=Paper=
{{Paper
|id=None
|storemode=property
|title=Computer-assisted Problem-based Learning for Word-based Mathematical Problem Solving
|pdfUrl=https://ceur-ws.org/Vol-991/paper4.pdf
|volume=Vol-991
|dblpUrl=https://dblp.org/rec/conf/ecis/AbdelhafidFK13
}}
==Computer-assisted Problem-based Learning for Word-based Mathematical Problem Solving==
https://ceur-ws.org/Vol-991/paper4.pdf
COMPUTER-ASSISTED PROBLEM-BASED LEARNING FOR
WORD-BASED MATHEMATICAL PROBLEM SOLVING
Chadli Abdelhafid, GEGI Lab - Ibn Khaldoun University of Tiaret, BP 78 Zaâroura,14000
Tiaret, Algeria, abdelhafith.chadli@univ-tiaret.dz
Bendella Fatima, University of Sciences and Technology of Oran, BP 1505 El M’naoeur,
31000 Oran, Algeria, bendella@univ-usto.dz
Belmabrouk Karima, University of Sciences and Technology of Oran, BP 1505 El M’naoeur,
31000 Oran, Algeria, karimabelmabrouk@yahoo.fr
Abstract
A focus on mathematical understanding and problem solving in math education has developed a need
to implement alternate ways of testing to better assess the students' understanding and problem
solving skills. Furthermore, previous computer-assisted problem-solving systems designed for
elementary school mathematical education have focused mainly on developing students’ cognitive
skills and less interest is dedicated to related procedural skills. However, procedural and conceptual
knowledge are highly correlated. This study proposes a computer-assisted system, whose design is
based on Polya’s problem-solving model. The system is designed to help low-achieving second
graders in mathematics with word-based addition and subtraction questions. The emphasis of using
the specific model was on dividing the problem solving procedure into stages and the concentration on
the students’ cognitive and procedural processes at each stage. In order to help students overcome
procedural obstacles, we developed an agent oriented evaluation so as to give them a meaningful
feedback to better monitor and support students learning performance.
Keywords: Problem based learning, Cognitive and procedural skills evaluation, Addition and
subtraction word problems resolution, Polya’s strategy.
1 Introduction
Descriptive evaluation is recognized as an effective method that requires students to write down the
problem solving process so that teachers could analyze what the students do not understand and help
improve their understanding. During the past 30 years, there has been an increasing emphasis on
assessing problem solving by examining the cognitive processes that students use while engaged in
problem solving. The multidimensionality of the problem-solving process is certainly made evident as
attempts are made to look at all thinking done to solve a problem.
Descriptive assessment does not ask simple questions that could be answered with a fact. Instead, they
ask students to describe their problem solving process and evaluate the students' advanced thinking
skills such as reasoning skills in mathematics. Whang (Whang, 2004) suggested that descriptive
assessment is one of the most effective evaluation methods because it allows teachers to know
explicitly the thought process of the students.
Furthermore, computer-assisted mathematical problem solving systems are rapidly growing in
educational usage. These systems help students to better cope with difficulties encountered in solving
problems and give them immediate feedback. Some of these systems are based on the four problem-
solving stages mentioned by Polya (Polya, 1945): (1) understanding the problem, (2) making a plan,
(3) executing the plan and (4) reviewing the solution. However, these computer-assisted problem-
solving systems have incorporated all the problem-solving steps within a single stage, making it
32
difficult to diagnose stages at which errors occurred when a student encounters difficulties and
imposing a too-high cognitive load on students in their problem solving (Chang et al., 2006).
Moreover, these systems focus more on cognitive thinking process, as well as abstract mathematical
concepts and little interest is devoted to procedural skills. However, procedural and conceptual
knowledge are highly correlated (Hallet et al., 2010) (Rittle-Johnson et al., 2001). Competence in
domains such as mathematics rests on children developing and linking their knowledge of concepts
and procedures (Silver, 1986), therefore we propose to develop a computer-assisted problem solving
system that rules on both students’ conceptual and procedural skills.
The purpose of this paper is to propose a new system that is based on the four problem-solving stages
mentioned by Polya. The system assists in achieving addition and subtraction problems for second
grade students by assessing cognitive reasoning at each stage and related procedural skills. Moreover,
a multi agent system is used to grade students’ answers and displays feedback after the problem
solving completion.
The paper is organized as follows: In section 2, we discuss the goals of problem based learning
strategy and its merits to enhance learning, such as creative thinking, problem solving, logical thinking
and decision making. Section 3 focuses mainly on the influence of computer-assisted environments on
mathematics instruction and their positive impact on students’ problem-solving. In section 4, we
present the proposed problem solving process and we describe student-machine interfaces that are
used in each stage besides embedded techniques to assist in achieving a successful outcome at each
stage. Section 5 presents the student assessment approach and depicts the role of each agent in the
assessment process. In section 6, we conclude on adopted strategy, and future work.
2 Problem Based Learning
A focus on mathematical understanding and problem solving in math education has developed a need
to implement alternate ways of testing to better assess the students' understanding and problem solving
skills. The purpose of education has shifted from simply delivering knowledge and information to
student-centered education that focuses on fostering creativity and enhancing problem solving skills.
In Algeria, evaluation in new mathematics curriculum now focuses more on assessing problem solving
skills and advanced mathematical thinking skills such as reasoning, communications and mathematical
connection skills.
In traditional teaching, assessment of whether students had understood a mathematical problem was
based on whether they could describe the correct arithmetic procedure. However, it was not enough to
evaluate students’ mathematics concepts and abilities of solving math problems merely depending on
their writing.
Several researches also pointed out that good problem solving skills are the key to acquiring a
successful solution in learning mathematics (Gagne, 1985) (Mayer, 1992).
Obviously, if a student could successfully solve a math problem by arithmetic calculation, that did not
mean the student really understood it. It has been maintained in the literature that PBL positively
influence learning outcomes along with learners’ higher order thinking skills such as creative thinking,
problem solving, logical thinking and decision making. For instance, Elshafei (Elshafei, 1999)
compared the Calculus achievement levels of second graders in five different high schools and 15
different classes where PBL and traditional instructional methods were implemented. Findings
indicated that students in PBL settings did prefer this method and had higher levels of achievement. In
addition, it was revealed that students in PBL settings had better solutions for given problems in
comparison to those who were in traditional classroom settings. Kaptan and Korkmaz (Kaptan and
Korkmaz, 2000) investigated the influence of PBL on problem solving skills and self-efficacy levels
of in-service teachers. Findings revealed that the experimental group which was exposed to
fundamental science activities through PBL had higher self-efficacy and logical thinking scores than
the control group.
33
The goal of PBL-based cognitive strategy instruction is to teach learners multiple cognitive and
metacognitive processes and strategies to facilitate and enhance performance in academic domains
(e.g., mathematical problem solving). The processes and strategies range from simple to complex
depending on task difficulty and context of the task (Montague and Van Garderen, 2008). Polya’s
Mathematics Problem-Solving Process is one of these PBL instructional strategies. He was the first to
introduce the concept of problem-solving model believing that mathematics is not all about the result.
According to Polya’s problem-solving model, the proposed system is designed to guide low-achievers
through the parts of the problem-solving process that they often ignore. Furthermore, the system
adopts schema representations strategy (Reusser, 1996) in the ”Making a plan“ stage to enable
students describe the solution steps in detail by ordering operands of the problem (see figure 3).
3 Relevant Research Work
Arithmetic word problems play an important role in the elementary school mathematics curricula in
terms of developing general problem-solving skills (Verschaffel et al., 2007). Studies of children's
solutions of addition and subtraction problems date to the early part of the last century (Arnet, 1905)
(Browne, 1906). Since that time a number of researchers have investigated how children solve
addition and subtraction problems. (For example, see (Carpenter et al., 1981) (Groen and Parkman,
1972) (Svenson, 1975)). With technological advancement and the arrival of the multimedia computer
instruction era, the attention of more and more studies has been fastened on interactive learning
methods through multimedia computers. The use of computers to implement findings from qualitative
research related to problem-solving teaching strategies can furnish more effective learning
opportunities for learners.
Over the last years there has been an increased research studies about the influence of computer-
assisted environments on mathematics instruction (see (Huang and Ke, 2009)). We present below
some of them that are interested in enhancing cognitive problem solving ability.
Chang et al. (Chang et al., 2006) proposed a computer-assisted system named MathCAL, the design of
which was based on the four polya’s problem-solving stages. A sample of 130 fifth-grade students
(average 11 years old) completed a range of elementary school mathematical problems. The result
showed that MathCAL was effective in improving the performance of students with lower problem
solving ability. These assistances improved students’ problem solving skills in each stage.
Huang et al. (Huang et al., 2012) developed a computer-assisted mathematical problem-solving system
in the form of a network instruction website to help low-achieving second- and third-graders in
mathematics with word-based addition and subtraction questions. According to Polya’s problem-
solving model, the proposed system was designed to guide these low-achievers through the parts of the
problem-solving process. They found that the mathematical problem solving ability of experiment
group students was significantly superior to that of control group students. Most of the participants
were able to continue the practice of solving word-based mathematical questions, and their willingness
to use the system was high. Their findings indicate that the computer-assisted mathematical problem
solving system can serve effectively as a tool for teachers engaged in remedial education.
Panaoura (Panaoura, 2012)] investigated the improvement of students’ mathematical performance by
using a mathematical model through a computerized approach. He developed an intervention program
and 11 years students worked independently on a mathematical model in order to improve their self-
representation in mathematics, to self-regulate their performance and consequently to improve their
problem solving ability. The emphasis of using the specific model was on dividing the problem
solving procedure into stages. The use of the computer offered the opportunity to give students general
comments, hints and feedback without the involvement of their teachers. Students had to communicate
with a cartoon animation presenting a human being who faced difficulties and cognitive obstacles
during problem solving procedure. Experiments involved 255 students (11 years old), who constituted
the experimental and the control group. Results confirmed that providing students with the opportunity
34
to self-reflect on their learning behavior when they encounter obstacles in problem solving is one
possible way to enhance students’ self-regulation and consequently their mathematical performance.
Leh and Jitendra (Leh and Jitendra, 2012) compared the effectiveness of computer-mediated
instruction and teacher-mediated instruction on the word problem-solving performance of students
struggling in mathematics. Both conditions integrated cognitive modeling that focused on the problem
structure using visual representations with critical instructional elements specifically targeting the
needs of at-risk students. Participants were 25 third-grade students with mathematics difficulties. But
results indicated no statistically significant between-condition differences at posttest and on a 4-week
retention test of word problem-solving.
Based on Polya’s four problem-solving steps (understanding the problem, devising a plan, carrying out
the plan and looking back), Ma and Wu (Ma and Wu, 2000) designed a set of interesting, active
learning materials for teaching. Research outcomes indicated both students’ learning interest and
achievement had improved. Chang (Chang, 2004) incorporated strategies such as key-point marking,
diagram illustration and answer review in the problem-solving process and developed a process-
oriented, computer-aided mathematics problem solving system. The system was applied mathematical
questions (mainly elementary-level arithmetic computation) with fifth graders as the subjects of the
empirical study. Results showed that the system was effective in enhancing low-achievers’ problem-
solving ability.
Summary of the examples cited above evince that computer-assisted mathematics-problem-solving
systems have a positive impact on children’s problem-solving ability. However all these systems focus
on cognitive skills used in problem solving and no interest is devoted to related problem solving
procedural skills. Here our focus is mainly on both cognitive and procedural skills training using
polya’s problem solving strategy and multi agent systems to analyze second grade students’ word
based problem solving ability. Precisely, we address the problem of how to evaluate the students’
skills objectively so as to provide them the best feedback.
4 System Design and Framework Outline
The purpose of this paper is to propose a computer-assisted Learning system that is based on the
mathematical problem-solving process proposed by Polya. It guides the second grade students to think
and solve the mathematical problems by using a graphical representation in the making plan stage
consisting of two operand nodes; one operator node and one result node (see Fig. 3). Each operand and
result node comes with two attributes, label and value, representing the meaning of the node and its
numerical value, respectively. The values for the two operand nodes and the operator node correspond
to the two operands and an operator in the mathematical expression. The value at the result node is the
result of the expression.
The schema representation is very helpful for conceptualizing the semantics of the problem [3]. The
problems would be divided into four types based on the classification of Vergnaud (Vergnaud, 1982):
(1) PUT-TOGETHER, (2) CHANGE-GET-MORE, (3) CHANGE-GET-LESS, and (4) COMPARE
(See table 1).
Because all problems involve three quantities and any of these quantities can be unknown, there are
three possible problem subtypes within each main problem type. Two of these require subtraction of
the two given numbers in the problem and one requires addition of the two givens.
35
Addition situations Subtraction situations
Change-Get-More Change-Get-Less
Missing end Missing end
Ali had 3 marbles. Ali had 8 marbles.
Then Omar gave him 5 more marbles. Then he gave 5 marbles to Omar.
How many marbles does Ali have now? How many marbles does Ali have now?
Missing Change Missing change
Ali had 3 marbles. Ali had 8 marbles.
Then Omar gave him some more marbles. Then he gave some marbles to Omar.
Now Ali has 8 marbles. Now Ali has 3 marbles.
How many marbles did Omar give him? How many marbles did he give to Omar?
Missing start Missing start
Ali had some marbles. Ali had some marbles.
Then Omar gave him 5 more marbles. Then he gave 5 marbles to Omar.
Now Ali has 8 marbles. Now Ali has 3 marbles.
How many marbles did Ali have in the beginning? How many marbles did Ali have in the beginning?
Put-Together Compare
Missing all Missing difference
Ali has 3 marbles. Ali has 8 marbles.
Omar has 5 marbles. Omar has 5 marbles.
How many marbles do they have altogether? How many more marbles does Ali have than Omar?
Missing first part Missing big
Ali and Omar have 8 marbles altogether. Ali has 3 marbles.
Omar has 3 marbles. Omar has 5 more marbles than Ali.
How many marbles does Ali have? How many marbles does Omar have?
Missing second part Missing small
Ali and Omar have 8 marbles altogether. Ali has 8 marbles.
Ali has 3 marbles. He has 5 more marbles than Omar.
How many marbles does Omar have? How many marbles does Omar have?
Table 1. Classification of word problems.
36
4.1 Students’ problem solving process
Students’ problem-solving guidance process is shown in Figure 1. Firstly, the adequate problem is
provided by the system among other problems stored in the problem solving information database. In
stage 1, the assessing module for understanding the problem proposes responses to be tagged by the
student and other techniques allowing to rule about comprehension of the problem. The plan making
stage enables the student to build a schema representation of his solution. Stage 3offers, according to
the operation type, a calculation interface and finally a multi questionnaire is proposed to the student
to validate his solution. Problem information is provided at each stage of the problem solving process
and assessment of each stage is recorded in the student tracking database. The system displays
feedback messages after the whole problem solving completion.
Figure 1. Students’ problem solving Process.
4.2 The stage of understanding the problem
In this stage, the system offers to students the possibility to circle important words in the problem.
Furthermore, students have to distinguish between what is known and what is requested in the problem
by selecting adequate responses. For illustration, figure 2 displays the problem in the problem frame
and check boxes for needed answers.
37
Buttons for: getting help, Ali had 13 marbles. Then
Reading the exercise, Next he gave 8 marbles to Omar.
stage and previous stage. How many marbles does
Ali have now?
Third step: cheek boxes that Second step: cheek boxes First step: showing and
indicate what is requested. that indicate what you know hiding a pencil to highlight
know important words.
Figure 2. The screenshot of the first stage (Understanding the problem)
4.3 The stage of making the plan
The guiding process of plan elaboration is divided in four steps as illustrated in figure 3 so as to help
students express graphically the problem solving. The first step consists of identifying the first
operand and its value among a list of operands; the student selects the appropriate one and enters its
value. The second step proposes an operator choice between addition and subtraction. In the third
step, the student selects the second operand and its value and finally the fourth step requires only a
result label. According to the problem missing part a result label may either be requested in first or
third step.
In the example of figure 3, the student has chosen the second label for the first operand and enters the
value 13, for the second operand he chosen also the second label with a value of 8 and tries subtraction
between these two operands. Labels are presented so as to know if student understands the meaning of
the operator.
After the student has pressed the ‘‘next’’ button, the system compares the solution plan made by the
student with the solution plan built into the system, the suggestions regarding the student’s problem
solving are stored in the student tracking database and displayed after the student completes the
problem solving.
38
Forth step: Select the Third step: Select the second Second step: First step: Select the first
result label among a operand label and its value Select the operand label and its value
list of labels. among a list of operands. operator. among a list of operands.
Figure 3. The screenshot of the second stage (Making the plan)
4.4 The stage of plan execution
As shown in figure 4, the system provides a graphic preview for all of the addition and subtraction
worksheets in a vertical problem format where large cases are reserved for digits of operands and little
cases are used if regrouping is required for subtraction (exchanging one of the tens for 10 units or one
of the hundreds for 10 tens) or for addition when process involved a carryover number. In this stage,
the system evaluates student’s procedural knowledge and uses a multi agent evaluation approach.
Three steps are required at most to complete this stage, each step aims at manipulate ones, tens and
hundreds. The student has to fill in the large cases (ones, tens and hundreds) of result and little cases
if regrouping is required for subtraction or if addition needs carrying over. After finishing calculation
of all columns, the system assesses student’s answer and feedback is stored. A last stage is needed to
validate student’s problem solution.
Third step: Second step: First step:
manipulating manipulating tens manipulating ones
hundreds column column column
Figure 4. The screenshot of the third stage (Executing the plan)
39
4.5 The stage of reviewing the solution
In this stage the student answers questions as shown in figure 5. In order to validate the solution given
at previous stage, the system proposes some questions that are related to the problem and student must
answer by true or false. After completing this stage, the student presses the Evaluation button which
triggers the system to evaluate the results, and messages appear that indicate whether any mistake was
made. Also, the correct problem-solving steps are displayed simultaneously on the same stage
interface of student’s answers.
False True Select the right Variants of the problem, obtained by
answer exchanging the missing part with operands
Figure 5. The screenshot of the fourth stage (Reviewing the solution)
5 Student Assessment
One of the most common strategies for studying the problem-solving process involves the use of an
analytic scoring scale. Analytic scoring is an evaluation method that assigns point values to various
dimensions of the problem-solving episode (Charles et al., 1987).
The grading rubric graded the solutions in 4 specific areas. A total of 10 maximum possible points
were awarded to each problem by assigning 2 maximum possible points for understanding the
problem, 3 maximum possible points for making a plan stage, 3 maximum possible points for
procedural skills and finally 2 maximum possible points for reviewing the solution. Detail of stages’
scoring is given in table 2.
Furthermore, one of interesting research issue in Computer-Assisted Instruction Systems is Intelligent
Agents. Some Intelligent Agents are used for helping students doing science experiments in Virtual
Experiment Environment (Huang et al., 1999) (Kuo et al., 2001); the others are used to help student
solving problems with a kind of knowledge structure and Knowledge Map (Kuo et al., 2002). In this
paper, intelligent agents are designed to diagnose students' learning status in problem solving system.
40
Stage Understanding the Making a plan Executing the plan Reviewing the
problem solution
Criteria Complete Accuracy of setting Accuracy of Correct validation of
understanding of the the plan and degree of computation with problem solution by
problem with describing and correct manipulation of selecting the correct
recognition of what is interpreting the numbers problem solution
given and what is operands and their (adding/subtracting of variants. Variants are
requested in the values, the operation units, tens and obtained by
problem with correct and the missing value. hundreds) and right use Combining addition
identification of of regrouping and and subtraction of
important words in the carrying over concepts. problem operands and
problem. missing part.
Rubrics What is known: 0.7 First operand label Manipulation of First problem solution
and scores pt identification: 0.5 units: 1pt variant: 0.5 pt.
What is requested: First operand value: Manipulation of Second problem
0.7 pt 0.5 tens: 1pt solution variant: 0.5 pt.
Identifying the Second operand label Manipulation of Third problem solution
important words: 0.6 identification: 0.5 hundreds: 1pt variant: 0.5 pt.
pt Second operand In case of Fourth problem
value: 0.5 manipulating numbers solution variant: 0.5 pt.
Identification of the without hundreds, the
operator: 0.5 rating score of this
Identification of category is affected
label of missing: 0.5 equally to units and
tens manipulations.
Table 2. Assessment grading rubric
5.1 Stage assessor agents
At the end of each problem solving stage, and when the student presses the next stage button the stage
assessor agent is started. The evaluations for stages: understanding the problem, making a plan and
reviewing the solution is the same and consists of some operations to be designed in an Intelligent
Agent: 1. Load stage solution of the problem; 2. Evaluate student’s answers: comparing student’s
answers with stage solution; 3.generate feedback and calculate stage score: feedback is generated
according to mastered concepts and developed skills and score is awarded. All stage solving
informations are stored in the student tracking database.
5.2 Procedural skills assessment agents
Assessment of plan execution stage is different from the other stages assessment and requires a multi
agent assessment to diagnose student’s addition and subtraction skills. For this purpose, four agents
are needed: ones agent, tens agent, hundreds agent and assessment agent, each of the first three agents
is responsible of evaluating one column operation and skills related to both addition and subtraction (if
regrouping is required for subtraction or if addition needs carrying over). The assessment agent
consults the problem solving information database to know the number of columns (units, tens and
hundreds) used in the problem solution, afterward he creates the agents needed for evaluation. After
evaluating his column, each agent sends a report to the assessment agent which assesses the whole
student’s procedural skills (see figure 6). The motivation for applying this assessment method is to
understand all computing details used by the student to complete addition and subtraction operations.
41
5.2.1 The ones agent
The ones assessment agent checks the digits’ computation of the ones column and verifies if
techniques related to operator type are used.
If needed operation is addition, the agent carries out the following operations:
Calculates the sum of digits of the ones column,
Verifies if the result units digit is correct,
Checks if the student has not miss the carry over number if the operation requires so, and sends a
message to tens agent to inform him that carrying over is required after computing ones column.
Generates a report according to results and sends it as evaluation grid to assessment agent.
If the problem solution requires a subtraction operation, the agent completes the following actions:
Calculates the difference between digits of the ones column,
Verifies if the result units digit is correct,
Checks if the student has used the regrouping technique if the subtraction requires so, and sends a
message to tens agent to inform him that regrouping is used to compute ones column.
Generates the feedback according to results and sends it as evaluation grid (See tables 3 and 4) to
assessment agent. The 3 maximum possible points that can be awarded in this stage are divided
depending on whether the solution of the problem requires one, two or three columns.
5.2.2 The tens/hundreds agent
This agent performs the same operations as the previous agent and makes sure that student adds the
carry over number to the sum of digits in tens (hundreds) column if needed operation is addition. In
the subtraction case, the agent checks up if the student adds the regrouping number to the subtracted
number of tens (hundreds) column. Finally, he sends details of evaluation to the assessment agent.
5.2.3 The assessment agent
After receiving reports from the three other agents, the assessment agent proceeds to the assessment of
the student’s procedural skills. The scores are awarded according to previous agents’ evaluation grids.
Results of assessment are displayed and stored in the student tracking database.
Hundreds Tens Units Evaluation
Agent Agent Agent grid
Assessment
Agent
Figure 6. Agent oriented assessment of procedural skills.
42
Skill Needed in Performed? Awarded
computation? score
Alignment of digits on worksheet Yes Yes 0.1
Arrangement of numbers on subtraction worksheet Yes Yes 0.1
Subtracting numbers less than 10 No No
Subtracting numbers greater than 10 Yes No 0
Management of regrouping technique Yes No 0
Table 3. Example of the ones agent’s evaluation grid (case of subtraction).
Skill Needed in Performed? Awarded
computation? score
Alignment of digits on worksheet Yes Yes 0.1
Subtracting numbers less than 10 Yes Yes 0.2
Subtracting numbers greater than 10 Yes No 0
Increment by 1 the value of tens to subtract Yes No 0
Management of regrouping technique No No
Table 4. Example of the tens agent’s evaluation grid (case of subtraction).
6 Conclusion
Mathematics education in Algeria lacked practical and effective descriptive methods that could be
readily used in the schools and students who experienced mathematical learning difficulties became
unable to attend expanded mathematical curricula. Our study was designed to offer one possible
solution to the problem. We developed a Computer-assisted problem-based learning system to help
low-achieving elementary students improve their ability to solve basic word-based addition and
subtractions questions, and enhance their willingness to continue the learning. Our system is based on
Polya’s four problem-solving steps; the emphasis of using this model was on dividing the problem
solving procedure into stages so as to diagnose stages at which errors occurred when a student
encounters difficulties. Furthermore, we focus on remedial computation of addition and subtraction
operations by developing an agent based evaluation approach that can furnish a meaningful feedback
to be effective in improving the performance of students with lower problem solving ability. Many
researches proposed problem-solving assistance to help students with their problem solving, and one
of the most suggested problem-solving assistances is visualization. As far as that goes this study
continues the convention of using such assistance, it included a few major differences from previous
studies. The first is the use of multiple-choice question in the ”Understanding the problem“ stage
where student have to identify what is known and what is requested in the problem. The second is
using of schema representations strategy in the ”Making a plan“ stage to enable students describe the
solution steps in detail by ordering operands of the problem. The third is the graphic presentation of
addition and subtraction worksheets so as to enable students to perform regrouping if subtraction is
needed to solve the problem or carrying over if addition is requested. These improvements allowed us
to objectively evaluate students’ cognitive and procedural skills.
Future research is planned to empirically demonstrate the effectiveness of our system on elementary
school mathematical problems that involve the operations of addition and subtraction. Another
improvement concerns student modeling so as to better monitor and support his learning.
43
In summary, this study improves assistance used in previous computer-assisted systems to help low-
achieving second-graders in mathematics by combining schema representation, graphical worksheets,
and other assistance in the problem-solving procedure.
Acknowledgment
This work is part of AMIAC research project 20/U311/4227, supported by the Algerian Ministry of
Higher Education and Scientific Research.
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