An Innovative Approach to Teaching Structural Induction for Computer Science

Proofs by induction are central to many computer science areas such as data structures, theory of computation, programming languages, program efficiency-time complexity, and program correctness. Proofs by induction can also improve students’ understanding of and performance with computer science concepts such as programming languages, algorithm design, and recursion, as well as serve as a medium for teaching them. Even though students are exposed to proofs by induction in many courses of their curricula, they still have difficulties understanding and performing them. This impacts the whole course of their studies, since proofs by induction are omnipresent in computer science. Specifically, students do not gain conceptual understanding of induction early in the curriculum and as a result, they have difficulties applying it to more advanced areas later on in their studies. The goal of my dissertation is twofold: 1. identifying sources of computer science students’ difficulties with proofs by induction, and 2. developing a new approach to teaching proofs by induction by way of an interactive and multimodal electronic book (e-book). For the first goal, I undertook a study to identify possible sources of computer science students’ difficulties with proofs by induction. Its results suggest that there is a close correlation between students’ understanding of inductive definitions and their understanding and performance of proofs by induction. For designing and developing my e-book, I took into consideration the results of my study, as well as the drawbacks of the current methodologies of teaching proofs by induction for computer science. I designed my e-book to be used as a standalone and complete educational environment. I also conducted a study on the effectiveness of my e-book in the classroom. The results of my study suggest that, unlike the current methodologies of teaching proofs by induction for computer science, my e-book helped students overcome many of their difficulties and gain conceptual understanding of proofs induction.

An innovative approach to teaching structural induction for computer science

Proofs by induction are central to many computer science areas such as data structures, theory of computation, programming languages, program efficiency-time complexity, and program correctness. Proofs by induction can also improve students’ understanding and performance of computer science concepts such as programming languages, algorithm design, and recursion, as well as serve as a medium for teaching them. Even though students are exposed to proofs by induction in many courses of their curricula, they still have difficulties understanding and performing them. This impacts the whole course of their studies, since proofs by induction are omnipresent in computer science. Specifically, students do not gain conceptual understanding of induction early in the curriculum and as a result, they have difficulties applying it to more advanced areas later on in their studies. The goal of my dissertation is twofold: (1) identifying sources of computer science students’ difficulties with proofs by induction, and (2) developing a new approach to teaching proofs by induction by way of an interactive and multimodal electronic book (e-book). For the first goal, I undertook a study to identify possible sources of computer science students’ difficulties with proofs by induction. Its results suggest that there is a close correlation between students’ understanding of inductive definitions and their understanding and performance of proofs by induction. For designing and developing my e-book, I took into consideration the results of my study, as well as the drawbacks of the current methodologies of teaching proofs by induction for computer science. I designed my e-book to be used as a standalone and complete educational environment. I also conducted a study on the effectiveness of my e-book in the classroom. The results of my study suggest that, unlike the current methodologies of teaching proofs by induction for computer science, my e-book helped students overcome many of their difficulties and gain conceptual understanding of proofs induction.

The applied computer science of economic analyses: Internet prioritization and Internet pricing, and software engineering and software pricing for the mass market

This research examines evolving issues in applied computer science and applies economic and business analyses as well. There are two main areas. The first is internetwork communications as embodied by the Internet. The goal of the research is to devise an efficient pricing, prioritization, and incentivization plan that could be realistically implemented on the existing infrastructure. Criteria include practical and economic efficiency, and proper incentives for both users and providers. Background information on the evolution and functional operation of the Internet is given, and relevant literature is surveyed and analyzed. Economic analysis is performed on the incentive implications of the current pricing structure and organization. The problems are identified, and minimally disruptive solutions are proposed for all levels of implementation to the lowest level protocol. Practical issues are considered and performance analyses are done. The second area of research is mass market software engineering, and how this differs from classical software engineering. Software life-cycle revenues are analyzed and software pricing and timing implications are derived. A profit maximizing methodology is developed to select or defer the development of software features for inclusion in a given release. An iterative model of the stages of the software development process is developed, taking into account new communications capabilities as well as profitability. ^

The development and analysis of a field project model curriculum and its impact on achievement and attitude toward science and the environment with at-risk eleventh and twelfth grade students

This study was an evaluation of a Field Project Model Curriculum and its impact on achievement, attitude toward science, attitude toward the environment, self-concept, and academic self-concept with at-risk eleventh and twelfth grade students. One hundred eight students were pretested and posttested on the Piers-Harris Children's Self-Concept Scale, PHCSC (1985); the Self-Concept as a Learner Scale, SCAL (1978); the Marine Science Test, MST (1987); the Science Attitude Inventory, SAI (1970); and the Environmental Attitude Scale, EAS (1972). Using a stratified random design, three groups of students were randomly assigned according to sex and stanine level, to three treatment groups. Group one received the field project method, group two received the field study method, and group three received the field trip method. All three groups followed the marine biology course content as specified by Florida Student Performance Objectives and Frameworks. The intervention occurred for ten months with each group participating in outside-of-classroom activities on a trimonthly basis. Analysis of covariance procedures were used to determine treatment effects. F-ratios, p-levels and t-tests at p $<$.0062 (.05/8) indicated that a significant difference existed among the three treatment groups. Findings indicated that groups one and two were significantly different from group three with group one displaying significantly higher results than group two. There were no significant differences between males and females in performance on the five dependent variables. The tenets underlying environmental education are congruent with the recommendations toward the reform of science education. These include a value analysis approach, inquiry methods, and critical thinking strategies that are applied to environmental issues. ^

The relationship of attitudes toward science, cognitive style, and self-concept to achievement in chemistry at the secondary school level

There is currently a crisis in science education in the United States. This statement is based on the National Science Foundation's report stating that the nation's students, on average, still rank near the bottom in science and math achievement internationally. ^ This crisis is the background of the problem for this study. This investigation studied learner variables that were thought to play a role in teaching chemistry at the secondary school level, and related them to achievement in the chemistry classroom. Among these, cognitive style (field dependence/independence), attitudes toward science, and self-concept had been given considerable attention by researchers in recent years. These variables were related to different competencies that could be used to measure the various types of achievement in the chemistry classroom at the secondary school level. These different competencies were called academic, laboratory, and problem solving achievement. Each of these chemistry achievement components may be related to a different set of learner variables, and the main purpose of this study was to investigate the nature of these relationships. ^ Three instruments to determine attitudes toward science, cognitive style, and self-concept were used for data collection. Teacher grades were used to determine chemistry achievement for each student. ^ Research questions were analyzed using Pearson Product Moment Correlation Coefficients and t-tests. Results indicated that field independence was significantly correlated with problem solving, academic, and laboratory achievement. Educational researchers should therefore investigate how to teach students to be more field independent so they can achieve at higher levels in chemistry. ^ It was also true that better attitudes toward the social benefits and problems that accompany scientific progress were significantly correlated with higher achievement on all three academic measures in chemistry. This suggests that educational researchers should investigate how students might be guided to manifest more favorable attitudes toward science so they will achieve at higher levels in chemistry. ^ An overall theme that emerged from this study was that findings refuted the idea that female students believed that science was for males only and was an inappropriate and unfeminine activity. This was true because when the means of males and females were compared on the three measures of chemistry achievement, there was no statistically significant difference between them on problem solving or academic achievement. However, females were significantly better in laboratory achievement. ^

An analysis of teachers' perceptions of informal science professional development

Science professional development, which is fundamental to science education improvement, has been described as being weak and fragmentary. The purpose of this study was to investigate teachers' perceptions of informal science professional development to gain an in-depth understanding of the essence of the phenomenon and related science-teaching dispositions. Based on the frameworks of phenomenology, constructivism, and adult learning theory, the focus was on understanding how the phenomenon was experienced within the context of teachers' everyday world. ^ Data were collected from eight middle-school teachers purposefully selected because they had participated in informal programs during Project TRIPS (Teaching Revitalized Through Informal Programs in Science), a collaboration between the Miami-Dade school district, government agencies (including NASA), and non-profit organizations (including Audubon of Florida). In addition, the teachers experienced hands-on labs offered through universities (including the University of Arizona), field sites, and other agencies. ^ The study employed Seidman's (1991) three-interview series to collect the data. Several methods were used to enhance the credibility of the research, including using triangulation of the data. The interviews were transcribed, color-coded and organized into six themes that emerged from the data. The themes included: (a) internalized content knowledge, (b) correlated hands-on activities, (c) enhanced science-teaching disposition, (d) networking/camaraderie, (e) change of context, and (f) acknowledgment as professionals. The teachers identified supportive elements and constraints related to each theme. ^ The results indicated that informal programs offering experiential learning opportunities strengthened understanding of content knowledge. Teachers implemented hands-on activities that were explicitly correlated to their curriculum. Programs that were conducted in a relaxed context enhanced teachers' science-teaching dispositions. However, a lack of financial and administrative support, perceived safety risks, insufficient reflection time, and unclear itineraries impeded program implementation. The results illustrated how informal educators can use this cohesive model as they develop programs that address the supports and constraints to teachers' science instruction needs. This, in turn, can aid teachers as they strive to provide effective science instruction to students; notions embedded in reforms. Ultimately, this can affect how learners develop the ability to make informed science decisions that impact the quality of life on a global scale. ^

Signal processing of physiological signals for automated assessment of stress in computer users

The need to provide computers with the ability to distinguish the affective state of their users is a major requirement for the practical implementation of affective computing concepts. This dissertation proposes the application of signal processing methods on physiological signals to extract from them features that can be processed by learning pattern recognition systems to provide cues about a person's affective state. In particular, combining physiological information sensed from a user's left hand in a non-invasive way with the pupil diameter information from an eye-tracking system may provide a computer with an awareness of its user's affective responses in the course of human-computer interactions. In this study an integrated hardware-software setup was developed to achieve automatic assessment of the affective status of a computer user. A computer-based "Paced Stroop Test" was designed as a stimulus to elicit emotional stress in the subject during the experiment. Four signals: the Galvanic Skin Response (GSR), the Blood Volume Pulse (BVP), the Skin Temperature (ST) and the Pupil Diameter (PD), were monitored and analyzed to differentiate affective states in the user. Several signal processing techniques were applied on the collected signals to extract their most relevant features. These features were analyzed with learning classification systems, to accomplish the affective state identification. Three learning algorithms: Naïve Bayes, Decision Tree and Support Vector Machine were applied to this identification process and their levels of classification accuracy were compared. The results achieved indicate that the physiological signals monitored do, in fact, have a strong correlation with the changes in the emotional states of the experimental subjects. These results also revealed that the inclusion of pupil diameter information significantly improved the performance of the emotion recognition system. ^

An analysis of the themes of environmental sustainability in the United States curriculum science content standards

This study examined how the themes of environmental sustainability are evident in the national, state and local standards that guide k–12 science curriculum. The study applied the principles of content analysis within the framework of an ecological paradigm. In education, an ecological paradigm focuses on students' use of a holistic lens to view and understand material. The intent of this study was to analyze the seventh grade science content standards at the national, state, and local textbook levels to determine how and the extent to which each of the five themes of environmental sustainability are presented in the language of each text. The themes are: (a) Climate Change Indicators, (b) Biodiversity, (c) Human Population Density, (d) Impact and Presence of Environmental Pollution, (e) Earth as a Closed System. The research study offers practical insight on using a method of content analysis to locate keywords of environmental sustainability in the three texts and determine if the context of each term relates to this ecological paradigm. Using a concordance program, the researcher identified the frequency and context of each vocabulary item associated with these themes. Nine chi squares were run to determine if there were differences in content between the national and state standards and the textbook. Within each level chi squares were also run to determine if there were differences between the appearance of content knowledge and skill words. Results indicate that there is a lack of agreement between levels that is significant p < .01. A discussion of these results in relation to curriculum development and standardized assessments followed. The study found that at the national and state levels, there is a lack of articulation of the goals of environmental sustainability or an ecological paradigm. With respect to the science textbook, a greater number of keywords were present; however, the context of many of these keywords did not align with the discourse of an ecological paradigm. Further, the environmental sustainability themes present in the textbook were limited to the last four chapters of the text. Additional research is recommended to determine whether this situation also exists in other settings.

DIMUSE: An integrated framework for distributed multimedia system with database management and security support

With the recent explosion in the complexity and amount of digital multimedia data, there has been a huge impact on the operations of various organizations in distinct areas, such as government services, education, medical care, business, entertainment, etc. To satisfy the growing demand of multimedia data management systems, an integrated framework called DIMUSE is proposed and deployed for distributed multimedia applications to offer a full scope of multimedia related tools and provide appealing experiences for the users. This research mainly focuses on video database modeling and retrieval by addressing a set of core challenges. First, a comprehensive multimedia database modeling mechanism called Hierarchical Markov Model Mediator (HMMM) is proposed to model high dimensional media data including video objects, low-level visual/audio features, as well as historical access patterns and frequencies. The associated retrieval and ranking algorithms are designed to support not only the general queries, but also the complicated temporal event pattern queries. Second, system training and learning methodologies are incorporated such that user interests are mined efficiently to improve the retrieval performance. Third, video clustering techniques are proposed to continuously increase the searching speed and accuracy by architecting a more efficient multimedia database structure. A distributed video management and retrieval system is designed and implemented to demonstrate the overall performance. The proposed approach is further customized for a mobile-based video retrieval system to solve the perception subjectivity issue by considering individual user's profile. Moreover, to deal with security and privacy issues and concerns in distributed multimedia applications, DIMUSE also incorporates a practical framework called SMARXO, which supports multilevel multimedia security control. SMARXO efficiently combines role-based access control (RBAC), XML and object-relational database management system (ORDBMS) to achieve the target of proficient security control. A distributed multimedia management system named DMMManager (Distributed MultiMedia Manager) is developed with the proposed framework DEMUR; to support multimedia capturing, analysis, retrieval, authoring and presentation in one single framework.

Towards simulation and emulation of large-scale computer networks

Developing analytical models that can accurately describe behaviors of Internet-scale networks is difficult. This is due, in part, to the heterogeneous structure, immense size and rapidly changing properties of today's networks. The lack of analytical models makes large-scale network simulation an indispensable tool for studying immense networks. However, large-scale network simulation has not been commonly used to study networks of Internet-scale. This can be attributed to three factors: 1) current large-scale network simulators are geared towards simulation research and not network research, 2) the memory required to execute an Internet-scale model is exorbitant, and 3) large-scale network models are difficult to validate. This dissertation tackles each of these problems. ^ First, this work presents a method for automatically enabling real-time interaction, monitoring, and control of large-scale network models. Network researchers need tools that allow them to focus on creating realistic models and conducting experiments. However, this should not increase the complexity of developing a large-scale network simulator. This work presents a systematic approach to separating the concerns of running large-scale network models on parallel computers and the user facing concerns of configuring and interacting with large-scale network models. ^ Second, this work deals with reducing memory consumption of network models. As network models become larger, so does the amount of memory needed to simulate them. This work presents a comprehensive approach to exploiting structural duplications in network models to dramatically reduce the memory required to execute large-scale network experiments. ^ Lastly, this work addresses the issue of validating large-scale simulations by integrating real protocols and applications into the simulation. With an emulation extension, a network simulator operating in real-time can run together with real-world distributed applications and services. As such, real-time network simulation not only alleviates the burden of developing separate models for applications in simulation, but as real systems are included in the network model, it also increases the confidence level of network simulation. This work presents a scalable and flexible framework to integrate real-world applications with real-time simulation.^

Leveraging symbiotic relationships for emulation of computer networks

The lack of analytical models that can accurately describe large-scale networked systems makes empirical experimentation indispensable for understanding complex behaviors. Research on network testbeds for testing network protocols and distributed services, including physical, emulated, and federated testbeds, has made steady progress. Although the success of these testbeds is undeniable, they fail to provide: 1) scalability, for handling large-scale networks with hundreds or thousands of hosts and routers organized in different scenarios, 2) flexibility, for testing new protocols or applications in diverse settings, and 3) inter-operability, for combining simulated and real network entities in experiments. This dissertation tackles these issues in three different dimensions. First, we present SVEET, a system that enables inter-operability between real and simulated hosts. In order to increase the scalability of networks under study, SVEET enables time-dilated synchronization between real hosts and the discrete-event simulator. Realistic TCP congestion control algorithms are implemented in the simulator to allow seamless interactions between real and simulated hosts. SVEET is validated via extensive experiments and its capabilities are assessed through case studies involving real applications. Second, we present PrimoGENI, a system that allows a distributed discrete-event simulator, running in real-time, to interact with real network entities in a federated environment. PrimoGENI greatly enhances the flexibility of network experiments, through which a great variety of network conditions can be reproduced to examine what-if questions. Furthermore, PrimoGENI performs resource management functions, on behalf of the user, for instantiating network experiments on shared infrastructures. Finally, to further increase the scalability of network testbeds to handle large-scale high-capacity networks, we present a novel symbiotic simulation approach. We present SymbioSim, a testbed for large-scale network experimentation where a high-performance simulation system closely cooperates with an emulation system in a mutually beneficial way. On the one hand, the simulation system benefits from incorporating the traffic metadata from real applications in the emulation system to reproduce the realistic traffic conditions. On the other hand, the emulation system benefits from receiving the continuous updates from the simulation system to calibrate the traffic between real applications. Specific techniques that support the symbiotic approach include: 1) a model downscaling scheme that can significantly reduce the complexity of the large-scale simulation model, resulting in an efficient emulation system for modulating the high-capacity network traffic between real applications; 2) a queuing network model for the downscaled emulation system to accurately represent the network effects of the simulated traffic; and 3) techniques for reducing the synchronization overhead between the simulation and emulation systems.

The impact of a Classroom Performance System on learning gains in a biology course for science majors

This study was conducted to determine if the use of the technology known as Classroom Performance System (CPS), specifically referred to as "Clickers", improves the learning gains of students enrolled in a biology course for science majors. CPS is one of a group of developing technologies adapted for providing feedback in the classroom using a learner-centered approach. It supports and facilitates discussion among students and between them and teachers, and provides for participation by passive students. Advocates, influenced by constructivist theories, claim increased academic achievement. In science teaching, the results have been mixed, but there is some evidence of improvements in conceptual understanding. The study employed a pretest-posttest, non-equivalent groups experimental design. The sample consisted of 226 participants in six sections of a college biology course at a large community college in South Florida with two instructors trained in the use of clickers. Each instructor randomly selected their sections into CPS (treatment) and non-CPS (control) groups. All participants filled out a survey that included demographic data at the beginning of the semester. The treatment group used clicker questions throughout, with discussions as necessary, whereas the control groups answered the same questions as quizzes, similarly engaging in discussion where necessary. The learning gains were assessed on a pre/post-test basis. The average learning gains, defined as the actual gain divided by the possible gain, were slightly better in the treatment group than in the control group, but the difference was statistically non-significant. An Analysis of Covariance (ANCOVA) statistic with pretest scores as the covariate was conducted to test for significant differences between the treatment and control groups on the posttest. A second ANCOVA was used to determine the significance of differences between the treatment and control groups on the posttest scores, after controlling for sex, GPA, academic status, experience with clickers, and instructional style. The results indicated a small increase in learning gains but these were not statistically significant. The data did not support an increase in learning based on the use of the CPS technology. This study adds to the body of research that questions whether CPS technology merits classroom adaptation.

The relationship between selected standardized test scores and performance in advanced placement math and science exams: Analyzing the differential effectiveness of scores for course identification and placement

There is a national need to increase the STEM-related workforce. Among factors leading towards STEM careers include the number of advanced high school mathematics and science courses students complete. Florida's enrollment patterns in STEM-related Advanced Placement (AP) courses, however, reveal that only a small percentage of students enroll into these classes. Therefore, screening tools are needed to find more students for these courses, who are academically ready, yet have not been identified. The purpose of this study was to investigate the extent to which scores from a national standardized test, Preliminary Scholastic Assessment Test/ National Merit Qualifying Test (PSAT/NMSQT), in conjunction with and compared to a state-mandated standardized test, Florida Comprehensive Assessment Test (FCAT), are related to selected AP exam performance in Seminole County Public Schools. An ex post facto correlational study was conducted using 6,189 student records from the 2010 - 2012 academic years. Multiple regression analyses using simultaneous Full Model testing showed differential moderate to strong relationships between scores in eight of the nine AP courses (i.e., Biology, Environmental Science, Chemistry, Physics B, Physics C Electrical, Physics C Mechanical, Statistics, Calculus AB and BC) examined. For example, the significant unique contribution to overall variance in AP scores was a linear combination of PSAT Math (M), Critical Reading (CR) and FCAT Reading (R) for Biology and Environmental Science. Moderate relationships for Chemistry included a linear combination of PSAT M, W (Writing) and FCAT M; a combination of FCAT M and PSAT M was most significantly associated with Calculus AB performance. These findings have implications for both research and practice. FCAT scores, in conjunction with PSAT scores, can potentially be used for specific STEM-related AP courses, as part of a systematic approach towards AP course identification and placement. For courses with moderate to strong relationships, validation studies and development of expectancy tables, which estimate the probability of successful performance on these AP exams, are recommended. Also, findings established a need to examine other related research issues including, but not limited to, extensive longitudinal studies and analyses of other available or prospective standardized test scores.

Investigating the Effects of Cognitive Apprenticeship-Based Instructional Coaching on Science Teaching Efficacy Beliefs

The overall purpose of this collected papers dissertation was to examine the utility of a cognitive apprenticeship-based instructional coaching (CAIC) model for improving the science teaching efficacy beliefs (STEB) of preservice and inservice elementary teachers. Many of these teachers perceive science as a difficult subject and feel inadequately prepared to teach it. However, teacher efficacy beliefs have been noted as the strongest indicator of teacher quality, the variable most highly correlated with student achievement outcomes. The literature is scarce on strong, evidence-based theoretical models for improving STEB. This dissertation is comprised of two studies. STUDY #1 was a sequential explanatory mixed-methods study investigating the impact of a reformed CAIC elementary science methods course on the STEB of 26 preservice teachers. Data were collected using the Science Teaching Efficacy Belief Instrument (STEBI-B) and from six post-course interviews. A statistically significant increase in STEB was observed in the quantitative strand. The qualitative data suggested that the preservice teachers perceived all of the CAIC methods as influential, but the significance of each method depended on their unique needs and abilities. STUDY #2 was a participatory action research case study exploring the utility of a CAIC professional development program for improving the STEB of five Bahamian inservice teachers and their competency in implementing an inquiry-based curriculum. Data were collected from pre- and post-interviews and two focus group interviews. Overall, the inservice teachers perceived the intervention as highly effective. The scaffolding and coaching were the CAIC methods portrayed as most influential in developing their STEB, highlighting the importance of interpersonal relationship aspects in successful instructional coaching programs. The teachers also described the CAIC approach as integral in supporting their learning to implement the new inquiry-based curriculum. The overall findings hold important implications for science education reform, including its potential to influence how preservice teacher training and inservice teacher professional development in science are perceived and implemented. Additionally, given the noteworthy results obtained over the relatively short durations, CAIC interventions may also provide an effective means of achieving improvements in preservice and inservice teachers’ STEB more expeditiously than traditional approaches.

Factors influencing university performance of associate in arts graduates transferring to the state university system

The purpose of this study was to examine the factorsbehind the failure rates of Associate in Arts (AA)graduates from Miami-Dade Community College (M-DCC) transferring to the Florida State University System (SUS). In M-DCC's largest disciplines, the university failure rate was 13% for Business & Management, 13% for Computer Science, and 14% for Engineering. Hypotheses tested were: Hypothesis 1 (H1): The lower division (LD) overall cumulative GPA and/or the LD major field GPA for AA graduates are predictive of the SUS GPA for the Business Management, Computer Science, and Engineering disciplines. Hypothesis 2 (H2): Demographic variables (age, race, gender) are predictive of performance at the university among M-DCC AA graduates in Engineering, Business & Management, and Computer Science. Hypothesis 3 (H3): Administrative variables (CLAST -College Level Academic Skills Test subtests) are predictive of university performance (GPA) for the Business/Management, Engineering, and Computer Science disciplines. Hypothesis 4 (H4): LD curriculum variables (course credits, course quality points) are predictive of SUS performance for the Engineering, Business/Management and Computer Science disciplines. Multiple Regression was the inferential procedureselected for predictions. Descriptive statistics weregenerated on the predictors. Results for H1 identified the LD GPA as the most significant variable in accounting for the variability of the university GPA for the Business & Management, Computer Science, and Engineering disciplines. For H2, no significant results were obtained for theage and gender variables, but the ethnic subgroups indicated significance at the .0001 level. However, differentials in GPA may not have been due directly to the race factor but, rather, to curriculum choices and performance outcomes while in the LD. The CLAST computation variable (H3) was a significant predictor of the SUS GPA. This is most likely due to the mathematics structure pervasive in these disciplines. For H4, there were two curriculum variables significant in explaining the variability of the university GPA (number of required critical major credits completed and quality of the student's performance for these credits). Descriptive statistics on the predictors indicated that 78% of those failing in the State University System had a LD major GPA (calculated with the critical required university credits earned and quality points of these credits) of less than 3.0; and 83% of those failing at the university had an overall community college GPA of less than 3.0.