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Secondary Education Mathematics and Performance Assessment Tasks
Melissa A. Ellis
Kutztown University
Abstract
During the research of performance assessment tasks, I looked at numerous books,
articles, and Internet sources to gather the overall consensus of what performance
assessment tasks are. PATs are a form of testing that requires students to perform a
task rather than taking a formal exam. The following are the main aspects of my
research focus: what is Performance Assessment and PATs, why use PATs,
theories and research behind PATs, pros and cons, types, suggestions and
constructing PATs, and rubrics. The reasons for researching PATs was to get a
better understanding of the overall process of creating and incorporating alternative
assessment in mathematics curriculum. This research illustrates the importance and
concerns about the importance for teachers to use PATs in their classroom.
PERFORMANCE ASSESSMENT TASKS 2
Secondary Education Mathematics and Performance Assessment Tasks
Throughout education, there has been continuous debate on what is the best method for
assessment. Assessment serves a variety of purposes in today's classroom (Appalachia
Educational Lab [AEL], & Virginia Education Association [VEA], 1992). For the students,
assessment aids learning and measures knowledge. For the teachers, it provides diagnosis of
student learning and data for making instructional decisions. Lastly, for the administration and
public, it indentifies the effectiveness of the program and displays the overall achievement (AEL,
& VEA, 1992). This is where the debate begins. Does either traditional or authentic assessment
fulfill the purpose of the student, teacher, administration, and public better? Authentic
assessment or performance assessment, asks students to analyze, apply, and sometimes
synthesize what they have learned (Blaz, 2008, p. 56). Performance assessment provides students
with tangible products that can serve as evidence of student achievement (Ronis, 2007, p. 22).
What is a Performance Assessment Task?
According to The Office of Technology Assessment of the U.S. Congress, performance
assessment is "any form of testing that requires a student to create an answer or a product that
demonstrates his or her knowledge or skills (Mahler & Chriest, n.d.)." In other terms, the product
is the student's outcome of a performance assessment task, and the skill is what the student
learned through classroom instruction. Performance assessment tasks (PATs) are activities that
students undertake to show what they know and can do (Ronis, 2007). A PAT can involve a
group of students, or an individual student. It is a mathematical task that can take only a half an
PERFORMANCE ASSESSMENT TASKS 3
hour to several days to complete and solve (Darling-Hammond, 1993). These tasks are measured
by a given criterion or standards that are applied by the teacher explaining the purposes of
evaluation. With the criteria, the students' quality of performances can be evaluated. Students
performing in a given task can apply their mathematical knowledge and skills to complete a
high-level mathematical task (Posamentier, Smith, & Stepelman).
All performance assessment tasks in mathematics classrooms' should be correlated with
the goals, objectives, and content of the curriculum (Posamentier et al.). During a PAT, students
are provided with little intervention or instructions from the teacher. This is why the task should
be understood by the student and a concept they can achieve. The task should also be important,
realistic, and have merit. Students should be able to display mathematics as a process allowing
them to show their conceptual understanding and thinking within a mathematical problem
(Posamentier et al.). A PAT is effective, in the way that it promotes motivation, critical thinking,
and is related to real-life situations. The best task a student can be offered is one that involves
open-ended tasks, more than one methodology, and other mathematical extensions and questions
(Posamentier et al.).
Assessment tasks can come in many forms. Students can be presented with a problem
related to what they are already doing in class and listening to the responses (Darling-Hammond,
1993). The evaluation can also be completed by observing what the students do and say while
working on a performance task. Another assessment is interviewing the given student during and
after a task. Overall, PATs in mathematics classrooms teach students real-life skills, when they
will use mathematical concepts, and the importance of quality (Blaz, 2008).
PERFORMANCE ASSESSMENT TASKS 4
Why Should Secondary Mathematic Classrooms Use PATs?
Unlike traditional assessment, performance assessment tasks require students to actively
demonstrate what they know (Sweet & Zimmermann, 1992). According to Education Research
Consumer Guide, performance assessment can be a more valid indicator of students' knowledge
and abilities. They will also provide improvement in instruction and increase in students'
understanding of what they need to know and be able to do (Sweet & Zimmermann, 1992).
Traditional assessment measures fundamental facts and concepts in mathematics. However,
PATs require students to use the fundamental facts and concepts learned during instruction.
PATs measure the methods, procedures, and analysis skills in mathematics (Slater & Ryan,
1993).
The most important factor of performance assessment tasks is the presence of
scaffolding. Scaffolding in PATs provides the following: clear directions, motivation and
purpose, students staying on task, students using time efficiently, clear expectations based on the
rubric, and no surprises or disappointments. The presence of scaffolding in a PAT takes the form
of narrowing down the topic and incorporating some creativity for the students (Blaz, 2008).
Another four important purposes of performance assessment tasks are keeping track, checking
up, finding out, and summing up (Maurer, 1996). As a teacher, it is important to gather
information about a student to see what the student has accomplished during the school year.
This is a form of monitoring or keeping track in that the PAT is designed to provide the teacher
with accountable information (Maurer, 1996). Checking-up is the formative function of the PAT.
It provides the teacher with information as to where the student is in achieving their
PERFORMANCE ASSESSMENT TASKS 5
understanding about the curriculum. Depending on the students' understanding, the teacher uses
this information to change the focus of the instructional program. The reason for the change in
focus is to ensure that the students are gaining and understanding what is needed in the
curriculum. The third purpose for performance assessment tasks is to find out and discover how
the student has built meaning from the instruction. This is where the teacher differentiates the
curriculum to meet the needs of every student. The reason for differentiated curriculum is simple,
each student takes new knowledge and relates it to old knowledge or experiences differently
(Maurer, 1996). Summing up is provide judgment information to the student, parent, or
community. This is known as feedback from the teacher. The report of a PAT is the
accountability purpose. It is the final word on whether a student has been able to demonstrate
understanding (Maurer, 1996).
The National Council of Teachers of Mathematics (NCTM) addresses the Assessment
Principle. The book Principles and Standards for School Mathematics, states that:
Assessment should be more than merely a test at the end of instruction to see how
students perform under special conditions; rather, it should be an integral part of
instructions. Assessment should not merely be done to students; rather, it should also be
done for students, to guide and enhance their learning.... It is important that assessment
tasks be worthy of students' time and attention. Activities that are consistent with (and
sometimes the same as) the activities used in instruction should be included. When
teachers use assessment techniques such as observations, conversations, and interviews
with students, or interactive journals, students are likely to learn through the process of
articulating their ideas and answering the teacher's questions (The National Council of
Teachers of Mathematics [NCTM], pp. 22-24).
PERFORMANCE ASSESSMENT TASKS 6
NCTM addresses the purpose of performance assessment tasks, stating that students learn to
articulate their ideas and answer teacher's questions. Therefore, by incorporating effective PATs
students will learn how to think and be more interactive during classroom instruction.
What Theory and Research Has to Say
According to the American Association for the Advancement of Science in Washington,
DC:
Studies that have looked closely at performance assessments find that, if the criteria is
clear and that examples are available to show levels of competency, performance
assessments are highly consistent across different evaluators (Kulm & Malcom, 1991).
Moreover, clear indication of what is expected of students improves student performance.
There are some indications at the K-12 levels that students perform inconsistently from
one PAT to the next (Shavelson, Baxter, & Pine, 4(4): 347). This suggests that studentsā€™
grades will be most reliably determined from a number of Performance Assessment with
other forms of assessment.
This excerpt shows that performance assessment tasks are effective when used with other forms
of assessment in curriculum. If there is any inconsistency in performance, the PAT should be
reevaluated.
Cognitive Learning Theory (CLT) defines knowledge as being constructed, while
learning is a process of creating personal meaning from new information and prior knowledge
(Maher & Chriest, n.d.). CLT shows assessment implies divergent thinking, multiple links and
solution, critical thinking skills, prior knowledge, and applying information to new situations
(Maher & Chriest, n.d.). When students work on PATs, they are using critical thinking skills,
using prior knowledge, building on their knowledge, finding multiple solutions, and using
application. Cognitive Learning Theory and performance assessment both mention the
PERFORMANCE ASSESSMENT TASKS 7
importance of the social components in group work, which is, taking a variety of roles, and
considering group products and processes. CLT states that people perform better when they
know the goal, see models, and know how their performance compares to the standard (Maher &
Chriest, n.d.). PATs emphasize what the goal is and what the quality of the work should be. Both
CLT and PATs, address a variety in learning styles, attention spans, memory, developmental
paces, and intelligences (Maher & Chriest, n.d.). For certain PATs, students have the choice of
how to show mastery of a concept. Students all learn at different paces. PATs give the students
the opportunity to work at their pace, use personal experiences, attention span, memory, and
learning styles in their individual task. Furthermore, PATs incorporates Cognitive Learning
Theory research by giving students real-world opportunities to apply and adapt new knowledge,
self-evaluate, and engage in problem solving a nonlinear progression of discrete skills (Maher &
Chriest, n.d.).
Well-designed assessment tasks not only assess student understanding but teach concepts
and require students to explain and communicate their solutions (Morrison, McDuffie, &
Akerson, 2002). American Educational Researchers, Fuchs, Karns, and Katzaroff , found that
students in performance assessment-driven instruction classes demonstrated stronger problem
solving skills than comparison groups that were not performance assessment-driven (Morrison et
al., 2002). This corresponds with research by the Office of Educational Research and
Improvement. They researched and stated:
Research suggests that learning how and where information can be applied, should be a
central part of all curricular areas. Also, students exhibit greater interest and levels of
learning when they are required to organize facts around major concepts and actively
PERFORMANCE ASSESSMENT TASKS 8
construct their own understanding of the concepts in a rich variety of contexts (Sweet &
Zimmermann, 1992).
They also observed that performance assessments created by teachers familiar with particular
state, district, or school curriculum, allowed the curriculum to "drive" the test, rather than be
weighted down by testing requirements that disrupt instruction (Sweet & Zimmermann, 1992).
The Pros and Cons of PATs
Performance assessment tasks provide students and teachers with countless advantages
when talking about assessing and learning. PATs emphasize having multiple correct answers and
creative solutions, ongoing throughout the unit of study, and provide an accurate picture of
student achievement (Ronis, 2007). Diane Ronis, author and professional educator states that
PATs allow teachers to develop meaningful curricula, create an environment where each child
has the opportunity to succeed, and provides multiple sources of evaluation that give an in-depth
view of student progress (Ronis, 2007). Meanwhile, Measurement and Assessment in Teaching
expresses PATs clearly communicate instructional goals that involve complex performances in
natural settings in and outside of school, plus, provide instructional targets (Miller, Linn, &
Gronlund). The book also addresses that performance assessment provides freedom to respond in
own one's own way, which, enables students to display originality (Miller et al.). This minimizes
students guessing. When grading, performance assessment encourages teacher feedback verses
ranking students' performance (Blaz, 2008). Overall, students are more accountable for their
own work, skills, knowledge they acquire, and self-reflection on their growth of performance by
actively participating in PATs (Blaz, 2008).
PERFORMANCE ASSESSMENT TASKS 9
On the other hand, PATs address fewer learning objectives than other forms of
assessment and are typically inappropriate for measuring student knowledge of facts (Maher &
Chriest). In addition to objectives, PATs are more difficult to achieve consistent scoring results,
and data simplified to a single number (Ronis, 2007). Most assessment tasks require pre-
assessment activities, which prepare students for the task. This takes too much time (Maurer,
1996).
A major downfall for performance assessment tasks is the bias that still emerges in
grading. Bias and reliability of ratings raises a lot of issue with professionals. Teachers must pay
careful attention to the learning outcomes that the task is intended to assess and to the scoring
rubrics that will be used in rating the performances (Miller, et al.). Going along with the
professional aspect of PATs, it is difficult to determine comparability between states. Each state
implements his or her own assessment tasks and interprets them differently (Maurer, 1996).
Overall, one of the main concerns with teachers is time. Performance assessments require
a greater expense of time, planning, and thought from students and teachers. The teachers who
use PATs must also pay close attention to technical and equity issues to ensure the assessments
are fair to all students (Sweet & Zimmermann, 1992). Students also spend an enormous amount
of time creating, for example, portfolios. Some professionals point out that most colleges and
universities still use test scores and grades for admission, so portfolios would need to somehow
translate into a grade (Blaz, 2008).
Types of Performance Assessment Tasks
PERFORMANCE ASSESSMENT TASKS 10
When deciding on the best type of performance assessment task, as a teacher, there are a
few decisions. Overall, there are two paths to take when creating or choosing a PAT: restricted-
response performance task or extended-response performance task. The freedom provided by
extended-response performance tasks enable students to display such important skills as problem
solving, planning, organization, integration, and creativity (Miller et al.). This type of PAT has
multiple goals that might be assigned at the beginning of a term or unit of study and used long
term (Ronis, 2007). On the other hand, restricted-response performance tasks are generally easier
to score and require less time than extended-response performance tasks. However, extended-
response performance tasks are better suited when measuring higher-order skills (Miller et al.).
One of the most comprehensive means of evaluating a learner's growth and progress
using a PAT is the use of portfolio creations. NCTM states that portfolios use problem solving,
communication, reasoning, and connections. They also are very specific in that they collect
information at the course level about the program standards (Maurer, 1996). Portfolios are
organized, a purposeful collection of documents, artifacts, records of achievement, and
reflections (Ronis, 2007). Artifacts are work students complete throughout the course. Whenever
a teacher leaves comments or observations on a test, paper, or assignment, the comments are
creating records of achievement. The most important purpose of a portfolio is to measure the
students' progress. However, the purpose is not for only the teacher to evaluate progress.
Reflections are the student's personal thoughts on his or her own learning throughout the course
(Ronis, 2007). This provides students with motivation, explicit examples, and engagement in
their own education. The reflections can include descriptions about how they feel about
PERFORMANCE ASSESSMENT TASKS 11
mathematics and/or an autobiography of their experience with mathematics. Portfolios also have
goal-setting sheets, journal entries, standardized tests or information on such tests, students'
choice of materials, projects, diagrams, pictures, reports, real-world applications, and problems
created by the students (Blaz, 2008). In creating portfolios and using self-monitoring tools,
teachers and students are working together to monitor progress more effectively. Therefore, as
students reread their reflections or journal entries, they may see that what was once confusing or
frustrating is now trivial. It also, empowers students next time they struggle to understand new
concepts and acquire new skills (Posamentier et al.).
How to create a Performance Assessment Task
When first creating a performance assessment task, start with an idea and carefully
construct the learning goals for the instructional unit (Slater & Ryan, 1993). Then decide if the
idea supports learning and assessment for these goals. Once the goals are created, clearly define
the knowledge and skills students need to apply. The students will also have to demonstrate these
skills in solving a problem (Slater & Ryan, 1993). Then determine criteria or standards at which
students will be judged. This will indicate the levels of competence (Slater & Ryan, 1993). Also,
determine which components of the task need to be analyzed. Make sure to design a task that can
have multiple entries, solutions, and exit points.
To determine all of the criteria and standards of a PAT, it is necessary to establish the
purpose of the PAT. There are three types of assessment purposes, which include diagnostic
purposes, instructional purposes, and monitoring purposes. Diagnostic purposes include what
students know about how to solve certain types of problems (Maher & Chriest, n.d.). Do students
PERFORMANCE ASSESSMENT TASKS 12
know how to evaluate findings or know how to use information learned (Maher & Chriest, n.d.)?
Instructional purposes are often indistinguishable from a learning activity. Lastly, monitoring
purposes are to judge the level of competency students achieved in doing mathematics.
Before completing the construction of a PAT, determine whether the criterion reflects the
most valued elements of student performance. This can be done by testing the idea, converting
the idea into a prompt, considering embellishments, consider what a student will need to know,
test the prompt out, and revise according to your experience (Darling-Hammond, 1993). After
revisiting the PAT, you will be able to determine if it emphasizes depth of knowledge and gain
mastery of skills (Maurer, 1996). After distributing the PAT, either directly observe students or
have students complete a structured student-answer sheet to evaluate various components of the
task (Slater & Ryan, 1993). In form of a rubric, teachers can match student performance with
criteria and determine which level most closely matches their performance. Make sure to also
provide written feedback of their performance.
It is important that there in a clear, logical set of activities that students are expected to
follow. Students must be aware of the expectations before starting on the performance
assessment task. The instructions must be specific, simple, not containing any complex sentence
structures, or difficult vocabulary. This will help make sure students have the prerequisite skills
and abilities needed to make the response (Miller et al.). In creating instruction, make sure to
avoid any racial, ethnic, or gender bias. Furthermore, it is important to create instructions and a
task that are in the appropriate reading level of all students (Miller et al.).
PERFORMANCE ASSESSMENT TASKS 13
Other steps professionals should following while creating PATs are to make sure the task
is a meaningful task in context. What real issues, problems, themes, and student interests can
help determine this context (Maher & Chriest, n.d.)? When creating a PAT, determine how
much the task will allow for student choice. Other choices to consider are: will there be student
choice in using outside resources, choice in working individually, with a partner, or in a group
(Maher & Chriest, n.d.). After creating the performance assessment task, it is important to not
only test out the task, it is important to create multiple responses. When creating multiple
responses, make sure each one shows a different performance level. They should follow the
rubric that you created. This can minimize bias and inconsistent grading.
How to create a rubric
In 1995, the NCTM released a document called Assessment Standards for School
Mathematics, to help reform traditional thinking about assessment in mathematics. It stated with
the understanding that:
All students are capable of learning mathematics, and highlighted six assessment
standards: assessment should reflect the mathematics that students need to know and be
able to do, enhance mathematics learning, promote equity, be an open process, promote
valid inferences about mathematics, and be a coherent process.... The key to these
standards is that assessment be used not to separate or rank students as examinations
often do, but as a tool to improve instruction as well as report the results of that
instruction (Posamentier, et al., pp. 159-163).
In doing so, the decision on the best way to improve instruction and report the results of
instruction is done by deciding what is the best use of rubric.
PERFORMANCE ASSESSMENT TASKS 14
Rubrics usually fall between one of two categories: analytic and holistic (Posamentier et
al.). A rubric that breaks the task into specific assessment categories and evaluated on each
separately is called an analytic rubric. In mathematics, teachers could grade students on their
conceptual understanding, mathematical reasoning and problem-solving strategies, and their
communication. For example, a student could receive a "Satisfactory" rating in problem-solving
strategies but an "Unsatisfactory" in communication (Posamentier, et al.). On the other hand, a
holistic rubric considers the product as a whole. In this case, students could be graded on a five
point scale (zero through four).
In creating the goals and objectives in the rubric, the teacher may decide on concepts,
mathematical reasoning, and communication skills. In this analytic rubric, the teacher identifies
each category understanding. For example, the description for communication as unsatisfactory
is identified as "Usage of mathematical terms is incorrect.ā€ The description for satisfactory is,
"mathematical terminology and notation is used effectively (Posamentier, et al.)." This step is
describing the levels of performance for each criterion. It is important to organize your rubric
and determine whether it is an analytic or a holistic model. Teachers may want to create rubrics
that reflect the model used in high stakes assessments to better prepare their students for success
on those types of tests (Posamentier, et al.). Then test the rubric that was created. There may be
flaws which need revisions. In creating an effective PATs, it is crucial that you create different
levels of student work in anticipating common student errors and use the rubric to assess the
examples. Finally, be able to correctly categorize the errors of students' work.
PERFORMANCE ASSESSMENT TASKS 15
Depending on the PATs, it may be more necessary to create number-based rubrics on
performance. For example, here is a generic rubric that represents a scale from one to six, with
six being the highest:
6 - Demonstrates conceptual understanding; is complete and goes beyond what is
expected; presents clear rationale; presents specific, relevant details as evidence;
represents exemplary achievement.
5- Demonstrates understanding; is complete; presents rationale; presents supporting
evidence; represents commendable achievement
4- Demonstrates some understanding, is fairly complete, presents a somewhat flawed
rationale, presents supporting evidence that lacks detail, represents adequate achievement
3- Attempts to show understanding but is unclear; is incomplete; presents a flawed
rationale; lacks supporting details; represents some evidence of achievement.
2- Demonstrates obvious misconceptions; is sorely incomplete; presents no evidence or
rationale; represents no examples; represents limited evidence of achievement
1- Demonstrates no understanding; shows no real attempt; presents a restatement of the
question; represents no evidence of achievement (Lim, 1997, p. 63).
This rubric can be applied to any topic in Mathematics by adding on the specific goals and
objectives to each level. For certain PATs, a separate rubric may be necessary for an
explanation. Here is a generic rubric that can be applied to any topic in Mathematics:
Answer: 4 - correct, 3 - almost correct or partially correct, 2 - incorrect but reasonable
attempt, 1 - incorrect with no relationship to the problem, and 0 - no answer
Explanation: 4 - complete, clear, logical, 3 - essentially correct but incomplete or not
entirely clear, 2 - vague or unclear but with redeeming features, 1 - irrelevant, incorrect,
or no explanation (Miller et al., p. 272).
This rubric shows that a teacher can grade the student on his or her final product (answers to
problems) and their explanation throughout the process of the task.
The next type of rubric can be organized in a way that the teacher is assessing the
students individually and as a whole (group). The following are categories for a generic rubric
that can be integrated to mathematics. These assessments are done by observations of the teacher
PERFORMANCE ASSESSMENT TASKS 16
during and post activity. The categories are: student learning styles (do the individuals), student
ideas (do the individuals), communication (do the students), cooperation (do the groups),
manipulative (individually or within group, do the students) (Darling-Hammond, 1993). Each of
these categories signifies whether it is assessing the student individually or all together. To
assess individual students on learning styles, the rubric can include the following questions: Do
the individuals consistently work alone or with others, try to help others, in what ways, succeed
in asking for and getting needed help, and from whom, stick to the task or become easily
distracted, and become actively involved in the problem (Darling-Hammond, 1993)? All of these
questions evaluate the studentsā€™ progress within the group.
Other possible questions a teacher can have to evaluate the individual student within a
group are: Do the individuals try to explain their organizational and mathematical ideas, their
arguments with evidence, consider seriously and use the suggestions and ideas of others, attempt
to convince others that their own thinking is best (Darling-Hammond, 1993)? The majority of
questions a teacher can use to evaluate a students' performance in communication can be done by
observing the students in the classroom. The questions consist of whether or not the student is
staying on task, communicating with group members, making reports to the whole class, making
a group consensus as well as their own, and synthesizing and summarizing their own or group's
thinking. The teacher may also grade the students on their cooperation as a group. These
questions include: whether they divided work among the members, agree on a plan or structure
for completing the task, taking time to ensure they all understand the task, use time in a
productive way, provide support for each member, think about recording, and allow for
PERFORMANCE ASSESSMENT TASKS 17
development of leadership. It is important to also evaluate if individuals and the group choose
and use appropriate manipulatives, share concrete objects, and appear not to need the actual
objects to be able to visualize within themselves.
No matter the method for creating a rubric, a teacher should help students understand
rubrics when giving assignments, so that students become familiar with and try to accomplish
what is required of them (Posamentier, et al.).
Reflection
After researching performance assessment tasks, I have concluded that they are a great
method for assessing students' full understanding of classroom instruction as long as the tasks
follow the objects and standards. In my opinion, the most effective way to incorporate PATs is as
a summative assessment. Allowing students to inductively work on a task after learning a few
lessons or the whole unit best measures the students' conceptual understanding. The length of my
PATs would vary throughout the course, but the best length to assess students understanding
after a few lessons is a one-to-two day PAT. This allows for students to work with classmates or
individually. It also allows for the elimination of classroom instruction, which, I feel is good for
student motivation. By observing students in the classroom, I gathered that they enjoy taking
control of the class by working on projects or tasks. Students are motivated by real-life
application and incorporating real-life application to every PAT, I feel students' conceptual and
critical thinking skills will evolve more effectively. PATs also provide feedback for the students
and the teacher. After administering and collecting a PAT from the students, I will look for
PERFORMANCE ASSESSMENT TASKS 18
concepts that the class had difficulty with. Before giving a formal exam, I would have the chance
to go over any concept with the class as a whole before giving a unit exam. Overall, my research
topic was insightful. I became aware of the downfalls and how to construct a PAT that avoids
limitations.
References
Slater, T.F. & Ryan, J.M. (1993) Laboratory Performance Assessment. Performance Assessment,
Retrieved December 1, 2011 from
http://www.flaguide.org/extra/download/cat/perfass/perfass.pdf
Maher, J. & Chriest, A. (n.d.). Developing Performance Assessment Tasks. Retrieved December
1, 2011 from the Prince George's County Public Schools at
http://www.pgcps.org/~elc/developingtasks.html
Kulm, G. & Malcom, S. M. (1991) Science Assessment in the Service of Reform. American
Association for the Advancement of Science, Washington, DC.
Shavelson R.J., Baxter, G.P. & Pine J. (1991) Performance Assessment in Science. Applied
Measurement in Education, 4(4): 347.
Blaz, D. (2008). Differentiated Assessment for Middle and High School Classrooms. Larchmont,
New York: Eye on Education.
Ronis, D. (2007). Brian-compatible Assessments. Thousand Oaks, CA: Corwin Press.
Maurer, R. E. (1996). Designing Alternative Assessments for Interdisciplinary Curriculum in
Middle and Secondary Schools. Needham Heights, MA: A Simon & Schuster Company.
Lim. L. (1997). How to Assess Student Work. Upper Saddle River, NJ: Prentice Hall.
PERFORMANCE ASSESSMENT TASKS 19
The National Council of Teachers of Mathematics. (2000). Principles and Standards for School
Mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc.
Posamentier, A.S., Smith, B.S., & Stepelman, J. (2010). Teaching Secondary Mathematics:
Teaching and Enriching Units. Boston, MA: Pearson.
Miller, D. M., Linn, R. L., & Gronlund, N.E. (2009). Measurement and Assessment in Teaching.
Upper Saddle River, NJ: Pearson.
Sweet, D., & Zimmermann, J. (1992). Education Research Consumer Guide. Performance
Assessment. Washington, DC: Office of Educational Research and Improvement.
Retrieved November 29, 2011 from ERIC.
Morrison, J., McDuffie, A., & Akerson, V. (2002). A Focus for Collaboration: Developing and
Implementing Science and Mathematics Performance Assessment Tasks. Retrieved
November 29, 2011 from ERIC.
Darling-Hammond, L. (1993). Authentic Assessment in Practice: A Collection of Portfolios,
Performance Tasks, Exhibitions, and Documentation. Retrieved November 29, 2011
from ERIC.
Appalachia Educational Lab, & Virginia Education Association, R. D. (1992). Alternative
Assessments in Math and Science: Moving toward a Moving Target. A Joint Study.
Retrieved November 29, 2011 from ERIC.

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Term Paper

  • 1. 1 Secondary Education Mathematics and Performance Assessment Tasks Melissa A. Ellis Kutztown University Abstract During the research of performance assessment tasks, I looked at numerous books, articles, and Internet sources to gather the overall consensus of what performance assessment tasks are. PATs are a form of testing that requires students to perform a task rather than taking a formal exam. The following are the main aspects of my research focus: what is Performance Assessment and PATs, why use PATs, theories and research behind PATs, pros and cons, types, suggestions and constructing PATs, and rubrics. The reasons for researching PATs was to get a better understanding of the overall process of creating and incorporating alternative assessment in mathematics curriculum. This research illustrates the importance and concerns about the importance for teachers to use PATs in their classroom.
  • 2. PERFORMANCE ASSESSMENT TASKS 2 Secondary Education Mathematics and Performance Assessment Tasks Throughout education, there has been continuous debate on what is the best method for assessment. Assessment serves a variety of purposes in today's classroom (Appalachia Educational Lab [AEL], & Virginia Education Association [VEA], 1992). For the students, assessment aids learning and measures knowledge. For the teachers, it provides diagnosis of student learning and data for making instructional decisions. Lastly, for the administration and public, it indentifies the effectiveness of the program and displays the overall achievement (AEL, & VEA, 1992). This is where the debate begins. Does either traditional or authentic assessment fulfill the purpose of the student, teacher, administration, and public better? Authentic assessment or performance assessment, asks students to analyze, apply, and sometimes synthesize what they have learned (Blaz, 2008, p. 56). Performance assessment provides students with tangible products that can serve as evidence of student achievement (Ronis, 2007, p. 22). What is a Performance Assessment Task? According to The Office of Technology Assessment of the U.S. Congress, performance assessment is "any form of testing that requires a student to create an answer or a product that demonstrates his or her knowledge or skills (Mahler & Chriest, n.d.)." In other terms, the product is the student's outcome of a performance assessment task, and the skill is what the student learned through classroom instruction. Performance assessment tasks (PATs) are activities that students undertake to show what they know and can do (Ronis, 2007). A PAT can involve a group of students, or an individual student. It is a mathematical task that can take only a half an
  • 3. PERFORMANCE ASSESSMENT TASKS 3 hour to several days to complete and solve (Darling-Hammond, 1993). These tasks are measured by a given criterion or standards that are applied by the teacher explaining the purposes of evaluation. With the criteria, the students' quality of performances can be evaluated. Students performing in a given task can apply their mathematical knowledge and skills to complete a high-level mathematical task (Posamentier, Smith, & Stepelman). All performance assessment tasks in mathematics classrooms' should be correlated with the goals, objectives, and content of the curriculum (Posamentier et al.). During a PAT, students are provided with little intervention or instructions from the teacher. This is why the task should be understood by the student and a concept they can achieve. The task should also be important, realistic, and have merit. Students should be able to display mathematics as a process allowing them to show their conceptual understanding and thinking within a mathematical problem (Posamentier et al.). A PAT is effective, in the way that it promotes motivation, critical thinking, and is related to real-life situations. The best task a student can be offered is one that involves open-ended tasks, more than one methodology, and other mathematical extensions and questions (Posamentier et al.). Assessment tasks can come in many forms. Students can be presented with a problem related to what they are already doing in class and listening to the responses (Darling-Hammond, 1993). The evaluation can also be completed by observing what the students do and say while working on a performance task. Another assessment is interviewing the given student during and after a task. Overall, PATs in mathematics classrooms teach students real-life skills, when they will use mathematical concepts, and the importance of quality (Blaz, 2008).
  • 4. PERFORMANCE ASSESSMENT TASKS 4 Why Should Secondary Mathematic Classrooms Use PATs? Unlike traditional assessment, performance assessment tasks require students to actively demonstrate what they know (Sweet & Zimmermann, 1992). According to Education Research Consumer Guide, performance assessment can be a more valid indicator of students' knowledge and abilities. They will also provide improvement in instruction and increase in students' understanding of what they need to know and be able to do (Sweet & Zimmermann, 1992). Traditional assessment measures fundamental facts and concepts in mathematics. However, PATs require students to use the fundamental facts and concepts learned during instruction. PATs measure the methods, procedures, and analysis skills in mathematics (Slater & Ryan, 1993). The most important factor of performance assessment tasks is the presence of scaffolding. Scaffolding in PATs provides the following: clear directions, motivation and purpose, students staying on task, students using time efficiently, clear expectations based on the rubric, and no surprises or disappointments. The presence of scaffolding in a PAT takes the form of narrowing down the topic and incorporating some creativity for the students (Blaz, 2008). Another four important purposes of performance assessment tasks are keeping track, checking up, finding out, and summing up (Maurer, 1996). As a teacher, it is important to gather information about a student to see what the student has accomplished during the school year. This is a form of monitoring or keeping track in that the PAT is designed to provide the teacher with accountable information (Maurer, 1996). Checking-up is the formative function of the PAT. It provides the teacher with information as to where the student is in achieving their
  • 5. PERFORMANCE ASSESSMENT TASKS 5 understanding about the curriculum. Depending on the students' understanding, the teacher uses this information to change the focus of the instructional program. The reason for the change in focus is to ensure that the students are gaining and understanding what is needed in the curriculum. The third purpose for performance assessment tasks is to find out and discover how the student has built meaning from the instruction. This is where the teacher differentiates the curriculum to meet the needs of every student. The reason for differentiated curriculum is simple, each student takes new knowledge and relates it to old knowledge or experiences differently (Maurer, 1996). Summing up is provide judgment information to the student, parent, or community. This is known as feedback from the teacher. The report of a PAT is the accountability purpose. It is the final word on whether a student has been able to demonstrate understanding (Maurer, 1996). The National Council of Teachers of Mathematics (NCTM) addresses the Assessment Principle. The book Principles and Standards for School Mathematics, states that: Assessment should be more than merely a test at the end of instruction to see how students perform under special conditions; rather, it should be an integral part of instructions. Assessment should not merely be done to students; rather, it should also be done for students, to guide and enhance their learning.... It is important that assessment tasks be worthy of students' time and attention. Activities that are consistent with (and sometimes the same as) the activities used in instruction should be included. When teachers use assessment techniques such as observations, conversations, and interviews with students, or interactive journals, students are likely to learn through the process of articulating their ideas and answering the teacher's questions (The National Council of Teachers of Mathematics [NCTM], pp. 22-24).
  • 6. PERFORMANCE ASSESSMENT TASKS 6 NCTM addresses the purpose of performance assessment tasks, stating that students learn to articulate their ideas and answer teacher's questions. Therefore, by incorporating effective PATs students will learn how to think and be more interactive during classroom instruction. What Theory and Research Has to Say According to the American Association for the Advancement of Science in Washington, DC: Studies that have looked closely at performance assessments find that, if the criteria is clear and that examples are available to show levels of competency, performance assessments are highly consistent across different evaluators (Kulm & Malcom, 1991). Moreover, clear indication of what is expected of students improves student performance. There are some indications at the K-12 levels that students perform inconsistently from one PAT to the next (Shavelson, Baxter, & Pine, 4(4): 347). This suggests that studentsā€™ grades will be most reliably determined from a number of Performance Assessment with other forms of assessment. This excerpt shows that performance assessment tasks are effective when used with other forms of assessment in curriculum. If there is any inconsistency in performance, the PAT should be reevaluated. Cognitive Learning Theory (CLT) defines knowledge as being constructed, while learning is a process of creating personal meaning from new information and prior knowledge (Maher & Chriest, n.d.). CLT shows assessment implies divergent thinking, multiple links and solution, critical thinking skills, prior knowledge, and applying information to new situations (Maher & Chriest, n.d.). When students work on PATs, they are using critical thinking skills, using prior knowledge, building on their knowledge, finding multiple solutions, and using application. Cognitive Learning Theory and performance assessment both mention the
  • 7. PERFORMANCE ASSESSMENT TASKS 7 importance of the social components in group work, which is, taking a variety of roles, and considering group products and processes. CLT states that people perform better when they know the goal, see models, and know how their performance compares to the standard (Maher & Chriest, n.d.). PATs emphasize what the goal is and what the quality of the work should be. Both CLT and PATs, address a variety in learning styles, attention spans, memory, developmental paces, and intelligences (Maher & Chriest, n.d.). For certain PATs, students have the choice of how to show mastery of a concept. Students all learn at different paces. PATs give the students the opportunity to work at their pace, use personal experiences, attention span, memory, and learning styles in their individual task. Furthermore, PATs incorporates Cognitive Learning Theory research by giving students real-world opportunities to apply and adapt new knowledge, self-evaluate, and engage in problem solving a nonlinear progression of discrete skills (Maher & Chriest, n.d.). Well-designed assessment tasks not only assess student understanding but teach concepts and require students to explain and communicate their solutions (Morrison, McDuffie, & Akerson, 2002). American Educational Researchers, Fuchs, Karns, and Katzaroff , found that students in performance assessment-driven instruction classes demonstrated stronger problem solving skills than comparison groups that were not performance assessment-driven (Morrison et al., 2002). This corresponds with research by the Office of Educational Research and Improvement. They researched and stated: Research suggests that learning how and where information can be applied, should be a central part of all curricular areas. Also, students exhibit greater interest and levels of learning when they are required to organize facts around major concepts and actively
  • 8. PERFORMANCE ASSESSMENT TASKS 8 construct their own understanding of the concepts in a rich variety of contexts (Sweet & Zimmermann, 1992). They also observed that performance assessments created by teachers familiar with particular state, district, or school curriculum, allowed the curriculum to "drive" the test, rather than be weighted down by testing requirements that disrupt instruction (Sweet & Zimmermann, 1992). The Pros and Cons of PATs Performance assessment tasks provide students and teachers with countless advantages when talking about assessing and learning. PATs emphasize having multiple correct answers and creative solutions, ongoing throughout the unit of study, and provide an accurate picture of student achievement (Ronis, 2007). Diane Ronis, author and professional educator states that PATs allow teachers to develop meaningful curricula, create an environment where each child has the opportunity to succeed, and provides multiple sources of evaluation that give an in-depth view of student progress (Ronis, 2007). Meanwhile, Measurement and Assessment in Teaching expresses PATs clearly communicate instructional goals that involve complex performances in natural settings in and outside of school, plus, provide instructional targets (Miller, Linn, & Gronlund). The book also addresses that performance assessment provides freedom to respond in own one's own way, which, enables students to display originality (Miller et al.). This minimizes students guessing. When grading, performance assessment encourages teacher feedback verses ranking students' performance (Blaz, 2008). Overall, students are more accountable for their own work, skills, knowledge they acquire, and self-reflection on their growth of performance by actively participating in PATs (Blaz, 2008).
  • 9. PERFORMANCE ASSESSMENT TASKS 9 On the other hand, PATs address fewer learning objectives than other forms of assessment and are typically inappropriate for measuring student knowledge of facts (Maher & Chriest). In addition to objectives, PATs are more difficult to achieve consistent scoring results, and data simplified to a single number (Ronis, 2007). Most assessment tasks require pre- assessment activities, which prepare students for the task. This takes too much time (Maurer, 1996). A major downfall for performance assessment tasks is the bias that still emerges in grading. Bias and reliability of ratings raises a lot of issue with professionals. Teachers must pay careful attention to the learning outcomes that the task is intended to assess and to the scoring rubrics that will be used in rating the performances (Miller, et al.). Going along with the professional aspect of PATs, it is difficult to determine comparability between states. Each state implements his or her own assessment tasks and interprets them differently (Maurer, 1996). Overall, one of the main concerns with teachers is time. Performance assessments require a greater expense of time, planning, and thought from students and teachers. The teachers who use PATs must also pay close attention to technical and equity issues to ensure the assessments are fair to all students (Sweet & Zimmermann, 1992). Students also spend an enormous amount of time creating, for example, portfolios. Some professionals point out that most colleges and universities still use test scores and grades for admission, so portfolios would need to somehow translate into a grade (Blaz, 2008). Types of Performance Assessment Tasks
  • 10. PERFORMANCE ASSESSMENT TASKS 10 When deciding on the best type of performance assessment task, as a teacher, there are a few decisions. Overall, there are two paths to take when creating or choosing a PAT: restricted- response performance task or extended-response performance task. The freedom provided by extended-response performance tasks enable students to display such important skills as problem solving, planning, organization, integration, and creativity (Miller et al.). This type of PAT has multiple goals that might be assigned at the beginning of a term or unit of study and used long term (Ronis, 2007). On the other hand, restricted-response performance tasks are generally easier to score and require less time than extended-response performance tasks. However, extended- response performance tasks are better suited when measuring higher-order skills (Miller et al.). One of the most comprehensive means of evaluating a learner's growth and progress using a PAT is the use of portfolio creations. NCTM states that portfolios use problem solving, communication, reasoning, and connections. They also are very specific in that they collect information at the course level about the program standards (Maurer, 1996). Portfolios are organized, a purposeful collection of documents, artifacts, records of achievement, and reflections (Ronis, 2007). Artifacts are work students complete throughout the course. Whenever a teacher leaves comments or observations on a test, paper, or assignment, the comments are creating records of achievement. The most important purpose of a portfolio is to measure the students' progress. However, the purpose is not for only the teacher to evaluate progress. Reflections are the student's personal thoughts on his or her own learning throughout the course (Ronis, 2007). This provides students with motivation, explicit examples, and engagement in their own education. The reflections can include descriptions about how they feel about
  • 11. PERFORMANCE ASSESSMENT TASKS 11 mathematics and/or an autobiography of their experience with mathematics. Portfolios also have goal-setting sheets, journal entries, standardized tests or information on such tests, students' choice of materials, projects, diagrams, pictures, reports, real-world applications, and problems created by the students (Blaz, 2008). In creating portfolios and using self-monitoring tools, teachers and students are working together to monitor progress more effectively. Therefore, as students reread their reflections or journal entries, they may see that what was once confusing or frustrating is now trivial. It also, empowers students next time they struggle to understand new concepts and acquire new skills (Posamentier et al.). How to create a Performance Assessment Task When first creating a performance assessment task, start with an idea and carefully construct the learning goals for the instructional unit (Slater & Ryan, 1993). Then decide if the idea supports learning and assessment for these goals. Once the goals are created, clearly define the knowledge and skills students need to apply. The students will also have to demonstrate these skills in solving a problem (Slater & Ryan, 1993). Then determine criteria or standards at which students will be judged. This will indicate the levels of competence (Slater & Ryan, 1993). Also, determine which components of the task need to be analyzed. Make sure to design a task that can have multiple entries, solutions, and exit points. To determine all of the criteria and standards of a PAT, it is necessary to establish the purpose of the PAT. There are three types of assessment purposes, which include diagnostic purposes, instructional purposes, and monitoring purposes. Diagnostic purposes include what students know about how to solve certain types of problems (Maher & Chriest, n.d.). Do students
  • 12. PERFORMANCE ASSESSMENT TASKS 12 know how to evaluate findings or know how to use information learned (Maher & Chriest, n.d.)? Instructional purposes are often indistinguishable from a learning activity. Lastly, monitoring purposes are to judge the level of competency students achieved in doing mathematics. Before completing the construction of a PAT, determine whether the criterion reflects the most valued elements of student performance. This can be done by testing the idea, converting the idea into a prompt, considering embellishments, consider what a student will need to know, test the prompt out, and revise according to your experience (Darling-Hammond, 1993). After revisiting the PAT, you will be able to determine if it emphasizes depth of knowledge and gain mastery of skills (Maurer, 1996). After distributing the PAT, either directly observe students or have students complete a structured student-answer sheet to evaluate various components of the task (Slater & Ryan, 1993). In form of a rubric, teachers can match student performance with criteria and determine which level most closely matches their performance. Make sure to also provide written feedback of their performance. It is important that there in a clear, logical set of activities that students are expected to follow. Students must be aware of the expectations before starting on the performance assessment task. The instructions must be specific, simple, not containing any complex sentence structures, or difficult vocabulary. This will help make sure students have the prerequisite skills and abilities needed to make the response (Miller et al.). In creating instruction, make sure to avoid any racial, ethnic, or gender bias. Furthermore, it is important to create instructions and a task that are in the appropriate reading level of all students (Miller et al.).
  • 13. PERFORMANCE ASSESSMENT TASKS 13 Other steps professionals should following while creating PATs are to make sure the task is a meaningful task in context. What real issues, problems, themes, and student interests can help determine this context (Maher & Chriest, n.d.)? When creating a PAT, determine how much the task will allow for student choice. Other choices to consider are: will there be student choice in using outside resources, choice in working individually, with a partner, or in a group (Maher & Chriest, n.d.). After creating the performance assessment task, it is important to not only test out the task, it is important to create multiple responses. When creating multiple responses, make sure each one shows a different performance level. They should follow the rubric that you created. This can minimize bias and inconsistent grading. How to create a rubric In 1995, the NCTM released a document called Assessment Standards for School Mathematics, to help reform traditional thinking about assessment in mathematics. It stated with the understanding that: All students are capable of learning mathematics, and highlighted six assessment standards: assessment should reflect the mathematics that students need to know and be able to do, enhance mathematics learning, promote equity, be an open process, promote valid inferences about mathematics, and be a coherent process.... The key to these standards is that assessment be used not to separate or rank students as examinations often do, but as a tool to improve instruction as well as report the results of that instruction (Posamentier, et al., pp. 159-163). In doing so, the decision on the best way to improve instruction and report the results of instruction is done by deciding what is the best use of rubric.
  • 14. PERFORMANCE ASSESSMENT TASKS 14 Rubrics usually fall between one of two categories: analytic and holistic (Posamentier et al.). A rubric that breaks the task into specific assessment categories and evaluated on each separately is called an analytic rubric. In mathematics, teachers could grade students on their conceptual understanding, mathematical reasoning and problem-solving strategies, and their communication. For example, a student could receive a "Satisfactory" rating in problem-solving strategies but an "Unsatisfactory" in communication (Posamentier, et al.). On the other hand, a holistic rubric considers the product as a whole. In this case, students could be graded on a five point scale (zero through four). In creating the goals and objectives in the rubric, the teacher may decide on concepts, mathematical reasoning, and communication skills. In this analytic rubric, the teacher identifies each category understanding. For example, the description for communication as unsatisfactory is identified as "Usage of mathematical terms is incorrect.ā€ The description for satisfactory is, "mathematical terminology and notation is used effectively (Posamentier, et al.)." This step is describing the levels of performance for each criterion. It is important to organize your rubric and determine whether it is an analytic or a holistic model. Teachers may want to create rubrics that reflect the model used in high stakes assessments to better prepare their students for success on those types of tests (Posamentier, et al.). Then test the rubric that was created. There may be flaws which need revisions. In creating an effective PATs, it is crucial that you create different levels of student work in anticipating common student errors and use the rubric to assess the examples. Finally, be able to correctly categorize the errors of students' work.
  • 15. PERFORMANCE ASSESSMENT TASKS 15 Depending on the PATs, it may be more necessary to create number-based rubrics on performance. For example, here is a generic rubric that represents a scale from one to six, with six being the highest: 6 - Demonstrates conceptual understanding; is complete and goes beyond what is expected; presents clear rationale; presents specific, relevant details as evidence; represents exemplary achievement. 5- Demonstrates understanding; is complete; presents rationale; presents supporting evidence; represents commendable achievement 4- Demonstrates some understanding, is fairly complete, presents a somewhat flawed rationale, presents supporting evidence that lacks detail, represents adequate achievement 3- Attempts to show understanding but is unclear; is incomplete; presents a flawed rationale; lacks supporting details; represents some evidence of achievement. 2- Demonstrates obvious misconceptions; is sorely incomplete; presents no evidence or rationale; represents no examples; represents limited evidence of achievement 1- Demonstrates no understanding; shows no real attempt; presents a restatement of the question; represents no evidence of achievement (Lim, 1997, p. 63). This rubric can be applied to any topic in Mathematics by adding on the specific goals and objectives to each level. For certain PATs, a separate rubric may be necessary for an explanation. Here is a generic rubric that can be applied to any topic in Mathematics: Answer: 4 - correct, 3 - almost correct or partially correct, 2 - incorrect but reasonable attempt, 1 - incorrect with no relationship to the problem, and 0 - no answer Explanation: 4 - complete, clear, logical, 3 - essentially correct but incomplete or not entirely clear, 2 - vague or unclear but with redeeming features, 1 - irrelevant, incorrect, or no explanation (Miller et al., p. 272). This rubric shows that a teacher can grade the student on his or her final product (answers to problems) and their explanation throughout the process of the task. The next type of rubric can be organized in a way that the teacher is assessing the students individually and as a whole (group). The following are categories for a generic rubric that can be integrated to mathematics. These assessments are done by observations of the teacher
  • 16. PERFORMANCE ASSESSMENT TASKS 16 during and post activity. The categories are: student learning styles (do the individuals), student ideas (do the individuals), communication (do the students), cooperation (do the groups), manipulative (individually or within group, do the students) (Darling-Hammond, 1993). Each of these categories signifies whether it is assessing the student individually or all together. To assess individual students on learning styles, the rubric can include the following questions: Do the individuals consistently work alone or with others, try to help others, in what ways, succeed in asking for and getting needed help, and from whom, stick to the task or become easily distracted, and become actively involved in the problem (Darling-Hammond, 1993)? All of these questions evaluate the studentsā€™ progress within the group. Other possible questions a teacher can have to evaluate the individual student within a group are: Do the individuals try to explain their organizational and mathematical ideas, their arguments with evidence, consider seriously and use the suggestions and ideas of others, attempt to convince others that their own thinking is best (Darling-Hammond, 1993)? The majority of questions a teacher can use to evaluate a students' performance in communication can be done by observing the students in the classroom. The questions consist of whether or not the student is staying on task, communicating with group members, making reports to the whole class, making a group consensus as well as their own, and synthesizing and summarizing their own or group's thinking. The teacher may also grade the students on their cooperation as a group. These questions include: whether they divided work among the members, agree on a plan or structure for completing the task, taking time to ensure they all understand the task, use time in a productive way, provide support for each member, think about recording, and allow for
  • 17. PERFORMANCE ASSESSMENT TASKS 17 development of leadership. It is important to also evaluate if individuals and the group choose and use appropriate manipulatives, share concrete objects, and appear not to need the actual objects to be able to visualize within themselves. No matter the method for creating a rubric, a teacher should help students understand rubrics when giving assignments, so that students become familiar with and try to accomplish what is required of them (Posamentier, et al.). Reflection After researching performance assessment tasks, I have concluded that they are a great method for assessing students' full understanding of classroom instruction as long as the tasks follow the objects and standards. In my opinion, the most effective way to incorporate PATs is as a summative assessment. Allowing students to inductively work on a task after learning a few lessons or the whole unit best measures the students' conceptual understanding. The length of my PATs would vary throughout the course, but the best length to assess students understanding after a few lessons is a one-to-two day PAT. This allows for students to work with classmates or individually. It also allows for the elimination of classroom instruction, which, I feel is good for student motivation. By observing students in the classroom, I gathered that they enjoy taking control of the class by working on projects or tasks. Students are motivated by real-life application and incorporating real-life application to every PAT, I feel students' conceptual and critical thinking skills will evolve more effectively. PATs also provide feedback for the students and the teacher. After administering and collecting a PAT from the students, I will look for
  • 18. PERFORMANCE ASSESSMENT TASKS 18 concepts that the class had difficulty with. Before giving a formal exam, I would have the chance to go over any concept with the class as a whole before giving a unit exam. Overall, my research topic was insightful. I became aware of the downfalls and how to construct a PAT that avoids limitations. References Slater, T.F. & Ryan, J.M. (1993) Laboratory Performance Assessment. Performance Assessment, Retrieved December 1, 2011 from http://www.flaguide.org/extra/download/cat/perfass/perfass.pdf Maher, J. & Chriest, A. (n.d.). Developing Performance Assessment Tasks. Retrieved December 1, 2011 from the Prince George's County Public Schools at http://www.pgcps.org/~elc/developingtasks.html Kulm, G. & Malcom, S. M. (1991) Science Assessment in the Service of Reform. American Association for the Advancement of Science, Washington, DC. Shavelson R.J., Baxter, G.P. & Pine J. (1991) Performance Assessment in Science. Applied Measurement in Education, 4(4): 347. Blaz, D. (2008). Differentiated Assessment for Middle and High School Classrooms. Larchmont, New York: Eye on Education. Ronis, D. (2007). Brian-compatible Assessments. Thousand Oaks, CA: Corwin Press. Maurer, R. E. (1996). Designing Alternative Assessments for Interdisciplinary Curriculum in Middle and Secondary Schools. Needham Heights, MA: A Simon & Schuster Company. Lim. L. (1997). How to Assess Student Work. Upper Saddle River, NJ: Prentice Hall.
  • 19. PERFORMANCE ASSESSMENT TASKS 19 The National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc. Posamentier, A.S., Smith, B.S., & Stepelman, J. (2010). Teaching Secondary Mathematics: Teaching and Enriching Units. Boston, MA: Pearson. Miller, D. M., Linn, R. L., & Gronlund, N.E. (2009). Measurement and Assessment in Teaching. Upper Saddle River, NJ: Pearson. Sweet, D., & Zimmermann, J. (1992). Education Research Consumer Guide. Performance Assessment. Washington, DC: Office of Educational Research and Improvement. Retrieved November 29, 2011 from ERIC. Morrison, J., McDuffie, A., & Akerson, V. (2002). A Focus for Collaboration: Developing and Implementing Science and Mathematics Performance Assessment Tasks. Retrieved November 29, 2011 from ERIC. Darling-Hammond, L. (1993). Authentic Assessment in Practice: A Collection of Portfolios, Performance Tasks, Exhibitions, and Documentation. Retrieved November 29, 2011 from ERIC. Appalachia Educational Lab, & Virginia Education Association, R. D. (1992). Alternative Assessments in Math and Science: Moving toward a Moving Target. A Joint Study. Retrieved November 29, 2011 from ERIC.