PROBLEM SOLVING AND REASONING Flashcards

1
Q

is drawing a general conclusion from a repeated observation or limited sets of observations of specific examples.

A

Inductive Reasoning

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

specific case to general case.

A

Inductive Reasoning

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Conjecture

A

is drawing conclusion using inductive reasoning.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

The conjecture may be true or false depending on the truthfulness of the argument.

A

True

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Is this example of conjecture or not?

1 is an odd number.
11 is an odd number.
21 is an odd number.

Thus, all number ending with 1 are odd numbers.

A

Conjecture

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

is drawing general to specific examples or simply from
general case to specific case.

A

Conjecture

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Deductive starts with ?

A

a general statement (or hypothesis)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Logical reasoning may be valid but nit necessarily true.

A

True

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Srinivasa Ramanujan wrote a letter to Godfrey Harold Hardy on

A

infinite sums, products, fractions, and roots.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Intuitive can be found in mathematical literature and discovery.

A

True

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Ramanujan’s formulas prove there is

A

mathematical intuition,
though he didn’t prove them.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

made a sound judgment without directly proving the formulas of Ramanujan’s were correct.

A

Hardy

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

a reliable mathematical belief without being
formalized and proven directly and serves as an essential part of mathematics.

A

Mathematical intuition

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

carries a heavy load of mystery and ambiguity and it is not legitimate substitute for a formal proof.

A

intuition

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

is being visual and is absent from the rigorous formal or abstract version.

A

Intuitive

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

As a student, you can build and improve your intuition by doing the following :

A

i. Be observant and see things visually towards with your critical thinking.
ii. Make your own manipulation on the things that you have noticed and observed.
iii. Do the right thinking and make a connections with it before doing the solution.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

A __________ demonstrates that a certain statement is always true
in all possible cases.

A

mathematical proof

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

is an essential defining attribute of mathematics and
mathematical knowledge.

A

Mathematical certainty

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

By definition, a _________ is an inferential argument for a mathematical statement
while __________ are an example of mathematical logical certainty.

A

proof, proofs

20
Q

Let us say P and Q are two propositions. In an if-then statement, proposition P would be the ___________ while the proposition Q would be our
___________ denoted by: _____

A

hypothesis, conclusion, P → Q

21
Q

TWO WAYS ON HOW TO PRESENT THE PROOF

A

a. Outline Form
b. Paragraph Form

22
Q

Proposition: If P then Q.
1. Suppose/Assume P
2. Statement
3. Statement
.
.
. Statement
Therefore Q .

A

a. Outline Form

23
Q

Proposition: If P then Q.

Assume/Suppose P. ____________. ___________.

_____________________. ____________ . . . _____________. _______________.
Therefore Q.

A

b. Paragraph Form

24
Q

is a mathematical argument that uses rules of inference to derive the conclusion
from the premises.

A

direct proof

25
The steps in taking a direct proof would be:
1. Assume P is true. 2. Conclusion is true.
26
is a type of proof in which a statement to be proved is assumed false and if the assumption leads to an impossibility, then the statement assumed false has been proved to be true.
Indirect proof or contrapositive proof
27
In an indirect proof, let us say we need to prove a given theorem in a form of P → Q. The steps or outline in taking an indirect proof would be:
27
In an indirect proof, let us say we need to prove a given theorem in a form of P → Q. The steps or outline in taking an indirect proof would be:
Assume/Suppose ~Q is true. . . . Therefore ~P is true.
28
There is a special name for an example that disproves a statement
COUNTEREXAMPLE.
29
This method works by assuming your implication is not true, then deriving a contradiction.
Proving by Contradiction
30
Proof by contradiction is given by this way;
1. Assume p is true. 2. Suppose that ~q is also true. 3. Try to arrive at a contradiction. 4. Therefore q is true
31
Proof by contradiction is given by this way; (give the four steps)
1. Assume p is true. 2. Suppose that ~q is also true. 3. Try to arrive at a contradiction. 4. Therefore q is true
32
POLYA’S FOUR-STEPS IN PROBLEM SOLVING
Step 1: Understand the problem. Step 2: Devise a plan. Step 3: Carry out the plan. Step 4: Look back.
33
was a mathematics educator who strongly believed that the skill of problem solving can be taught.
George Polya (1887-1985)
34
was a mathematics educator who strongly believed that the skill of problem solving can be taught.
George Polya (1887-1985)
35
He developed a framework known as Polya’s Four-Steps in Problem Solving.
George Polya
36
The process addressed the difficulty of students in problem solving.
POLYA’S FOUR-STEPS IN PROBLEM SOLVING
37
Mathematics is useful to predict.
True
38
Number pattern
leads directly to the concept of functions in mathematics.
39
is applied to problem-solving whether a pattern is present and used to generalize a solution to a problem.
Number pattern
40
can be in the form counting up or down and the missing number is of the form of completing count up or down.
Pattern
41
is a type of figurative number represented as dots or pebbles arranged in the shape of a regular polygon.
polygonal number
42
Examples of polygonal number
Triangular number, Square number
43
Alphametic
is a type of number puzzle containing sum (or other arithmetic operation) in which digits (0 to 9) are replaced by letters of the alphabet.
44
One of the most famous alphametic puzzles is the one introduced by
Henry Dudeney in 1924.
45
He was an English author and mathematician who specialized in logic puzzles and mathematical games.
Henry Dudeney