Multimedia CAI Program for Students With Mathematics Difficulties

Abstract

This study investigated the effectiveness of Math Explorer at enhancing the word problem-solving skills of students with mathematics difficulties (MD). The study, which had a multiple-probe-across-subjects design, was conducted over 18 weeks. Four students with MD in Grades 2 and 3 participated. All students were able to use the four-step cognitive and three-step metacognitive strategies to solve addition and subtraction word problems and improved their word problem-solving performance on the computer- and paper/pencil-based tests. After the intervention phase, three out of the four students successfully maintained their improved word problem-solving performance levels during the follow-up phase. Implications for teachers and future software programmers are discussed, and directions for future computer-assisted instruction (CAI) research are suggested.

Keywords

students with mathematics difficulties computer-assisted instruction mathematical word problem solving cognitive and metacognitive strategies

Mathematical problem solving is a complex process that involves the application of mathematical knowledge, skills, and strategies to a wide variety of problems (Fuchs, Fuchs, Finelli, Courey, & Hamlett, 2004; Xin & Jitendra, 2006). It has been argued that mathematical problem solving is critical for students to construct their own conceptual understanding of fundamental mathematical ideas and processes and to develop their logical thinking, thereby influencing their performance on a variety of mathematics tasks, such as estimation, word problems, and computation (National Mathematics Advisory Panel, 2008). Over the past few years, more emphasis has been placed on mathematical problem solving as an essential means for students to deal with unexpected problems in their everyday life (Bottge & Hasselbring, 1993; Van de Walle, 2004). Accordingly, the National Council of Teachers of Mathematics (2000) has emphasized that problem solving should be the first priority of the curriculum at all grade levels, and students should be encouraged to explore and solve many mathematical problems in meaningful real-life contexts.

Despite the increasing emphasis on problem solving in the mathematics curriculum and instruction, students with mathematics difficulties (MD) have considerable difficulties solving mathematical word problems and show significantly poorer word problem-solving performance compared to their typically achieving peers (Montague & Applegate, 2000; Powell, Fuchs, Fuchs, Cirino, & Fletcher, 2009). Interestingly, even students with MD who possess competent reading and computation skills often display particular difficulties with mathematical word problem solving (Montague & Bos, 1986, 1990; Nuzum, 1987). Therefore, researchers have focused on the cognitive and metacognitive knowledge and skills necessary for successful mathematical word problem-solving performance of students with MD and have found that these students typically have cognitive and metacognitive deficits (Miller & Mercer, 1997; Montague & Bos, 1986, 1990; Zawaiza & Gerber, 1993).

To remediate the deficits in cognitive and metacognitive knowledge and skills among students with MD, researchers in a number of intervention studies have attempted to teach these students cognitive and metacognitive strategies for mathematical word problem solving. The results have provided clear evidence that when these students are explicitly taught such strategies, they can develop their word problem-solving knowledge and skills (Jitendra & Hoff, 1996; Jitendra, DiPipi, & Perron-Jones, 2002; Montague, 1992; Montague & Bos, 1986; Xin, Jitendra, & Deatline-Buchman, 2005; Zawaiza & Gerber, 1993). However, several constraints may limit teachers’ successful application of cognitive and metacognitive strategies in mathematics instruction for students with MD, such as (a) a lack of sufficient time for teachers to provide additional instructional support and strategies, (b) teachers’ limited understanding and knowledge of the underlying theory, processes, and components of these strategies, (c) lack of pre- and in-service teacher training on the strategies, and (d) lack of instructional resources and adaptation plans for the strategies (Montague, 1992; Montague, Warger, & Morgan, 2000). These difficulties are further compounded by insufficient time for instructional preparation (Harkamp & Suhre, 2006).

Computer-assisted instruction (CAI) may be an effective method for providing students with MD with cognitive and metacognitive strategies for mathematical word problem solving. In general, CAI has been defined as the use of a computer as a medium for providing instructional content. CAI includes several sophisticated computer-technology functionalities and features applicable to the effective delivery of cognitive and metacognitive strategy instruction on mathematical word problem solving for students with MD. First, CAI can provide students with a sufficient number of practice problems contextualized to various real-world situations. Second, various instructional tools (e.g., number line and computing tool) embedded in CAI programs can provide students with MD additional support when they use cognitive and metacognitive strategies. Third, the variety of virtual manipulatives (e.g., symbols and pictorial representations) used in CAI programs can help students with MD facilitate their interactive learning and understanding of cognitive and metacognitive strategies. Last, CAI can include attractive animations and graphics that help students with MD improve their academic interest, motivation, and persistence, which have been identified as attribute factors of their poor word problem-solving performance (Montague & Applegate, 1993).

Despite the promising features of CAI for delivering cognitive and metacognitive strategies for mathematical word problem solving to students with MD, no study has examined its impact on these students’ mathematical word problem-solving performance. One difficulty in conducting such a study is finding commercially available mathematics CAI programs that incorporate cognitive and metacognitive strategies (Seo & Bryant, 2009). As a result, we designed, developed, and implemented an interactive multimedia CAI program, Math Explorer, to teach one-step addition and subtraction word problem-solving skills to students with MD. Math Explorer incorporates four-step cognitive strategies and corresponding three-step metacognitive strategies adapted from previous research on these strategies for the mathematical word problem-solving performance of students with MD (Montague, 1992).

The purpose of this study was to investigate the effectiveness of Math Explorer in enhancing the one-step addition and subtraction word problem-solving skills of students with MD in Grades 2 to 3. The following research questions guided this study: (a) To what extent does the use of Math Explorer affect the accuracy performance of students with MD on computer-based tasks with one-step addition and subtraction word problem solving? (b) To what extent does the use of Math Explorer generalize to the accuracy performance of these students on paper/pencil-based tasks with one-step addition and subtraction word problem solving? (c) To what extent does the use of Math Explorer maintain the accuracy performance of these students on computer- and paper/pencil-based tasks with one-step addition and subtraction word problem solving?

Method

Participants

Four second and third grade students attending a public elementary school in a midsized city participated in this study. The school enrolled a total of 850 students, of whom 0.35% were Asian, 12.82% were African American, 82.94% were Hispanic, and 3.76% were White. The majority of the students (92%) were from low socioeconomic backgrounds. The four students had been identified as having MD based on their teacher’s rating (i.e., poor or below average level) of their mathematical competence relative to the entire class and to the school district’s mathematics curriculum standards. The students were in the process of LD identification based on the response to intervention model and had below-grade-level mathematics scores on Texas’s standardized test (released Texas Assessment of Academic Skills). Once the students returned the signed parental consent and assent forms, they took a screening test to confirm their eligibility for the study. The students had a score of 30% or less on the screening test (see the Measures section), identified as the recommended criterion level in previous research focusing on learning strategy interventions (Montague & Bos, 1986; Schumaker, Deshler, Alley, Warner, & Denton, 1982). Table 1 presents detailed demographic information and mathematics test scores for the four participating students.

Table 1.

Participant Demographics and Testing Information

Variable	Student 1	Student 2	Student 3	Student 4
Age (years)	7	7	9	8
Grade	2nd	2nd	3rd	3rd
Gender	Female	Male	Male	Male
Areas of difficulty	Math	Math, reading	Math	Math, reading
Ethnicity	White	African American	Hispanic	Hispanic
Socioeconomic status	Free or reduced lunch	Free or reduced lunch	Free or reduced lunch	Free or reduced lunch
Standardized test scores^a
Student score	14	19	21	17
School mean	45	45	53	53
District mean	49	49	51	51
Screening test percentage scored	5	0	11	11

Released Texas Assessment of Academic Skills/Math.

Setting

The study was conducted in a second- and third-grade tutoring area or a conference room at the school. The tutoring areas, which were located in the classroom hallway, were primarily used for the study. If the tutoring areas were too noisy because of other tutoring groups, the study was conducted in the conference room located inside of the school’s main office. A Windows-based laptop computer on which Math Explorer was installed was set up for the study. Other computer equipment, such as mouse and earphones, was also provided.

Dependent Variable

The dependent variable was one-step addition and subtraction word problem-solving performance. The students’ addition and subtraction word problem-solving performance was assessed based on the number of addition and subtraction word problems that they solved correctly on the computerized and paper/pencil-based tests.

Measures

Computer- and paper/pencil-based tests

The computer- and paper/pencil-based tests developed by the researcher served as the screening, baseline, intervention, and follow-up assessments of the students’ addition and subtraction word problem-solving performance. These tests contained a total of 18 one-step addition and subtraction word problems randomly selected from the problem database of Math Explorer. Of the 18 problems, 9 were from each problem difficulty level (Levels 1 and 2) based on the instructional hierarchy for addition and subtraction proposed by Mercer and Mercer (2001). The 9 problems in each level included 3 word problem types and 2 or 3 subtypes based on the addition and subtraction word problem classifications by Riley, Greeno, and Heller (1983), such as (a) change (an unknown result quantity, an unknown change quantity, and an unknown start quantity), (b) combine (an unknown whole quantity and an unknown part quantity), and (c) compare (an unknown difference quantity, an unknown compared quantity, and an unknown referent quantity). The problem sequence within each test was arranged based on the problem types and difficulty levels ranging from easy to difficult.

The students had 10 min to complete the computer- and paper/pencil-based tests administered by the researcher. When they completed the computer-based test, total numbers of correct and incorrect responses were recorded and compiled into each student’s individual file. When the students completed the paper/pencil-based test, the researcher checked their responses and recorded total numbers of correct and incorrect responses. A graduate student checked 25% of the paper/pencil-based tests scored by the researcher to assess the scoring reliability. Mean interrater reliability was 99%, calculated by dividing the number of agreements by the number of agreements plus disagreements and multiplying by 100.

Student implementation checklist

The student implementation checklist developed by the researcher was used to assess the fidelity of each student’s correct use of Math Explorer. The checklist consisted of seven statements to determine whether a student followed instructions and actively engaged in activities during a session, for example, “A student follows instructions for all cognitive and metacognitive strategy steps.” During at least 25% of the computer training and intervention sessions for each student, the researcher and tutors who worked at the school observed each student’s performance and independently assigned a rating from 1 to 3 points (i.e., 1 = disagree, 2 = neutral, 3 = agree) for each statement on the implementation checklist. Mean interrater reliability was 96%.

Independent Variable

The intervention was the interactive multimedia CAI program, Math Explorer. Math Explorer integrated four-step cognitive and three-step metacognitive strategies adapted from previous research on cognitive and metacognitive strategies for the mathematical word problem-solving performance of students with MD (Montague, 1992). The four cognitive strategy steps were Reading, Finding, Drawing, and Computing. For each of the cognitive strategy steps, three metacognitive strategy steps were included: Do Activity, Ask Activity, and Check Activity. The students completed each cognitive strategy step by executing the three metacognitive strategy steps. Table 2 summarizes the four-step cognitive and three-step metacognitive strategies in Math Explorer and presents screenshots.

Table 2.

Cognitive and Metacognitive Strategy Components in Math Explorer

Step	Cognitive strategy	Metacognitive strategy
1	Reading	Do Activity: I read the problem aloud for understanding.
		Ask Activity: Have I read and understood the problem?
		Check Activity: I understand the problem. I read the problem again.
2	Finding	Do Activity: I find and click the important information in the problem.
		Ask Activity: Have I found and clicked the important information correctly?
		Check Activity: I check the important information that goes with the problem.
3	Drawing	Do Activity: I draw or click a picture to show the problem using my drawing tool.
		Ask Activity: Does the picture fit the problem?
		Check Activity: I check the picture against the problem information.
4	Computing	Do Activity: I write the number sentence and find the answer using my computing tool.
		Ask Activity: Are the number sentence and answer correct?
		Check Activity: I check that the number sentence and answer are correct.

Several instructional design features that have been identified as crucial for the successful mathematical learning of students with MD (Bryant et al., 2008; Steel, 2002; Swanson, Hoskyn, & Lee, 1999) were also included in Math Explorer. Those features were (a) clear instructional goals, (b) explicit instructional modeling, (c) guided and independent practice opportunities, (d) prerequisite mathematics skill review, (e) vocabulary skill review, (f) visual representations, (g) instructional, ability, and effort feedback, and (h) text-to-speech function. Figure 1 offers screenshots of the instructional design features of Math Explorer.

Figure 1.

Screenshots of the instructional features of Math Explorer

Development procedures of Math Explorer

Math Explorer was developed via an advanced multimedia authoring tool, Macromedia Flash Professional 8 (Macromedia, 2006), based on the multimedia development periods proposed by Alessi and Trollip (2001). The researcher created a program evaluation checklist based on the multimedia evaluation checklist presented by Alessi and Trollip (2001) to examine program fidelity. The program evaluation checklist consisted of 60 statements to determine whether Math Explorer was well designed in terms of instructional, interface, and interaction design; language and grammar; and offline resources (e.g., “Instructional objectives are stated.”) The researcher and a graduate student independently assigned a rating from 1 to 3 points (i.e., 1 = disagree, 2 = neutral, 3 = agree) for each statement on a program evaluation checklist. Mean interrater reliability was 96%. Disagreements or any concerns about the program between the researcher and graduate student were also discussed and considered for revision. Last, the researcher conducted usability testing with six students and teachers to assess whether Math Explorer was usefully designed for students with MD. All procedures and questionnaires for the usability testing were prepared according to the usability testing guidelines outlined by Nielsen, Snyder, Molich, and Farrell (2000). This feedback was used to revise Math Explorer.

Problem template and database systems of Math Explorer

To construct the problem pool of Math Explorer, one-step addition and subtraction word problems with single- and/or double-digit numbers were collected from mathematical textbooks (i.e., SRA Math, Scott Foresman, and Everyday Mathematics) for Grades 2 and 3. The problems in the problem pool were divided into the eight problem subtypes of Riley and his colleagues (1983), and then three word problems were randomly selected from each problem subtype in the problem pool. For each of the three problems, problem templates that included subject, object, and number variables were developed. To generate actual problems from the problem templates, subject and number variables were assigned by randomly choosing an entity from predefined subject (e.g., Tom and Jamie) and object (e.g., apple and cookie) sets. The number variables were restrictively assigned depending on the problem difficulty levels based on the instructional hierarchy of Mercer and Mercer (2001). The result was 288 problems across the problem difficulty levels in the problem database of the program.

Research Design and Data Analysis

The students’ performance in each intervention session needed to be checked specifically to analyze their word problem-solving performance characteristics when using Math Explorer. Also, the strengths and limitations of Math Explorer needed to be identified specifically to evaluate its effectiveness in improving the word problem-solving performance of students with MD. Therefore, a multiple-probe-across-subjects design was used to assess the effects of Math Explorer on students’ one-step addition and subtraction word problem-solving skills. Four students received the Math Explorer intervention at different points in time, and each student’s baseline data were collected once a week.

Visual inspection was conducted to analyze students’ performance within and between the phases in terms of stability, level change, and trend direction. According to Gast (2009), data within a phase are considered stable if 80% of the data points fall within a 15% range of the mean of all data points of the phase. Level change was identified based on the difference in the last data point value of the first phase and the first data point value of the second phase. Trend direction (i.e., accelerating, decelerating, or zero-celerating) was identified based on the split-middle analysis described by Gast (2009).

Data Collection Procedures

The study was conducted over 18 weeks. Students individually participated in the introduction, screening test, and computer training sessions with the researcher and then started the intervention sessions.

Baseline

During the baseline phase, the students took computer- or paper/pencil-based baseline tests once a week without having been given any instruction on the cognitive and metacognitive strategies. Each student’s baseline data were collected in three consecutive sessions prior to the introduction of Math Explorer. The test sequence for each student during the baseline phase was counterbalanced on a daily basis to avoid a possible order effect. The test sequence was also counterbalanced across the students.

Intervention

During each intervention session, the students were asked to work with Math Explorer for 20 to 30 min and then take the computer- or paper/pencil-based test for 10 min. The students participated in, at most, five intervention sessions per week. After stable data with zero-celerating trends were collected during the baseline phase, Student 1 started the intervention. When Student 1 correctly responded to at least 13 out of 18 problems (i.e., 70% accuracy) on at least four consecutive tests, Student 2 immediately started the intervention. This criterion level was determined based on the review of previous research focusing on learning strategy interventions (Montague & Bos, 1986; Schumaker et al., 1982). The same procedure was applied to Students 2, 3, and 4.

Follow-up

Approximately 2 weeks after the intervention phase was completed, each student met with the researcher individually once a week to check the maintenance of Math Explorer’s effects over time. Each student was asked to take a 10-min computer- or paper/pencil-based test. The tests were randomly selected from the screening, baseline, and intervention tests. Before each follow-up session, the four-step cognitive and three-step metacognitive strategies were briefly reviewed to help the students remember them.

Results

Figure 2 provides data on each student’s accuracy percentage scores on the computer- and paper/pencil-based tests during the baseline, intervention, and follow-up phases.

Figure 2.

Accuracy percentage scores across the baseline, intervention, and follow-up phases for the students

Research Question 1 examined the effects of Math Explorer on the students’ accuracy performance on computer-based tasks with one-step addition and subtraction word problem solving. During the baseline session, accuracy performance on the computer-based tests remained stable with a zero trend for each student, except Student 3. After the intervention, an immediate increase in level occurred, with an accuracy percentage score of 16%, 16%, 27%, and 22% for Students 1 to 4, respectively. Each student’s accuracy performance on the computer-based tests gradually improved over time, showing an accelerating trend. All four students were able to achieve scores exceeding the criterion level on the computer-based tests. Except for Student 2, the students maintained those scores for the reminder of the intervention phase. All four students achieved relatively higher accuracy percentage scores for the change (i.e., unknown result and unknown start) and combine word problem types on the computer-based tests. Specifically, the average accuracy percentage scores for the change–unknown result, change–unknown start, combine–unknown whole, and combine–unknown part problems across the four students were 100%, 97%, 100%, and 93%, respectively, whereas the students achieved relatively lower scores for the change (i.e., unknown change) and compare problem types on the computer-based tests. Specifically, the average accuracy percentage scores for the change–unknown change, compare–unknown compared, compare–unknown difference, and compare–unknown referent problems across the four students were 82%, 89%, 69%, and 65%, respectively.

Research Question 2 examined whether performance gains on the computer-based tests generalized to paper/pencil-based tests. Visual inspection of each student’s accuracy percentage scores on the paper/pencil-based tests revealed that student’s performance remained stable with a zero trend during the baseline phase. After the intervention started, an increase in level occurred, with an accuracy percentage score of 22%, 16%, 22%, and 22% for Students 1 to 4, respectively. Each student’s accuracy performance gradually increased over time, with an accelerating trend. All four students were able to achieve scores that exceeded the criterion level (i.e., 70% accuracy) on the paper/pencil-based tests. Once scores beyond the criterion level were obtained, three students maintained their scores for the remainder of the intervention phase. As shown on the computer-based tests, all four students achieved relatively higher accuracy percentage scores for the change (i.e., unknown result and unknown start) and combine problem types on the paper/pencil-based tests. Specifically, the average accuracy percentage scores for the change–unknown result, change–unknown start, combine–unknown whole, and combine–unknown part problems across the four students were 100%, 97%, 100%, and 94%, respectively. They achieved slightly lower scores for the change (i.e., unknown change) and compare problem types on the paper/pencil-based tests. Specifically, the average accuracy percentage scores for the change–unknown change, compare–unknown compared, compare–unknown difference, and compare–unknown referent problems across the four students were 85%, 86%, 79%, and 75%, respectively. However, all of these scores remained above the criterion level.

Research Question 3 examined whether students maintained their accuracy performance on the computer- and paper/pencil-based tasks of one-step addition and subtraction word problem solving. After the 3- to 6-week follow-up phase started, Students 1, 3, and 4 maintained their intervention gains on their accuracy performance. A decrease in level occurred, with the average accuracy percentage score of 11%, for Students 1 and 2, but there was no level change for Students 3 and 4. Trend direction was not examined because of the limited number of data points for each student during the follow-up phase. An analysis of the data on the average accuracy percentage scores revealed that the increase in scores for three students on the computer- and paper/pencil-based tests during the follow-up phase was greater than those achieved on the computer- and paper/pencil-based tests during the intervention phase. In addition, a comparison of the data from the computer- and paper/pencil-based tests during the follow-up phase revealed that the average accuracy percentage scores on the computer-based tests were as great as or greater than those on the paper/pencil-based tests. All four students had accuracy percentage scores of 100% for most of the change and combine problem types but had relatively lower scores for the compare problem type on the computer- and paper/pencil-based tests during the follow-up phase. For example, on the computer-based tests, the average accuracy percentage scores for the compare–unknown difference and compare–unknown referent problems across the four students were 35% and 29%, respectively. On the paper/pencil-based tests, the average accuracy percentage scores for the compare–unknown difference and compare–unknown referent problems across the four students were 72% and 68%, respectively.

Discussion

This study investigated the effects of Math Explorer on the one-step addition and subtraction word problem-solving skills of four students with MD in Grades 2 and 3. The findings of the study revealed that all students were able to use the four-step cognitive and three-step metacognitive strategies to solve addition and subtraction word problems and improved their word problem-solving performance on the computer- and paper/pencil-based tests during the intervention phase. The positive findings of this study may be related to the presentation of the cognitive and metacognitive strategies in Math Explorer. As the students learned how to solve various types of word problems using the four-step cognitive and three-step metacognitive strategies in Math Explorer, they became much more adept at solving word problems correctly. These findings are consistent with previous research on cognitive and metacognitive strategies use for students with MD in which it was demonstrated that explicit instruction on cognitive and metacognitive strategies was a promising approach for successful mathematical word problem-solving performance of these students (Montague, 1992). Considering that most of the previous research on cognitive and metacognitive strategies has been conducted with secondary school students with MD, the findings of this study provide preliminary evidence that elementary school students with MD can also benefit from cognitive and metacognitive strategy instruction through CAI to improve their addition and subtraction word problem-solving skills.

Another possible factor explaining the positive findings of this study may be the instructional design features for students with MD in Math Explorer (e.g., step-by-step explicit instructional modeling of cognitive and metacognitive strategies, guided and independent practice sessions, and representational tools). There has been consensus that the instructional principles and features embedded in CAI programs are important positive factors for students’ learning (Clark, 1983). However, research has found that most existing CAI programs in mathematics fail to incorporate the critical instructional features for the successful mathematical learning of students with MD (Seo & Bryant, 2009). Emphasis must be placed on developing commercially available CAI programs that effectively present the critical instructional features for students with MD as part of appropriate CAI instruction suited to meet their instructional needs.

This study had several interesting results. First, the participants still displayed difficulties in solving the change–unknown change, compare–unknown compared, compare–unknown difference, and compare–unknown referent problems on both computer- and paper/pencil-based tests during the intervention phase. These findings are consistent with previous research on difficulty levels of different word problem types, indicating that compare word problems are more difficult to solve for elementary school students than other word problems (e.g., combine and change problems; Arendasy, Sommer, & Ponocny, 2005; Fuson, Carroll, & Landis, 1996; Stern, 1993).

Second, gains on the computer-based tests generalized to the paper/pencil-based tests. However, each student’s accuracy percentage scores were slightly greater on the computer-based tests than the paper/pencil-based tests during the intervention phase. This finding provides evidence that the generalization ability of students with MD was somewhat limited. The differences in the students’ accuracy scores between the computer- and paper/pencil-based tests may be explained by the fact that on the paper/pencil-based tests the students often made several types of mistakes, for example, backward number writing and ones and tens confusion. Those mistakes did not occur on the computer-based tests because the students were able to make number sentences by clicking numbers on the computing tool. Another reason may be a faster performance rate on the computer-based tests than the paper/pencil-based tests. On the computer-based tests, the students were able to apply each step of the strategies at a fast rate and quickly move on to the next problem; thus, they had more chances to solve problems on the computer-based tests. These findings were confirmed by data showing that the number of problems the students solved was slightly higher on the computer-based tests than the paper/pencil-based tests across intervention sessions.

Interestingly, most of the students’ accuracy percentage scores for the difficult problem types (e.g., change–unknown change and compare) were slightly lower on the computer-based tests than the paper/pencil-based tests. On the contrary, for the easy problem types (e.g., change–unknown result and combine), most of the students’ accuracy percentage scores were as high as or slightly higher on the computer-based tests than the paper/pencil-based tests. It may be that those difficult problem types required students to spend enough time to apply the strategies with careful attention to solve the problem correctly.

Limitations of the Research

There are several limitations that need to be considered when interpreting the results of this study. First, the computer- and paper/pencil-based tests used as an outcome measure in the study were developed by the researcher, and their reliability and validity had not been adequately assessed. Even though the tests were developed through random selection procedures, the students’ performance was not assessed with standardized tests. Second, the students took the 10-min computer- or paper/pencil-based tests every other day after the intervention. Because of such a high frequency of testing, there may be a concern as to whether each student’s improved accuracy performance was primarily because of practice effects rather than the intervention effects. Therefore, caution is necessary in interpreting the students’ test performance. Third, the social validity of the study was not adequately assessed. Formal interviews with the students and their teachers were not conducted, so the students’ perspectives on the effectiveness of Math Explorer and the teachers’ observations on the students’ mathematical performance progress in their classroom were not obtained. Fourth, although the students received the intervention for 5 to 7 weeks, they also received mathematics instruction regarding three-digit addition or multiplication from their classroom teacher. Therefore, the students’ improved accuracy performance may have been influenced not only by the Math Explorer intervention but also by their classroom instruction. A replication study with a research design that can control for this issue is necessary.

Implications for Practice

The approaches addressed within Math Explorer can be used as one tool to introduce the promise of CAI to teachers in a variety of workshops, conferences, and other professional development opportunities. Such efforts may increase the possibility that teachers use available CAI programs as part of their mathematics instruction and teach mathematical concepts and skills to students with MD effectively. Another implication of the study is that Math Explorer can be used as a tool for teachers to learn cognitive and metacognitive strategies and develop their own abilities to successfully teach the strategies to students during mathematics instruction. Math Explorer was designed to incorporate the cognitive and metacognitive strategies in a systematic way so that teachers can easily learn the processes and components of the strategies using the program. In addition, the study points out the importance of the critical instructional design features for students with MD in Math Explorer. Future software programmers can be aware of these features to design and develop mathematics CAI programs for students with MD. Also, teachers or other educators can refer to these features when they evaluate or select mathematics CAI programs for students with MD and, furthermore, utilize them to prepare their mathematics instruction for students with MD.

Implications for Future Research

Several suggestions for future research have emerged. First, the effectiveness of Math Explorer must be further explored by including additional students with MD or other special education populations in other educational settings. Second, higher level word problems (e.g., multiplication and division) should be addressed by expanding the problem database of Math Explorer for students in Grades 2 and 3 and in upper grade levels to practice solving word problems that correspond to the mathematics content at their grade level. Incorporating such higher level word problems could help students with MD to more fully benefit from the mathematics instruction and curriculum at their grade level. Third, another area that warrants further research is the suitable duration of CAI to maximize its effectiveness and hold its novelty over time for students with MD. Anecdotally, Student 2, who interacted with Math Explorer for the longest time, appeared to gradually lose interest in learning to use a computer and showed distracted and off-task behaviors during the intervention phase. Therefore, it is necessary to explore ways to maintain the novelty effects of CAI over time and to identify the appropriate duration of CAI for students with MD in future research. Fourth, in the midst of current trends in CAI research using advanced technology, studies validating the potential of e-learning and m-learning in mathematics using sophisticated computer software and mobile devices should be conducted. Furthermore, an investigation of how the contents of e-learning and m-learning are developed and delivered with particular attention to the deficits that students with MD have in memory, attention, and cognitive processing is necessary to maximize mathematical learning outcomes.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interests with respect to the authorship and/or publication of this article.

Financial Disclosure/Funding

The author(s) received no financial support for the research and/or authorship of this article.

About the Authors

You-Jin Seo, PhD, is a research professor at Korea University in Seoul, Korea. Her research interests include assistive technology and mathematics interventions for students with learning disabilities and instructional adaptations for students with disabilities in inclusive settings.

Diane Bryant, PhD, is a research professor in the Department of Special Education and the Meadows Center for Preventing Educational Risk at the University of Texas at Austin. Her research interests focus on the validation of interventions for students with mathematics disabilities and the role of assistive technology in instructional settings.

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