The identification,implementation, and evaluation of critical user interface design features of computer-assisted instruction programs in mathematics for students with learning disabilities

Critical user interface design features of computer-assisted instruction programs in mathematics for students with learning disabilities and corresponding implementation guidelines were identified in this study. Based on the identified features and guidelines, a multimedia computer-assisted instruction program, ‘Math Explorer’, which delivers addition and subtraction word problem-solving instruction for students with learning disabilities at the early elementary level, was designed and developed. Lastly, usability testing was conducted to assess whether Math Explorer was well-designed in terms of the interface for students with learning disabilities. Given the results of the usability testing, this study corroborated the fact that the critical user interface design features and guidelines in mathematics computer-assisted instruction programs would be essential for facilitating the mathematical learning of students with learning disabilities. Implications for practice and future research were discussed.     

Schoenfeld’s problem solving theory in a student controlled learning environment

This paper evaluates the effectiveness of a student controlled computer program for high school mathematics based on instruction principles derived from Schoenfeld’s theory of problem solving. The computer program allows students to choose problems and to make use of hints during different episodes of solving problems. Crucial episodes are: analyzing the problem, selecting appropriate mathematical knowledge, making a plan, carrying it out, and checking the answer against the question asked.     

Control of numerical effects of dispersion and dissipation in numerical schemes for efficient shock-capturing through an optimal Courant number

Composite schemes consist of several steps of a dispersive scheme followed by one step of a dissipative scheme [Liska Richard, Wendroff Burton. Composite schemes for conservation laws. SIAM J Numer Anal 1998;35(6):2250-71]. The latter [Liska Richard, Wendroff Burton. 2D shallow water equations by composite schemes. Int J Numer Meth Fluids 1999;30:461-79] acts as a filter reducing oscillations in regions of discontinuity. Liska and Wendroff have derived the composite Lax-Wendroff/Lax-Friedrichs (LWLF) [Liska Richard, Wendroff Burton, 1998] scheme which blends the Lax-Wendroff (LW) scheme with the 2-step Lax-Friedrichs (LF) scheme. The formulation of the 2-step Lax-Friedrichs scheme [Liska Richard, Wendroff Burton, 1998] is different from that of the classic Lax-Friedrichs scheme and has been devised by Liska [Liska Richard, Wendroff Burton, 1998]. In this work, we propose to replace LW scheme by MacCormack (MC) scheme since the latter is less dispersive. We obtain a new composite scheme in 1-D and in 2-D by blending the MacCormack scheme with the 2-step Lax-Friedrichs scheme which we term as the composite MacCormack/Lax-Friedrichs (MCLF) scheme. This is followed by analytical work on the effective amplification factor (EAF) and the relative phase error (RPE) for both families of schemes in 1-D and 2-D: LWLFn and MCLFn, consisting of (n − 1) steps of the dispersive scheme (LW or MC) and 1 step of the dissipative LF scheme. We introduce a new concept, baptised as Curbing of Dispersion by Dissipation for Efficient Shock-capturing, CDDES in which a cfl number is computed whereby dissipation curbs dispersion. This cfl number is termed as optimal in this work. We conduct a comparative study based on numerical experiments in 2-D namely: contact-discontinuity problem [Ould Kaber SM. A legendre pseudospectral viscosity method. J Comput Phys 1996;128:165-80], rotating hill problem [Ould Kaber SM, 1996] and the deformative flow of Smolarkiewicz [Dabdub Donald, Seinfeld John H. Numerical advective schemes used in air quality models-sequential and parallel implementation. Atmos Environ 1994;28(20):3369-85, Ghods A, Sobouti F, Arkani-Hamed J. An improved second order method for solution of pure advection problems. Int J Numer Meth Fluids 2000;32:959-77, Nguyen K, Dabdub D. Two-level time-marching scheme using splines for solving the advection equation. Atmos Environ 2001;35:1627-37] to show that the MacCormack/Lax-Friedrichs (MCLF) scheme is more efficient than LWLF scheme to capture shocks in regions of discontinuity. We also show that better results are obtained at optimal cfl numbers for some variants of LWLFn and MCLFn schemes, with n = 2, 3, 4 and 5.     

Implementation of Web-based dynamic assessment in facilitating junior high school students to learn mathematics

This research adopts the Graduated Prompting Assessment Module of the WATA system (GPAM-WATA) and applies it to the remedial teaching of junior high school mathematics. The theoretical basis of the development of GPAM-WATA is the idea of ‘graduated prompt approach’ proposed by Campione and Brown, 1985, Campione and Brown, 1987. In GPAM-WATA, when examinees fail to answer items correctly, they obtain instructional prompts (IPs) in a graduated way. This research developed the contents of IPs based on the mathematical problem-solving theory of Mayer (1992, pp. 458–460). A quasi-experimental design was adopted. Ninety-six junior high school seventh graders from three different classes participated in this research. The three classes were randomly divided into the GPAM-WATA group (n = 31), the N-WBT group (n = 31) and the PPT group (n = 34). All students received traditional mathematics instruction from the same teacher. After traditional mathematics instruction, all students took the pre-test of the summative assessment. The students in the three different groups then respectively received remedial teaching in the form of GPAM-WATA, normal Web-based test (N-WBT), and paper-and-pencil test (PPT). After the remedial teaching, all students took the post-test of the summative assessment. The results indicate that compared with other groups, performing remedial teaching using GPAM-WATA has significantly better effectiveness. Moreover, it is found that the IPs in GPAM-WATA are effective in remedial teaching for not only those students most lacking in different types of mathematical problem-solving knowledge but also all the other students.     

Space-time discretizing optimal DRP schemes for flow and wave propagation problems

The present paper reports constrained optimization of explicit Runge–Kutta (RK) schemes, coupled with optimal upwind compact scheme to achieve dispersion relation preservation (DRP) property for high performance computing. Essential ideas of optimization employed in arriving at the proposed time integration scheme are extension of the earlier work reported in Rajpoot et al. (J Comput Phys 2010;229:3623–51). This is in turn an application of the correct error evolution equation in Sengupta et al. (J Comput Phys 2007;226:1211–8). Resultant DRP scheme demonstrated the idea for explicit spatial central difference schemes. Present work is similar, extending it for near-spectral accuracy compact schemes. Practical utility of the developed method is demonstrated by solution of model problems and for flow problems by solving Navier–Stokes equation, some of which cannot be solved by conventional schemes, as the problem of rotary oscillation of cylinder.Developed method is calibrated with: (i) flow past a circular cylinder performing rotary oscillation at Re = 150 and (ii) flow inside a 2D lid-driven cavity (LDC) at Reynolds numbers of Re = 1000 and Re = 10,000. Quantitative and qualitative comparisons show excellent match for rotary oscillation cylinder cases with the experimental results of Thiria et al. (J Fluid Mech 2006;560:123–47). Results for LDC for Re = 1000 are compared with that in Botella & Peyret (Comp Fluids 1998;27:421–33) and results for Re = 10,000 are compared with recent published ones showing triangular vortex in the core.     

Transitional feedback schedules during computer-based problem-solving practice

Feedback has a strong influence on effective learning from computer-based instruction. Prior research on feedback in computer-based instruction has mainly focused on static feedback schedules that employ the same feedback schedule throughout an instructional session. This study examined transitional feedback schedules in computer-based multimedia instruction on procedural problem-solving in electrical circuit analysis. Specifically, we compared two transitional feedback schedules: the TFS-P schedule switched from initial feedback after each problem step to feedback after a complete problem at later learning states; the TFP-S schedule transitioned from feedback after a complete problem to feedback after each problem step. As control conditions, we also considered two static feedback schedules, namely providing feedback after each practice problem-solving step (SFS) or providing feedback after attempting a complete multi-step practice problem (SFP). Results indicate that the static stepwise (SFS) and transitional stepwise to problem (TFS-P) feedback produce higher problem solving near-transfer post-test performance than static problem (SFP) and transitional problem to step (TFP-S) feedback. Also, TFS-P resulted in higher ratings of program liking and feedback helpfulness than TFP-S. Overall, the study results indicate benefits of maintaining high feedback frequency (SFS) and reducing feedback frequency (TFS-P) compared to low feedback frequency (SFP) or increasing feedback frequency (TFP-S) as novice learners acquire engineering problem solving skills.     

Assessing problem solving in expert systems using human benchmarking

The human benchmarking approach attempts to assess problem solving in expert systems by measuring their performance against a range of human problem-solving performances. We established a correspondence between functions of the expert system GATES and human problem-solving skills required to perform a scheduling task. We then developed process and outcome measures and gave them to people of different assumed problem-solving ability. The problem-solving ability or “intelligence” of this expert system is extremely high in the narrow domain of scheduling planes to airport gates as indicated by its superior performance compared to that of undergraduates, graduate students and expert human schedulers (i.e. air traffic controllers). In general, the study supports the feasibility of using human benchmarking methodology to evaluate the problem-solving ability of a specific expert system.     

Speech versus text supported hints in learning to solve word problems

The aim of this research was to test whether the effectiveness of hints offered in a computer programme for word problem solving can be enhanced by combining visual schemas with spoken instruction (audio and visual input) instead of written instruction with visual schemas (visual only input). In complex tasks, audio/visual information is easier to comprehend than visual only information (Clark and Mayer, 2011, call this the ‘modality effect'). In a first study, it was tested on the basis of 6 word problems whether grade 5 students (n = 20) better improved their solution plans using audio plus visual schemas than students who were provided with text plus visual schemas (n = 21). We found that students who worked with audio/visual hints had less difficulty in translating the hints information into their solution plans. The second study was based on a programme containing 48 word problems in which hints use was optional. The students in the audio-visual condition (n = 28) solved more problems correctly and performed better on a post-test than the students in the text-visual condition (n = 30). These results seem to support our expectation that the modality of hints affects students' comprehension and ability levels in solving word problems.     

Improving mathematical problem solving: A computerized approach

Mathematics teachers often experience difficulties in teaching students to become skilled problem solvers. This paper evaluates the effectiveness of two interactive computer programs for high school mathematics problem solving. Both programs present students with problems accompanied by instruction on domain-specific knowledge required in different episodes of problem solving. The first program is based on a direct instructional approach to learning, the second on a constructivist view of learning. The latter approach is expected to be particularly beneficial to weak students.The effectiveness of both computer programs was evaluated by means of an experiment. Four classes worked with the constructivist based computer program, and four worked with the direct instructional program. Five classes that had received traditional mathematics education served as the control group. The computer programs were used in three periods of two consecutive weeks each. The results show that both computer programs improved problem-solving ability more strongly than had traditional mathematics instruction. Contrary to our expectations, both weak and skilled students benefited equally from both computer programs. Specifically, the programs helped the students to improve the quality of their analysis and verification skills during problem solving.     

Effects of identical example–problem and problem–example pairs on learning

Examples are often an integral part of online learning environments directed at the acquisition of problem-solving skills. An unresolved issue, however, is when examples should be provided to learners. Prior research has suggested that example–problem pairs are more effective than problem–example pairs for novice learners. However, in those studies, the problem–example pairs condition may have been hindered by the fact that the examples and problems were not identical within and across pairs. The present experiment therefore employed a between-subjects design with two conditions to compare the effects of learning to solve one particular problem from studying/practicing either in an example–problem–example–problem sequence (EP condition; n = 16) or in a problem–example–problem–example sequence (PE condition; n = 16). Results show that participants in the EP condition outperformed their counterparts in the PE condition during the learning phase, but that this difference had disappeared on the test tasks after participants in the PE group had also studied the example a second time.     

A Cognitive Model and Computer Tutor for Programming Recursion

This article discusses cognitive models of learning to program recursion and their relation to lessons on recursion in an intelligent computer tutor for LISP programming (the LISP Tutor). The cognitive models are implemented as production systems in which programming skill is characterized as the decomposition of programming goals into subgoals and elementary actions via the application of programming plans. Two sets of learning mechanisms are used in the cognitive models. Analogical problem-solving mechanisms use declarative knowledge of example program solutions to overcome problem-solving impasses. Knowledge compilation mechanisms summarize problem solutions into efficient problem-solving skill. Analyses and simulations of novice and expert programming were used to develop ideal models of the programming knowledge to confer upon students and bugs that characterize common misconceptions. The LISP Tutor uses the ideal models and bugs to guide its interactions with students. Experimental evaluations of the LISP Tutor indicate that it is more efficient and effective than classroom instruction.     

Trends and issues of regulative support use during inquiry learning: Patterns from three studies

This paper looks across three experimental studies that examined supports designed to assist high-school students (age 15–19) with cognitive regulation of their physics inquiry learning efforts in a technology-enhanced learning environment called Co-Lab. Cognitive regulation involves the recursive processes of planning, monitoring, and evaluation during learning, and is generally thought to enhance learning gains for students. The research synthesis described in this paper examined the usage effects of a support tool called the process coordinator (PC) on learning outcomes. This tool incorporated goal-lists, hints, prompts, cues, and templates to support the cognitive regulation skills of students during a fluid dynamics task. Students were asked to produce two learning outcomes of their investigations: system dynamics models and lab reports. Results from the three studies indicated trends in frequent use of the PC for planning activities, but low usage for monitoring and evaluation. Correlational analysis revealed two trends with regard to how these regulative activities impacted learning outcomes. First, consistent positive correlations were apparent between regulative activities and lab report scores of students and second, consistent negative correlations between the use of supports and model quality scores. Trends with regard to how task complexity, time, and student prior experience impacted these findings are also presented with suggestions for future research.     

The effect of the timing of instructional support in a computer-supported problem-solving program for students in secondary physics education

Many students experience difficulties in solving applied physics problems. Researchers claim that the development of strategic knowledge (analyze, explore, plan, implement, verify) is just as necessary for solving problems as the development of content knowledge. In order to improve these problem-solving skills, it might be profitable to know at what time during problem solving is the use of instructional support most effective: before, during or after problem solving.     

Approximating the buffer allocation problem using epochs

The correctness of applications that perform asynchronous message passing typically relies on the underlying hardware having a sufficient amount of memory (message buffers) to hold all undelivered messages—such applications may deadlock when executed on a system with an insufficient number of message buffers. Thus, determining the minimum number of buffers that an application needs to prevent deadlock is an important task when writing portable parallel applications. Unfortunately, both this problem (called the Buffer Allocation Problem) and the simpler problem of determining whether an application may deadlock for a given number of available message buffers are intractable [A. Brodsky, J. Pedersen, A. Wagner, On the complexity of buffer allocation in message passing systems, Journal of Parallel and Distributed Computing 65 (2005) 692–713].     

Improving literacy and metacognition with electronic portfolios: Teaching and learning with ePEARL

Can an electronic portfolio that is both a multimedia container for student work and a tool to support key learning processes have a positive impact on the literacy practices and self-regulated learning skills of students? This article presents the findings of a yearlong study conducted in three Canadian provinces during the 2007–2008 school year initially involving 32 teachers and 388 students. Due to varying levels of implementation our final data set included 14 teachers and 296 students. Using a non-equivalent pre-test/post-test design, we found that grade 4–6 students who were in classrooms where the teacher provided regular and appropriate use of the electronic portfolio tool ePEARL (i.e., medium–high implementation condition, n = 7 classrooms and 121 students), compared to control students (n = 7 classrooms and 175 students) who did not use ePEARL, showed significant improvements (p < .05) in their writing skills on a standardized literacy measure (i.e., the constructed response subtest of the Canadian Achievement Test-4th ed.) and certain metacognitive skills measured via student self-report. The results of this study indicate that teaching with ePEARL has positive impacts on students’ literacy and self-regulated learning skills when the tool is used regularly and integrated into classroom instruction.     

Searching for the two sigma advantage: Evaluating algebra intelligent tutors

This study evaluated 2 off-the-shelf, computer-based, mathematics intelligent-tutoring systems that provide instruction in algebra during a remedial mathematics summer program. The majority of the enrolled high school students failed to pass algebra in the previous semester. Students were randomly assigned in approximately equal proportions to work with the Carnegie Learning Algebra Cognitive Tutor or the ALEKS Algebra Course. Using the tutoring system exclusively, the students completed a 4-h-a-day, 14-day summer school high school algebra class for credit. The results revealed that both tutoring systems produced statistically and practically meaningful learning gains on measures of arithmetic and algebra knowledge.     

Cognitive outcomes from the Game-Design and Learning (GDL) after-school program

The Game-Design and Learning (GDL) initiative engages middle school students in the process of game-design in a variety of in-school, after-school, and summer camp settings. The goal of the GDL initiative is to leverage students' interests in games and design to foster their problem-solving and critical reasoning skills. The present study examines the effectiveness of an after-school version of the GDL program using a quasi-experimental design. Students enrolled in the GDL program were guided in the process of designing games aimed at solving problems. Compared to students in a control group who did not attend the program (n = 24), the children who attended the GDL program (n = 20) showed a significant increase in their problem-solving skills. The results provide empirical support for the hypothesis that participation in the GDL program leads to measurable cognitive changes in children's problem-solving skills. This study bears important implications for educators and theory.     

LevelScheme: A level scheme drawing and scientific figure preparation system for Mathematica

LevelScheme is a scientific figure preparation system for Mathematica. The main emphasis is upon the construction of level schemes, or level energy diagrams, as used in nuclear, atomic, molecular, and hadronic physics. LevelScheme also provides a general infrastructure for the preparation of publication-quality figures, including support for multipanel and inset plotting, customizable tick mark generation, and various drawing and labeling tasks. Coupled with Mathematica's plotting functions and powerful programming language, LevelScheme provides a flexible system for the creation of figures combining diagrams, mathematical plots, and data plots.

Program summary

Title of program:LevelSchemeCatalogue identifier:ADVZProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVZOperating systems:Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and LinuxProgramming language used:Mathematica 4Number of bytes in distributed program, including test and documentation:3 051 807Distribution format:tar.gzNature of problem:Creation of level scheme diagrams. Creation of publication-quality multipart figures incorporating diagrams and plots.Method of solution:A set of Mathematica packages has been developed, providing a library of level scheme drawing objects, tools for figure construction and labeling, and control code for producing the graphics.     

Instructional effectiveness of a computer-supported program for teaching reading comprehension strategies

This article examines the effectiveness of a computer-based instructional program (e-PELS) aimed at direct instruction in a collection of reading comprehension strategies. In e-PELS, students learn to highlight and outline expository passages based on various types of text structures (such as comparison or cause-and-effect) as well as to paraphrase, self-question, and summarize. The study involved 1041 fourth-grade elementary students from 21 schools distributed in three regions in central Chile. Participant teachers integrated this program into the Spanish language curriculum, instructing their students during thirty sessions of 90 min each during one school semester. Pretest-to-posttest gains in reading comprehension scores were significantly greater for students instructed with this program than for students who received traditional instruction (d = .5), with particularly strong effects for lower-achieving students (d = .7). The findings support the efficacy of direct instruction in specific learning strategies in a computer-based environment.