Mathematical process , Reasoning , Examples,Types of Reasoning, Argumentation, Examples How to argument, Justification and Advantages , How to justify equation.
7. MATHEMATICAL REASONING.
• Mathematical reasoning happens through
making conjectures, investigating, and
representing and finding and explains and
justifying conclusions.
• Reasoning can be thought of as the process of
drawing conclusions on the basis of evidence or
stated assumption and sence making can be
defined as developing and understanding of a
situation, context, or concept by connecting it
with existing knowledge.
8. MATHEMATICAL REASONING.
The (NCTM) National
council of teacher of
mathematics defines
reasoning as the “A
productive way of
thinking that
becomes common in
the process of
mathematical inquiry
and sence making”.
Ex:- Solve (20)^2
10. EXAMPLE OF REASONING.
Ex:- Solve 18+27=__+29
Here twenty nine is two more than 27 , So the
number which is added has to be two less
than 18 to making the eqution.
Instead of adding 18+27 then figuring out the
number to add 29 to get 45,simplify the
calculation by comparing the numbers on both
sides one who realised 29 is two more than
27.So the number added had to be two less
than 18 that is 16.
11. MATHEMATICAL
REASONING TWO TYPES.
• 1) Inductive reasoning.
• 2) Deductive reasoning.
• Inductive reasoning:-Inductive reasoning is a
logical process in which multiple premises, all
believed true or found true most of the time,
are combined to obtain a specific conclusion.
• Inductive reasoning is a method of logical
thinking that combines observations with
experiential information to reach a
conclusion.
15. DEDUCTIVE REASONING.
Deductive reasoning is a logical process
in which a conclusion is based on the
concordance of multiple premises that are
generally assumed to be true.
Example
• All numbers ending in 0 or 5 are divisible
by 5.
• The number 35 ends with a 5.
• so it must be divisible by 5.
19. ADVANTAGES OF MATHEMATICAL
REASONING.
• Helps children to think logically and
make sense of mathematics.
• Help children to test hypothesis.
• Help chldren to make predictions.
• Helps children to explain their
thinking.
22. MATHEMATICAL
ARGUMENTATION EXAMPLE
• Statement 1:- Numbers ending with 0 and 5 are
divisable by 5) How?
• Statement 2:-Numbers ending with 0 divisable
by 10.} How?
• Statement 3:- Numbers ending with 3 and 9
divisable by 2] How?
• Statement 1:-True
• Statement 2:-True
• Statement 3:-False
25. MATHEMATICAL ARGUMENTATION
ARE LIKE THIS.
• Can you explain?
• What happened before?
• What would happen if you used this number?
• What would change if.....
• Show me where.....
• What could you add to strengthen this part?
• How would that work?
26. ADVANTAGES OF
MATHEMATICAL
ARGUMENTATION.
• Discover new mathematical ideas.
• Argumentation supports for the
conclusion.
• Contributed to the class understanding.
• Tool for student reasoning.
• Provides evidence and reasoning for new
idea.
27. MATHEMATICAL JUSTIFICATION.
• Mathematical justification in a mathematical
setting teaches a important writing style,
writing a brief, information packed statement
that gives the reader a solid reason to
believe your conclusion, without wasting a
readers time.
• OR
• Mathematical justification is the use appropriate
mathematical language to give reasons for the
particular approach used to solve a problem.
28. EXAMPLE
• Determine when the first equation is cheaper than
the second
• C = 40t+200
• C=30t+300
• Developing a solution
• Students will work on the solution of the problem.
Either graphically, or by solving simultaneous
equations, the time for which costs are equal is 10
hours.
•
• Note: The time for which the first rate is more than
the second is any time greater than 10 hours.
31. ADVANTAGES OF MATHEMATICAL
JUSTIFICATION.
• Students learn better when they self justify and
and explain the solution.
• It supports logical reasoning and analytical
thinking.
• It improves problem solving skills.
• Teachers need to know how students arrive at
their answer.
• Explanations encourage students to explain the
why and not just the how.