FORMATIVE ASSESSMENTS
WITH EMPHASIS ON GROUP
WORK
Dr. Revathy Parameswaran
Fulbright Distinguished Awards in Teaching Program
Capstone Project
12-12-13
Contents
BACKGROUND OF THE STUDY ........................................................................................................... 1
AIM OF THE STUDY .............................................................................................................................. 2
LITERATURE ........................................................................................................................................... 3
COLLABORATIVE LEARNING ...................................................................................................................... 3
GROUP WORTHY TASKS ............................................................................................................................. 5
CHALLENGES IN CONDUCTING GROUP TASKS .................................................................................... 8
COMPLEX INSTRUCTION: ........................................................................................................................... 9
CODING OF ABILITY LEVEL ...................................................................................................................... 11
GRADING METHODS FOR GROUP WORK ........................................................................13
INSTRUCTOR ASSESSMENT OF GROUP PRODUCT ....................................................................... 13
ASSESSMENT OPTION ............................................................................................................................. 13
ADVANTAGES.............................................................................................................................................. 13
DISADVANTAGES ....................................................................................................................................... 13
Shared Group Grade ...............................................................................................................................13
Group Average Grade.............................................................................................................................13
Individual Grade - Allocated task .....................................................................................................13
Individual Grade - Individual report ................................................................................................. 13
Individual Grade - Examination .........................................................................................................13
MY INQUIRY ........................................................................................................................................14
ANALYSIS OF THE DATA ....................................................................................................................15
EFFECTIVE FORMATIVE ASSESSMENTS .............................................................................................. 15
USING GROUP WORK AND THE PERCEIVED ADVANTAGES ......................................................... 15
USING THE RESULTS OF FORMATIVE ASSESSMENTS IN TEACHING PRACTICES .....................17
ASSESSING GROUP WORK ...................................................................................................................... 17
ASSESSING INDIVIDUAL WORK IN A GROUP TASK ......................................................................... 18
DISCUSSION AND CONCLUSION ......................................................................................................19
REFERENCE ..........................................................................................................................................20
1. HELEN FEATHERSTONE, SANDRA CRESPO, LISA M. JILK, JOY A. OSLUND, AMY NOELLE PARKS, MARCY
B.WOOD. (2011), SMARTER TOGETHER! COLLABORATION AND EQUITY IN THE ELEMENTARY MATH
CLASSROOM. .................................................................................................................................................... 20
ACKNOWLEDGEMENTS .................................................................................................................21
BACKGROUND OF THE STUDY
There is a paradigm shift in the assessment processes as the Central Board of
Secondary Education in India moved from traditional schooling to empowered
schooling. In this context learning is meant to be experience centered with focus on
developing multiple literacies and to de-stress memory based learning.
The CCE (Continuous Comprehensive Evaluation) was introduced with its main focus
on evaluation of students’ knowledge, understanding, comprehension, application,
analysis and creativity. The formative assessments were designed to help both the
teacher and the learner. For example when poor performance is observed using
diagnostic tests, it is followed by appropriate interventions including retesting.
This new trend in assessment is in its infancy in India. Since In my host country
formative assessments has been an integral part of the curriculum for a long time it is
meaningful and a learning experience for me to study the different kinds of formative
assessments used here.
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AIM OF THE STUDY
Broad study: To get a broad overview of formative assessments used in mathematics
by school teachers in their classroom. To understand how the results are used to
inform teaching practices and learning options. Also to study the potential of group
tasks and assessment of group work as effective formative assessments.
Specific study: In India the teaching methods are mostly teacher centric and in
recent times the importance of having collaborative learning practices is being
emphasized. Hence a detailed study of group work in the host country would help me
understand its role in classrooms.. The focus of my study is to understand the different
criteria which contribute to enhancement of personal and group achievement in a
collaborative activity as opposed to independent work Also I wish to understand how
teachers assess group work. The challenge is to test an individual understanding when
he or she works in a collaborative setting, working as a part of a group towards a
solution to a mathematical problem. Also to study how the transactions that take
place during group work and group discussions can effect teaching practices and serve
as good formative assessments. This study will help me in incorporating the best
practices in my own teaching and teaching in my school
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LITERATURE
COLLABORATIVE LEARNING
DEFINITION: Collaborative learning is defined as students working together in a group
small enough that everyone can participate on a collective task that has been clearly
assigned. The students are expected to carry out their task without direct and
immediate supervision of the teacher.
PRODUCTIVITY: The productivity of collaborative learning ranges from achievement
of basic skills, memorization of factual materials and application of routine algorithms
to conceptual learning and higher order thinking skills. A small group is suggested for
productivity of conceptual learning and higher order thinking skills since many
researchers believe that such knowledge outcomes cannot happen without the
possibility of suitable discourse or conversations within small groups having potential
for processes of discovery.
Productivity can be measured in terms of desirable prosaically behavior, such as being
cooperative while engaging in group tasks, and, being friendly and respectful towards
other members in the group.
INTERACTIONS DURING GROUP TASKS: The type of interaction which is very effective
and which is most needed will depends on two things namely the nature of task that
is being executed and the instructional objective. We have two types of tasks namely
1 Tasks which have clear procedures and right answers and the objective being
routine academic learning or knowledge acquisition of standard concepts and facts.
2. Tasks which are thought provoking and exploratory in nature and the objective is
conceptual learning and building higher order thinking skills.
Hence we have at least two different types of tasks with two different objectives. For
the first type of task which requires learning from each other and making routine
calculations, discussing and verifying, a group can be heterogeneous. Children of
varying abilities will profit from each other. Those who explain their understanding to
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others have to arrange their thought processes in a logical order and hence in their
effort to communicate gain in the process and the others who learn from them gain in
their understanding. For the second type of task having a homogeneous group of
students with a reasonably good mathematical ability will accelerate achievement. In
such a setting where the tasks are open ended and requiring higher order thinking
skills, having students with mixed ability can cause tension and lower the confidence
level in low ability students. In such a context students with different strengths like
possessing problem solving strategies, visualization skills etc can further accelerate the
achievement ofthe group. Hence selecting group members can be a non-trivial task
depending on the instructional goals. In the case of tasks of the second type if they are
too structured they can become dysfunctional because it can impede free thought and
conceptually oriented interactions. In the case of tasks of the first type structuring of
the tasks can foster learning and understanding.
Complex instruction is not a magic pill. It contains no formula or checklist to
follow. In addition to strong content knowledge and knowledge about students
and knowledge about how students think and learn math, successfully
implementing complex instruction requires a deep belief that all students can
learn, that teaching is more than delivering information and learning is more
than listening. Complex instruction is in fact complex. Its components interwine.
Lisa Jilk
Collaboration and Equity in the elementary math classrooom
4
GROUP WORTHY TASKS:
One of the important questions that arises in the literature is what kind of tasks are
worthy of group work since it does not make sense to have tasks which could be done
individually to be given as a group task.
What are worthwhile tasks suitable for group work?
1. Tasks that do not separate mathematical thinking from mathematical
concepts and skills.
2. Tasks that capture students’ curiosity.
3. Tasks that invite students to speculate and pursue their hunches.
4. Tasks that can be approached in more than one interesting and legitimate
way.
5. Tasks which have more than one reasonable solution.
6. Procedures with connections invite students to figure out relationships and
build connections.
EXAMPLES OF GROUP WORTHY TASKS
1. Construct a poster that shows 4 ways of solving and explaining the
following number sentence 15 x 49 = ?
Your explanation could include
grids, pictures, charts, algorithm, written expression or any other way your
group can think of explaining the equation. Each member in the group
should be prepared to show and explain your group’s answers.
Suggestion: To look for connections among the multiplication strategies.
2. (Adapted from Deborah Ball’s 1992 hypermedia materials)
Each of you should work alone for the first 10 minutes writing as many
number sentences equal to 10 as you can. (For example. 6 +4 =10, 1+9 =
10). After 10 minutes I will flash the lights and you should stop writing new
number sentences and look at all the number sentences that everyone in
your group has written. Look for patterns. Write down as many patterns as
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your group can find. Make sure that everyone in the group understands
and agrees to each pattern that you write down and that each person in
the group can explain each pattern. Each of you should explain your
thinking in your math journal.
Make a poster that has at least 4 number sentences from each person in
your group. Use these number sentences as well as words, symbols, and
pictures to describe the patterns your group found. If you have time after
you have made your poster, talk about this question in your group. What is
the largest number of sentences equal to 10 that anyone could write? Be
ready to explain to the rest of the class both your answer to this question
and the answers of others in your group.
For the second task some of the patterns that the group members wrote
down were:
1. If you write a number sentence that is equal to 10 you can make
another number sentence by making the first one smaller and the
second one bigger.
2. If you make the first number bigger then you have to make the second
one smaller.
3. If the first number is bigger than 10 then the second one has to be a
take away.
4. You can start with any number and make a number sentence equal to
10.
5. If you have a number sentence like 21-11 = 10 you can make another
number sentence by making the first number bigger and making the
second one bigger.
These responses suggest that group worthy tasks of the above nature have the
potential to stimulate such rich mathematical thinking and in fact help students see so
many connections and patterns that may not be possible with routine tasks. Also
preparation for whole group discussion tells teachers what might be the focus for the
discussion. Teachers use the inputs they derive from the group tasks to work on the
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focus of the whole group discussion. Thus the group tasks are effective formative
assessments. Also during the whole group discussions when students articulate their
mathematical thinking, it offers great possibilities for teachers to make sense of their
understandings and misunderstandings.
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CHALLENGES IN CONDUCTING GROUP TASKS
There is evidence throughout literature on the advantages of collaborative learning.
There is also evidence that conducting group work, choosing group worthy tasks that
facilitates interactive learning and mathematical discourse comes with plenty of
challenges.
1. To create group worthy tasks it needs teachers to choose suitable tasks with
the above mentioned criteria but also in a way to anticipate the possible
interactions, the different solutions and possible misconceptions as well.
2. To ensure that every student in the group participate and that some student
does not dominate is also a challenge.
3. To make children open-minded to the arguments of others is important for a
fruitful discussion and useful dialogue.
4. It can happen that those who participate in the group discussions that follow
the tasks learn the most while those who do not learn the least.
5. The role of the teacher is to facilitate the discussions in a way that fosters
mathematical communication and justification. It is important that when
children discuss and argue different viewpoints that they understand what is a
mathematically correct argument. In other words the activity can promote
mathematical thinking and justifications.
6. To maintain the dynamics between launching worthy tasks, allowing
independent exploration or solving mathematical problems and justification
through group discussions is the biggest challenge. Tasks can be group worthy
but not necessarily have the scope for good mathematical discourse. In that
case it is still an advantage for the teacher to conduct the group task . What is
important is that the teachers know what they are looking for in a group task.
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COMPLEX INSTRUCTION:
It is a set of ideas and strategies for addressing the problems that seem to challenge
group work and block powerful learning for children. Elizabeth Cohen (2002) coined
the term complex instruction. According to her
Complex instruction is a set of strategies for creating equitable classrooms. Using
these strategies, teachers can teach to a high intellectual level in academically and
linguistically heterogeneous classrooms.
Her ideas on complex instruction have its roots on the following theory of learning. For
centuries the model that dominated thinking about teaching and learning is a linear
one. In this model the teacher’s role is to decide what lessons to teach, divide this
content into manageable units, organize them in a logical order and then walk the
learners through them in a logical order. This model is like that of a ladder, each skill
builds on the one before, and if we break them down appropriately and present them
in a logical order then we can deliver the content without confusing the learner. In
fact mathematics is not a ladder but a web. Almost always there are many ways to
solve a math problem even a simple one. The different ways build on different
understandings and different ways of making sense of mathematics. In the ladder
model there is more scope for people to settle down with one way of understanding
an idea, solve a problem, move on to another. On the other hand complex instruction
derives from
1. Different understanding of how people learn.
2. Different image of what it means to understand a mathematical idea.
It builds on the idea that learning is complex and that learners because they bring
different ideas and understandings to a novel problem will make sense of the problem
in multiple ways.
Hence in complex instruction certain features listed below are in place.
1. Children are working in groups of three to five on group worthy tasks.
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2. The teacher has composed the groups randomly. The membership of the group
varies at regular intervals.
3. The teacher structures the assignment in such a way that all children must
participate in the intellectual work of problem solving.
4. The teacher holds all children in each group responsible for understanding the
work that their group has done together. Every student must be prepared to
report to the rest of the class on his or her group’s problem-solving strategy.
5. Each child has a role to play both intellectually and in terms of practical work.
Complex instruction is not a magic pill. It contains no formula or checklist to
follow. In addition to strong content knowledge and knowledge about students
and knowledge about how students think and learn math, successfully
implementing complex instruction requires a deep belief that all students can
learn, that teaching is more than delivering information and learning is more
than listening. Complex instruction is in fact complex. Its components interwine.
Lisa Jilk
Collaboration and Equity in the elementary math classrooom
10
Cohen’s work on complex instruction is based on research focused on learning how to
teach, students who have a diverse range of prior knowledge, language abilities and
social status. Importantly it assumes every child is academically competent.
The social and academic status often impedes students’ participation and learning. For
example some communities have assigned more values to English than any other
language because people sometimes assume that others who do not speak English
fluently do not have the same competence as native English speakers. The outcome of
such a belief is that a black student may actively disengage himself from doing a
mathematics task because he believes that white students in his group have more
mathematical skills.
Some students do not want to participate because they do not feel smart. Also when a
person dominates the conversation and takes over the task and does all the work is
also not learning enough mathematics.
CODING OF ABILITY LEVEL: To determine the effect of ability level on
performance and behavior, pretests are administered at the beginning of the study.
After the group work, the students are assessed using a rubric which involves
components pertaining to the task in question. When a group is working on a problem
some of the factors that will be considered are whether the students
1. Made mistakes which were corrected and were told the correct procedures for
solving them.
2. The learners in the group indicated non understanding of the methods of
solving and were told the correct procedures
3. Copied other students’ work.
4. They did not contribute verbally to group discussions.
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GROUP ASSESSMENT AND GROUP PROCESSES:
Group assessment without knowledge of group processes cannot be valid indicators of
individual competence.
1. Study of group processes can only help to distinguish among students who learn to
solve problems with little or no help from the group,
2. Students who solve by working collectively with others
3. Students who use resources from the group to obtain the correct solution by
copying others’ work or being told what to do without any recourse to understanding.
Group assessments will not be able to distinguish between these categories. All these
students will score high in group assessments. Hence group assessment can
overestimate individual scores without knowledge of group processes. Knowledge of
group processes help to measure the productivity of students when working in groups,
measure collaboration skills and problem solving processes.
Assessing group work is a non-trivial task. Depending on the aims of the task, both the
process and the product related skills must be assessed. Second group performance
must be translated into individual grades which lends itself into the question of
fairness and equity. Also because very often neither group processes nor individual
contribution are necessarily apparent in the final product. Thus the instructor needs to
devise methods of obtaining that information.
Here is an example of grading methods for group work produced by Eberly Center for
teaching excellence, Carnegie Mellon.
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Grading Methods for Group Work
Instructor Assessment of Group Product
Assessment Option
Shared Group Grade
The group submits one product and all group
members receive the same grade, regardless
of individual contribution.
Group Average Grade
Individual submissions (allocated tasks or
individual reports) are scored individually.
The group members each receive the average
of these individual scores.
Individual Grade - Allocated task
Each student completes an allocated task
that contributes to the final group product
and gets the marks for that task
Individual Grade - Individual report
Advantages
Disadvantages
encourages group work - groups
sink or swim together
decreases likelihood of plagiarism
(more likely with individual
products from group work)
relatively straightforward method
individual contributions are not
necessarily reflected in the marks
stronger students may be unfairly
disadvantaged by weaker ones
and vice versa
may provide motivation for
students to focus on both
individual and group work and
thereby develop in both areas
may be perceived as unfair by
students
stronger students may be unfairly
disadvantaged by weaker ones
and vice versa
a relatively objective way of
ensuring individual participation
may provide additional motivation
to students
potential to reward outstanding
performance
difficult to find tasks that are
exactly equal in size/complexity
does not encourage the group
process/collaboration
dependencies between tasks may
slow progress of some
ensures individual effort
perceived as fair by students
precise manner in which
individual reports should differ
often very unclear to students
likelihood of unintentional
plagiarism increased
may increase motivation to learn
from the group project including
learning from the other members
of the group
may diminish importance of
group work
additional work for staff in
designing exam questions
may not be effective, students
may be able to answer the
questions by reading the group
reports
Each student writes and submits an individual
report based on the group's work on the
task/project
Individual Grade - Examination
Exam questions specifically target the group
projects, and can only be answered by
students who have been thoroughly involved
in the project
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MY INQUIRY
The objective of the inquiry is to have a dialogue with teachers about what kind of
formative assessments they use in their classroom and how they use the results to
inform their teaching practices. In particular to know if they use group work in their
classrooms and how they assess the group work and individual learning during group
work. A questionnaire was prepared and sent to many teachers. The questionnaire
contained the following questions.
1. What are the types of formative assessments that you employ in your class room?
(Formative assessments are assessments used to inform teaching and learning
practices.)
Select as many as are applicable:
Personal interviews
Class room observation
Interactions with the student
Group Work
Tests
Assignments
Written Quiz
Other:
2. How do you use the results of these assessments to inform your teaching
practices?
3.In your experience what type of formative assessment have you found to be most
effective? Give an example.
4. Have you used group work anytime in your class? What do you perceive are
advantages of group work?
5.For what kind of tasks do you think group work is more effective than individual
work?
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6 .How do you assess group work?
7.What tools do you use to measure individual learning in a group task?
ANALYSIS OF THE DATA
EFFECTIVE FORMATIVE ASSESSMENTS
SAMPLE RESPONSES:
1. Quizzes are most effective as they give a quick snapshot on a few topics.
2. Open note exit quizzes are very effective.
3. Interactions with individual students are helpful in finding what help they require
4. Open ended questions are very effective formative assessments.
5. Quizzes are best the ways for students to convincingly demonstrate their
knowledge.
6. Exit tickets are useful to identify mistakes.
7. Assignments with clear learning intentions are very good formative assessments.
USING GROUP WORK AND THE PERCEIVED ADVANTAGES
SAMPLE RESPONSES:
1. Groups of 4 and think/pair share type of group work help students to learn
from their peers. In math sometimes they can explain better to each other.
Also they learn from each other’s mistakes.
2. Group work gives opportunities for collaboration and richer and more
engaging student interaction and dialogue. Students of different ability levels
and interests/expectations working with and learning with and from one
another. Students learn to negotiate and work with one other.(Social inter
personal learning).
3. The kids learn to talk better. I let them do problem solving in groups if they
want to. I use group work as a way for students to review previously taught
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concepts, skills. The advantage is that students feel comfortable with the
learning goals because they have already been taught. They are able to work
together and figure out solutions.
4. I use group work and partner work. It gives them someone else to talk to about
the problem especially in a big classroom where it is difficult to talk to everyone
and the group tends to generate more than one idea or method to solve a
problem and students seem to be more flexible and willing to try something in
a group. We try to give group work since it allows me to spend less time
answering questions and doing informal assessments. Students can cooperate
on the problem that they individually may not be able to do so but can each
bring a piece to the table. To do review and explain concepts to one another.
5. I use group work in every reading and math class. Also when I need to do
sorting. I think student discourse is very helpful. I like to use heterogeneous
groups so students have more opportunity to learn from one another. Group
members determine the effectiveness of a group.
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USING THE RESULTS OF FORMATIVE ASSESSMENTS IN TEACHING
PRACTICES
SAMPLE RESPONSES:
1. See what concepts are missing most and reteach those concepts. Provide
additional support.
2. Alter next year’s lesson plan.
3. Make my teaching better.
4. Sometimes the material is too easy and we need to move on. Identify students
in need. Scaffold and differentiate tasks. Common mistakes addressed through
warm-up problems.
ASSESSING GROUP WORK
1. I use rubrics to measure participation, cooperation and the quality of the final
product, student talk, student work and group dynamics.
2. .Usually I use sometimes a grading rubric. I have given all the students the same
grade. I have given students different grades based on peer reviews. I have given
students different grades based on how they participated in the group or group
presentation. Sometimes I allow students to turn in one assessment for the entire
group and sometimes I expect each individual to turn in the assessment.
3. Group work is harder to assess formally since I do not know where ideas came from.
I try to have different students take ownership from different pieces, which works a
little, but mainly avoid assessing group work more than just checking in and seeing if
they are all working and seem to be understanding
4. Observing what they leaned in final test I don’t assess group work
5. Grading the groups’ papers completion grade at times and other times each person
must turn in an assignment. Depending on the activity I will assess each person
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individually or give the entire group the same grade. Sometimes informally by
observing the participation.
My group work is not assessed but when I assess it, I use either a rubric or a
monitoring tool to do it. Sometimes I have students present projects or findings. I have
students fill out their own worksheet (never a common sheet). I have students grade
each other’s work or swap each others’ work for a grade.
6. Observation sheets, Videos, Checklists and rubrics. Teacher, peer and self. Fish bowl
technique. It depends on the assignment. Most of the time I have students self assess
as part of the assignment. If I see anything I can objectively judge, such as a student
not doing any work while the others are working then I can deal with that on an
individual basis.
ASSESSING INDIVIDUAL WORK IN A GROUP TASK
1. Same as individual task. Using student work and anecdotal records.
2. I try to keep everyone in the group working but there are times when not
everyone in the group is progressing. Hence I use group work only as a part of
my lesson and make sure to have individual work as well.
3. Review of individual assessments, individual exit slips, quizzes, walk around and
assess informally.
4. Asking individual students to explain in a specific activity. Each group gets 4
problems ( 4 people in a group). Each person is responsible for one problem
and the group cannot move on until each problem is correct.
5. I find it difficult to differentiate between group members in these tasks as I
cannot necessarily rely on the group to self-assess effectively. (Either they are
too harsh or too forgiving.) and reliably observe everyone in hand.
6.
Measure or assess? Observation sheets, videos, checklists and rubrics, Teacher,
peer and self- rubrics, observation in the classroom setting, worksheet, exit slip,
follow up quiz, individual problem completion after group completion problem
solving.
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DISCUSSION AND CONCLUSION
I had set out to study different kinds of formative assessments used in mathematics
classrooms in schools in the US, with particular emphasis on assessment of
collaborative work as well as individuals involved in collaborative work. I had the
opportunity to observe classrooms in the US, discuss with the teachers on issues
concerning assessment of individuals engaged in group work or collaborative learning.
I also studied the paper of Cohen analyzing research on the topic of effectiveness of
collaborative learning.
I had prepared a questionnaire on formative assessment encompassing assessment of
understanding an individual engaged in self-study, collaborative learning, as well as
assessment of the group work as a whole. Based on the responses and my own
understanding based on discussions with the teachers and classroom observations, I
am lead to the following conclusions:
•
Quizzes emerge as the single most favored assessment tool. Open ended
questions lead to better understanding of learner’s level of understanding of
concepts.
•
There are definite advantages to group learning. As they talk to each other and
express their views on a problem, their understanding of the concepts
improves. They learn from their peers and from each other’s mistakes. It helps
in improving communication skills and social interactions.
•
The formative assessment helps teachers to change their lesson plans as the
need arises, re-teach certain concepts, do the lessons differently in the
following year.
•
Various methods are used to assess group work. A common tool is to use
rubrics. But there seems to general consensus that this is not an easy task.
Some teachers seem to prefer to test individuals after the group task is
completed. Some merely observe but not assess group task.
•
As for evaluating individuals, again, there is no common assessment tool
uniformly preferred among the teachers. Some teachers prefer to supplement
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the group task with an individual task. Some teachers give, say four problems
for a group of four and hold each student responsible for one problem.
In summary, group tasks enhance learning. When a group of children work on a
problem together, the network of ideas they bring to the problem serves as a resource
to the members of the group. Since learners come up with new ideas with different
background knowledge, they will find different paths into the problem. Hence multiple
representations of mathematical problems serve as a resource for the group.
According to my study Quizzes are one of the most widely used formative assessments.
Also there is enough evidence in the literature to substantiate the fact that frequent
quizzing does promote learning. It calls for regular study hours, provides a more
focused review of content. Researchers have found that quizzes facilitates “effort
retrieval” process which aids learning.
REFERENCE
1. Helen Featherstone, Sandra Crespo, Lisa M. Jilk, Joy A. Oslund, Amy Noelle Parks,
Marcy B.Wood. (2011), Smarter Together! collaboration and equity in the
elementary math Classroom.
2. Cohen, E.G. (1994) Restructuring the classroom. Conditions for productive small
groups. Review of educational research 64(1) 1-35
3. Felix Kwan. (2011) Formative assessment: the one-minute paper vs. the daily quiz.
Journal of Instructional Pedagogies.
4. Assessing Group Work-Enhancing Education-Carnegie Mellon. www.cmu.edu.
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