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Quantitative Reasoning & Problem Solving
14 © 2014 Pacific Crest
What Do You Already Know? Tapping into your existing knowledge
1. What mathematical content have you found easy to learn? Why do you think that was?
2. What do you need to do in order to learn mathematics?
3. What do you need to do in order to teach someone a mathematical concept or process?
4. When and how do you use mathematics to solve problems in your life?
5. What is the role of thinking in learning and problem solving?
6. Is it easier to achieve understanding by 1) solving a series of problems or 2) by critically analyzing
a model and then working a series of problems? Why?
Mathematical Language Terms and notation
answer key — the expected solutions for given problems
examples — the step-by-step illustration of how to solve a quantitative reasoning problem in any
mathematics-related subject
information — the section of an activity where the expert’s explanation shared how and why you can
do something to increase your understanding of mathematics
notation — the established preferences of mathematicians for representing mathematical concepts in
abbreviated form
presentation of answers — a defined and required form for solutions
problems — an application of knowledge where information is given with the expectation of a solution
as a result of that knowledge
properties — the well-developed and proven rules that exist with a given set of assumptions
worked solution — a step-by-step development of an answer to a problem that documents the
mathematical reasoning used to produce the answer
Information What you need to know
Readings Resources
Methodology Elevating Knowledge
In this methodology, “Level” refers to the Level of Learner Knowledge (from activity 1.1).
Step Explanation Level
1. Informational
base
Establish and solidify an informational base. 1
2. Prior knowledge Identify the cornerstones for the knowledge. Knowledge is built upon
a foundation of prior knowledge.
2