Download Problem Solving

SWTJC STEM – ENGR 1201
Problem Solving Strategies
11. describe a successful problem solving strategy
a.
b.
c.
d.
identify types and elements of problem solving
identify characteristics of a successful problem solver
list problem solving steps
list problem solving techniques
Content Goal 11
SWTJC STEM – ENGR 1201
Problem Types
1. Research problems
2. Knowledge problems
3. Troubleshooting problems
4. Mathematical problems
5. Resource problems
6. Social problems
7. Design problems
Content Goal 11a - 1
SWTJC STEM – ENGR 1201
Problem Elements
1. Problem identification - In the classroom by your instructor; in the
real world by a manager or creative engineer/scientist.
2. Analysis - Problem is dissected into pieces, analyzed and
modeled. Focus of this class and much of your formal education!
3. Synthesis - Creative step in which parts (sometimes seemingly
unrelated) are integrated into a whole
4. Application - Appropriate information from problem-at-hand is
identified and applied.
5. Comprehension - Analysis and application results are used to
actually solve the problem.
Content Goal 11a - 2
SWTJC STEM – ENGR 1201
Problem Solver Characteristics - 1
1. Approach
Skilled solver - Motivated, confident, and persistent.
Novice solver - Easily discouraged; lacks confidence; careless.
2. Knowledge
Skilled solver - Understands requirements, facts, and principles; rereads
and studies problems carefully.
Novice solver - Lacks understanding; careless with facts; reads once or
skims; makes unfounded assumptions.
Content Goal 11b -1
SWTJC STEM – ENGR 1201
Problem Solver Characteristics - 2
3. Attack
Skilled solver - Doesn't start until understands; breaks problem into
pieces.
Novice solver - Guesses and uses intuition carelessly; jumps to
conclusions; plunges into problem prematurely.
4. Logic
Skilled solver - Uses basic principles; proceeds logically from one step
to another.
Novice solver - Disorganized; jumps from one step to another.
Content Goal 11b -2
SWTJC STEM – ENGR 1201
Problem Solver Characteristics - 3
5. Analysis
Skilled solver - Clearly defines terms; researches and organizes
information; thinks carefully and clearly.
Novice solver - Uncertain about meaning of terms, steps, and symbols;
hopes the answer will come; "Takes the logarithm and turns it in!".
6. Perspective
Skilled solver - Has a "feel" for the correct answer; uses the "rule of
thumb" to estimate answer; discerns the relevant issues.
Novice solver - Uncritical about answers; cannot use estimation
techniques; confused by importance of issues.
Content Goal 11b -3
SWTJC STEM – ENGR 1201
Problem Steps – Given
Step 1 - Given: (Synthesis)
i. Record statement of problem.
ii. Draw a figure or diagram.
iii. Indicate on the figure properties with their units!
iv. State the assumptions.
Given:
"A 12 v battery is connected to a 10 ohm resistor. How much
electric current flows?" (Statement)
Battery and connecting wires have no
internal resistance. (Assumptions)
(Diagram)
Content Goal 11c - 1
SWTJC STEM – ENGR 1201
Problem Steps – Find
Step 2 - Find: (Synthesis)
i. State what is to be found using symbols.
ii. Label the unknown(s) on diagram with a question mark.
iii. Restate in words exactly what is to be found.
Find: I, current flowing in circuit in A (amperes)?
Content Goal 11c - 2
SWTJC STEM – ENGR 1201
Problem Steps – Relationship
Step 3 - Relationships: (Analysis)
i. State principle(s) and derive modeling equation(s).
ii. Solve for the desired quantity.
iii. Show sufficient detail to logically follow derivation.
Relationships:
Ohm's law applies to a direct current source (the battery) and
resistor connected in series. (Scientific Principle)
V = voltage (v) (Symbols used)
I = current (A)
R = resistance ( = v / A
V = R . I (Main relation – Ohm’s Law)
Solving for I,
I = V / R (Solve for desired unknown)
Content Goal 11c - 3
SWTJC STEM – ENGR 1201
Problem Steps – Solution 1
Step 4. Solution: (Application & Comprehension)
i. Make appropriate substitutions with their units.
ii. Ensure that units cancel appropriately to give expected
results.
iii. Compute the answer using appropriate computational
tools.
iv. Clearly mark the final answer(s) with their units.
v. Compare with "Find" to ensure that all questions have
been answered.
vi. Consider the reasonableness of the answer
Content Goal 11c - 4
SWTJC STEM – ENGR 1201
Problem Steps – Solution 2
Solution:
I = V / R = 12V / 10 = 12V / (10V/A)
Note that  = V / A
I = 1.2 A, current flowing in circuit  Ans
Content Goal 11c - 4
SWTJC STEM – ENGR 1201
Problem Steps – Check
Step 5. Check: (Quality Control)
i. Does the answer makes sense, both numerically and its
units?
ii. Verify by applying the scientific and engineering principles
as directly and independently as possible. Avoid simply
rechecking calculation steps; you could make the same
mistake twice!
Check:
V = 1.2A . 10  = 12V  OK
Note that the check reverts to Ohm’s Law to avoid making the
same mistake twice.
Content Goal 11c - 5
SWTJC STEM – ENGR 1201
Problem Steps – Example
Click to link to complete example.
Content Goal 11c - 5
SWTJC STEM – ENGR 1201
Problem Solving Techniques – Slide 1
1. Checks his/her solution by applying logic, not just reworking the
steps as done.
2. Asks if the solution "makes sense"?
3. Uses engineering analysis paper, if available, or four/five square
grid paper (a must).
4. Uses an appropriate computational tool.
5. Is neat and orderly, working left-to-right and down the page.
Content Goal 11d - 1
SWTJC STEM – ENGR 1201
Problem Solving Techniques – Slide 2
6. Works on scratch paper and transfers to final copy when done.
7. Shows enough intermediate steps to permit someone to follow
his/her thought process.
8. Uses scientific or engineering notation with three significant
digits and shows units.
9. Completes on a single page if possible. Cuts and pastes or
attaches computational listings if appropriate.
10. Uses proper headings and numbers pages (see pages 68-70 of
text).
Content Goal 11d - 2