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Error Analysis Case Study
Introduction
Wyatt’s scenario is case study level c, case one. In reviewing Wyatt’s assignment, he was
struggling with fractions, more specifically his errors occur when multiplying fractions with the
same number in the denominator. He seems to get this skill mixed up with adding fractions with
the same denominator. He failed to multiply problems like this correctly. This is an error in
conceptual understanding. Correcting the pattern errors will help Wyatt keep from making the
same errors over and over. Just teaching a student a formula is not always enough. This will
cause gaps in their learning of a particular mathematical concept. To determine the reason why
students like Wyatt are making the pattern errors teachers can conduct an error analysis to target
certain areas instead of reteaching the whole concept again. Conceptual errors may sometimes
require concrete or visual demonstrations. Teachers can address the concepts by allowing
students to use concrete objects to solve problems. “The type of instruction a teacher uses to
correct conceptual errors will likely differ from that used to address factual or procedural errors.
Simply teaching a student the formula or the steps to solve a mathematics problem will not help
the student gain conceptual understanding” (Brown & Skow, 2016). The conceptual knowledge is
used by many countries but the way and procedure the symbols are used may differ from other
countries. For example, using a multiplication problem here in the United States may look like
4*3 but in other countries that could be seen as a subtraction problem. So, it is also important for
the teacher to make sure it is not a cultural diversity issue causing the errors in the math
problems as well. Having a student use manipulative will help the student better understand
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conceptual skills and gain confidence in themselves while practicing the mathematical concept.
Another strategy is to use the explicit, systematic instruction approach.
Summary
Two strategies that will help Wyatt’s scenario are the use of manipulatives and the explicit
systematic instruction. Manipulatives are used to have a concrete model of the problems that are
being taught. The purpose of using manipulatives are so the students are provided with concrete
and visual examples to represent a mathematical idea. “A strategy that works for one student
may be completely ineffective with another, even for a student with the same exceptionality”
(Bay-Williams, Karp, & Van De Walle, 2019). The use of manipulatives may not always work for
every student. For example, students with visual deficits may have difficulty using
manipulatives. “After a student has gained a basic understanding of the mathematical concept,
the concrete objects should be replaced by visual representations such as images of a number line
or geoboard (a small board with nails on which students stretch rubber bands to explore a variety
of basic geometry concepts)” (Brown & Skow, 2016). The use of fraction blocks or fraction strips
could be used to help students like Wyatt build that foundation of using fractions and then later
replace the objects with visual representations of the numbers and symbols. The next strategy is
using the explicit, systematic instruction strategy. “Explicit, systematic instruction involves
teaching a specific skill or concept in a highly structured environment using clear, direct
language…” (Brown & Skow, 2016). When a teacher is using explicit, systematic instruction they
need to incorporate modeling, guided practice, and independent practice into their lesson. In the
step of modeling one example would be for the teacher to lead the students through sample
problems and point out difficult aspects of the problems. During the guided practice step the
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student will complete problems with the help of the teacher or practice problems with their peers
in a group activity. The teacher will offer feedback during this step as well. The final step before
assessment would be independent practice. The student will complete problems on their own and
the teacher will make sure to check for understanding. “When engaging in explicit instruction
you do not merely demonstrate the strategy and have students practice it; instead, you try to
illuminate the decision making along the way – a process that may be troublesome for some
leaders without this level of support. After you assess students, so you know what to target, use a
tightly organized sequence, from modeling the concept or strategy, to prompting students
through the model, to practice” (Bay-Williams, Karp, & Van De Walle, 2019). The use of concrete
models goes hand in hand with explicit, systematic instruction. There are several instructional
tips that will help aid in the process, they are: check for prerequisite skills, model examples and
nonexamples, pinpoint error, provide ample opportunities for practice, start with simple
problems, mover the error around. All of these are great tips in helping students with
mathematical errors. The tips that would work the best in Wyatt’s scenario would be to pinpoint
the error and provide ample opportunities to practice problems that require multiplying fractions
with like denominators. As the teacher moves through the pinpointing the error which will
happen during the modeling and guided practice step the teacher should focus on the part of the
problem that the error occurred in not the entire problem.
Conclusion
Wyatt’s scenario gave an example of a student that was struggling with multiplying fractions.
After reading the case study the two strategies that would work for students like Wyatt would be
to use the explicit, systematic instruction and use concrete objects like manipulatives. These two
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strategies can be combined and used together. The explicit, systematic instruction strategy is a
more structured plan on teaching a mathematical concept. The use of objects like manipulatives
gives the students a hands-on concrete visual of how mathematical problems can be solved. The
teacher should pinpoint the error and provide ample practice opportunities on problems that
involve the student to multiply fractions with like denominators. The teacher should also
remember to try different strategies to help aid each of his or her students due to the diversities in
the classroom. The case study gave good practice to aiding students in fixing mathematical
errors.
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References
Bay-Williams, J. M., Karp, K. S., & Van De Walle, J. A. (2019). Elementary and Middle School
Mathmatics Teaching Developmentally. Pearson Education.
Brown, J., & Skow, K. (2016). Mathematics: Identifying and Addressing Student Errors.
Retrieved from http://iris.peabody.vanderbilt.edu/case_studies/ics_matherr.pdf
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