MINNESOTA "HIGH" STANDARDS OMIT MULTIPLICATION AND DIVISION!
\doc\web\98\08\minnstan.txt
http://children.state.mn.us/grad/highstandards.htm#math
-----Original Message-----
From: Wagner, Cathy [SMTP:Cathy.Wagner@state.mn.us]
Sent: Wednesday, October 28, 1998 12:41 PM
To: Skoglund, Barbara; 'arthurhu@raima.com'
Hello again, I found the curriculum standards, and I have determined
that the normal or gaussian distribution is _not_ in your stated
standards at any grade level. I am also perplexed that division is
not covered at all, not even on a calculator, and the only
multiplication is single digit multiples of ten. Nowhere is is
expected that students should be able to compute 2x2, let alone
102x311, even with a calculator. Can you explain this oversight?
Minnesota High Standards 1998
3501.0463 PREPARATORY CONTENT STANDARDS IN LEARNING AREA FOUR: MATHEMATICAL APPLICATIONS
Analysis by Arthur Hu
Here's some of the grade level assignments I've found:
number sense
K-3 counting
K-3 place value
G4-5 addition (normally 1st grade)
G4-5 multiplication 1 digit (normally 2/3rd grade)
G4-5 simple fractions
G6-8 fractions
G6-8 exponents
G6-8 prime numbers
G6-8 factors
G6-8 scientific notation
G6-8 ratio
G6-8 proportion
G6-8 percent
G6-8 transform algebraic expressions
High triginometry
*** NOT EXPECTED OF MINNESOTA STUDENTS ***
NA multiplication multiple digit
NA division, any digits
NA square roots
K-3 measurement
G4-5 metric
G6-8 unit conversion
G6-8 area of rectangle
G6-8 area of circle (pi)
statistics
rough centrality
G4-5 mean, median mode
G6-8 calculate probability
NA standard deviation
NA normal distribution
geometry
2D shapes
G4-5 3D shapes
G6-8 symmetry
G6-8 coordinates
G6-8 transformations
G6-8 pythagorean theorem
High standards?
There is no mention in these standards of division of any kind,
even with calculators. Multiplication is only mentioned in
terms of single digit multiples of 10. Square roots are also
not mentioned.
Normal distribution, normally found only in college or college
prep statistics, but found in one of the sample 5th grade test
problems, is _not_ in the standards.
There is a very high emphasis of experimental probability,
charts, graphs, and communication, which are typically needed
to support arguments that some groups in society are unfairly
treated, or that the earth is dying. Yet they do not teach
multiplication or division.
--------------------------------------------------------------
The High Standards define what students should know and be able to
do. Preparatory standards require K-8 students to master important
concepts, skills, and ideas
Students who enter the 9th grade in 1998 and beyond must complete 24
of 48 possible High Standards as one Minnesota public high school
graduation requirement.
Primary content standards (math)
K-3
Number Sense
A student shall use number relationships to represent information and
solve problems by:
using whole numbers to represent numbers in more than one way, count
and order, name and locate, measure, and describe and extend pattern;
demonstrating an understanding of place value, number relationships,
relative size, and reasonableness of answers in problem-solving
situations; and
solving problems and justifying thinking by selecting appropriate
numbers and representations; using operations, patterns, and
estimation; generating multiple solutions; organizing data using
pictures and charts; and using concrete objects, diagrams, or maps to
solve simple problems involving counting, arrangements, or routes.
Shape, Space, and Measurement
A student shall apply concepts of shape, space, and measurement to
solve problems involving two- and three-dimensional shapes by
demonstrating an understanding of:
patterns by describing, extending, and completing existing patterns;
creating new patterns; representing spatial patterns pictorially,
numerically, or both; and identifying, creating, or identifying and
creating symmetrical patterns;
measurement, given familiar objects, to identify type of measurement
required, estimate measurement, select appropriate tools and units of
measurement, measure accurately, and use measurements to order a
group of objects according to size;
familiar two- and three-dimensional shapes by identifying shapes in
real-world contexts; drawing, building, or drawing and building
familiar shapes; sorting and classifying shapes; and predicting the
results of flipping, sliding, or turning a shape; and
geometric terms used to describe spatial relations.
Intermediate 4-5
3501.0463 PREPARATORY CONTENT STANDARDS IN LEARNING AREA FOUR: MATHEMATICAL APPLICATIONS
Intermediate Content Standards
Shape, Space, and Measurement
A student shall:
describe and analyze two- and three-dimensional shapes and spaces
using appropriate whole and partial units, including metric, to
measure length, time, weight, volume, temperature, angle, and area,
and using names and properties of common two- and three-dimensional
shapes;
describe and compare two- and three-dimensional geometric figures
existing in the physical world;
analyze and create new shapes by combining, dissecting, or
transforming existing shapes;
extend or create geometric patterns to solve problems;
represent a three-dimensional space in two-dimensional view;
measure, including identifying type of measurement required,
selecting appropriate tools and units of measurement, and measuring
accurately;
estimate measurements by using appropriate units and comparisons to
known objects or quantities; and
use maps or graphs to determine the most efficient routes.
Number Sense
A student shall:
demonstrate understanding of concepts of place value, variables, and
equations; when and how to use number operations; when and how to use
a variety of estimation strategies; addition, subtraction, and
multiplication of single-digit multiples of powers of ten; and the
reasonableness of calculator results;
use number concepts and a variety of math operations to represent
information and solve problems;
solve a variety of multiple-step problems using number relationships
and properties, number patterns, and appropriate computation or
estimation procedures;
generate and describe more than one method to solve problems;
use whole numbers, simple fractions, and money amounts to quantify,
label, measure, and locate numerical information;
represent real-life situations mathematically;
represent patterns using words, pictures, and numbers; and
use lists or diagrams to solve counting and arrangement problems.
Chance and Data Handling
A student shall:
demonstrate understanding of how to find range, mean, and median
simple concepts of likelihood including impossible, unlikely, equal
chance, likely, certain, fair, and unfair; and information displayed
in graphs, tables, and charts;
answer questions by collecting and organizing data, representing
data, and communicating results;
conduct experiments involving uncertainty including listing possible
outcomes; tally, record, and explain results; and use the results to
predict future outcomes;
describe patterns, trends, or relationships in data displayed in
graphs, tables, or charts; and
represent data using at least two graphic forms.
grade 6-8
3501.0463 PREPARATORY CONTENT STANDARDS IN LEARNING AREA FOUR:
MATHEMATICAL APPLICATIONS
Middle-level Content Standards
Space, Shape, and Measurement
A student shall:
demonstrate understanding of basic concepts of coordinate systems,
know precise mathematical names and properties of two- and
three-dimensional shapes, convert common measurement units within the
metric system and customary systems, and understand how properties of
shapes affect stability and rigidity of objects;
recognize and describe shape, size, and position of two- and
three-dimensional objects and the images of the objects under
transformations;
create complex designs using transformations and tilings to
generalize properties of shapes;
connect geometric concepts and use them to test conjectures and solve
problems, including distances (rational and irrational), the
Pythagorean Theorem, similarity and congruence, slope, properties of
polygons and polyhedra, and symmetry;
measure length, mass, perimeter, and area of quadrilaterals and
circles, surface area and volume of solids and angles, including
determining type of measurement (exact, approximate, derived),
selecting appropriate measurement tools and units, and measuring to
the appropriate accuracy; and
describe how changes in the dimensions of figures affect perimeter,
area, and volume.
Number Sense
A student shall:
demonstrate understanding of number concepts including place value,
exponents, prime and composite numbers, multiples, and factors;
fractions, decimals, percents, integers, and numbers in scientific
notation by translating among equivalent forms; and compare and order
numbers within a set;
solve a variety of problems by representing numbers efficiently,
selecting appropriate operations, selecting appropriate methods to
estimate or compute, and generating and describing more than one
method to solve problems;
analyze and justify operations and methods used and evaluate the
reasonableness of computed results to problems with proposed
solutions;
apply proportional reasoning to solve a variety of problems using
rates, ratios, proportions, and percents; and
create a real-world communication that demonstrates the ability to
use a variety of numbers in context.
Chance and Data Handling
A student shall:
calculate basic measures of center and variability, to demonstrate
understanding of basic concepts of probability and calculate simple
probabilities;
formulate a question and design an appropriate data investigation;
organize raw data and represent it in more than one way;
analyze data by selecting and applying appropriate data measurement
concepts;
critique various representations of data;
devise and conduct a simulated probability situation; and
predict future results based on experimental results.
Patterns and Functions
A student shall:
analyze patterns and use concepts of algebra to represent
mathematical relationships, including demonstrating understanding of
the concepts of variables, expressions, and equations;
recognize, analyze, and generalize patterns found in linear and
nonlinear phenomena; data from lists, graphs, and tables; number
theory; sequences; rational numbers; and formulas;
represent and interpret cause and effect relationships using
algebraic expressions, equations and inequalities, tables and graphs,
verbal descriptions, and spread sheets;
connect verbal, symbolic, and graphical representations; identify
constraints; translate algebraic expressions into equivalent forms;
and propose and justify solutions in problem situations; and
use properties of mathematics to informally justify reasoning in a
logical argument.
High School
3501.0444 LEARNING AREA FOUR: MATHEMATICAL APPLICATIONS
High School Standards
Students must complete three
Discrete Mathematics OR Chance and Data Analysis
AND
Algebraic Patterns OR Technical Applications
AND
Shape, Space, and Measurement
Discrete Mathematics
A student shall use discrete structures to demonstrate mathematical
relationships and solve problems by:
describing the difference between discrete and continuous models of
data and permutations, combinations, and other principles of
systematic counting;
translating between real-world situations and discrete mathematical
models using vertex-edge graphs, matrices, verbal descriptions, and
sequences;
analyzing and modeling iterative and recursive patterns;
analyzing and solving problems by building discrete mathematical
models, developing and comparing algorithms or sequences of
procedures, and determining whether solutions exist, the number of
possible solutions, and the best solutions; and
using properties of mathematics to justify reasoning in a logical
argument.
Chance and Data Analysis
A student shall:
demonstrate understanding of the statistical concepts of measures of
center, variability, and rank; differences between correlation and
causation; sampling procedures; line or curve of best fit; and
concepts related to uncertainty of randomness, permutations,
combinations, and theoretical and experimental probabilities;
investigate a problem of significance by formulating a complex
question, designing a statistical study, collecting data,
representing data appropriately, using appropriate statistics to
summarize data, determining whether additional data and analysis are
necessary, drawing conclusions based on data, and communicating the
results appropriately for the intended audience;
analyze and evaluate the statistical design, survey procedures, and
reasonableness of mathematical conclusions in a published study or
article;
use probability experiments, simulations, or theory to model
situations involving uncertainty; and make predictions based on the
model.
Algebraic Patterns
A student shall:
demonstrate the ability to identify rates of change in different
models of linear relationships and know characteristics of
polynomial, exponential, and periodic functions and relations;
functional notation; and terminology;
translate between real-world situations and mathematical models using
graphs; matrices; data tables, spread sheets, or both; verbal
descriptions; and algebraic expressions;
generalize patterns and build mathematical models to describe and
predict real situations including linear, exponential growth and
decay, and periodic;
use algebraic concepts and processes to represent and solve problems
involving variable quantities; and
use properties of algebra to justify reasoning using a logical
argument.
Technical Applications
A student shall:
demonstrate knowledge of computational technologies; how to use
complex measurement equipment for several systems; how to convert
between measuring systems; how to measure to scale; how to calculate
quantities using algebraic formulas; how to read and interpret
information in complex graphs, tables, and charts; scientific and
exponential notation used in complex systems; trigonometric
applications appropriate to technical situations; and fundamental
geometric constructions or calculations used in drafting or
construction;
create a set of plans to design or modify a complex structure,
product, or system by researching background information, calculating
mathematical specifications, and developing a materials list that
matches mathematical specifications;
construct a complex structure, product, or model to mathematical
specifications; and
analyze existing complex structure, product, or system for purposes
of maintenance, repair, trouble shooting, or optimizing function.
Shape, Space, and Measurement
A student shall:
demonstrate understanding of the characteristics of geometric figures
in both two and three dimensions, including reflections, rotations,
and translations; congruence and similarity; perimeter, area, and
volume; distance; scaling; and symmetry;
use spatial visualization to model geometric structures and solve
problems;
analyze characteristics of shape, size, and space in art,
architecture, design, or nature;
translate between numerical relationships and geometric
representations to analyze problem situations, scale models, or
measurement;
use properties of shape, location, or measurement to justify
reasoning in a logical argument; and
demonstrate understanding of measurement accuracy, error, and
tolerances.
feedback:
I cannot believe you are actually defending this sort of nonsense.
As one of the kids that _did_ make it into the top 1%, let me tell
you that we learned exactly the same program as the other kids.
The only difference is that we got 99.9% of our exercises right, not
that we did all this "higher order thinking" nonsense.
By abandoning basic skills, all you are doing is insure that you
don't even have the top 10% that you used to have. No one will
master the multiplication tables or division because it will not
be taught any more.
The WASL assessment bird feeder question rubric specifically
states that incorrect arithmetic will not count against a perfect
score. With assessments like this, what incentive is there to
teach accurate no-calculator arithmetic?
Subject: Re: Minnesota omits multiplication, division from "High Standards"
Date sent: Thu, 29 Oct 98 12:22:35 -0800
From: Bob Sotak
To: ,
Copies to: ,
,
> Yes, you are probably correct, multiplication and division are not
explicitly mentioned, BUT, to be able to do the activities math
literate students are asked to do, they will have to be able to DO
the multiplication and division. This is not a dumming down, rather
it makes sense. These oporations will be taught, only the focus is
not on how but why. For too long we have stopped with teaching the
operations - or run out of time - before getting to the application
of math in real world situations. By engagi
> As a parent and educator I want my children to be able to use the
math they learn rather than just score high on a standardized test
which only measures math and division facts.
From: "arthur hu"
To: Bob Sotak
Date sent: Thu, 29 Oct 1998 15:41:58 -0800
Subject: Re: Minnesota omits multiplication, division from "High Standards"
Send reply to: arthurhu@halcyon.com
Priority: normal
I cannot believe you are actually defending this sort of nonsense.
As one of the kids that _did_ make it into the top 1%, let me tell
you that we learned exactly the same program as the other kids.
The only difference is that we got 99.9% of our exercises right, not
that we did all this "higher order thinking" nonsense.
By abandoning basic skills, all you are doing is insure that you
don't even have the top 10% that you used to have. No one will
master the multiplication tables or division because it will not
be taught any more.
The WASL assessment bird feeder question rubric specifically
states that incorrect arithmetic will not count against a perfect
score. With assessments like this, what incentive is there to
teach accurate no-calculator arithmetic?
Subject: Re: Minnesota omits multiplication, division from
"High Standards"
Date sent: Thu, 29 Oct 98 12:22:35 -0800
From: Bob Sotak
To: ,
Copies to: ,
,
> Yes, you are probably correct, multiplication and division are not
> explicitly mentioned, BUT, to be able to do the activities math literate
> students are asked to do, they will have to be able to DO the
> multiplication and division. This is not a dumming down, rather it makes
> sense. These
oporations will be taught, only the focus is not on how but why. For too
long we have stopped with teaching the operations - or run out of time -
before getting to the application of math in real world situations. By
engagi > As a parent and educator I want my children to be able to use the
math they learn rather than just score high on a standardized test which
only measures math and division facts.
arthur hu kirkland WA arthurhu@halcyon.com
"fairness in diversity"
http://www.leconsulting.com/arthurhu