This body of research focuses on supporting problem-stakeholders, decision-makers and problem-solvers faced with an ill-defined and complex real world problem. An ill-defined problem has a characteristic trait of continual refinement. That is, the definition of the problem changes throughout the problem investigation and resolution process. The central theme of this research is that a support system should provide problem stakeholders with a problem definition model for constructing and manipulating a representation of the definition of the problem as they understand it. The approach adopted herein is to first develop a problem definition model for ill-defined problems— the 6-Component problem definition model. With this model, it is then possible to move on to identifying the types of changes or modifications to the problem definition that problem stakeholders, decision makers and problem solvers may wish to explore. Importantly, there must be a connection between the surface representation of the problem and the underlying implementation of the support system. This research argues that by focusing the support system around the problem definition, it is possible to reduce the mismatch between the problem objectives and the representation of the problem that the support system offers. This research uses the Unified Modelling Language to record and explore the requirements that problem stakeholders, faced with an evolving problem definition, place on a support system. The 6-Component problem definition model is then embedded within a design for an evolutionary support system. This embedding, supported by collaboration diagrams, shows how a system using the 6-Component problem definition model will support stakeholders in their exploration, evaluation and resolution of an ill-defined and complex real-world problem. A case study provides validation of the effectiveness of the 6-Component problem definition model proposed and developed in this work. The case study uses the 6-Component problem definition model as a basis for implementing the Integration Workbench, an evolutionary support system for land-use planning. Stakeholders explore, communicate, evaluate and resolve the Tasmanian Regional Forest Agreement problem with assistance from the Integration Workbench.

A relatively large number of 8th-grade public middle school students in the United States, particularly in urban communities, are not performing at acceptable levels in mathematics. One concept that poses significant difficulty for these students and negatively affects their overall mathematics achievement is fractions. Many researchers have attributed these difficulties primarily to traditional fraction instruction that emphasizes procedural rather than conceptual knowledge. Therefore this study was designed to investigate how students use their computational and conceptual knowledge and fraction representations to solve fraction-related performance-based mathematical tasks. Social constructivism was used as the theoretical framework in examining conceptual knowledge related to learning fractions. This qualitative study was implemented in an urban middle school in the southeast. It involved an initial sample of 37, 8th-grade, African American pre-algebra students who completed a fraction interest questionnaire and two fraction pretests. During the implementation period, 34 students in the researcher’s pre-algebra class completed three performance-based tasks, three reflection logs, and participated in an interview after completing each task. Of the 34 students who completed all tasks, three were purposefully selected as the informants for the study. In addition, observations, field notes, and artifacts (student work) were utilized to facilitate triangulation of the data. The findings of the study indicated the informants could compute fractions with an average of 85% of mastery but could conceptualize fractions only to a small extent. This validated prior findings and led to the conclusion that student deficiency with fractions results primarily from their level of conceptual knowledge. In the investigation of the ways in which 8th-grade students use fraction representations, this study found the informants used representations to develop a visual map of their mathematical thinking and reasoning and to check the accuracy of their computations. Therefore, this study suggests, when students’ mathematical learning experiences relative to fractions have not emphasized the use of representations to develop conceptual knowledge, they may not be comfortable with the accuracy of the solutions demonstrated in their fractions models.

<p>This qualitative study was conducted to understand the instructional strategies used by high school integrated STEM (iSTEM) teachers to apply real-world problem solving in their classrooms in the state of Indiana. The problem addressed by this study was the need to understand the instructional strategies employed by iSTEM teachers in their classrooms. Using a basic qualitative approach, data was collected through teacher interviews, classroom observations, and documents. The thematic analysis revealed several themes: (a) there is no single instructional strategy, but teachers adapt their strategies to the context, (b) the importance of preparation using various sources and building on student’s prior knowledge, (c) a focus on asking "why" questions as a priority, (d) the necessity of making group work tangible, (e) the use of modeling as a common strategy, including data collection and analysis, sketching and documentation, (f) the promotion of student independence by being aware and performing tasks independently, (g) the integration of real-world issues to relate learning to student lives, and (h) the challenges posed by time and diversity of student abilities. These findings suggest that iSTEM teachers should be flexible in their approach and emphasize preparation, questioning, modeling, group work, and real-world connections to improve student learning in an integrated STEM approach. The findings contribute to the existing literature on iSTEM teaching and have implications for iSTEM teachers, school administrators, and policymakers. The findings of this study can inform professional development programs for iSTEM teachers and can help school administrators design collaborative and problem-solving learning environments. Lastly, policymakers can use the findings to develop policies that promote the integration of real-world problem-solving into STEM education, thereby contributing to the development of a workforce that is prepared to meet the challenges of the 21st century.</p>

The concept of function is crucial to a great extent in modern mathematics and is considered a major barrier to many mathematics students. Students have difficulty interpreting information related to functions in general, and quadratic functions in particular. Quadratic Function is one of the topics which are covered in a course which is compulsory for a large number of students in the General Education Program of Zayed University. This program leads to different majors, including Mathematics Education, Business, Information Technology, and other majors. The challenge in teaching Quadratic Function in a course like this is mostly based on the fact that many students think that Quadratic Function is a difficult topic to understand and learn, and some teachers would agree with them that it is difficult to teach. In this paper, I demonstrate real world problems aimed to improve the students understanding of Quadratic Functions; life problems on this topic support developing student’s knowledge, critical thinking, quantitative reasoning, and analytical skills. This paper also includes examples of the techniques used with graphing of quadratic function, the algebra, and inverses of the same function. International move to improve mathematics curriculum have supported new goals for student’s learning which highlights problem solving skills, reasoning, ability to work in groups and individually, and use of technology. Knowing that information technology plays considerable role in achieving the above goals, teaching students the concept of Quadratic Functions can be smoothly achieved by using Information Technology in solving real world problems.

The concept of function is crucial to a great extent in modern mathematics and is considered a major barrier to many mathematics students. Students have difficulty interpreting information related to functions in general, and quadratic functions in particular. Quadratic Function is one of the topics which are covered in a course which is compulsory for a large number of students in the General Education Program of Zayed University. This program leads to different majors, including Mathematics Education, Business, Information Technology, and other majors. The challenge in teaching Quadratic Function in a course like this is mostly based on the fact that many students think that Quadratic Function is a difficult topic to understand and learn, and some teachers would agree with them that it is difficult to teach. In this paper, I demonstrate real world problems aimed to improve the students understanding of Quadratic Functions; life problems on this topic support developing student’s knowledge, critical thinking, quantitative reasoning, and analytical skills. This paper also includes examples of the techniques used with graphing of quadratic function, the algebra, and inverses of the same function. International move to improve mathematics curriculum have supported new goals for student’s learning which highlights problem solving skills, reasoning, ability to work in groups and individually, and use of technology. Knowing that information technology plays considerable role in achieving the above goals, teaching students the concept of Quadratic Functions can be smoothly achieved by using Information Technology in solving real world problems.