Tmn 3704 revision guide
,CHAPTER
EXPLORING WHAT IT MEANS TO DO MATHEMATICS
Traditional views of mathematics
Traditional teaching, still the predominant instructional pattern, typically begins with an explanation of what
ever idea is on the current page of the text followed by showing children how to do the assigned exercises.
Even with a hands on activity, the traditional teacher is guiding students, telling them exactly how to use the
materials in the prescribed manner. The focus of the lesson is primarily on getting answers. Students rely
on the teacher to determine if their answers are correct.
Mathematics as a science of pattern and order
Mathematics is the science of pattern and order. Science is a process of figuring things out or making
sense of things. It begins with problem-based situations. Although you may never have thought of it in quite
,this way, mathematics is a science of things that have a pattern of regularity and logical order. Finding and
exploring this regularity order and then making sense of it is what doing mathematics is all about.
The world is full of pattern and order: in nature, in art, in buildings, in music. Pattern and order are found in
commerce, science, medicine, manufacturing, and sociology. Mathematics discovers this order, makes
sense of it, and uses it in a multitude of fascinating ways, improving our lives and expanding our
knowledge.
What does it mean to do mathematics?
Doing mathematics = engaging in the science of pattern and order
There is a time in a place for drill but drill should never come before understanding.
The verbs of doing mathematics are:
Explore
Investigate
Conjecture
Solve
Justify
Represent
Formulate
Discover
Construct
Verify
Explain
Predict
Develop
Describe
Use
These are science verbs indicating the process of making sense and figuring out.
What is basic in mathematics?
The most basic idea in mathematics is that mathematics makes sense!
Everyday students must experience that mathematics makes sense.
Students must come to believe that they are capable of making sense of mathematics.
Teachers must stop teaching by telling and start letting students make sense of the mathematics
they are learning.
To this end, teachers must believe in the student’s - all of them!
An environment for doing mathematics
The classroom must be an environment where doing mathematics is not threatening and where
every student is respected for his or her ideas.
Students should feel comfortable taking risks, knowing that they will not be ridiculed if they are
wrong.
The teacher’s role is to create this spirit of enquiry, trust, and expectation.
The focus is on students actively figuring things out, testing ideas and making conjectures,
developing reasons and offering explanations.
No answer book
In the real world of problem solving outside the classroom, there are no teachers with answers and no
answer books. Doing mathematics includes deciding if an answer is correct or and why. It also includes
being able to justify your reasoning to others.
1
, 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.
2
,CHAPTER
EXPLORING WHAT IT MEANS TO DO MATHEMATICS
Traditional views of mathematics
Traditional teaching, still the predominant instructional pattern, typically begins with an explanation of what
ever idea is on the current page of the text followed by showing children how to do the assigned exercises.
Even with a hands on activity, the traditional teacher is guiding students, telling them exactly how to use the
materials in the prescribed manner. The focus of the lesson is primarily on getting answers. Students rely
on the teacher to determine if their answers are correct.
Mathematics as a science of pattern and order
Mathematics is the science of pattern and order. Science is a process of figuring things out or making
sense of things. It begins with problem-based situations. Although you may never have thought of it in quite
,this way, mathematics is a science of things that have a pattern of regularity and logical order. Finding and
exploring this regularity order and then making sense of it is what doing mathematics is all about.
The world is full of pattern and order: in nature, in art, in buildings, in music. Pattern and order are found in
commerce, science, medicine, manufacturing, and sociology. Mathematics discovers this order, makes
sense of it, and uses it in a multitude of fascinating ways, improving our lives and expanding our
knowledge.
What does it mean to do mathematics?
Doing mathematics = engaging in the science of pattern and order
There is a time in a place for drill but drill should never come before understanding.
The verbs of doing mathematics are:
Explore
Investigate
Conjecture
Solve
Justify
Represent
Formulate
Discover
Construct
Verify
Explain
Predict
Develop
Describe
Use
These are science verbs indicating the process of making sense and figuring out.
What is basic in mathematics?
The most basic idea in mathematics is that mathematics makes sense!
Everyday students must experience that mathematics makes sense.
Students must come to believe that they are capable of making sense of mathematics.
Teachers must stop teaching by telling and start letting students make sense of the mathematics
they are learning.
To this end, teachers must believe in the student’s - all of them!
An environment for doing mathematics
The classroom must be an environment where doing mathematics is not threatening and where
every student is respected for his or her ideas.
Students should feel comfortable taking risks, knowing that they will not be ridiculed if they are
wrong.
The teacher’s role is to create this spirit of enquiry, trust, and expectation.
The focus is on students actively figuring things out, testing ideas and making conjectures,
developing reasons and offering explanations.
No answer book
In the real world of problem solving outside the classroom, there are no teachers with answers and no
answer books. Doing mathematics includes deciding if an answer is correct or and why. It also includes
being able to justify your reasoning to others.
1
, 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.
2
