Formative and
Summative Assessments
Classroom assessments
fall into the following categories: formative and summative. Formative
assessments are the most valuable, as they present the teacher and the student
with day-by-day opportunities for discovering the studentŐs current processing
of the teacherŐs current lesson style regarding the skill being learned.
Summative assessments generally provide an evaluation of the effectiveness of
the instructional program along with student competency and are given at the
end of instruction.
The Tennessee Department
of Education has updated how we evaluate our studentŐs thinking skills.
Presently, we think of tasks in terms of BloomŐs Taxonomy when designing
objectives and target skills. We will now incorporate another set of data
called the WebbŐs Depth of Knowledge scale. The newly updated standards are
designed to implement this scale using the checks for understanding included in
each grade level.
WebbŐs Depth of Knowledge (DOK)
Level 1:
requires simple recall of information: facts, definitions, terms, and
procedures.
Level 2:
involves the studentŐs ability to make decisions about how to approach a
problem or activity such as classifying, organizing, estimating, and the
collection and comparison of data.
Level 3:
requires strategic thinking such as reasoning, planning, and using data to
think at a higher level.
Level 4:
requires complex reasoning, planning, developing to make connections both
within and among subject domains.
http://www.ride.ri.gov/instruction/curriculum/rhodeisland/resources/dokMath.htm
www.education.ky.gov/users/jwyatt/CoreContent/DOK%2012-151.PPT
Formative Assessments
Observation
Observation of students
as they use mathematics in various learning experiences is one of the most
important components of assessment. Observation involves much more than
teachers simply interacting with students or watching and listening to students
in the classroom. Observation involves the systematic collection and
analysis of observable data while comparing it to the checks for understanding
in each skill set. These observations can be used to plan and adjust
instruction and to provide key information for feedback to students and
parents.
Checklists
and Anecdotal Comments
Checklists and anecdotal
comments are useful tools to structure, direct, and record observations.
These tools are usually supplemented by conversations, conferences, and
interviews. Sometimes, when appropriate, student activities may be audio
or video taped.
Checklists - Checklists can be used to observe how students use the mathematical
processes as they listen, calculate, interact, view, and represent.
StudentsŐ mathematical products- oral, written, visual can also be assessed.
Anecdotal notes - Anecdotal notes provide ongoing records about an
individual studentŐs performance in listening, speaking, reading, writing,
viewing and representing activities, as well as their needs and language
development over a period of time. Methods of recording and keeping
anecdotal records on individual students, small groups, or the entire class
vary. Some teachers like to use self-stick notes, labels, or maintain a
separate blank page for each student in a binder. All observations should
be dated and focused on what students know and can do. If you choose to
create labels, you may keep a label sheet on a clipboard as you move around the
room. You may jot down notes to peel and stick in a notebook later. Writing
notes while you are actually observing will help you keep accurate notes on a
studentŐs progress.
Label example:
Student:_____________________
Date:________________________
Observations/Comments
Student Anecdotes form
to print
http://www.timesaversforteachers.com/index_page0059.htm
Standards-based
Rubrics
The following
information is derived from an excellent website (see below) for rubrics used
for the purpose of assessing writing assignments. The rubric information,
however, is applicable to a variety of tasks, and may be developed using the
following guidelines.
Rubrics provide clear
criteria for evaluating a product or performance on a continuum of quality.
Rubrics are not simply checklists with point distributions or lists of
requirements. Well-designed rubrics have the following in common:
1. They are task specific: The more specific a rubric is to a particular task,
the more useful it is to the students and the teacher. The descriptors
associated with the criteria should reference specific requirements of the
assigned task and clearly describe the quality of work at each level on the
rubric.
2. They are accompanied by exemplars:
The levels of quality
described in the rubric need to be illustrated with models or exemplars.
These anchor papers or sample products help both the students and the teacher
to see and understand what quality work looks like as it is described in the
rubric. These models or exemplars can come from past student work or the
teacher can create a model to share with the class.
3. They are used throughout the
instructional process: The
criteria used to evaluate student work should be shared as the task is
introduced to help students begin with the end in mind. Rubrics and
models should also be referenced while the task is being completed to help
students revise their work. They should also be used after the task is
complete, not only to evaluate the product or performance, but also to engage
students in reflection on the work they have produced.
Ideally, students should
be involved in the process of generating rubrics through the careful analysis of
exemplars: by studying the models, students draw inferences about the
criteria that are important to a successful product and then describe different
levels of performance for each criterion. http://www.greece.k12.ny.us/instruction/ELA/6-12/Rubrics/Index.htm
Diagnostic
Interview
Diagnostic Interview is
the basic technique used to assess a broad area for each child. The teacher
meets with each student one-on-one to identify the studentsŐ skills
acquisition. This information can be used to plan and adjust instruction.
Self
Assessment
Self-assessment is a
flexible and useful tool. Self-assessment helps students develop higher
order metacognitive skills and to identify individual learning goals.
Students participate in self-assessment in order to find out what they have
learned so they will know what to focus on next.
Math
Journals
Journal writing is a way
to make written communication a regular part of doing mathematics.
Students write
about such things as:
á
Their conceptual understandings and
problem solving, descriptions of ideas, solutions, and justifications of
problems, graphs, charts, and observations.
á
Their questions concerning the current
topic, an idea that they may need help with, or an area they donŐt quite
understand.
á
Their feelings about aspects of
mathematics, their confidence in their understanding, or their fears of being
wrong.
The work for many
performance tasks should go into the journal. Students should understand
that the work is important and the teacher wants to see it, but it is not
graded. A graded journal communicates that there is a specific ŇrightÓ
response you are seeking. It is essential, however, that you read and
respond to journal writing. If you do not read and respond to journals,
students will quickly come to regard them as busywork and conclude that you do
not value their efforts. On a regular basis, it is manageable to
read and respond to about five journals a night. Students can flag
entries that they want teacher attention or a response.
Writing Prompts and Ideas
á
ŇI think the answer is...I think this
becauseÉ
á
Write an explanation for other
students (or for students in a lower grade) of why 5x6 is the same as 6x5.
á
Explain to a student in grade X (or a
student who is absent today) what you learned in math class today.
á
What did you think was easy about
todayŐs math lesson? What was difficult? What do you still have questions
about?
á
After you solved todayŐs problems,
what did you do so that you were convinced that your answer was correct?
á
Write a story problem that goes with
this picture (this graph, this diagram, this equation)
Journals for Early Learners - Students respond to a topic or a prompt on a
large flipchart. The teacher writes their ideas, adding their
contributorŐs name, and even drawings when appropriate.
http://www.pbs.org/teachersource/whats_new/math/assessment0999.shtm
http://www2.ups.edu/community/tofu/lev2/journaling/writemath.htm
http://facultystaff.vwc.edu/~dwilkinson/journal_writings.htm
http://math.about.com/library/weekly/aa123001a.htm
Folders
and Portfolios
Folders and portfolios
are collections of studentsŐ work that exhibit the individual studentŐs effort,
progress, and achievements in one or more areas. The collection must
include student participation in selecting the contents, the criteria for
judging merit, and evidence of studentsŐ self-reflection. Portfolios can
be placed in three-ring binders or folders and students can have regular
scheduled times to update their portfolios. Folders and portfolios can be an
important part of the assessment and evaluation process. These tools also
help students become more accountable, more independent, and more responsible
for their learning. Folders and portfolios can assist in reporting, and
can be used as a basis for conversation between the teachers, the student, and
the parent. Students can also take time to reflect on what they have achieved,
what they are including in their portfolios, and the goals that they have set
for themselves. Folders and portfolios can include a number of work
samples that reflect the objectives of their curriculum, the studentsŐ
processes and products, and self-evaluations including personal achievements
and goals). After parent-student-teacher conference, parent comments can
be added.
Performance
Assessment (student work)
Performance assessment
in mathematics allows students to demonstrate their understanding of a
mathematical concept. There is more emphasis on studentsŐ thinking and demonstrating than traditional paper and pencil tests.
Since students are able to show what they understand, performance assessments
allow for students at all achievement levels to be successful. A low
achiever can demonstrate what he or she knows, and a high achiever can use the
same assessment to show a more in-depth understanding of the same concept, all
while using the same assessment questions.
Performance assessments
allow teachers to evaluate the mathematical process standards as set forth in
the NCTM Principles and Standards. Processes such as problem solving, reasoning, and
communication can best be assessed through student observation. These processes
are difficult to assess by traditional tests alone. Performance
assessments allow educators to get a more Ňthree-dimensionalÓ view of studentsŐ
thinking.
Homework
Homework can serve
several purposes. It can be used to reinforce, apply, or extend the math
children are learning in class (Burns and Silbey, 2000). All homework should be
based on skills and concepts that have already been taught and never anything
new. Homework assignments given for reinforcement lets students practice newly
learned skills through drills (Van De Walle, 2004). Other homework allows for
the practical application of mathematical concepts through problem-based tasks.
Extension exercises permit individualized and creative thinking by emphasizing
student initiative and research (Eddy, 1984). Homework also allows parents to
stay abreast of what their children are learning.
Additionally, homework
can be a source of informal assessment. Teachers can view homework after being
checked, and identify those concepts or skills with which students had the most
difficulty. This is valuable information that can be used during the planning
phase of instruction. Homework, too, can provide data regarding individual
students that is helpful in diagnosing their strengths and weaknesses (Burns
and Silbey, 2000).
There are four
generalizations that can guide the teachers in the use of Homework (Marzano,
Pickering, & Pollock, 2001):
3
The estimated
amount of homework assigned to students should be different given the grade
level.
á Grades K-1 10 minutes
á Grades 2-3 30 minutes
á Grades 4-5 40 minutes
3
Parental involvement in homework
should be kept to a minimum.
3
The purpose of homework should be
identified and articulated.
3
If homework is
assigned, it should be commented on.
Summative Assessments
Testing
Testing will always be a
part of teaching. We test to get an idea of student performance on
certain concepts and skills. Testing should reflect the instruction being
taught. However, tests should not only be used for computation and basic
skill knowledge, but they need to allow students to demonstrate a conceptual
basis for the process. Tests should go beyond the basics and give the
teacher an idea of how the students think, process, and connect ideas. The goal
of these evaluations should be to
determine if students have mastered specific competencies and to identify
instructional areas that need revision. Examples of summative tests include
chapter tests, final exams, statewide exams, and national exams.
More information on assessments:
http://fcit.usf.edu/assessment/basic/basica.html
http://my.nctm.org/eBusiness/ProductCatalog