Problem Solving Strategies

1. SWTJC STEM – ENGR 1201 • 11. describe a successful problem solving strategy • identify types and elements of problem solving • identify characteristics of a successful problem solver • list problem solving steps • list problem solving techniques Problem Solving Strategies Content Goal 11

2. SWTJC STEM – ENGR 1201 • Research problems • Knowledge problems • Troubleshooting problems • Mathematical problems • Resource problems • Social problems • Design problems Problem Types Content Goal 11a - 1

3. SWTJC STEM – ENGR 1201 • Problem identification - In the classroom by your instructor; in the real world by a manager or creative engineer/scientist. • Analysis - Problem is dissected into pieces, analyzed and modeled.  Focus of this class and much of your formal education! • Synthesis - Creative step in which parts (sometimes seemingly unrelated) are integrated into a whole • Application - Appropriate information from problem-at-hand is identified and applied. • Comprehension - Analysis and application results are used to actually solve the problem. Problem Elements Content Goal 11a - 2

4. SWTJC STEM – ENGR 1201 1. Approach Skilled solver - Motivated, confident, and persistent.Novice solver - Easily  discouraged; lacks confidence; careless. Problem Solver Characteristics - 1 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

5. SWTJC STEM – ENGR 1201 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. Problem Solver Characteristics - 2 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

6. SWTJC STEM – ENGR 1201 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!". Problem Solver Characteristics - 3 • 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

7. SWTJC STEM – ENGR 1201 • Step 1 - Given: (Synthesis) • Record statement of problem. • Draw a figure or diagram. • Indicate on the figure properties with their units! • State the assumptions. Problem Steps – Given 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

8. SWTJC STEM – ENGR 1201 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. Problem Steps – Find Find: I, current flowing in circuit in A (amperes)? Content Goal 11c - 2

9. SWTJC STEM – ENGR 1201 • 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. Problem Steps – Relationship 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

10. SWTJC STEM – ENGR 1201 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 Problem Steps – Solution 1 Content Goal 11c - 4

11. 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

12. SWTJC STEM – ENGR 1201 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! Problem Steps – Check 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

13. SWTJC STEM – ENGR 1201 Problem Steps – Example Click to link to complete example. Content Goal 11c - 5

14. SWTJC STEM – ENGR 1201 • Checks his/her solution by applying logic, not just reworking the steps as done. • Asks if the solution "makes sense"? • Uses engineering analysis paper, if available, or four/five square grid paper (a must). • Uses an appropriate computational tool. • Is neat and orderly, working left-to-right and down the page. Problem Solving Techniques – Slide 1 Content Goal 11d - 1

15. SWTJC STEM – ENGR 1201 • Works on scratch paper and transfers to final copy when done. • Shows enough intermediate steps to permit someone to follow his/her thought process. • Uses scientific or engineering notation with three significant digits and shows units. • Completes on a single page if possible.  Cuts and pastes or attaches computational listings if appropriate. • Uses proper headings and numbers pages (see pages 68-70 of text). Problem Solving Techniques – Slide 2 Content Goal 11d - 2