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An Analysis of Standards and Curriculum. How well do they fit together? Christina Gavin SEED 607 August 2, 2002.

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An analysis of standards and curriculum

An Analysis of Standards and Curriculum

How well do they fit together?

Christina Gavin

SEED 607

August 2, 2002


Back in 1989, The National Council of Teachers of Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?


Nctm standards vs sol s
NCTM Standards vs. SOL’s Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?


Nctm standards vs text
NCTM Standards vs. Text Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?

  • Glencoe Geometry: Integration, Applications, Connections. (1998). NY, NY: McGraw Hill.


Nctm standards vs taught curriculum
NCTM Standards vs. Taught Curriculum Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?


Sol s vs text
SOL’s vs. Text Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?

  • Glencoe Geometry: Integration, Applications, Connections. (1998). NY, NY: McGraw Hill.


Sol s vs taught curriculum
SOL’s vs. Taught Curriculum Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?


Nctm vs sol vs text vs taught
NCTM vs SOL vs Text vs Taught Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?

NCTM

SOL’s

Text

Taught


Differences between the nctm standards and the va sol s

NCTM’s Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?

General standards

Are not subject specific

More authentic assessment needed

More technology

Less traditional

SOL’s

Specific Standards

Subject centered

Multiple Choice/

Memorization

More traditional

Differences between the NCTM Standards and the VA SOL’s.


Nctm standards
NCTM Standards Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?

  • 1: Mathematics as Problem Solving

  • 2: Mathematics as Communication

  • 3: Mathematics as Reasoning

  • 4: Mathematical Connections

  • 5: Algebra

  • 6: Functions

  • 7: Geometry from a Synthetic Perspective

  • 8: Geometry from an Algebraic Perspective

  • 9: Trigonometry

  • 10: Statistics

  • 11: Probability

  • 12: Discrete Mathematics

  • 13: Conceptual Underpinnings of The Calculus

  • 14: Mathematical Structure


Nctm vs sol vs text vs taught1

NCTM Standards Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?

Virginia’s SOL’s

Text

Taught Curriculum

More process based

More product based

Some process, some product

Product based

More emphasis on using technology

Less emphasis on technology

Use of technology

Dependent on teacher

More emphasis on connections

Subject centered

Some connections to real world (in the introductions)

Subject centered

More emphasis on applications

Some application

Application examples

Dependent on teacher and time

Estimation/ approximation/ graphing

Factoring/simplifying/point-plotting

Factoring/simplifying/point-plotting. Some graphing

Factoring/simplifying/point-plotting. Some graphing

Deductive Reasoning/Paragraph Proofs

Deductive Reasoning

Deductive Reasoning/Two Column/Paragraph proofs

Some proofs

Less circle segment/

angle theorems

Circle segment/angle theorems

Circle segment/angle theorems

Circle segment/angle theorems

NCTM vs SOL vs Text vs Taught


Nctm vs sol vs text vs taught2

Geometry SOL Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?

NCTM Standard/ Taught

Text

1

1, 2, 3, 4,

1, 3

Chapter 2

2

2, 7, 8

7, 8

Chapter 1-4, 1-5, 3-3, 3-5, 4-3, 10-4,13

3

1, 7

1, 7

Chapter 3, 6

4

1, 3, 7, 8

1, 3, 7, 8

Chapter 3

5

1, 3, 7, 8

1, 3, 7, 8

Chapter 4

6

1, 4, 5, 7

5, 7,

Chapter 4, 5

7

1, 4, 5, 7, 9,

5, 7, 9

Chapter 8

8

1, 2, 3, 4, 5, 7,

1, 5, 7

Chapter 6

9

1, 2, 5, 8,

5, 8

Chapter 10

10

1, 2, 3, 4, 5, 7, 10

1, 3, 5, 7

Chapter 9

11

8

8

Chapter 1, 2

12

1, 2, 3, 4, 7,

1, 4, 7

Chapter 11, 13 (?)

13

1, 2, 5, 7,

1, 5, 7

Chapter 11

14

1, 2, 3, 4, 5, 6, 7,

1, 3, 5, 7

Chapter 10 (?)

15

1, 2, 5, 8,

1, 5, 8

Chapter 12

NCTM vs SOL vs Text vs Taught


Cautions between sol s and nctm s
Cautions between SOL’s and NCTM’s. Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?

  • Problem Solving vs. Application

  • NCTM move away from Standard 7, SOL emphasis on Standard 7

  • The teaching is a large factor on the correlation between standards.

  • Time is a big pressure.

  • SOL’s are tested; NCTM Standards are not.


Interpretation
Interpretation Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?

  • SOL’s state types of problems that students need to be able to do.

  • NCTM standards show how the students should be able to use and connect these problems.

  • These two can only overlap well, when they are taught simultaneously.

  • Textbooks cannot dominate learning for this to happen.

  • Professional Development to incorporate NCTM standards within the curriculum is a necessity.

  • More time needs to be given to each concept in order to cover the NCTM standards, rather than incorporating all concepts covered in the SOL’s.


Interpretation1
Interpretation Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?

  • Can a student move from VA to another state and do well?

    • Does the other state standards line up with VA?

    • Does the teacher incorporate the NCTM Standards.

    • The use of NCTM standards nationally will greatly address the problem of moving from state to state, because students will be learning connections between concepts rather than just rote memorization of concepts.


References
References: Mathematics published their standards for Grades 9-12. Those standards altered the ideas of what a mathematics curriculum should include. How well have those standards changed what is actually a part of the mathematics curriculums and state standards today?

  • Glencoe Geometry: Integration, Applications, Connections. (1998). NY, NY: Glencoe/McGraw Hill.


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