capstone paper on cumulative review.pdf - The Benefits of...

The Benefits of Review in the Math Classroom
Math Education Seminar Series
Capstone Paper

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Introduction: Why I Chose to Research Cumulative Review
Before delving into the topic of cumulative review, I want to give context into why I chose
this topic. As a math teacher, I have often found that many students have a difficult time
retaining material from the beginning of the year. As a math teacher, this becomes a frustrating
situation when students need to take cumulative tests, like midterms and finals. When they start
reviewing, it is clear that students often need to be “retaught” the material and are unable to
“recall” the material from the beginning of the year. I have also found that almost everything that
they have already learned in past years looks familiar to them, yet they have a difficult time
knowing what tools or how to actually solve problems that they have supposedly already
“mastered.” This also becomes frustrating as a teacher when I need to “reteach” concepts that
students claim they do not remember or were never taught.
Many questions arise from these frustrations. Why is it that students seem to have
mastered a concept but are unable to reproduce it after some time has passed? If students
need to see an example of an old problem done out again to remember how to work out a
problem, have they truly mastered the concept or have we only trained students to work
robotically and not necessarily have the depth of understanding that they should? Do we need
to pull out problems from past units every now and then for students to attempt again so that
they do not forget “how to do” a problem? Or should we be incorporating previously acquired
skills into the new concepts that they are currently learning in the classroom? Is there too much
compartmentalizing in the curriculum with respect to concepts and problems throughout the
year and should we be linking concepts and units within the curriculum more clearly with
students?
As I ponder these questions regularly as a teacher, I decided to look into any research
available regarding cumulative review and mathematical retention, in the hopes of finding

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applications for my own teaching practice. One of the things I found in my research is that
cumulative review can really only be understood and implemented after understanding the types
of practice that are given to students. Otherwise, cumulative review can look different from class
to class. Thus, I started my research by first defining the different types of practice.
Different Types of Review and Practice
In the classroom, cumulative review is generally understood to be a review of all the
concepts that have been taught up to the present time in a class. For example, in a math
classroom, a cumulative review for the midterm would consist of all the topics that have been
taught since the beginning of the year up to the most recent lesson. However, it is difficult to
label something as “cumulative review” without first understanding the different types of practice
that are given.