Assessing Learning through Classroom Research: The Supporting Teachers
as Researchers Project
By Sheela Diederich
As every teacher knows, a positive classroom environment helps children learn.
But what are the characteristics of a classroom culture that helps every
child achieve?
Teachers need to maintain a classroom culture that challenges students to
give support for their ideas and that accepts every student's input in order
for all students to be successful learners. Without such a culture, teachers
will have difficulty discovering the varied ways their students think and
understand. If teachers are not fully aware of the differences between their
students' reasoning abilities, how can they teach to diverse learners so
that they all succeed? Without such awareness, students will be forced to
work at levels either too sophisticated or too limiting for their current
skills.
I know well the span of abilities and readiness levels that can be found
in a single classroom. I taught kindergarten for several years, and my students
ranged from those who started school already reading to those who knew only
a few letters and could barely write their names. The diverse needs of these
children required a differentiated style of instruction.
During this past summer, I attended a math academy where a group of teachers
avidly worked to define successful classroom culture. After several intense
meetings and discussions, an effective classroom culture was established
as one that allows and encourages children to share their ideas without fear
of being "right" or "wrong." While the right answer is important, it is equally
important for a child to feel comfortable communicating his ideas to his
classmates.
I work the entire school year to establish a classroom culture where students
take responsibility for their learning and that of their peers. I talk explicitly
with my students about how we work together and learn from each other. We
challenge each other by asking one another to prove that our answers are
acceptable and by explaining our strategies.
An Emphasis on How
Early in September, my first graders had to address the following math problem:
"If I have six apples and four bananas, how many do I have altogether?" Each
student was asked to use pictures, numbers, and/or words to show the rest
of the class how she came up with the answer. Manipulatives, such as unifix
cubes, buttons, and plastic counters were available for them, and many of
the children preferred to take a tub of the manipulatives to begin.
One child told me that the answer was ten. "How do you know it's ten?" I
asked. "Easy, I just knew," Jason told me. "What can you draw or write to
show me that six and four really make ten? How do you know it won't be eleven
tomorrow? What evidence do you have?" These are the kinds of questions I
ask to encourage my students to share their thinking strategies with the
class. For a child who doesn't know how to solve the problem, I ask him,
"where might you begin," or "what could you do first?" "Maybe, you will want
to draw pictures," I suggest. The children need to know that while we want
the right answer, we need to be able to explain how we got that answer. The
children are then made aware that they can use the strategy again to help
them solve other similar problems.
As they worked to solve the problem, I saw some children draw six apples
and four bananas and count each item individually. Some used other methods.
This task was open-ended enough to allow all of the children to participate
comfortably and to work at their differing ability levels. The children were
able to demonstrate the complexity of their thinking by writing and explaining
their solutions. Any way the children choose to use writing to share their
thinking, whether it be words, pictures, or numbers, is especially helpful
for finding out what they are thinking and what they already know. The emphasis
is on explaining and justifying how the strategies they use work, and all
answers are accepted. Children working at their own ability level use what
is comfortable to them—pictures, words, numbers, manipulatives—to solve a
problem and complete a task.
When the children finished writing their solutions, we talked about what
strategies they used to solve the problem. On chart paper, I recorded the
solutions I had seen the children using as I interacted with them during
our work session. Not only did they hear their peer's explanation, but they
also saw it being modeled on the chart paper. The next time we solve a similar
problem, they may want to try solving it by using one of the strategies that
was recorded.
Finding Solutions at Their Own Pace
Early in the year, there was evidence of concrete thinking. All students
used manipulatives to show their work for solving problems. Some children
showed only two different ways while other children conceived multiple strategies
to complete the task.
Later in the year, my students moved into increasingly abstract levels of
thinking using more developed strategies. Many children began to use manipulatives
and write with pictures, numbers, and even words to tell how they approached
a task. For example, when using cuisenaire rods to make ten in as many ways
as they could, Robin drew pictures of her rods and wrote sentences to describe
her procedures while Jack drew his rods and wrote numbers to show how he
made ten.
By January, all children were asked to record on paper how they solved a
problem. They could still use manipulatives, if they chose. For each problem,
they first worked on their own, and after a few minutes, they shared their
ideas with a partner. Then as a group they shared their strategies and recorded
them on chart paper. At least four different strategies were modeled as the
children told their peers how they worked on these tasks.
Until this point, the strategies hadn't been given formal names, but I could
see that many of them were using the "counting on," "making tens," and "finding
doubles plus one" strategies for addition. The strategies came from the children—not
from the teacher. While telling children about these different addition strategies
may be faster, in the end it is not as meaningful for the children or as
successful. Allowing children to develop the strategies as if they were their
own fosters a real sense of independence, ownership, and empowerment. Eventually,
as different strategies are used repeatedly and are discussed in our group
sessions, we label the strategies by formal names.
Some children progress at different rates than others. Allowing children
to learn at their own pace is a real challenge for teachers. The pressures
of time and expectation of immediate results place heavy demands on teachers
to move children through an expansive and overwhelming curriculum. A teacher
must trust that his students want to learn and that they have the capacity
to do so—even if their pace is different from his.
Different Solutions for Different Kids
In early January we read Each Orange has Eight Slices by Paul Giganti, Jr.
Our conversation centered around how groups of seeds and oranges could be
combined together. Then, the children decided to make flip books about number
combinations. They could choose any number up to twenty to be the sum of
their number combinations.
Kari chose the number twenty and wrote "five flowers with four petals each
makes twenty." She drew five flowers, each with four petals. (Sounds a bit
like early multiplication.)
Ellie is at a completely different level. She chose to write about thirteen.
She drew one red dot and twelve black dots. She recorded one number combination
and was stuck. Together, we pulled out the manipulatives. After working with
them she was able to find three other ways to make thirteen.
Without opportunities to work at their own individual readiness levels, these
children would not have been challenged successfully. Had I chosen the sum
for the number combinations and directed how to write the books, Kari would
have been stifled and Ellie would have felt frustrated. This activity opened
the door for these children to be successful at their own levels. An accepting
classroom culture that allows children to learn at their own pace enables
them to be successful and gain a real understanding of the concepts we try
to teach.
Assessment Strategies
Teachers can collect evidence of their students' learning through day to
day interaction with them and through their paper records of strategies and
solutions. As a teacher interacts with a child, asking questions and examining
the child's oral and written explanations, she can observe and assess whether
or not the child is learning. A child who is making progress uses increasingly
complex strategies. He will explain his thinking in increasingly explicit
terms orally and show clearer organization of his thoughts on paper. The
child will represent solutions and strategies in different ways with numbers,
pictures, and words. A student who is improving also asks questions about
his peers' thinking in an attempt to understand the strategies they use.
If a child exhibits these traits, he is learning.
As a classroom teacher, I collect written samples of students' work and keep
them in a portfolio. These work samples inform my teaching and guide the
types of math problems I will present to students. I record brief notes about
a few children each day as I observe them making connections and trying something
new. These assessments keep record of the development of my students' progress.
To ensure that all children with different abilities and readiness levels
achieve, a teacher can provide a wide range of open-ended activities. However,
without properly establishing a nurturing, challenging classroom culture,
even open-ended lessons will not be completely successful. In an classroom
full of students with diverse learning styles and needs, teachers need to
create a culture where probing questions are asked, open-ended activities
are provided, all students' responses are accepted, students explain their
thinking, and all children are expected to participate actively.
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