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Q
uantitative
R
easoning &
P
roblem
S
olving
238
© 2014 Pacific Crest
D
iscovery
Finding out for yourself
If you have used a spreadsheet before, find three or four spreadsheet examples stored on your computer
that you can use for this exercise. Another possibility is to find someone who has spreadsheets that
you can use as examples. As a last resort, use the information available at the URL provided below.
In each spreadsheet, determine what part of the spreadsheet data was entered (or imported from other
sources) and what part of the data was calculated within the spreadsheet environment. In inventorying
these calculations, identify at least five different types of transformations (from the Transforming Data
Techniques) found in the spreadsheet’s calculations.
If you can’t find your own spreadsheets, a link to sample Excel spreadsheets is available from the
companion website.
W
hat Do You Already Know?
Tapping into your existing knowledge
1. Are there reasons that functions from the family of function cards cannot be used to mathematically
transform data with spreadsheet expressions and functions?
2. What is the relationship between a calculation and a function?
3. Why do you put the transformed data into new variables?
4. In a spreadsheet, how do you implement a mathematical transformation of one or more variables?
M
athematical Language
Terms and notation
lagging data
—
shifting the position in the sequence of the observations forward or backwards in a
defined specific variable
transforming data
—
the process of converting original data into a new structure (expanded, reduced,
or even remapped) that will provide a stronger base for analytical use
I
nformation
What you need to know
In this book, four major quantitative reasoning components have been developed: new mathematical
concepts
,
tools
,
methodologies
, and
heuristics
. The depth and breadth of mathematical conceptual
understanding affects the level of quantitative reasoning and problem solving performance. The tools
include truth tables, Venn diagrams, spreadsheets, equations, functions, graphs, etc. The methodologies
are processes (Learning Process, Problem Solving, Solving Equations, Determining Likelihoods, and
Analyzing a Function, etc.). The fourth component, heuristics, is what differentiates the expert in
quantitative reasoning from an everyday practitioner.
The tables that have been shared throughout the book should now be revisited for their importance in
building heuristics. For example, in Experience 1.4, a set of “Best Practices in Learning Mathematics”
was presented. The key to using this table is choosing the most appropriate practice for the current
learning or problem solving challenge. Just as you can pound a nail with a screwdriver and drive in
a screw with a hammer, so can you use an inappropriate practice for a given context. In every case,
however, the work goes better and faster when the right tool is used for the right context. Much of the
value of this book is found in these heuristic tables that are the result of many years of experience in
quantitative reasoning and problem solving. In addition, the learning challenges and experiences in the