Delta-Phi: Jurnal Pendidikan Matematika, vol. 1, pp. 01–06, 2023
Received 16 Feb 2023 / published 30 Apr 2023
https://doi.org/10.61650/dpjpm.v1i1.30

Newman and Scaffolding Stages in
Analyzing Student Errors in Solving
Algebraic Problems
Lelly Nur Rachmawati1, Retno Wahyu Arian Sah2, Siti Nur Hasanah3 and Anurag Hazarika4
1. Universitas Muhammadiyah Malang, East Java, Indonesia
2. MTs PP Unggulan Singa Putih, East Java, Indonesia
3. SMKS An-Nasyiin Grujukan Pamekasan, East Java, Indonesia
4. Tezpur Central University, Assam, India
E-mail correspondence to: lellyrachmawati10@gmail.com

Abstract
Algebra is a branch of mathematics that is abstract in form, so students
make errors in solving Algebra problems. This research aims to describe (1)
the error form made by students in solving algebraic operation story
problems based on the Newman stage and (2) the scaffolding form given
to students who make errors in solving problems of algebraic form
operations. This qualitative research is descriptive with research subjects of
3 class VIII students at MTs Unggulan Singa Putih. The results of the study
state that: (1) the errors form on the reading step is students cannot read
the problems by beheading or stopping correctly, and on the
comprehension step, the students need to learn the meaning of the
problem. In the transformation step, the students need help to model
variables appropriately. In the process skill step, the students need help to
operate algebraic forms appropriately. On the encoding step, the students
cannot answer correct conclusions; (2) the scaffolding forms given to
students are students requested to recheck or reread the results of their
work, students are given questions that lead students to think more about
the problem and give praise to motivate students to improve their work.

Keywords: Algebraic Operation; Error; Newman’s Step; Scaffolding.

Introduction
Mathematics is a subject published at all levels of education, from
elementary to high school (Hutajulu et al., 2019; Meiliasari et al., 2021)
l. Based on the Law of the Republic of Indonesia number 20 of 2003
concerning the National Education System Chapter X Article 37
paragraph 1 states that the primary and secondary education
curriculum must contain mathematics (Aguilar et al., 2022; Inganah et
al., 2023; Saundarajan et al., et al., 2020). Students at the elementary
school education level only know arithmetic (Tokgoz et al., 2021). In
contrast, students only know number symbols that represent specific

numbers (Turidho et al., 2021), while at the Junior High School
education level, students begin to be introduced to abstract letter
symbols where the letter symbols represent specific numbers called
Algebra (Ngado et al., 2020; Rahmawati & Soekarta, 2021; Syaifuddin et
al., 2022).
Algebra is one of the branches of mathematics, algebraic material at
the Junior High School education level, namely the operation of
algebraic forms given in class VII (Curriculum, 2013) (Anjarwati et al.,
2023; Pratiwi et al., 2021). Junior High School students tend to
experience mistakes when doing abstract algebra problems. This is
based on the results of a preliminary study conducted by researchers at
MTs Unggulan Singa Putih, Prigen, and Pasuruan, which showed that
students needed help to solve the problem of algebraic shape operation
story 100% correctly.
The Newman stage method is one theory that can be used to
discover the location of students' mistakes in doing story problems
(Saundarajan et al. et al., 2020). This is to White's statement, which
states that the analysis of errors based on the Newman stage has high
credibility in finding out the mistakes made by students in doing math
assignments (Sari et al., 2018; Sugianto, Darmayanti et al., 2022;
Sulistiawati & Surgandini, 2019). The effort to overcome the occurrence
of mistakes students make is by scaffolding students who experience
mistakes in doing questions.
Scaffolding is a form of assistance provided by others to students to
assist them in solving problems (Sah et al., 2023; Vamsi et al., Kishore,
2019; Wood et al., 1976). The purpose of giving scaffolding to students
who make mistakes is so that students realize where the mistakes they
have made so that students can correct the mistakes they have made
(Ardıç & İşleyen, 2018; Sekaryanti et al., 2022; Sinaga et al., 2021). Based
on this, this study aims to (1) describe the forms of mistakes made by
students in solving algebraic form operation story problems based on
Newman stages (2) describe the scaffolding form given to students who
experience errors in solving algebraic form operation story problems.

© 2023 Rahmawati (s). This is an open-access article licensed under the Creative Commons Attribution License 4.0.
(http://creativecommons.org/licenses/by/4.0/).

Rachmawati et al.: Newman and Scaffolding... Delta-Phi: Jurnal Pendidikan Matematika, 1, 01–05, 2023

selected subjects based on the results of the I test score in the form of
an algebraic form operation story. Subject 1 (SU1) is a subject of the
upper group, while subject 2 (SU2) is a subject of the middle group, and
subject 3 (SU3) is a subject of the lower group. Then, the results of the
work of the three subjects were analyzed for errors based on the
indicators of the Newman stages test questions I can see in Figure 1.

Research Methode
This research is a qualitative descriptive research. The purpose of
descriptive research is to systematically describe the facts and
characteristics of the object and subject under study precisely (Yuliana
et al., 2021). This study's purpose is to describe the mistakes made by
students in doing mathematical problems of algebraic form operation
material based on the Newman stage and its scaffolding. The study
subjects were three students of class VIII MTs Unggulan Singa Putih,
Prigen, and Pasuruan, each of whom came from the upper, middle, and
lower groups. The grouping of students' mathematical abilities is based
on the range of grades, which are categorized according to (Annisa &
Kartini, 2021).
Data analysis was carried out by focusing the research on three

Figure 1. Test questions

The indicators used to analyze students' errors with test questions
can be seen in Table 2 (Kurniawati & Hadi, 2021).

Table 2. Error indicators based on Newman stages
Error Types Based on Newman
Stages
Reading error
Comprehension error

Transformation error

Process skill error

Encoding error

Indicator
Students can not read questions with appropriate beheadings or pauses.
Students do not understand and do not write down the information
known and asked about the questions.
Students write down known information and are asked questions but do
not understand the meaning of the information.
Students do not write down variable calculations and cannot plan
solutions to solve problems.
Students can plan solutions and write down variables but not precise
calculations.
Students do not write down and cannot plan the operations or formulas
that will be used to solve the problem.
Students write down operations or formulas to solve problems but are
not precise.
Students do not write down and cannot perform count operations.
Students write down and perform count operations, but they are not
precise.
Students do not write down and cannot complete the count operation
down to the simplest form.
Students do not write down the final answer
Students write down the final answer, but it is incomplete and precise.

After analyzing errors based on error indicators, Newman
continued with interviews and scaffolding in each research subject.
The scaffolding used in this study is based on Anghileri's theory, which
uses the second level of scaffolding, namely reviewing (Ivars et al.,
2020; Sekaryanti et al., 2023; Sugianto, Cholily et al., 2022; Supiarmo
et al., 2021). Subjects who have received scaffolding are given test II,
a question about the story of the operation of algebraic forms. Test II
questions can be seen in Figure 2.

Figure 2. Test questions II Media Validation
Results and Discussion
In learning mathematics, especially in algebra, students often
have difficulty solving problems given by the teacher. To learn more
about the extent of students' difficulties in solving mathematical
problems, the following will explain Newman's stages and the
student scaffolding process.

Figure 3. SU1 answer results on test
Students from the upper group make mistakes while writing the
final answer. The form of the mistake made is that the student
cannot write down the conclusion of the answer completely. This is
supported by the results of research conducted by Kulsum, which
states that competent students make mistakes when writing the
final answer (Darmayanti et al., 2022; Humaidi et al., 2022; Kulsum,
2019).

Error Analysis and Scaffolding of Subject 1 (SU1)
Error analysis and scaffolding to SU1 are based on the results of
the SU1 answer on test I. SU1 answer results can be seen in Figure 3.

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Rachmawati et al.: Newman and Scaffolding... Delta-Phi: Jurnal Pendidikan Matematika, 1, 01–05, 2023

Error Analysis and Scaffolding of Subject 2 (SU2)

Wati et al., 2023), and final answer writing errors.

Error analysis and scaffolding to SU2 are based on the results of
the SU2 answers on test I. SU2 answer results can be seen in Figure
4.

The form of error at the reading stage is that students cannot
read the questions with proper correction or pause. Meanwhile,
the form of mistakes made by students at the understanding
stage is that students do not know the meaning of the questions
correctly (Astuti et al., 2023; Rofiah et al., 2023). At the
transformation stage, the form of error made by students is that
students cannot do the proper distribution of variables. At the
process skill stage, the form of error that the student makes is that
the student cannot perform the operations of addition,
subtraction, or multiplication of algebraic forms. Meanwhile, the
form of error made by students at the stage of writing the final
answer is that the student does not write the conclusion or the
student writes the conclusion, but it is not complete and
appropriate

Figure 4. SU2 answer results on test I

Conclusion

Based on the interview results and the SU2 answers, the
mistakes made were at the stage of transformation, process skills,
and writing the final answer. The results of the analysis of the form
of error and scaffolding given to SU2. Students from the middle
group make mistakes at the transformation stage, process skills,
and write the final answer (Gunawan et al., 2023; In’am et al.,
2023). This is by the results of Kulsum's research, which states that
capable students are making transformation errors, process skills
errors, and final answer writing errors (Khoiriyah et al., 2022;
Kulsum, 2019; MM Effendi et al., 2022; Rakes & Ronau, 2019).

Suggestions that can be given to educators are (1) at the
reading stage can apply scaffolding types of verbalising,
prompting and probing questions, and interpreting students'
actions and talk to overcome reading errors to lower group
students, (2) at the understanding stage can apply scaffolding
types of looking, prompting and probing questions, and
interpreting students' actions and talk to lower group students to
overcome misunderstanding errors, (3) at the transformation
stage, they can apply scaffolding types of prompting and probing
questions and interpreting students' actions and talk to middle
group students to overcome transformation errors, but for lower
group students who are still unable to apply this type of
scaffolding, educators must train the ability to do variable shaping
appropriately, (4) at the process skill stage, they can apply
scaffolding type prompting and probing questions and
interpreting students' actions and talk to middle group students
who make process skill mistakes, but the type of scaffolding still
cannot be applied to lower group students, then educators must
train the ability to perform algebraic form operations (algebraic
form operation requirements), (5) at the stage of writing the final
answer can apply scaffolding Types of looking, prompting and
probing questions, and interpreting students' actions and talk to
upper and middle group students to overcome errors in writing
final answers, but these types of scaffolding cannot yet be applied
to lower group students, so educators must train and remind
students to write complete and precise descriptions in doin.

Error Analysis and Scaffolding of Subject 3 (SU3)
Error analysis and scaffolding to SU3 are based on the results of
SU3 answers on test I. SU3 answer results can be seen in Figure 5.

Figure 5. SU3 answer results on test I

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