Download Tools for Mathematics Reasoning

Tools for Mathematical Reasoning
Deductive and inductive reasoning have a long history in mathematics; however, this
does not mean that these two basic types of reasoning are used rigourously and explicitly
every time one does mathematics. A formal proof by deductive logic is a cornerstone of
the foundation of mathematics. However, even for mathematicians, it is not possible or
desirable to start from first principles (axioms) every time a problem is tackled. In most
cases, previous proofs are accepted as facts to form a body of knowledge. This body of
knowledge is used to create new knowledge, test knowledge and use it in applications
such as problem solving. All of these activities—create, test, use—involve deductive and
inductive reasoning whether this is done explicitly or implicitly.
Although there are many fields of mathematical knowledge, the concepts and procedures
from basic arithmetic, algebra, geometry and statistics are the tools often used in
mathematical reasoning.

arithmetic: deals with numbers, their properties and operations

algebra: deals with symbols and equations for showing relations, generalizing
or modeling

geometry: deals with size, shape and relative position of figures

statistics: deals with the collection and analysis of large quantities of data
Some Pitfalls of Mathematical Tools

arithmetic: inadequate consideration of constraints or conditions

algebra: confusion between symbols used as unknowns and symbols for
variables

geometry: inaccurate use of concepts or lack of internal consistency in
applying concepts to a figure

statistics: insufficient size and/or relevancy of data or evidence.
M4ReasoningTools
www.CRYSTALAlberta.ca
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