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.