What Does Successful Geometry Curriculum Look Like?

Emily PlunkettNovember 25, 2008

History of Geometry and Geometry Curriculum

Important Geometry Events

• Pythagoras and his followers made many advancements around 500 B.C.

• Elements by Euclid about 300 B.C.

• 19th Century saw development of non-Euclidean geometry

Important Curriculum Advancements

• Geometry education moved into secondary education in the mid-1800s

• Geometry education became a part of primary school mathematics curriculum at the turn of the 20th century

ON GOING DEBATES

• Place of non-Euclidean geometry

• Place of informal geometry

• Place of formal proofs

• Is geometry the best place to teach students the axiomatic nature of math?

US Curriculum

• There is not a federal curriculum.• Standards published by National Council of

Teachers of Mathematics (NCTM) are used as the guide for most states.

• No Child Left Behind Act of 2000 mandates that states have a curriculum that is tested in key years.

NCTM Standards

NCTM Standards for Geometry

These principles are Instructional programs that students from prekindergarten through grade 12 should enable to— * analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; * specify locations and describe spatial relationships using coordinate geometry and other representational systems; * apply transformations and use symmetry to analyze mathematical situations; * use visualization, spatial reasoning, and geometric modeling to solve problems.

Two guiding ideas:1. Need for real world representation, application, and problem solving.2. Introduction of axioms and proofs.

Geometry Lesson Example

http://www.teachertube.com/view_video.php?viewkey=535e0b862ae12245c890

NORTH CAROLINA

Statistics on Geometry EOC in North Carolina

In 2006 – 2007, 78021 students took the EOC for Geometry and 49882 passed making the percent proficient 63.9.

In 2006 – 2007, Durham County had 45% proficient.

In 2006 – 2007, Hillside High School had only 37% proficient.

Iran- General Info

• World’s largest youth population• General Education– Obligatory:

• 5 years of primary • 3 years of lower secondary

– Optional:• 3 years of upper secondary• 1 year of pre-university

• One track in secondary school is Mathematics and Physics

• National Curriculum

Geometry Curriculum in Iran

On the Books• Last reform 1992-1993• 2 geometry classes in upper

secondary• 1 Analytic Geometry course

in pre-university• Move toward applications

and problem solving• Proofs are part of the

curriculum but not the focus

In Practice• Many teachers did not follow

the reforms of 1992-1993• Most teachers stay strictly to

an axiomatic, proof driven geometry curriculum

• Studies have been done to confirm students mostly memorize and repeat procedures in geometry courses within Iran

England – General Info

• National curriculum designated by the Ministry of Education

• School is compulsory until age 16• During the last decade and a half, many

educational reforms have been put in place specially in mathematics.

Geometry Curriculum in England

• Process oriented approach• Proofs are studied as a place to make a

hypothesis and test it • No formal study of proof• Hands-on activity is emphasized• Applications

Spectrum of Geometry Curriculum

Which is best?

There is not much research on which is most effective.

Further Research

1. Which curriculum leads to best understanding in geometry?2. How do application problems factor into students

understanding and retention of the material?3. How important are formal proofs to mathematics and

success in mathematics at the university level?

References• Coleman Jr, Robert. The Development of Informal Geometry. New York: Columbia University, 1942.• Education in Iran. “The Iranian Educational System” 23 Nov. 2008. <

http://www.iranchamber.com/education/articles/educational_system.php>• Education Reform. “Education Reform Lessons from England” 23 Nov. 2008 <

http://www.educationsector.org/analysis/analysis_show.htm?doc_id=344385> • Euclid. 22 Nov. 2008 <http://cs.clarku.edu/~djoyce/java/elements/elements.htm>.• Gooya, Zahra. “Mathematics teachers’ beliefs about a new reform in high • school geometry in Iran.” Educational Studies in Math 65 (2007): 331-347.• Hoyles, C and Jones, K., Proof in Dynamic Geometry Contexts. Ed. Mammana and V. Villani, Perspectives on the

Teaching of Geometry for the 21st Century. Dordrecht: Kluwer (1998): 121-128. • Masingila, Joanna O. “Secondary Geometry: A Lack of Evolution.” School Science and Mathematics 93 (1993): 38-44.• MSN Geometry. “Geometry” 23 Nov. 2008 <http://encarta.msn.com/encyclopedia_761569706_6/geometry.html>.• MSN United Kingdom. “United Kingdom” 23 Nov. 2008. <

http://uk.encarta.msn.com/text_761553483__1/United_Kingdom.html>. • NCTM. Principles and Standards for School Mathematics. Oregon: Graphic Arts Center, 2000.• Timeline. “A Time-line for the History of Mathematics” 22 Nov. 2008. <

http://www.math.wichita.edu/~richardson/timeline.html>.• http://www.teachertube.com/view_video.php?viewkey=535e0b862ae12245c890 • http://www.ncreportcards.org/• http://www.flags.net/