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Case Study Level A, Case 1 - Dalton (pp. 19-20)
After reviewing the work in Dalton’s work, it is evident that while he is proficient in
basic computation, he struggles with aligning the decimals during decimal operations. This was
found by observing the student work and finding the error pattern, in this case it’s moving the
decimal. This specific error is considered a procedural error as it is as simple as misplaced
decimals. Procedural errors do not necessarily mean that the student doesn’t understand the
entire concept, such as regrouping during calculations, incorrectly converting mixed numbers to
fractions, or performing incorrect operations.
To address this specific error pattern, the teacher should give targeted re-teaching on
decimal operations for multiplication. For this section, Dalton would benefit from modeling the
process of decimal multiplication, then guided practice, then repeat independent practice.
Demonstration of a helpful technique, like counting decimal places, then using it in practice
could help students like Dalton master the concept. It is also important to observe Dalton’s
technique with adding and subtracting decimals to ensure similar errors are not occurring and
make any necessary corrections. Dalton shows mastery in the multiplication itself, and with
targeted re-teaching would be successful.
This would be the best method of addressing Dalton’s error pattern for several reasons.
The first is that it provides targeted intervention, the teacher is addressing the specific error and
providing targeted instruction and feedback. Modeling and guided practice are also helpful
interventions as they provide Dalton with visual displays of the correct methods and helpful
techniques, then experience of using the correct method during guided practice. The independent
practice portion gives the opportunity for repetition and mastery. Through the entire error
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correction, the teacher is sure to observe, make corrections as necessary, and adjust instruction to
meet Dalton’s needs.
Case Study Level A, Case 2 - Madison (pp. 21-22)
Madison is a third grade student with a math learning disability that necessitates an IEP
that encourages the use of hands-on or concrete objects to learn abstract ideas. She has shown
success with this method in the unit where students were completing a unit about money. Before
completing the worksheet, Madison has been working with a cardboard clock with moveable
hands. However, even with hands on manipulatives, Madison still seems to be struggling with
the concept of using the cock to tell the time.
After looking at Madison’s most recent test for error analysis, it appears that Maddison
has a good grasp of time when it is shown on a clock, and creates a clock face based on the
written time, but struggles when the description uses language like ‘quarter past’ or ‘quarter til’.
This type of mistake, using mathematics vocabulary, would fall under the banner of factual
errors. These errors can be simple to correct to help the student achieve mastery. Her teacher can
create targeted interventions to help Maddison learn time-related terminology and master the
concept.
A great method would be to refer back to the money lesson where Maddison has already
shown mastery. The teacher can emphasize how dollars can be divided into four quarters, the
teacher can then make a paper clock face cut into four pieces, and one cut into halves. This can
help Maddison visualize the difference between quarter and half as parts of a whole hour. The
teacher can also have Maddison label the divisions of time, half-past, quarter-past, etc.
Case Study Level B, Case 2 – Elias (pp. 25-26)
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Elias is a second grader who has a learning disability. His Special Education teacher is
gathering data, and has decided that she needs to conduct a diagnostic assessment to identify
specific weaknesses and instructional needs. In the assessment, Elias shows some procedural and
conceptual errors in his addition and subtraction calculations. In many of Elias’ problems he
struggled with carrying during addition and holding place value. However, Elias shows
understanding of these concepts when subtracting.
Through this data collection, and the following error analysis, Elias’ Special Education
teacher can provide customized support and learning options to help Elias reach mastery. There
are several interventions that his teacher could utilize to help Elias understand carrying over tens
values as well as holding correct place values. Elias would benefit greatly from hands-on
learning with place value manipulatives to represent the values being added. This would allow
him to visualize the concept and see exactly how carrying a value converts to the next place
value.
Case Study Level C, Case 1 - Wyatt (pp. 27-28)
Wyatt is a sixth grade student who seems to be struggling with fractions on his most
recent independent work. During the initial lesson, Mr. Goldberg observed that most students
were understanding the concepts quickly. When switching to multiplying fractions, more
students seemed to struggle which led Mr. Goldberg to give a mini-lesson to help students
achieve mastery. After this, only a handful of students still struggled with the concepts, and
Wyatt is one of them.
After reviewing Wyatt’s most recent independent practice, Wyatt seems to make
mistakes primarily when multiplying fractions. Many of Wyatt’s mistakes happen primarily with
multiplying the denominators as well as reducing fractions to their simplest form. His teacher
