PST201 F Study Notes
PST 201-F STUDY NOTES
CHAPTER 1
TEACHING MATHEMATICS IN THE ERA OF NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS (NCTM) STANDARDS
Principles and Standards for School Mathematics
The six principles for school mathematics
Equity – high expectations and strong support for all students
Curriculum – must be coherent, focused on important mathematics and well articulated.
Teaching – understand math; understand how children learn math; select tasks and strategies to maximise learning.
Learning – students must learn actively, building new knowledge from experience and prior knowledge.
Assessment – support learning of math and provide info for both teacher and learner
Technology – essential, it influences what is taught and enhances learning.
The five Content Standards (or strands of mathematics)
Number and operations
Algebra
Geometry
Measurement
Data Analysis and Probability
The five process standards
Problem solving
Reasoning and proof
Communication
Connections
Representation
These refer to the process through which students should acquire and use mathematical knowledge.
N.B SEE TABLE 1.1, PAGE 4 OF TEXT
The Professional Standards for Teaching Mathematics
Teachers must shift from a teacher-centred to a child-centred approach in their instruction.
Five shifts in Classroom Environment
The introduction to the professional standards lists five major shifts in the environment of the mathematics classroom that are necessary to allow students to develop mathematical power. Teachers need to shift
Toward classrooms as mathematics communities and away from classrooms as simply a collection of individuals
Toward logic and mathematical evidence as verification and away from the teacher as the sole authority for right answers
Toward mathematical reasoning and away from mere memorising procedures
Toward conjecturing, inventing, and problem solving and away from an emphasis on the mechanistic finding of answers
Towards connecting mathematics, its ideas, and its
CHAPTER 1
TEACHING MATHEMATICS IN THE ERA OF NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS (NCTM) STANDARDS
Principles and Standards for School Mathematics
The six principles for school mathematics
Equity – high expectations and strong support for all students
Curriculum – must be coherent, focused on important mathematics and well articulated.
Teaching – understand math; understand how children learn math; select tasks and strategies to maximise learning.
Learning – students must learn actively, building new knowledge from experience and prior knowledge.
Assessment – support learning of math and provide info for both teacher and learner
Technology – essential, it influences what is taught and enhances learning.
The five Content Standards (or strands of mathematics)
Number and operations
Algebra
Geometry
Measurement
Data Analysis and Probability
The five process standards
Problem solving
Reasoning and proof
Communication
Connections
Representation
These refer to the process through which students should acquire and use mathematical knowledge.
N.B SEE TABLE 1.1, PAGE 4 OF TEXT
The Professional Standards for Teaching Mathematics
Teachers must shift from a teacher-centred to a child-centred approach in their instruction.
Five shifts in Classroom Environment
The introduction to the professional standards lists five major shifts in the environment of the mathematics classroom that are necessary to allow students to develop mathematical power. Teachers need to shift
Toward classrooms as mathematics communities and away from classrooms as simply a collection of individuals
Toward logic and mathematical evidence as verification and away from the teacher as the sole authority for right answers
Toward mathematical reasoning and away from mere memorising procedures
Toward conjecturing, inventing, and problem solving and away from an emphasis on the mechanistic finding of answers
Towards connecting mathematics, its ideas, and its