From Commercial Arithmetic to Life Annuities: The Early History of ...

From Commercial Arithmetic to Life Annuities: The Early History of ...

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  • cours - matière potentielle : education
  • cours - matière potentielle : textbook
  • expression écrite - matière potentielle : security pricing problems by economists
25/8/96 From Commercial Arithmetic to Life Annuities: The Early History of Financial Economics, 1478-1776.* Geoffrey Poitras Faculty of Business Administration Simon Fraser University Burnaby, B.C. CANADA V5A 1S6 and Department of Economics and Statistics National University of Singapore 10 Kent Ridge Crescent SINGAPORE 0511 ABSTRACT This paper considers the early history of financial economics, focusing on the origins of security pricing theories. The period under examination, 1478-1725, starts with the first printed commercial arithmetic and ends with de Moivre' s contributions to the pricing of life annuities.
  • stock companies
  • life annuities
  • early security market participants
  • origins of security pricing theories
  • shares of profit
  • commercial arithmetics
  • early history of financial economics
  • period under examination
  • life annuity
  • interest

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CONNECTING
COLLEGEREADINESS
TMSTANDARDS
TOTHECLASSROOM
For Mathematics TeachersACT endorses the Code of Fair Testing Practices in
Education and the Code of Professional Responsibilities
in Educational Measurement, guides to the conduct of
those involved in educational testing. ACT is committed
to ensuring that each of its testing programs upholds the
guidelines in each Code.
A copy of each Code may be obtained free of charge
from ACT Customer Services (68), P.O. Box 1008,
Iowa City, IA 52243-1008, 319/337-1429.
Visit ACT’s website at: www.act.org
© 2008 by ACT, Inc. All rights reserved. 11672TABLE OF CONTENTS
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
The College Readiness Standards Report for
EXPLORE Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Description of the College Readiness Standards . . . . . . . . . . . . . . . . . . 5of the EXPLORE Mathematics Test . . . . . . . . . . . . . . . . . . .14
The Need for Thinking Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
Thinking Your Way Through the EXPLORE Test . . . . . . . . . . . . . . . . . . . 26
The Assessment-Instruction Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Using Assessment Information to Help Support
Low-Scoring Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Instructional Activities for EXPLORE Mathematics . . . . . . . . . . . . . . . . 57
Putting the Pieces Together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
List of Tables
1 The College Readiness Standards for the
EXPLORE Mathematics Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 EXPLORE Mathematics Strands and
Corresponding Content Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
3 EXPLORE Sample Test Questions by Score Range . . . . . . . . . . . . . .19
4 College Readiness Benchmark Scores . . . . . . . . . . . . . . . . . . . . . . . 30
5 Estimated PLAN Composite Score Ranges . . . . . . . . . . . . . . . . . . . . 31
6 The Link Between ACT Composite Scores
and College Admission Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
List of Figures
1 EXPLORE Mathematics Test Content Areas and
Cognitive Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14INTRODUCTION
ACT has developed this guide to help classroom Local comparisons to the national norm group are
teachers, curriculum coordinators, and counselors most appropriate when EXPLORE is administered
TMinterpret the College Readiness Standards report for under conditions similar to those in the norming
®EXPLORE Mathematics. The guide includes: study—with all four tests administered in a single
session in the standard order, and students having
■ A description of the College Readiness
calculators available for use on the Mathematics Test.
Standards for EXPLORE
Eighth-grade students who test in August through
■EXPLORE Mathematics Test
January will receive Fall Eighth-Grade Norms. Eighth
graders who test in February through July will receive■ A set of sample test questions
Spring Eighth-Grade Norms. Ninth-grade students
■ A description of the Assessment- will receive Ninth-Grade Norms regardless of their
Instruction Link test date. (If your school chooses to test ninth-grade
students in the spring, keep in mind that these■ A set of classroom instructional activities
students will have had several more months of
The College Readiness Standards for EXPLORE instruction than the norm group. Therefore, spring-
are statements that describe what students who score tested ninth graders may show higher levels of
in the four score ranges 13–15, 16–19, 20–23, and achievement when compared to the fall-tested norm
24–25 are likely to know and to be able to do. The group than if they had tested in the fall.) Students who
statements are generalizations based on the are not in the eighth or ninth grade when they take
performance of many students scoring in these four EXPLORE will receive Fall Eighth-Grade Norms on
score ranges. College Readiness Standards have not their student reports.
been developed for students whose scores fall in the
EXPLORE is a curriculum-based assessment1–12 range because these students, as a group,
program developed by ACT to help eighth and ninthdo not demonstrate skills similar to each other
graders devise a high school course work plan thatconsistently enough to permit useful generalizations.
prepares them to achieve their post-high school
The College Readiness Standards for EXPLORE goals. As part of ACT’s Educational Planning and
TMare accompanied by ideas for progress that help Assessment System (EPAS ), EXPLORE is comple-
®teachers identify ways of enhancing student learning mented by PLAN , ACT’s tenth-grade program, and
®based on the scores students receive. by the ACT , for eleventh and twelfth graders. We
hope this guide helps you assist your students as theyds Information
plan and pursue their future studies.
Services provide five aggregate reports for EXPLORE.
Four of these reports are content specific: each
presents the scores of your students in each of the “The role of standardized testing
four content areas the EXPLORE test measures— is to let parents, students, and
English, Mathematics, Reading, and Science. These
institutions know what students four content-specific reports present EXPLORE results
are ready to learn next.”using ACT’s College Readiness Standards. The fifth
report, the Summary Profile, summarizes the scores of
— Ralph Tyler, October 1991your students across all four content areas. All five
Chairman Emeritus ofreports provide data that compare the performance of
ACT’s Board of Trustees
your school’s students with all students in a nationally
representative comparison group (norm group).
1THE COLLEGE READINESS
STANDARDS REPORT FOR
EXPLORE MATHEMATICS
The College Readiness Standards wereThe College Readiness Standards report for D developed by identifying the knowledge andEXPLORE Mathematics allows you to compare the
skills students need in order to respond successfully toperformance of students in your school with the
questions on the EXPLORE Mathematics Test. As youperformance of students nationwide. The report
review the report for EXPLORE Mathematics, you willprovides summary information you can use to map
note that the Standards are cumulative, which meansthe development of your students’ knowledge and
that if students score, for example, in the 16–19 scoreskills in mathematics. Used along with your own
range, they are likely to be able to demonstrate mostclassroom observations and with other resources,
or all of the knowledge and skills in the 13–15 and thethe test results can help you to analyze your students’
16–19 score ranges. Students may be able toprogress in mathematics and to identify areas of
demonstrate some of the skills in the next score range,strength and areas that need more attention. You can
20–23, but not consistently enough as a group tothen use the Standards as one source of information
reach that score range. A description of the way thein the instructional planning process.
College Readiness Standards were developed can be
A sample report appears on the next page. found on pages 5–6.
An explanation of its features is provided below.
This section briefly explains the uses of the The “ideas for progress” are statements thatA report to help you interpret the test results. E provide suggestions for learning experiences
that students might benefit from. These ideas for
progress are arranged by score range and strand.These are the five score ranges reported for the
Although many of the ideas cross more than oneB College Readiness Standards for EXPLORE. To
strand, a primary strand has been identified for each determine the number of score ranges and the width
in order to facilitate their use in the classroom. Ideasof each score range, ACT staff reviewed normative
for progress are provided for students who score in data, college admission criteria, and information
the 24–25 score range, the highest score range forobtained through ACT’s Course Placement Service.
EXPLORE. The ideas for the 24–25 score range areFor a more detailed explanation of the way the score
shown to suggest educational experiences from whichranges were determined, see page 5.
students may benefit before they take PLAN and
the ACT.
This section compares the percent of students
C who scored in a particular score range at an
Page 2 of the report profiles the test results,individual school (Local) with the percent of all F College Readiness Standards, and ideas for
students in the norm group who scored in the same
progress for score ranges 20–23 and 24–25.range. The percent of students for the norm group is
based on the most current set of nationally represen-
tative norms. The number of local-school students who
scored in each of the five score ranges is provided in
the column to the left of each bar graph; the total
number of students tested locally is provided at the
top of the report.
2A
D
B
E
C
F
3DESCRIPTION OF THE
COLLEGE READINESS STANDARDS
After analyzing all the data and reviewing differentWHAT ARE THE COLLEGE
possible score ranges, ACT staff concluded thatREADINESS STANDARDS?
using the five score ranges 1–12, 13–15, 16–19,
The College Readiness Standards communicate 20–23, and 24–25 would best distinguish students’
educational expectations. Each Standard describes levels of achievement so as to assist teachers,
what students who score in the designated range are administrators, and others in relating EXPLORE test
likely to be able to do with what they know. Students scores to students’ attainment of specific skills and
can typically demonstrate the skills and knowledge understandings.
within the score ranges preceding the range in which
they scored, so the College Readiness Standards are HOW WERE THE COLLEGE READINESS
cumulative. STANDARDS DEVELOPED?
In helping students make the transition to high
After reviewing normative data, college admission
school, teachers, counselors, and parents can use
criteria, and information obtained through ACT’s
the College Readiness Standards for EXPLORE to
Course Placement Service, content experts wrote the
interpret students’ scores and to understand which
College Readiness Standards based on their analysis
skills students need to develop to be better prepared
of the skills and knowledge students need in order to
for the future.
successfully respond to the test questions in each
score range. Experts analyzed numerous test
HOW WERE THE SCORE RANGES questions that had been answered correctly by 80%
DETERMINED? or more of the examinees within each score range.
The 80% criterion was chosen because it offers those
To determine the number of score ranges and the
who use the College Readiness Standards a high
width of each score range for EXPLORE, ACT staff both
degree of confidence that students scoring in a given
reviewed EXPLORE normative data and considered the
score range will most likely be able to demonstrate
relationship among EXPLORE, PLAN, and the ACT.
the skills and knowledge described in that range.
In reviewing the EXPLORE normative data, ACT
staff analyzed the distribution of student scores across
“The examination should describe
the score scale. Because EXPLORE and PLAN have a
the student in meaningful terms—common score scale, ACT can provide EXPLORE
examinees with an estimated PLAN Composite score. meaningful to the student, the parent,
When the score ranges were being determined, and the elementary and high school
therefore, both the EXPLORE score scale, 1–25, and
teacher—meaningful in the sense
the PLAN score scale, 1–32, were reviewed side by
that the profile scores correspond side. And because many students take PLAN to
determine how well they might perform on the ACT, to recognizable school activities,
the course-placement research that ACT has
and directly suggest appropriate
conducted over the last forty years was also reviewed.
distributions of emphasis in learningACT’s Course Placement Service provides colleges
and universities with cutoff scores that are used to and teaching.”
place students into appropriate entry-level courses in
— E. F. Lindquist, February 1958college; and these cutoff scores were used to help
Cofounder of ACTdefine the score ranges.
5As a content validity check, ACT invited nationally It is important to recognize that the EXPLORE Test
recognized scholars from high school and university does not measure everything students have learned
Mathematics and Education departments to review nor does any test measure everything necessary for
the College Readiness Standards for the EXPLORE students to know to be successful in high school. The
Mathematics Test. These teachers and researchers EXPLORE Mathematics Test includes questions from a
provided ACT with independent, authoritative reviews large domain of skills and from areas of knowledge
of the ways the College Readiness Standards reflect that have been judged important for success in high
the skills and knowledge students need to school and beyond. Thus, the College Readiness
successfully respond to the questions on the Standards should be interpreted in a responsible way
EXPLORE Mathematics Test. that will help students understand what they need to
know and do if they are going to make a successful
Because EXPLORE is curriculum based, ACT and
transition to high school. As students choose courses
independent consultants conduct a review every three
they plan to take in high school, they can use the
to four years to ensure that the knowledge and skills
Standards to identify the skills and knowledge they
described in the Standards and outlined in the test
need to develop to be better prepared for their future.
specifications continue to reflect those being taught in
Teachers and curriculum coordinators can use the
classrooms nationwide.
Standards to learn more about their students’
academic strengths and weaknesses and can then
HOW SHOULD THE COLLEGE modify their instruction and guide students
READINESS STANDARDS BE accordingly.
INTERPRETED AND USED?
HOW ARE THE COLLEGE READINESSThe College Readiness Standards reflect the
STANDARDS ORGANIZED?progression and complexity of the skills measured in
EXPLORE. Because no EXPLORE test form measures As content experts reviewed the test questions
all of the skills and knowledge included in the College connected to each score range, distinct yet
Readiness Standards, the Standards must be overlapping areas of knowledge and skill were
interpreted as skills and knowledge that most identified. For example, there are many types of
students who score in a particular score range are questions in which students are asked to solve
likely to be able to demonstrate. Since there were arithmetic problems. Therefore, Basic Operations &
relatively few test questions that were answered Applications is one area, or strand, within the College
correctly by 80% or more of the students who scored Readiness Standards for EXPLORE Mathematics. The
in the lower score ranges, the Standards in these other strands are Probability, Statistics, & Data
ranges should be interpreted cautiously. The skills Analysis; Numbers: Concepts & Properties;
and understandings of students who score in the Expressions, Equations, & Inequalities; Graphical
1–12 score range may still be evolving. For these Representations; Properties of Plane Figures; and
students the skills and understandings in the higher Measurement.
score ranges could become their target achievement
outcomes.
6