Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…

A large body of research has shown that for novice learners, instruction that relies more heavily on worked examples than on problem solving, is more effective for learning as shown by higher test performance. Moreover, this beneficial effect is often obtained with less acquisition time and lower cognitive load during acquisition and test phase.…

This study examined whether and, if so, how word-problem features differentially affect problem difficulty as a function of mathematics difficulty (MD) status: no MD (n = 109), MD only (n = 109), or MD in combination with reading difficulties (MDRD; n = 109). The problem features were problem type (total, difference, or change) and position of…

In the transition years, Grades 7 to 9, the shift from natural numbers to rational numbers and the associated multiplicative concepts prove challenging for many learners. The new concepts, operations and notation must be mastered if the student is to thereafter rise to meet the challenges of algebra and more advanced and powerful mathematics. The…

The Taiwanese early intervention/early childhood special education (EI/ECSE) system is modeled after the federal legislation and practices of the U.S., incorporating specific cultural beliefs in Taiwan. Nonetheless, in EI/ECSE assessments, several challenges are presented, including: (a) limited resources and funding, (b) lack of reliable and…

This dissertation presents several studies designed to probe the mental representations that physics experts and novices form when interacting with typical instructional materials, such as diagrams and problem statements. By using recognition tasks and a change detection task, the mental representations of experts and novices are studied in a more…

Within the cognitive load theory framework, we designed and compared three alternative instructional solution formats that can be derived from a common static hierarchical network representation depicting problem structure. The interactive-solution format permitted students to search in self-controlled manner for solution steps, static-solution…

Counselors often engage in conflict mediation in professional practice. A model for understanding the complex and subtle nature of conflict resolution is presented. The ecosystemic complexity theory of conflict is offered to assist practitioners in navigating the fog of conflict. Theoretical assumptions are discussed with implications for clinical…

Contemporary debates on effective pedagogies for K-12 mathematics have called for shifts in the way teachers and teacher educators conceptualise mathematics as a subject and how it should be taught. This is reflected by changes in the curriculum including the inclusion of a strand called Working Mathematically within K-12 mathematics curriculum…

A new national survey of recent public high school graduates shows that approximately 50% of them report gaps in preparation for life after high school. Recent grads say they would have worked harder if they had fully understood the challenges that lay ahead. The research suggests that providing real academic challenge for high school students and…

The second phase of a new national survey conducted among college instructors and employers shows that 78% of college faculty and 62% of employers believe that public high schools are not doing enough to prepare students for the expectations they will face in college and the working world. Only roughly one in four recent high school grads report…

Isomorphs of a puzzle called m+m resulted in faster solution times and an easily reproduced solution path in a labeled version of the problem compared to a more difficult binary version. We conjecture that performance is related to a type of heuristic called direction that not only constrains search space in the labeled version, but also…

In assessment, the ability to construct test items that measure a targeted skill is fundamental to validity and alignment. The ability to do the reverse is also important: determining what skill an existing test item measures. This paper presents a model for classifying test items that builds on procedures developed by others, including Bloom…

This study investigated the influence of informational complexity and working memory capacity on problem-solving efficiency. We examined two predictions of the "situational efficiency hypothesis," which states that the efficiency of problem solving varies as a function of situational constraints. One prediction is that informational complexity…

In recent times, science education researchers have identified a lot of instruments for evaluating conceptual understanding as well as students' attitudes and beliefs about physics; unfortunately however, there are no broad based evaluation instruments in the field of problem-solving in physics. This missing tool is an indication of the complexity…