Assessment ◆ 155is incomplete. Teachers will contact me and say, “Nicki, the kids could
answer the question but they couldn’t do the tape diagram.” To which
I reply, “Well then they could only answer part of the question and so they
get partial credit because being able to model one’s thinking is part of
mathematical proficiency.” So, we have to get better at learning and being
completely comfortable with the models and strategies that the new state
standards across the U.S. are asking students to know and be able to do.
Analyzing the Data
So, when the data is collected, teachers should notice what is happening.
The data has to be analyzed and interpreted. Maybe as in the case just
mentioned, most of the students can’t make a tape diagram yet. This is
an issue. If it is a whole class issue, then it needs to be addressed in the
whole class problem-solving routine. If it is an issue with some of the
students, then it should be addressed in the small guided math groups.
Here is an example of a fourth-grade data analysis sheet (see Figure 11.8).
It is an Excel sheet so that the calculations can be easily scored and the
percentages given and groups formed accordingly. With this type of form,
teachers are able to see who is missing which questions. The actual error
analysis allows teachers to then pull small-guided math groups and address
the specific error patterns of the students. The groups will be sorted into
experts, practitioners, apprentices and novices. The experts are the students
that are working above grade level. The practitioners are the students who
are on grade level. The apprentices are approaching grade level and the
novices are working below grade level. The implications of this information
is that guided math groups are pulled accordingly and math workstations
have differentiated activities. So everyone is not solving the same problem
at the same time, always. Sometimes they are solving the same problem.
This occurs when students are working in groups or with partners. Usually,
they are working with partners at a similar level. Sometimes problem-solving
groups are heterogeneous and sometimes homogeneous.
The Problem with Word Problems
The research points out specific problems that students have with story
problems. There is the comprehension phase and the solving phase. Dur-
ing the comprehension phase, “problem solvers process the text of the
story problem and create corresponding internal representations of the
quantitative and situation based relationships expressed in the text”
(Nathan et al., cited in Koedinger). During the solution phase, students
try to find the solution. Several researchers have found that errors in the
comprehension phase account for problem-solving difficulties (Lewis &