The study was a quasi-experimental research conducted to investigate the effect of 4S(Sense Making, Showing of Representation, Solution and Explanation, and Summarization) Learning Cycle Model on students' mathematics comprehension. The participants of the study were the two intact classes of freshmen education students in College and Advanced Algebra course enrolled during the 1 st semester SY 2019-2020 at the University of Science and Technology of Southern Philippines. One section was assigned as control group who was exposed to Polya Method of Problem Solving while the other one was experimental group who was exposed to 4S Learning Cycle Model. The performance of the students were measured using their test scores. To determine if the 4S Learning Cycle Model significantly affects the students' mathematics comprehension, the Analysis of Covariance Model (ANCOVA) was utilized at 0.05 level of significance. Results revealed that the 4S Learning Cycle Model helped in the development of students' mathematics comprehension.

4S Learning Cycle Model
Summary of the mean and standard deviation

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American Journal of Educational Research, 20 20, Vol. 8, No. 3, 182-186

Available online at http://pubs.sciepub.com/education/8/3/9

Published by Science and Education Publishing

DOI:10.12691/education-8-3-9

4S Learning Cycle on Students' Mathematics

Comprehension

Maria Antonieta A. Bacabac *, Laila S. Lomibao

Department of Mathematics Education, University of Science and Technology of Southern Philippines,

Cagayan de Oro City, Philippines

*Corresponding author: antonieta.bacabac@ustp.edu.ph

Received February 15, 2020 ; R evised March 20, 2020; Accepted March 28, 2020

Abstract The study was a quasi -experimental research conducted to investigate the effect of 4S( S ense Making,

Showing of Representation, Solution and Explanation, and Summarization) Learning Cycle Model on students'

mathematics comprehension. The participants of the study were the two intact classes of freshmen education

students in College and Advanced Algebra course enrolled during the 1st semester SY 2019-2020 at the University

of Science and Technology of Southern Philippines. One section was assigned as control group who was exposed to

Polya Method of Problem Solving while the other one was experimental group who was exposed to 4S Learning

Cycle Model. The performance of the students were measured using their test scores. To determine if the 4S

Learning Cycle Model significantly affects the students' mathematics comprehension, the Analysis of Covariance

Model (ANCOVA) was utilized at 0.05 level of significance. Results revealed that the 4S Learning Cycle Model

helped in the development of students' mathematics comprehension.

Keywords: mathematics comprehension, 4S Learning Cycle Model, sense making, summarization

Cite This Article: Maria Antonieta A. Bacabac , and Laila S. Lomibao , "4S Learning Cycle on Students'

Mathematics Comprehension." American Journal of Educational Research, vol. 8, no. 3 (2020 ): 182 -186 . doi:

10.12691/education-8-3-9.

1. Introduction

Mathematics is one of the oldest scientific disciplines

yet, its applications are still very relevant for it is one

of the basic foundation in understanding almost all

phenomena in everyday life. Generally, the teaching and

learning of mathematics aim to improve reasoning

and cultivate the mind, that will provide students with

systematic ways of approaching a variety of problems and

as tools for analyzing and modeling situations and events

in the physical, biological and social sciences [1] .

However, it is not easy to understand mathematics.

Learning mathematics is learning a new language. For

mathematics is unique with its combination of words and

symbols and compact style [2] . Non-readers, slow-readers

or students with frustrating level in reading, or whose

primary language is not English, are often at a

disadvantage. Obviously the low performing students

made a higher number of comprehension and transformation

errors than high performing students [3] .

This is manifested in the latest Program for International

Student Assessment (PISA) results where Filipino students

average score in mathematics, science and reading rank

76th out of 77 participating countries, particularly 76th in

mathematics, 77th in both science and reading [4] . PISA

[5] assessment framework are specifically designed to

measure the 7 fundamental mathematical capabilities

namely the communication, mathematizing, representation,

reasoning and argument, devising strategies for solving

problems, using symbolic, formal and technical language

and operations, and using mathematical tools, which all

require mathematics comprehension. Particularly, PISA

stages of mathematization, including (1) comprehending a

task, (2) transforming the task into a mathematical

problem, (3) processing mathematical procedures, and (4)

interpreting or encoding the solution in terms of the real

situation [6] .Hence, these results exhibited that Filipino

students are poor in these mathematical capabilities.

The same observations were also found by Wijaya et al.,

[3] when they study Indonesian students, their data

analysis revealed that most of students' errors were related

to the understanding of meanings of the context-based

tasks and comprehension errors particularly, the selection

of relevant information. Further, researchers suggested

that many unsuccessful problem solvers often rely on the

direct translation strategy (like looking for numbers and

keywords) and fail to provide correct answers when

problems include important implicit information [7,8] .

To comprehend mathematics, every word and abstract

symbol must be read (or written) and understood with

precision such as solving word problems (WPs). It

requires numerical processing and comprehension, thus,

one has to know the meaning of individual words and also

possess the skills to integrate the meanings of these words

into semantically more complex meanings [9,10] . WPs

presented in written form place significant demands on

reading comprehension and other literacy skills, such as

vocabulary, at the same time, it is essential to identify the

183 American Journal of Educational Research

problem type in order to activate the existing mathematical

knowledge structures [10,11] . Hence, one has to have both

linguistic and mathematical knowledge, and be able to flexibly

operate between these different knowledge types to

be able to solve mathematical word problems [10] .

Non-routine WPs tasks require high levels of text

comprehension skills [8] . It was also emphasized by Fuchs,

Fuchs, Seethaler, & Craddock [12] that embedding

language comprehension within schema -based word

problem intervention provides students with an additional

boost in word problem performance. Thus, practicing with

more demanding WPs is not only beneficial for

mathematics learning but can also be an effective way to

improve advanced mathematics comprehension skills [8] .

It is essential then to focus on building students'

mathematics comprehension rather than merely developing

superficial understanding through procedural learning [13] .

Nagy stressed that all too often mathematics teaching

approaches set more emphasis on the importance of

'How?' and supersedes that of 'Why?', hence, teachers

need to be encouraged to present mathematics in a variety

of ways which enhance the systemic understanding of

concepts and the development of a systematic methodology.

In designing mathematical tasks, a teacher should

assure that it aims to improve students' mathematical

comprehension by giving students opportunities for making

sense and process its own comprehension through showing

representations of the tasks at hand. For according to

Fuentes [2] reading mathematics equations has a unique

directionality, quite different from ordinary language

patterns and frustrating for a newcomer to mathematics

because mathematics has unique vocabulary, for some

words are special to mathematics, some are borrowed

from ordinary usage, and some are familiar words with

new and different meanings. Moreover, giving time for

students to formulate their solution and explain how

they arrive in their answer will also enhance students

mathematics understanding [14] and summarizing

one's process may also promote comprehension [15] .

Hence, this study aimed to explore the application of

the 4S (Sense Making, Showing Representations, Solution

and Explanation, and Summarization ) Learning Cycle

Model in mathematics to enhance students' mathematics

comprehension. 4S Learning Cycle Model may change the

paradigm of learning, from the old paradigm where

teacher as center of learning into a new paradigm in which

students become the center of learning, and teacher as a

motivator and facilitator.

2. Theoretical Framework

Comprehension is the retrieval and integration of

information about something of which one is aware and

occurs in concrete and abstract contexts. The richness and

complexity of contexts that can be comprehended is one

measure of intelligence [16] . Comprehending a given

problem tasks requires essential other skills other than

simple reading of the text. Kyttälä & Björn [10] suggested

that the reading comprehension process involves the

construction of a mental representation based on the text.

Thus, showing representations as one of the component of

4S Learning Cycle Model through illustrating models will

help students to understand the word problems. The

concept of representations can be credited back to the

constructivist concepts of intellectual development theory

[17] which was outline from Piaget's [18] propositions.

Bruner enumerated three modes of representations namely

the concrete stage which involves a tangible hands

on method of learning. In mathematics education,

manipulative are the concrete objects with which the

actions are performed. Second, the pictorial stage which

involves images or visuals to represent the concrete

situation enacted in the first stage. One way of doing this

is to draw images of the objects on paper or to picture

them in one's head. Other ways could be through the use

of shapes, diagrams and graphs. Third, is the symbolic

(language-based) or the abstract stage which takes the

images from the second stage and represents them using

words and symbols. The use of words and symbols allows

student to organize information in the mind by relating

concepts together. The words and symbols are abstractions.

Language and words are ways to abstractly represent the

idea.

This study was also founded on Russell [19] sense

making model which theorized that sense making is the

process of searching for a representation and encoding

data in that representation to answer task-specific questions.

According to their theory, making sense of a body of data

is a common activity in any kind of analysis that requires

different operations both cognitive and external resources.

They argued that when a person was confronted with

problems that have large amounts of information, he or

she has an array of resources that can be used -- both

internal cognitive resources and external resources for

information storage and computation. The methods for

carrying out this task can be described in terms of

operations, such as representations through finding data,

encoding and using the encoded representations. So when

students were given problem tasks, which can be

considered as information-rich data, they will undergo a

process of operation such as retrieving cognitive resources

like recalling previous related concepts learned and

making connections, and if they are in groups, an

opportunity to interact and discourse among peers could

occur, hence helping them to comprehend the problem at

hand.

The third component of 4S Learning Cycle Model is

solutions and explanation. The theory of conceptual fields

[20] hypothesized that, to establish better connections

between the operational form of knowledge, which

consists in action in the physical and social world, and the

predicative form of knowledge, which consists in the

linguistic and symbolic expressions of this knowledge.

Vergnaud [20] further stressed that without words

and symbols, representation and experience cannot

be communicated; on top of that, thinking is often

accompanied, or even driven, by linguistic and symbolic

processes. As observed when students are asked to write

or pose their work on the board and explain it to the class,

what they do most of the time is to read what they have

written. They do not really explain the thinking that they

used which enabled them to develop a solution or

obtain the required answer. To enhance mathematics

comprehension and thinking, it is important that teachers

require students to provide reasons for what they did and

American Journal of Educational Research 184

not just to relate the procedures that they used to solve

problems.

Finally, summarization can be used successfully

in many ways in the mathematics classroom. It can

increase mathematics comprehension through giving them

opportunities to see and think about the material on

different context and discuss them with their peers. If

students are struggling with a concept, their peers'

explanations may be what they need to help them

understand it and those explanations can come through

summarizing. Synthesizing also makes understanding

visible to teachers [15].

Figure 1. 4S Learning Cycle Model

Grounded on the preceding theories, this study adopted

the model in Figure 1 above, the 4S Learning Cycle

Model with the following components: sense making,

showing representations, solution and explanation, and

summarization aimed to promote students' mathematics

comprehension. This study mainly investigated the effect

of 4S Learning Cycle Model to students' mathematics

comprehension

3. Objectives of the Study

Current researches in mathematics comprehension so

far explored on the relation of reading comprehension and

its implication to problem solving skills and conducted

mostly among elementary or secondary students. However,

seldom explored this variable among the tertiary students

preparing to be mathematics teachers. Building strong

foundation on concepts in mathematics and problem

solving for future mathematics teachers is essential for the

effectivity and efficiency of teachers depend greatly on its

capability and quality [21] . Henceforth, this study aimed

to determine whether the 4S Learning Cycle Model had

influenced the students' mathematics comprehension.

4. Methodology

The study used the pretest - posttest quasi-experimental

design to determine the effects of 4S Learning Cycle

Model to students' mathematics comprehension. The

experimental group was exposed to treatment which

utilized the 4S Learning Cycle Model while the control

group was exposed to Polya Method of Problem Solving.

The performances of the students were measured using

their test scores. The study utilized the validated 24- item

multiple choice teacher -made test. The study was conducted

for a semester.

The participants of the study were the two intact classes

of freshmen education students in College and Advanced

Algebra at the University of Science and Technology of

Southern Philippines. One section was randomly assigned

as the experimental group and the other as the control group.

At the start of the study, pretest was given to both

control and experimental groups. Teacher-researcher was

the one facilitating learning. The classroom environment

was created which facilitated an active, responsible and

engaged community of learners. The students were

divided into small groups and each student was given an

activity sheet. The activity began by giving an open-ended,

engaging, an d challenging task that the students had the

ability to solve.

In the experimental group, the 4S Learning Cycle was

employed to solve the problem. Students started the

activity through making sense of the problem by discussing

among peers in the group, using their prior knowledge and

experiences. During the discussion, students' draw

representations to visualize their understanding of the

problem which help strengthen their comprehension of the

tasks at hand. These led them to translate the given

conditions in the problem to an expression or equation to

arrive at the correct solution . After having the solution of

the problem, students were encouraged to communicate

their understanding of the task through explaining their

solution to their group-mates. Each group was asked to

present their solutions and summarized the concepts they

learned. Here, students were given the chance to discuss

the intended mathematical ideas developed with the

teacher's guidance to avoid misconceptions (if there is).

On the other hand, the control group was taught using

the Polya's method of problem solving. The first step was

understanding the problem. In order to show an

understanding of the problem, students need to read the

problem carefully. Once the problem was read, students

listed in the space provided all the components and data

that were involved. This was where they assigned

variables. The second step was devise a plan. Students

translated the conditions in the problem into an equation,

drawn the diagram or illustrate if needed. They devised a

plan in order to solve the problem. The next step which is

step 3 was carrying out the plan or this means solving the

problem. The students solved the problem. They discussed

with their group mates how to solve the problem and they

wrote on their activity sheet their solutions. The last step

for Polya's problem solving method was looking back.

The students checked their solution and tried to see if they

used all the information and if their answer made sense.

To describe the mathematics comprehension level,

mean and standard deviation of the pretests and posttests

were computed. To determine the influence of the

two methods of teaching on students' mathematics

comprehension, the one-way analysis of covariance

(ANCOVA) was used, with the pretest as the covariate.

185 American Journal of Educational Research

The K-12 descriptive level was adopted to interpret the

mathematics comprehension level as shown in the rating

scale below:

Table 1. Mathematics Comprehension Rating Scale

Mean Score Range Description/Interpretation

18.00-24.00 Mastery

12.00-17.99 Near Mastery

0.00-11.99 Low Mastery

5. Results and Discussion

Table 2 shows the pretest and posttest mean scores and

standard deviation and descriptive level of students'

mathematics comprehension on Linear Equations, Quadratic

Equations, Systems of Linear Equations and Linear

Inequality.

Table 2. Summary of the mean and standard deviation

n Mean SD Level

Pretest 4S 38 10.868 3.112 Low Mastery

Polya 38 11.921 3.044 Low Mastery

Posttest 4S 38 16.158 3.140 Near Mastery

Polya 38 15.131 3.256 Near Mastery

The results indicate that the students' mean scores from

both groups were in the low mastery level in the pretest,

an indication that they have little background in the

subject. It can be observed also that the pretest mean

scores have a difference of 1.052 only where the control

group is slightly higher than the experimental group. This

means that the two groups of students had comparable

mathematics comprehension before the treatment was

administered.

In the posttest, the students taught with 4S Learning

Cycle Model shows a mean score higher than the group

exposed to Polya Method of Problem Solving. The results

revealed that both groups have increased their posttest

mean scores indicating that both groups have manifested

improvement from low level before the treatment

was administered to near mastery after the treatment

was administered. However, it is noticeable that the

experimental group has improved more in mathematics

comprehension compared to the control group. The

posttest mean score of students taught with 4S learning

cycle is 1.027 higher and nearer to mastery level.

The standard deviation of the pretest scores of those

taught with 4S Learning Cycle Model is higher compared

to those students taught with Polya Problem Solving

Method. This means that before the treatment, the scores

of the students in the experimental group have a

wider spread compared to the scores of the students in

the control group. However, in the postest, the group

exposed to 4S Learning Cycle Model has a lower standard

deviation than the control group who were taught with

Polya Problem Solving Method. This result revealed

that the students in the experimental group have

more improved mathematics comprehension after the

treatment was administered. The students' scores in

the experimental group are more closely located about

the mean of 16.158 indicating a more consistent or

homogeneous set of students in terms of performance in

the mathematics comprehension test. To verify whether

the difference was significant, ANCOVA was further used.

Table 3. One - way ANCOVA Summary for Students' Mathematics

Comprehension

Adjusted Error 526.68 73 7.21

Table 3 presents the summary of the analysis of

covariance of pretest and posttest scores for students'

mathematics comprehension of the experimental and control

groups. The analysis yielded a computed probability value

lesser than the 0.05 level of significance. This led to the

non-acceptance of the null hypothesis. This means that

there is sufficient evidence to conclude that mathematics

comprehension of the students exposed to 4S Learning

Cycle Model is significantly higher than those exposed to

Polya Method of Problem Solving. This happened because

when the students were exposed to 4S Learning Cycle

Model, they were provided the opportunity to comprehend

the given tasks through an active process following the

four components-cycle. Communicating how one makes

sense of the task and showing representations by undergoing

a process of operation such as retrieving cognitive

resources like recalling previous related concepts learned

and making connections and breaking information-rich

data into smaller chunks of information [19,22] helped

students understand the problem. Explaining the solutions,

and summarizing concepts learned from the activity,

allowed students to interact and discourse among peers.

This also facilitates the struggling students' understanding

and comprehension of the problem at hand [15] .

6. Conclusion and Recommendation

Based on the findings of the study, 4S Learning Cycle

Model positively influenced the students' mathematics

comprehension. On this basis, the teachers may adapt

this teaching strategy to improve the mathematics

comprehension skills of their students. The mathematics

teachers may be given training on how to apply

this strategy in their mathematics class. School principal

and supervisors may support the implementation of

4S Learning Cycle Model in mathematics classroom to

enhance the mathematics comprehension skills of the

students. Similar studies maybe conducted in a wider

scope using different population in different learning

institution to promote the generalization of the results.

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ResearchGate has not been able to resolve any citations for this publication.

In this study we investigated word-problem (WP) item characteristics, individual differences in text comprehension and arithmetic skills, and their relations to mathematical WP-solving. The participants were 891 fourth-grade students from elementary schools in Finland. Analyses were conducted in two phases. In the first phase, WP characteristics concerning linguistic and numerical factors and their difficulty level were investigated. In contrast to our expectations, the results did not show a clear connection between WP difficulty level and their other characteristics regarding linguistic and numerical factors. In the second phase, text comprehension and arithmetic skills were used to classify participants into four groups: skilful in text comprehension but poor in arithmetic; poor in text comprehension but skilful in arithmetic; very poor in both skills; very skilful in both skills. The results indicated that WP-solving performance on both easy and difficult items was strongly related to text comprehension and arithmetic skills. In easy items, the students who were poor in text comprehension but skilful in arithmetic performed better than those who were skilful in text comprehension but poor in arithmetic. However, there were no differences between these two groups in WP-solving performance on difficult items, showing that more challenging WPs require both skills from students.

  • Robin Nagy Robin Nagy

It is essential to retain a focus on building students' mathematical reasoning and comprehension rather than merely developing superficial understanding through procedural learning. All too often this approach 'takes a back seat' because of examination and assessment pressure, where the importance of 'How?' supersedes that of 'Why?' It is not what we teach that is important so much as how we teach it. This session explores conceptual methods in the teaching of Secondary mathematics. It will appeal to both new and seasoned teachers, providing food for thought and suggesting practical approaches to teaching mathematics for understanding rather than regurgitation.

  • Laila Lomibao Laila Lomibao

The efficiency and effectivity of the learning experience is dependent on the teacher quality, thus, enhancing teacher's quality is vital in improving the students learning outcome. Since, the usual top-down one-shot cascading model practice for teachers' professional development in Philippines has been observed to have much information dilution, and the Southeast Asian Ministers of Education Organization demanded the need to develop mathematics teachers' quality standards through the Southeast Asia Regional Standards for Mathematics Teachers (SEARS-MT), thus, an intensive, ongoing professional development model should be provided to teachers. This study was undertaken to determine the impact of Lesson Study on Bulua National High School mathematics teachers' quality level in terms of SEARS-MT dimensions. A mixed method of quantitative–qualitative research design was employed. Results of the analysis revealed that Lesson Study effectively enhanced mathematics teachers' quality and promoted teachers professional development. Teachers positively perceived Lesson Study to be beneficial for them to become a better mathematics teacher.

The intention of this study was to clarify students' difficulties in solving context-based mathematics tasks as used in the Programme for International Student Assessment (PISA). The study was carried out with 362 Indonesian ninth- and tenth-grade students. In the study we used 34 released PISA mathematics tasks including three task types: reproduction, connection, and reflection. Students' difficulties were identified by using Newman's error categories, which were connected to the modeling process described by Blum and Leiss and to the PISA stages of mathematization, including (1) comprehending a task, (2) transforming the task into a mathematical problem, (3) processing mathematical procedures, and (4) interpreting or encoding the solution in terms of the real situation. Our data analysis revealed that students made most mistakes in the first two stages of the solution process. Out of the total amount of errors 38% of them has to do with understanding the meaning of the context-based tasks. These comprehension errors particularly include the selection of relevant information. In transforming a context-based task into a mathematical problem 42% of the errors were made. Less errors were made in mathematical processing and encoding the answers. These types of errors formed respectively 17% and 3% of the total amount of errors. Our study also revealed a significant relation between the error types and the task types. In reproduction tasks, mostly comprehension errors (37%) and transformation errors (34%) were made. Also in connection tasks students made mostly comprehension errors (41%) and transformation errors (43%). However, in reflection tasks mostly transformation errors (66%) were made. Furthermore, we also found a relation between error types and student performance levels. Low performing students made a higher number of comprehension and transformation errors than high performing students. This finding indicates that low performing students might already get stuck in the early stages of the modeling process and are unable to arrive in the stage of carrying out mathematical procedures when solving a context-based task.

The focus of this article is the role of language comprehension within word-problem solving (WPS). The role of the language comprehension in WPS is explained, and an overview of research illustrating language comprehension's contribution to WPS is described. Next, an innovative intervention that embeds word problem (WP)-specific language comprehension instruction within a validated form of schema-based WP intervention is described, and the methods and results of a randomized controlled trial assessing the added value of embedding WP-specific language comprehension instruction are outlined. Implications for practice and future research are drawn.

  • Gonca Usta Gonca Usta

This study aims to analyze the student and school level variables that affect students? self-efficacy levels in mathematics in China-Shanghai, Turkey, and Greece based on PISA 2012 results. In line with this purpose, the hierarchical linear regression model (HLM) was employed. The interschool variability is estimated at approximately 17% in China-Shanghai, approximately 22% in Turkey, and approximately 23% in Greece. This study showed a positive association between variables of self-confidence, teacher support, and attitude toward school, all of which are among Level 1 variables, and mathematics self-efficacy in all three countries. A negative association was observed to exist between the variables socio-cultural index and educational opportunities at home and mathematics self-efficacy in all three countries. While pre-school education in China-Shanghai and Turkey were negatively associated with students? mathematics self-efficacy levels, the same variable was positively associated with students? mathematics self-efficacy in Greece. While the variable mathematical anxiety was negatively associated with students? mathematics self-efficacy in China-Shanghai and Greece, it was positively associated with students? mathematics self-efficacy in Turkey. The variable interest in mathematics, in turn, was negatively associated with mathematics self-efficacy solely in China-Shanghai. Regarding the association between mathematics self-efficacy levels and the school level variables, a near-zero positive association was found between class size, deemed significant for Turkey, and self-efficacy levels. The association between teacher to student ratio in school and self-efficacy levels was found to be negative in all three countries. The variable teacher?s morale, however, was positively associated with self-efficacy level in China-Shanghai and Turkey.

  • Stephen J. Pape Stephen J. Pape

Many children read mathematics word problems and directly translate them to arithmetic operations. More sophisticated problem solvers transform word problems into object-based or mental models. Subsequent solutions are often qualitatively different because these models differentially support cognitive processing. Based on a conception of problem solving that integrates mathematical problem-solving and reading comprehension theories and using constant comparative methodology (Strauss & Corbin, 1994), 98 sixth- and seventh-grade students' problem-solving behaviors were described and classified into five categories. Nearly 90% of problem solvers used one behavior on a majority of problems. Use of context such as units and relationships, recording information given in the problem, and provision of explanations and justifications were associated with higher reading and mathematics achievement tests, greater success rates, fewer errors, and the ability to preserve the structure of problems during recall. These results were supported by item-level analyses.