Why take the time to learn the history of mathematics education?

1. Mathematics: The History, Theories, and Implications of Yesterday and Todayby: Tiffany Barnes Cathy Binetti Rachel IvieCathy Uhl

2. Whytake 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

3. 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.

4. 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

5. Contributions of Greek Mathematicians • Odd and even numbers • Geometry • Algebra • Trigonometry • Concept of continuous numbers

6. 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 mathematics • several Greek words were translated into Latin

7. Europe: After the Fall of the RomanEmpire • decline in education • first few centuries were very volatile • the plague devastated Europe in the 13th century; further decline in education • 14th century—the concept of rote learning was established

8. European Education during the Renaissance Education • major shift in ideas • children should be taught life skills, not just those required by their occupation • printing press invented; books more assessable • education in the 17th and 18th centuries was influenced by the close relationship between church and state.

9. 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

10. 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

11. The Early Days of American Education • 1650s—2 basic tracks of education which were based on the English system: • elementary schools for lower economic citizens to learn reading, writing, and religion • 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

12. 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

13. Current Theories and Implications • NCTM supports using manipulatives, open-ended word problems, real-world connections • less skill and drill activities • fewer worksheets • less “right answer” math approaches • more student self-reflection • two instructional approaches outlined that follow these guidelines and suggestions

14. Teaching Math Through Problem-Solving • big idea mentality • students 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

15. Investigations in Number, Data, and Spaces • built around four major goals: • offer students meaningful mathematical problems • emphasize depth in mathematical thinking • guide students in communicating effectively with their teachers about the math content • expand the overall number of mathematically literate students • Units are presented through investigations conducted by students.

16. 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

17. 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

18. Sample Sites for Integrating Technology • Online calculators http://www.1728.com/ • Online manipulatives http://www.matti.usu.edu/nlvm/nav/vlibrary.html • Problem Solving sites http://www.stfx.ca/special/mathproblems/grade5.html • Math Games http://www.kidscom.com/games/tangram/tangram.html • Internet Activity Hunts http://www.sbgmath.com/chaps_gr5.html • Parent Tutoring http://www.sbgmath.com/study_buddy.html

19. Obstacles to Integrating Technology • lack of computers and software • inadequate teacher training • low levels of instructional technology in curriculum and assessment

20. 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.

21. 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.