Error Analysis Case Study: Dalton 2
Dalton has made the following errors; factual error, procedural error, and procedural er-
ror when multiplying decimals. Dalton possibly could have made the common factual error in
the deficiency of information. In addition, in multiplying decimals, he also made the error of
procedures in not knowing what the next step would be in solving the problems. It seems that
he knew how to multiply the decimals, but is putting the decimal in the wrong area. The con-
ceptual errors that were present, consisted of the ideas and principles not being recognized ef-
fectively. The relationships with the concepts of multiplying decimals were not identified either.
The common factual error is that he has not grasped basic number facts, in which he made er-
rors when multiplying. The common procedural errors are defined as; Procedural knowledge is
an understanding of what stages or measures are essential to explain a problem. Procedural er-
rors occur when a student erroneously applies an instruction or an algorithm (i.e., the method
or step-by-step process for explaining a problem). Studying the assessments below to learn an
in-depth analysis about some common procedural errors. Execution of incorrect operation;
even though students are able to appropriately classify the signs (e.g., addition, minus), stu-
dents often subtract when they are supposed to add, or vice versa but, students might also at-
tain other improper processes such as; multiplying instead of adding. The mutual conceptual er-
rors are defined as; Conceptual knowledge is an understanding of primary ideas and values and
an acknowledgement of when to apply them. It also includes, understanding the associations
among concepts and ideologies. Conceptual errors occur when a student holds misconceptions
or nonexistent understanding of the original principles and philosophies related to a given
mathematical problem (e.g., the relationship between numbers, the characteristics and proper-
ties of shapes). Investigation of the common errors of the table allows the instructor to learn
Error Analysis Case Study: Dalton 3
more about some common conceptual errors. Confusion of place value; the pupil doesn’t un-
derstand place value and chronicles the response, so that the numbers are not in the proper
place value location Skow, J. B. (2016).
What needs to be revealed with Dalton, is that he is clearly gaining the misconceptions
that are present with multiplying decimals. What interested me was that Dalton answered all
the questions incorrectly in his assignment except for one problem. The problem he provided
the right answer for was the 3.25*12 problem, which only has one decimal in the problem
which became easier with him. In my opinion, had Dalton asked questions in the classroom, the
misconceptions he may have had would have been eased from the start. Dalton had made a
misconception that is categorized as longer is larger, which means in turn that he typically picks
longer decimals to become larger numbers ultimately missing the decimal places. The reason
the students have this misconception is due to not making the link to decimal to fraction, which
also provides difficulties in place value. The place value misrepresentation is linked to the deci-
mal place in the multiplication sector of the problem Steinle, S. (1998).
The strategies that would relate to multiplying decimals would be to multiply as you
would with whole numbers. Count how many digits you have after every decimal point in the
problem, and move the decimal point to the left as many places as there are digits behind the
decimal. This should be shown to the students in order for them to understand how to multiply
decimals effectively. Also, Dalton will need to understand place values, if he learns about the
place value of decimals, he will understand the places where the decimal will need to be.
Error Analysis Case Study: Dalton 4
Extra work at home would help Dalton in becoming more active in understanding how to multi-
ply decimals. The educator could also connect how fractions and decimals are intertwined with
one another, because if you comprehend the values of fractions, you will also comprehend the
values of decimals Spector, L. (2019).
Summary, Description of the Strategies, Purpose & how can we Improve
When dealing with the strategies you can refer to learning how to multiply in early
years. You can clearly see, when you break up numbers in multiple forms and reflecting ways
on understanding multiplication concepts from the base ten criteria. Allow Dalton to under-
stand the common misconceptions to multiplying decimals, which is adjusting their number
groups. Dalton seems to get the concept of multiplying whole numbers with decimals, but is
not understanding how to multiply decimal to decimal. The question may be asked, detailing
how he understood how to multiply the whole number with the decimal effectively. The com-
mon answer he would probably give is that it only had one decimal between the two-number
signifying money, which by habit only will have two numbers behind the decimal. With that in
mind, you can let the student know the power of understanding the number place in decimals.
In summation, Dalton just needed to follow the simple tasks when multiplying decimals which
are; Ignoring the decimal points and multiply as usual, counting how many total digits are on
the right side of the decimal points in the problem you are multiplying, and placing the decimal
point in your answer, so they are the same digits to the right Skow, J. B. (2016).
Dalton made what can be stated as, careless errors when multiplying decimals. There
are ways to depict the errors in a more effective way such as; Slow down, when you are in a
Error Analysis Case Study: Dalton 5
rush to finish your work, take your time to ensure that you complete the work efficiently, and
also to pay close attention to detail. Circle important information when looking at the assign-
ment. You can circle the directions to ensure that you are completing the assignment correctly,
and most importantly for him, would be to multiply the decimals and to pay close attention to
the place value of the decimals. In addition, when circling important information this would in
return provide the student with the strategy needed to successfully complete the assignment
the right way. When dealing with computational error, the student is dealing with a multi-step
problem that would imply that the rest of their work would ultimately be incorrect. The step
would be to show all stages when deriving at their answer, which is what Dalton did, but he
overlooked the decimals and adding the zeros. By not calculating the zeros and not placing the
decimal correctly, it made his answer incorrect. However; the ways to improve would be for the
student to check the answer after solving. Checking the answer would allow the answer to be
more accurate and the student could see where they went wrong in the problem. Dalton could
also have utilized a calculator, although it would not provide the steps for the answer, Dalton
would know the correct answer. To take it a step further, Dalton could answer the problem
with the steps and utilize the calculator to make sure his answer is accurate. The conceptual er-
ror Dalton made was misunderstanding the concepts or logic of multiplying the decimals. A
strategy in order to overcome conceptual errors would be for Dalton to learn how to originate
at the answer in different ways. Analyzation of errors would be for the student to go over their
work in more detail and in an analytical way. Now when Dalton looks back at his work, when
getting his paper back with the wrong answers, he would understand to efficiently review his
work before turning it in Bethany. (2016).
Error Analysis Case Study: Dalton 6
References
Bethany. (2016). 3 Types of Math Errors and How to Prevent Them. Retrieved from Math Geek
Mama: https://mathgeekmama.com/types-of-math-errors/
Curran, C., & the IRIS Center. (2003). Mathematics: Identifying and addressing student errors.
Retrieved from https://iris.peabody.vanderbilt.edu/wp-content/uploads/pdf_case_studies/
ics_matherr.pdf
Skow, J. B. (2016). Mathematics: Identifying and Addressing Student Errors. The Iris Center, 1-
26.
Spector, L. (2019). HOW TO MULTIPLY WHOLE NUMBERS HOW TO MULTIPLY DECIMALS. Re-
trieved from The Math Page : http://www.themathpage.com/Arith/multiply-whole-
numbers-multiply-decimals.htm
Steinle, S. (1998). Misconceptions about Decimal Numbers. Retrieved from Extranet Education :
https://extranet.education.unimelb.edu.au/SME/TNMY/Decimals/Decimals/tests/mis-
con.htm
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