Texas Mathematics Teacher Spring/Summer 2020 - 28

Cumulative Exam Review in Upper Secondary Mathematics Classrooms:
Observations on Best Practices
Elizabeth A. Gutermann

Part 1: Introduction
Cumulative exam review is a challenge for many
teachers. In the final weeks leading up to a high-stakes
test, teachers need to strike a delicate balance between
maintaining fidelity to their goals of learning outcomes
and adequately preparing students by "teaching to the
test." These concerns are amplified in upper-secondary
math classrooms in that the content is highly cumulative,
building upon itself in much the same way as a secondary
language acquisition course. Additionally, upper
secondary (and particularly twelfth-grade) students are
likely to be focused beyond the scope of high school at the
end of the school year, causing grades to slip as students'
attention wanes (Avoiding Senioritis, 2019). This makes it
all the more challenging to keep students focused on
high-stakes tests at the end of the year, including EOC
tests and semester exams as well as AP and IB tests.
Over the past six years, I have been refining my teaching
practice during the cumulative review portion of my
course as I prepare my students to take the AP Calculus
AB exam. This article seeks to share the elements of
cumulative exam review that have been most fruitful in
my classroom and to discuss importance of cumulative
review best practices in terms of desired student
outcomes. So, while my experience is specifically in
preparing for an AP exam, the techniques presented
will also be relevant to other tests, including EOC and
semester exams, in other grade bands. The reader should
come away with concrete ideas for how to formulate
a review unit in their own classroom and with the
understanding of general review best practices and their
rationale.
Part 2: Elements of Exam Review
2.1 Establishing a Baseline - the Mock Exam
I have found it most beneficial to start a review unit by
establishing an objective baseline of performance upon
which students can build. In order to achieve this, each
year my students take a mock exam as an objective
benchmark test. Typically, the most recently released
sample test is used for this purpose. I suggest that teachers
should use an objective benchmark assessment to establish
a baseline performance for students upon which they can
build during the course of the review unit. Because the
purpose of the mock exam is to give students a baseline
upon which to build, providing students with feedback on
their performance in a timely (Faxon-Mills et al., 2013) and
thorough manner is crucial to the intent of this activity.
Students should be involved in the analysis of their
scores on this benchmark, a practice which leads to
demonstrably higher performance (Marzano, 2009).
In order to involve students in the data-tracking process,
students filled out an analysis form that tied each
question to a course topic.

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| Spring/Summer 2020

Standards were not used because there were too few
questions on each standard for an individual student to
draw conclusions about their performance (Marzano,
2009); instead questions were lumped into broader course
topics so that students could establish trends. The analysis
form was created and shared by Jennifer Nicholson, North
Side High School, Fort Worth Independent School District,
and is reprinted with permission. An excerpt of the
analysis form is shown in Table 1.

Table 1: Mock Exam Analysis Form
Students marked the questions they got correct in each
topic and determined their percent mastery. Students
then made note of their best and worst topics, statistically
speaking.
Beyond just giving students a metric of their current
academic performance, the benchmark assessment can be
used for goal setting for the actual test. Because the AP
Exam is graded on a scale score, students need to be given
the opportunity to understand what their mock
exam results mean in the context of AP scores. AP
exams are scored on a scale of 1-5, with 5 being the
highest. Scores of 3, 4, and 5 are considered "qualifying
scores" and may be accepted for college credit (College
Board, 2019). The teacher should guide students to
understanding the results of their benchmark assessment
and should provide the students with concrete and
actionable steps that they can take to achieve their goals.

I suggest that teachers should use an
"
objective benchmark assessment to establish
a baseline performance for students upon
which they can build during the course of
the review unit.

"

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