Quantitative Problem Solving

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QUANTITATIVE PROBLEM-SOLVING

math

IN APPLIED SCIENCES, NATURAL SCIENCES, MATHEMATICS, AND COMMERCE

Avoid endless, ineffective problem-solving. Our Quantitative Problem-Solving resources are thorough and will help you make better use of your practice problems and avoid common problem-solving pitfalls.

Looking for something short and sweet? Read our quick tips for problem-solving.

Looking for tools? Check the tabs below.

  • General Strategies to Improve Problem-Solving Skills
  • How to Approach Homework Problems
  • How to Understand and Diagnose Mistakes
  • Range of Problems – Common Types of Difficult Problems
  • Using Cognitive vs Metacognitive Questions to Help You Learn
  • Decision Steps
  • Quantitative Concept Summary
  • Evidence-Based Components of Expert Problem-Solving – Self-Assessment
  • Systematic, General Problem-Solving

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Quick tipsWhat is 'quantitative problem-solving'?General strategies, guiding questions, and how to approach practice problems for homeworkDecision step process, Quantitative concept summaries, and common types of difficult problems

QUICK TIPS

FOR QUANTITATIVE PROBLEM-SOLVING

1. Solving problems tests your ability to apply theoretical concepts. Both abstract thinking and computation are required.

2. Most courses have only a few key concepts that will reappear in novel contexts. Look for the “spiral of learning”: identify and understand these concepts deeply.

3. Organize concepts to see connections, and improve recall.

4. Use a systematic approach to stay focused, isolate errors in logic or computation, and reduce the panic.

5. Read to define the question fully: what is known? unknown? asked for? what is the significance of each different part?

6. Solve what you can initially. Think about problems using the same concepts (Newton’s 2nd Law, complementarity in base- pairing, equilibrium and Le Chatelier’s principle, net asset) that may use similar methods of solution.

7. In class: pay attention to the steps the prof follows (the thought process) in addition to the computations.

8. Describe your thoughts as you solve a problem. Monitor yourself: are you on task? Do you remember your purpose in doing “x”? What’s the next step?

9. Work with a good problem solver and compare your thought process to theirs.

10. Working in groups can be helpful to share ideas, but do some of each problem type yourself…exams are solo events!

11. STOP if you plug in an equation that has the exact variables as the problem. Focus on identifying concepts…not memorizing formula.

12. STOP if you try to use solutions from other problems that don’t apply. Focus on identifying underlying concepts first.

13. Set time limits for homework questions (e.g., 20 minutes) and get help if needed.

14. Keep up with the homework…this material is taught sequentially.

15. In labs: relate experiment or process to problems in class. Do specific equations describe phenomenon being observed in the lab?

16. Check your work using a different method, if possible.

QUANTITATIVE PROBLEM-SOLVING:

WHAT, WHY, and HOW IT WORKS

Spoiler title
Characteristics of expert problem-solvers
Typical characteristics of novice problem-solvers
Strategies to improve problem-solving skills
Expert problem-solving self-assessment

STRATEGIES AND TOOLS

FOR QUANTITATIVE PROBLEM-SOLVING

General problem-solving strategy
Use cognitive and metacognitive questions to help you learn
Homework: Approaching practice problems
Homework: Diagnose the problem and connect it to a misconception

STRATEGIES AND TOOLS

FOR QUANTITATIVE PROBLEM-SOLVING

Decision step process
Example: Decision steps in Calculus for max/min word problems
Decision steps for rational expressions
Quantitative concept summary
Example: Concept summary for Ordinary Simple Annuities
Range of problems strategy: Common types of difficult problems
Further resources

 

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First photo courtesy of Clay Shonkwiler and second photo courtesy of fdecomite under the Creative Commons Attribution-Non-Commercial-No-Derivations 2.0 license.