Sample Proficiency Standards
The fol lowing general statements reflect ratings of
student work created in response to a
mathematically challenging task.
Advanced
Student work is distinguished in that it goes well beyond
the criteria for Proficient in an
insightful and creative approach to the task. It includes:
• evidence of reflection upon one’s work
• multiple solutions and/or solution strategies
• effective presentation of ideas, using a variety of forms (pictorial, graphic ,
symbolic,
algebraic , verbal)
• evidence of exploration, conjecturing, generalizing, validating and justifying
with use of
examples and counterexamples when appropriate.
Proficient
Student work completely addresses all aspects of the task.
It includes:
• appropriate application of concepts, procedures, and
structures although an occasional
minor computational error may be present
• clear and complete explanations
• coherent use of mathematical words, symbols, or other visual representations
that are
appropriate to the task
• logical conclusions based upon known facts, properties and relationships.
Basic
Student work addresses most of the essential conditions of
the task. It includes:
• some evidence of the application of appropriate
knowledge and skills
• reasonably clear explanations (which may not be complete)
• some accurate conclusions (although reasoning may be faulty or incomplete)
• evidence of some minor misconceptions
Minimal
Student work addresses some of the essential conditions of
the task. While it may include
some positive elements , the work is characterized by:
• the presence of at least one major conceptual or
procedural error
• unsatisfactory or missing communication
• a lack of detail/superficiality
• reasoning that is seriously f lawed or completely missing
Example: A task for fourth grade students.
Sample Proficiency Standards
B. Number Operations and Relationships
Content Standard
Students in Wisconsin will use numbers effectively for various purposes, such as
counting,
measuring, estimating, and problem solving.
PERFORMANCE STANDARD
B.4.5 In problem solving situations involving whole
numbers, select and efficiently use
appropriate computational procedures such as recalling the basic facts of
addition,
subtraction, multiplication and division
E. Statistics and Probability
Content Standard
Students in Wisconsin will use data collection and analysis, statistics and
probability in
problem solving situations, employing technology where appropriate.
PERFORMANCE STANDARDS
E.4.4 Determine if the occurrence of future events is
more, less, or equally likely, unlikely,
impossible, or certain
E.4.5 Predict outcomes of future events and test
predictions using data from a variety of
sources
SAMPLE TASK
Successful completion of the task involves a thorough
knowledge of the basic facts of
addition, good number sense, and a realization that chances of winning are
increased by: 1)
choosing the sums that are more likely to occur in the game than other sums, and
2) placing
those numbers in the optimal positions.
Advanced
Student work is distinguished in that it goes well beyond
the criteria for Proficient in an
insightful and creative approach to the task. It should include definite
evidence of the
recognition that the best chances of winning involve correct choice and
placement of those
numbers that will come up most often as sums. Written explanations should be
clear and
well organized.
Proficient
Student work completely addresses all aspects of the task.
It should include correct use of
computational procedures although an occasional minor error is allowed. Written
or
symbolic explanations should be easy to follow. Conclusions about the chances of
winning of
the two hypothetical students should be justified by examples, counter-examples,
or citation
of known mathematical properties.
Basic
Student work addresses most of the essential conditions of
the task. Students may fail to
address the chances of both hypothetical students. There might be some
misconception
about odd or even numbers. Respondent’s own game board may be well filled out,
but
rationale may be sketchy, missing, or with evidence of some misconceptions.
Minimal
Student work addresses only some, or even none, of the
essential conditions of the task.
Written explanations, if any, may not fit numerical evidence presented. Student
may
criticize the choice of the hypothetical students, but then repeat the same
choice in his/her
own board. Rationale is completely faulty. Rules for filling out the game board
are not
followed.
Samples of Student Work
Explanation of Ratings for Student Work
Proficient
All aspects of the task are addressed. The explanation for
Question 1 is clearly presented. Although
the explanation for the student’s own choice of a game board is non-verbal, it
is well presented in
such a way that one can easily understand why the various numbers were chosen.
Inclusion of
commutative pairs of addends (e.g., 9+6 and 6+9; 4+1 and 1+4) is important.
On the other hand, this response does not merit an Advanced Rating. The
organization on page 2 is
not completely systematic and the better choices of 12 and 13 were not even
considered. The location
of numbers on the student’s own game board suggests that optimal placement
(center square is best ,
four corners are next best) of sums that have the highest likelihood of being
called was not
considered.
Basic
All aspects of the task are addressed but there is no
recognition that Toni has some
impossible numbers. The explanation for Question 3 is clear and understandable,
but shows some misconception that chance of winning is based solely on a balance
of odd and even numbers, and not on choice of sums that are more likely to occur
than others.
Minimal
The explanation for Question 1 indicates a misinterpretation of the rules;
the student
believes the numbers on the board themselves must be added and the sum must also
be on
the board. The choice of numbers put on the student’s own gameboard violate the
rules of
the game—repetitions and impossibles sums (0 and 1). However, the student did
try and
that is an important fact in his/her favor. It must also be noted that all of
the indicated
sums and differences written on the paper are correct with the one exception of
22 + 24 =
26.
