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“Higher Standards for Our Students...

NCTM Presents

Higher Standards for Ourselves”

Principles• Learning

• Assessment

• Technology

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• Teaching

• Assessment

• Technology

Principles

The principles describe particular features of high-quality mathematics programsThe principles describe particular features of high-quality mathematics programs

• Equity

• Curriculum

• Learning

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Using Principles to Prepare Students

Equity

Curriculum

Technology

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Statement of PrinciplesThe Learning PrincipleStudents must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.

The Assessment Principle

Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.

The Technology Principle

Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.

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Learning

• Learning mathematics with understanding is essential, and

• Students can learn mathematics with understanding

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Learning mathematics with understanding is essential.

Three components of mathematics proficiency:

• Conceptual understanding;• Conceptual understanding;• Factual knowledge; and

• Conceptual understanding;• Factual knowledge; and• Procedural facility.

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Learning mathematics with understanding is essential.

• Learning with understanding makes subsequent learning easier.

• Mathematics makes more sense and is easier to remember and to apply when students connect new knowledge to existing knowledge in meaningful ways.

• Mathematics makes more sense and is easier to remember and to apply when students connect new knowledge to existing knowledge in meaningful ways.

• Well-connected, conceptually grounded ideas are more readily accessed for use in new situations .

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Students can learn mathematics

with understanding. • Students have a natural desire to understand

what they are asked to learn. • Students have a natural desire to understand

what they are asked to learn.

• Students' understanding of mathematical ideas can be built throughout their school years if they actively engage in tasks and experiences designed to deepen and connect their knowledge.

continued

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Students can learn mathematics

with understanding. • Classroom discourse and social interaction can

be used to promote the recognition of connections among ideas and the reorganization of knowledge .

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Assessment

• Enhance student learning, and

• A tool for making instructional decisions

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Assessment should enhance student’ learning.

• Good assessment enhances students' learning.

• Good assessment enhances students' learning.

• It is important that assessment tasks be worthy of students' time and attention.

• Good assessment enhances students' learning.

• It is important that assessment tasks be worthy of students' time and attention.

• A focus on self-assessment and peer assessment has been found to have a positive impact on students' learning.

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Assessment is a valuable tool for making instructional decisions.

• To ensure deep, high-quality learning for all students, assessment and instruction must be integrated so that assessment becomes a routine part of the ongoing classroom activity.

• Assessment is the primary source of information used by teachers in making instructional decisions.

• Assessment is the primary source of information used by teachers in making instructional decisions.

• Assessment should reflect the mathematics that all students need to know and be able to do.

continued

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Assessment is a valuable tool for making instructional decisions.

• Assessment should focus on students‘ understanding as well as their procedural skills.

• Assessments should allow for multiple approaches, thus giving a well-rounded picture and allowing each student to show his or her best strengths.

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Technology

• Enhances mathematics learning

• Supports effective mathematics teaching

• Influences what mathematics is taught

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Technology enhances mathematics learning

• The computational capacity of technological tools extends the range of problems accessible to students.

• The computational capacity of technological tools extends the range of problems accessible to students.

• Technology enables students to execute routine procedures quickly and accurately, thus allowing more time for conceptualizing and modeling.

• The computational capacity of technological tools extends the range of problems accessible to students.

• Technology enables students to execute routine procedures quickly and accurately, thus allowing more time for conceptualizing and modeling.

• Technology offers teachers options for adapting instruction to special student needs.

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Technology supports effective mathematics teaching.

• The effective use of technology in the mathematics classroom depends on the teacher. The teacher must decide if, when, and how technology will be used.

• Technology aids in assessment, allowing teachers to examine the processes used by students in their mathematical investigations as well as the results, thus enriching the information available for teachers to use in making instructional decisions.

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Technology influences what mathematics is taught.

• Students can explore and solve problems involving large numbers.

• Students can explore and solve problems involving large numbers.

• Students can investigate characteristics of shapes using dynamic geometry software.

• Students can explore and solve problems involving large numbers.

• Students can investigate characteristics of shapes using dynamic geometry software.

• Students can be asked to work at higher levels of generalization or abstraction.

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Impact of Technology on the Mathematics Curriculum

• Some mathematics becomes more important because technology requires it.

• Some mathematics becomes less important because technology replaces it.

• Some mathematics becomes less important because technology replaces it.

• Some mathematics becomes possible because technology allow it.

NCTM Curriculum and Evaluation Standards for School Mathematics, 1989.

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Summary

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Statement of PrinciplesThe Learning PrincipleStudents must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.

The Assessment Principle

Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.

The Technology Principle

Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.

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Assignment

Read:• Principles and

Standards, pages 29-31, 211-13, and 287-89.