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For many courses, mathematics included, there is an associated interactive e-learning system that provides assessment and tutoring. Some of these systems are classified as Intelligent Tutoring Systems. MyMathLab, Mathzone, and Assessment of LEarning in Knowledge Space (ALEKS) are just a few of the interactive e-learning systems in mathematics. In ALEKS, assessment and tutoring are based on the Knowledge Space Theory. Previous studies in a traditional learning environment have shown ALEKS users to perform equally or better in mathematics achievement than the group who did not use ALEKS. The purpose of this research was to investigate the effect of ALEKS on students’ achievement in mathematics in an online learning environment and to determine the cognitive complexity of mathematical tasks enacted by ALEKS’s initial (pretest) and final (posttest) assessments. The targeted population for this study was undergraduate students in College Mathematics I, in an online course at a private university in the southwestern United States. The study used a quasi-experimental One-Group non-randomized pretest and posttest design. Five methods of analysis and one model were used in analyzing data: t-test, correctional analysis, simple and multiple regression analysis, Cronbach’s Alpha reliability test and Webb’s depth of knowledge model. A t-test showed a difference between the pretest and posttest reports, meaning ALEKS had a significant effect on students’ mathematics achievement. The correlation analysis showed a significant positive linear relationship between the concept mastery reports and the formative and summative assessments reports meaning there is a direct relationship between the ALEKS concept mastery and the assessments. The regression equation showed a better model for predicting mathematics achievement with ALEKS when the time spent learning in ALEKS and the concept mastery scores are used as part of the model. According to Webb’s depth of knowledge model, the cognitive complexity of the pretest and posttest question items used by ALEKS were as follows: 50.5% required application of skills and concepts, 37.1% required recall of information, and 12.4% required strategic thinking: None of the questions items required extended thinking or complex reasoning, implying ALEKS is appropriate for skills and concepts building at this level of mathematics.

Educators in the United States (U.S.) are increasingly turning to intelligent tutoring systems (ITS) to provide differentiated math instruction to high school students. However, many struggling high school learners do not perform well on these platforms, which reinforces the need for more awareness about effective supports that influence the achievement of learners in these milieus. The purpose of this study was to determine what factors of the Assessment and Learning in Knowledge Spaces (ALEKS), an ITS, are predictive of struggling learners' performance in a blended-learning Algebra 1 course at an inner city technical high school located in the northeastern U.S. The theoretical framework consisted of knowledge base theory, the zone of proximal development, and cognitive learning theory. Three variables (student retention, engagement time, and the ratio of topics mastered to topics practiced) were used to predict the degree of association on the criterion variable (mathematics competencies), as measured by final course progress grades in algebra, and the Preliminary Scholastic Assessment Test (PSATm) math scores. A correlational predictive design was applied to assess the data of a purposive sample of 265 struggling students at the study site; multiple regression analysis was also used to investigate the predictability of these variables. Findings suggest that engagement time and the ratio of mastered to practiced topics were significant predictors of final course progress grades. Nevertheless, these factors were not significant contributors in predicting PSATm score. Retention was identified as the only statistically significant predictor of PSATm score. The results offer educators with additional insights that can facilitate improvements in mathematical content knowledge and promote higher graduation rates for struggling learners in high school mathematics.

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This research effort compared student learning gains and attitudinal changes through the implementation of two varying instructional approaches on the topic of functions in College Algebra. Attitudinal changes were measured based on the Attitude Towards Mathematics Inventory (ATMI). The ATMI also provided four sub-scales scores for self-confidence, value of learning, enjoyment, and motivation. Furthermore, this research explored and compared relationships between students' level of mastery and their actual level of learning. This study implemented a quasi-experimental research design using a sample that consisted of 56 College Algebra students in a public, state college in Florida. The sample was enrolled in one of two College Algebra sections, in which one section followed a self-adaptive instructional approach using ALEKS (Assessment and Learning in Knowledge Space) and the other section followed a traditional approach using MyMathLab. Learning gains in each class were measured as the difference between the pre-test and post-test scores on the topic of functions in College Algebra. Attitude changes in each class were measured as the difference between the holistic scores on the ATMI, as well as each of the four sub-scale scores, which was administered once in the beginning of the semester and again after the unit of functions, approximately eight weeks into the course. Utilizing an independent t-test, results indicated that there was not a significant difference in actual learning gains for the compared instructional approaches. Additionally, independent t-test results indicated that there was not a statistical difference for attitude change holistically and on each of the four sub-scales for the compared instructional approaches. However, correlational analyses revealed a strong relationship between students' level of mastery learning and their actual learning level for each class with the self-adaptive instructional approach having a stronger correlation than the non-adaptive section, as measured by an r-to-z Fisher transformation test. The results of this study indicate that the self-adaptive instructional approach using ALEKS could more accurately report students' true level of learning compared to a non-adaptive instructional approach. Overall, this study found the compared instructional approaches to be equivalent in terms of learning and effect on students' attitude. While not statistically different, the results of this study have implications for math educators, instructional designers, and software developers. For example, a non-adaptive instructional approach can be equivalent to a self-adaptive instructional approach in terms of learning with appropriate planning and design. Future recommendations include further case studies of self-adaptive technology in developmental and college mathematics in other modalities such as hybrid or on-line courses. Also, this study should be replicated on a larger scale with other self-adaptive math software in addition to focusing on other student populations, such as K - 12. There is much potential for intelligent tutoring to supplement different instructional approaches, but should not be viewed as a replacement for teacher-to-student interactions.

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