thought out and informed decisions concerning their teaching strategies.
Tremendous progress has been made in regard to math education.
References
Boyer, C.B., (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, Inc. Checkley, K. (1999, summer). Math in the Early Grades: Laying a foundation for later learning.
Curriculum Update, Association for Supervision and Curriculum Development. Dorward, J. (2002). Intuition and research: Are they compatible? Retrieved March 24, 2004,
from The National Council of the Teachers of Mathematics, Inc website: www.nctm.org
Hart, L.A. (2002). Human brain and human learning (3rd ed.). Covington, Washington: Books for Educators, Inc.
Kliman, M., Tierney, C., Russell, S.J., Murray, & Akers, J., (1998). Investigations in number, data, and space: Mathematical thinking at grade 5. White Plains, New York: Dale Seymore Publications.
Obretenov, C., (2003). History of Math Notes. Notes retrieved on February 10, 2004 from www.math.sfu.ca/histmath/math380notes/math380.html
The National Council for the Teachers of Mathematics (October, 2003). The use of technology in the learning and teaching of mathematics. Retrieved March 28, 2004, from
www.nctm.org/about/position_statements/ The National Museum of American History [NMAH], (2002). Slates, slide rules, and software:
Teaching math in America. Retrieved February 10, 2004 from the NMAH Web site: http://americanhistory.si.edu/teachingmath/
Teaching through problem solving. (n.d.). Presented at a Staff In-Service at Cheatham Hill Elementary School, 2002-03, Powder Spring, GA
Watson, E. (2000). The teaching of mathematics in ancient Greece. Retrieved January 30, 2004 from University of St. Andrews Web site: http://www.st-andrews.ac.uk/
Zemelman, S., Daniels, H., & Hyde, A. (1998). Best practice: New standards for teaching and learning in America's Schools (2nded.). Portsmouth, New Hampshire: Heinemann,
Inc.