Math 572 Home

Alignment with Standards

Goal Standards K-12 Standards Learning Experience Assessment
Students will learn how axiom systems and logical deductions (proofs) provide the foundation of mathematics
  • NCATE 1.5.9
  • CBMS Geo. 2
  • KS Lic Math 2
  • NCTM R&P
  • Regents
A pair of initial lectures on axiom systems and reasoning will be followed by a week of demonstration of how results are deduced. Students will then deduce results on their own. At the end of the course, a variant axiom system (hyperbolic geometry) will be studied and students will compare how changes in the axiom system change the mathematics. Homework and exams
 
Students will learn to read and write proofs
  • NCATE 1.5.9
  • CBMS Geo. 2
  • KS Lic Math 2
  • NCTM R&P
  • Regents
Students will work in groups to solve prove selected results and present their work to the class. Students will judge others proofs when presented. Students will also turn in written proofs and will have an assignment to find errors in false proofs. In-class assessment, homework, and exams
 
Students will learn basic ideas of synthetic geometry, especially Euclidean geometry.
  • NCATE 1.5.5
  • KS Lic Math 2
  • NCTM Geo 1
  • KS Stu Geo 1
  • Regents
Theorems proved in class by instructor and students will cover the basics of classical Euclidean geometry. Homework and exams
 
Students will learn to conjecture and prove new results.
  • CBMS Geo. 6
  • KS Lic Math 2
  • NCTM R&P
Students will conjecture new results after experimentation with dynamic geometry software. Students will then be responsible for proving their results. Homework
 
Students will understand geometric transformations.
  • CBMS 3
  • KS Lic Math 2
  • NCTM Geo 3
  • KS Stu Geo 3
  • Regents
Students will explore the effects of geometric transformations using dynamic geometry software. Afterward the class will develop in lecture a group-theoretic approach to transformations and apply this approach to the Poincare half-plane model of hyperbolic geometry. Homework and exams
 
Students will learn basic models and properties of hyperbolic geometry (a non-Euclidean geometry).
  • NCATE 1.5.5
As noted above, there will be lectures developing the Poincare half-plane model of hyperbolic geometry. These lectures will be supplemented with interactive on-line applets. The class will end by proving some basic results about hyperbolic geometry. Homework and exams
 
Students will develop communication skills to present mathematics, both in small groups and at the blackboard.
  • NCATE 1.3
  • KS Lic All 3
  • KS Lic Math 2
  • NCTM Comm.
Students will work in small groups both to develop and present proofs and when working with dynamic geometry software. Students will present proofs to the class at the blackboard. Efforts at the blackboard will be critiqued by the instructor (and possibly by other students) In-class assessment
 
Students will learn to use dynamic geometry software.
  • CBMS 6
  • KS Lic Math 2
  • KS Stu Geo 1
Students will work with dynamic geometry software in class (Geometer's Sketchpad) both to explore new conjectures and to examine the effects of geometric transformations. In-class assessment and homework

Explanation

Standards are the standards for the preparation of future teachers of mathematics developed by the following organizations.
NCATE
The National Center for Accreditation of Teacher Education Program Standards for Initial Preparation of Mathematics Teachers, prepared by the National Council of Teachers of Mathematics. References are to the standards for the preparation of grade 7-12 teachers.

CBMS
The Conference Board for the Mathematical Sciences Mathematical Draft Content Recommendations for High School Teachers

KS Lic
Licensure for Kansas Educators draft from the Kansas State Board of Education. "All" refers to the outcomes for all licensed educators and "Math" refers to the outcomes for the math concentration from early adolescent to late adolescent/adult level.

K-12 Standards are standards for K-12 students published by the following organizations.

NCTM
"Principles and Standards for School Mathematics" published by the National Council of Teachers of Mathematics. The references are all to the grade 9-12 band of the standards.

KS Stu
The Kansas Curricular Standards for Mathematics adopted by the Kansas State Board of Education. References are to the standards for grade 10.

Regents
The course description of the required geometry course for qualified admissions published by the Kansas Board of Regents.

Please report any problems with this page to bennett@math.ksu.edu