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Mathematics word problems provide students with an opportunity to apply what they are learning in their mathematics classes to the world around them. However, students often neglect their knowledge of the world and provide nonsensical responses (e.g., they may answer that a school needs 12.5 buses for a field trip). This study examined if the question design of word problems affects students' mindset in ways that affect subsequent sense-making. The hypothesis was that rewriting standard word problems to introduce inherent uncertainty about the result would be beneficial to student performance and sense-making because it requires students to reason explicitly about the context described in the problem. Middle school students (N = 229) were randomly assigned to one of three conditions. In the standard textbook condition, students solved a set of six word problems taken from current textbooks. In the modified yes/no condition, students solved the same six problems rewritten so the solution helped answer a "yes" or "no" question. In the disfluency control condition, students solved the standard problems each rewritten in a variety of fonts to make them look unusual. After solving the six problems in their assigned condition, all students solved the same three "problematic" problems designed to assess sense-making. Contrary to predictions, results showed that students in the modified yes/no condition solved the fewest problems correctly in their assigned condition problem set. However, consistent with predictions, they subsequently demonstrated more sense-making on the three problematic problems. Results suggest that standard textbook word problems may be able to be rewritten in ways that mitigate a "senseless" mindset.

We consider a discrete time financial market with proportional transaction cost under model uncertainty, and study a super-replication problem. We recover the duality results that are well known in the classical dominated context. Our key argument consists in using a randomization technique together with the minimax theorem to convert the initial problem to a frictionless problem set on an enlarged space. This allows us to appeal to the techniques and results of Bouchard and Nutz (2015) to obtain the duality result.

We consider the stochastic, single-machine earliness/tardiness problem (SET), with the sequence of processing of the jobs and their due-dates as decisions and the objective of minimizing the sum of the expected earliness and tardiness costs over all the jobs. In a recent paper, Baker (2014) shows the optimality of the Shortest-Variance-First (SVF) rule under the following two assumptions: (a) The processing duration of each job follows a normal distribution. (b) The earliness and tardiness cost parameters are the same for all the jobs. In this study, we consider problem SET under assumption (b). We generalize Baker's result by establishing the optimality of the SVF rule for more general distributions of the processing durations and a more general objective function. Specifically, we show that the SVF rule is optimal under the assumption of dilation ordering of the processing durations. Since convex ordering implies dilation ordering (under finite means), the SVF sequence is also optimal under convex ordering of the processing durations. We also study the effect of variability of the processing durations of the jobs on the optimal cost. An application of problem SET in surgical scheduling is discussed.

The fields of science have undergone dramatic reorganizations as they have come to terms with the realities of the growing complexities of their problem set, the costs, and the breadth of skills needed to make major progress. A field such as particle physics transformed from principal investigator-driven research supported by an electron synchrotron in the basement of your physics building in the 1950s, to regional centers when costs became prohibitive to refresh technology everywhere, driving larger teams of scientists to cooperate in the 1970s, to international centers where multinational teams work together to achieve progress. The 2013 Nobel Prize winning discovery of the Higgs boson would have been unlikely without such team science.[1] Other fields such as the computational sciences are well on their way through such a transformation. Today, we see precision medicine as a field that will need to come to terms with new organizational principles in order to make major progress, including everyone from individual medical researchers to pharma. Interestingly, the Cancer Moonshot has helped move thinking in that direction for part of the community and now the initiative has been transformed into law.[2]

Problem definition studies focus on the ways in which problems are characterized in the political domain, and how they can be used strategically to limit or expand policy participation. Nanotechnology entrepreneurs are vying for resources in the political domain while strategically linking their nano-solution to multiple and ambiguous problems. This article considers the evolution of nanotechnology as a solution, and the linked problems from a problem definition perspective. We consider how nanotechnology has been defined over time, in the scientific community and in the media, through development of a database of problem and solution definitional change. We find that, over time, advocates have defined the solution from a more narrow perspective while maintaining the overall ambiguity of the problem set. We suggest that the problem definition perspective is a viable framework for understanding the fluid and complex dynamics of science and technology issues and offer several suggestions for further research.

How do people evaluate their degree of mastery over a task? A series of four studies demonstrated that a potentially irrelevant cue can have a strong influence on such evaluations. In these studies, the total amount of work given to participants (the problem set size) influenced both (a) the amount of work participants completed before feeling that they had performed well and were adequately prepared for a related future task, and (b) participants' assessments of their performance and their feelings of preparedness for a related future task. These effects occurred even when a randomization procedure was used to emphasize the arbitrary nature of the problem set size. The effects vanished, however, when participants were given extra time to evaluate their progress after completing each problem. Copyright © 2001 John Wiley & Sons, Ltd.

This study examined the problem of assessing group process in a collaborative problem-solving situation. Students in seven collaborative groups worked on a two-part math and logic problem—first individually, then in groups, and finally, individually again. Groups engaging in behaviors that facilitated collaboration obtained higher group and individual accuracy scores on a challenging problem set. High-achieving students were influential in group problem-solving outcomes. Group scores did not reflect the individual achievement of low-achieving students. Examining collaborative group process and outcomes offers a new direction in functional and contextualized assessment for school psychologists. © 2001 John Wiley & Sons, Inc.

We examined how reinforcer rate, quality, delay, and response effort combined to influence the choices of 6 youths with learning and behavior difficulties, and the viability of an assessment methodology derived from matching theory for determining differential responsiveness to those reinforcer and response dimensions. The students were given two concurrent sets of math problems that were equal on two dimensions but competed on two other dimensions (e.g., one set yielded higher rate and lower quality reinforcement than the other). Competing dimensions were counterbalanced across the six conditions of the initial assessment phase, permitting assessment of each dimension on time allocation. The conditions resulting in the most and least time allocated to one problem set alternative relative to the other were then replicated. Time allocated to each of the problems within sets was differentially affected by the reinforcer and/or response dimensions, with allocation patterns varying across students. The results are discussed in the context of implications for the design of treatments and extrapolations from basic research on matching and behavioral economics.

Traditional approaches for modeling and solving dynamic demand lotsize problems are based on Zangwill's single-source network and dynamic programming algorithms. In this paper, we propose an arborescent fixed-charge network (ARBNET) programming model and dual ascent based branch-and-bound procedure for the two-stage multi-item dynamic demand lotsize problem. Computational results show that the new approach is significantly more efficient than earlier solution strategies. The largest set of problems that could be solved using dynamic programming contained 4 end items and 12 time periods, and required 475.38 CPU seconds per problem. The dual ascent algorithms averaged .06 CPU seconds for this problem set, and problems with 30 end items and 24 time periods were solved in 85.65 CPU seconds. Similar results verify the superiority of the new approach for handling backlogged demand. An additional advantage of the algorithm is the availability of a feasible solution, with a known worst-case optimality gap, throughout the problem-solving process.

FOREWORD. PREFACE. ACKNOWLEDGMENTS. 1. INTRODUCTION. The Meaning of Function. Reading FAST. FAST Logic. Some Observations. What Have We Learned? Applying FAST to Hardware Products. Reading a FAST Model. Analyzing a FAST Model. Some Unique Ways That a FAST Model Has Been Used. How It All Began. Toward an Innovation Process. Who Models Functions? Why an Interdisciplinary Team? Team Makeup. Unlocking Practical Ingenuity. When Should We Use FAST? Fundamental Questions. Distinguishing Between Problem and Opportunity. Difference Between FAST Diagrams and FAST Models. Validating Function Models. Outline of This Book. 2. PROBLEM-SOLVING TECHNIQUES. Verb-Noun Function Technique. Fuzzy Problem Technique. Setting Up the Problem in the Fuzzy Problem Technique. Hierarchical Technique. Verb-Noun and Fuzzy Problem Techniques Within the Hierarchical Technique. Closing Remarks. 3. FUNCTION ANALYSIS. Function Analysis Syntax. Active Verbs. Measurable Nouns. Using Two Words to Describe Functions. Defining and Classifying Functions. Types of Functions. Extrinsic Functions. Intrinsic Functions. Basic Functions. Secondary Functions. Practical Definitions. Rules Governing Basic Functions. Function Identification Example. Random Function Determination. Levels of Abstraction. Function and Component Selection. Function Cost Matrix. Simplifying the Process. Closing Remarks. 4. FUNCTION ANALYSIS SYSTEM TECHNIQUE. Process Overview. Some Misconceptions. "As Is" Versus "Should Be" Models. Syntax Used to Create and Read a FAST Model. Reading How-Why and Our Intentions. How-Why Versus Why-How Orientation. Reading When to Consider Causality and Consequential Functioning. Key Elements of a FAST Model. Scope Lines. Highest-Order Function(s). Lowest-Order Function(s). Basic Function(s). Content. Requirements or Specifications. Dependent Functions. Independent (Support) Functions. Logic Path Functions. Articulating Theories in FAST. Variations of How-Why Questions. Considering And-Or Along the Logic Path. Considering And in the When Direction. Considering Or in the When Direction. FAST Model-Building Process: Product Example. Expanding the Number of Functions. Case for Using Active Verbs. Purpose of Expanding Functions. Avoiding Duplicate Functions. Starter Kit Functions. Preparations for Building a FAST Model. Build How and Test Why. Relationship of the Left Scope Line to the Basic Function. Right Scope Line. Left Scope Line. What's the Problem? Defining the Problem. Three Questions Before Starting the FAST Process. How the Strategic Questions Are Asked in a Workshop. Symbols and Notations Used in FAST Modeling. Taking Exception to the FAST Rules. Independent Functions Above the Logic Path, Activities Below the Logic Path. No Activities in the Major Logic Path. Only Two Words Used to Describe Functions. Loop-Back Modeling. Validating the Logic Flow. Exploration Drilling Model. Closing Remarks. 5. DIMENSIONING THE FAST MODEL. Pre-event Stage. FAST Dimensioning Themes. Business Process and Soft Issues. Sensitivity Matrix. Facility Management Case Study. Determining Responsibility, Move to Action. Incorporating Other Dimensions in FAST Models. RACI/RASI Dimensioning. FAST and Organizational Effectiveness. Organizational Effectiveness Case Study. Model the Future or the Present? Incorporating Additional Dimensions. Product- and Equipment-Based FAST Models (Artifacts). Sensitivity Matrix in Product (Artifact) Analysis. Staple Remover Case Study Using FAST With the Sensitivity Matrix. Determining Component Function-Cost Details. Proposed Solution. Pipeline Case Study Using the Sensitivity Matrix. Other Case-Specific Dimensions. Budgeting Operating Expenses and the Sensitivity Matrix. Clustering Functions. Example Using Clustering. Closing Remarks. 6. ATTRIBUTES AND THE FAST MODEL. Defining an Attribute's Range of Acceptance. Ranking Attributes. Incorporating Attributes Into a FAST model. Linking Issues of Concern to a FAST model. Construction Management Case Study. Influence of Attributes and Incentives on FAST Modeling. Software Acquisition Case Study. Validity of a FAST Model. Pre-event's Role in FAST Modeling. Areas Defined by a Scope Line. Resolving the Incentive Issue. Determining the Incentive Earned Points Score. Closing Remarks. 7. ENABLING INNOVATION. Analyzing FAST Models. Distinguishing Outcomes and Ideas. Starting to Generate Ideas. Handling Negative Functions. Examples of Negative Functions. TRIZ and Negative Functions: Path to Creativity. Defining Problems: Prerequisite to Seeking Solutions. Problem Set Matrix. Identifying Critical Innovation Points. Realizing Innovation Through FAST Models. Toward Innovation That Makes a Difference. Importance of the Pre-event Phase. XYZ-3 Case Study. Defining XYZ-3's Problems. Setting Project Goals. Selecting Attributes. Selecting Random Functions. Constructing the FAST Model. Selecting Functions to Be Brainstormed. Using FAST for Brainstorming. Concluding the XYZ-3 Value Study. Closing Remarks. 8. FROM COMPETENCY TO CAPABILITY. Moving Toward Know-How and FAST models. Beyond Intuition. Discovering New Knowledge. Management of Functionality. Using FAST Modeling to Improve the Supply Chain. Using FAST Modeling to Enable Shared Understanding. Managing Intangible Value to Advantage. Automotive Parts Case Study. How Can We Unify? Functional Enquiry. Closing Remarks. END NOTES. REFERENCES. APPENDIX: FREQUENTLY ASKED QUESTIONS. INDEX.

Purpose: Pilot a new approach to teaching physics to Radiation Oncology residents that seeks to maximize the learning experience under the constraint of limited class time provided for teaching. The pilot is limited to a few lectures during the year. Method and Materials: Class time is devoted to the interactive learning of the key concepts instead of reciting the text book by rote to the students by means of prepared in‐class lectures. Two types of classes are given. The first class is spent asking the residents prepared questions on the key concepts of the subject material. These questions involve no calculations and are multiple‐choice. The second class consists of reviewing problem set questions that were distributed beforehand. The residents are encouraged to teach each other to help the class understand the concepts and problem solving methods with the instructor acting as the guide in the process. In order to be prepared for class, the residents are required to review the material beforehand. To facilitate this, audio/visual (A/V) lectures are created in Adobe Captive for them to view. These lectures are kept short (∼20 min) and are focused on the key concepts instead of the details. Results: The residents viewed the A/V lectures and came to class prepared for discussion. The in‐class question sessions on concepts supported by a group learning approach enabled the residents to teach their peers and focus on the essential material. The problem sessions allowed them to apply their knowledge of the concepts to learn the details and calculation process. Conclusions: This pilot study has been successful as evidenced by the residents' increased exam scores and attendance to class. This program will be expanded to cover more lectures. In addition, the material (lectures, questions, problem sets and detailed answers) will be made available via the department website.

This business problem for microeconomic students might be used as part of a problem set or as a take-home exam. It highlights the importance of marginal analysis, and the implications of the fact that rational individuals will undertake the most cost-effective measures first.

The purpose o f this study was to examine the consistency with which students applied procedural rules for solving signed-number operations across identical items presented in different orders. A test with 64 open-ended items was administered to 161 eighth graders. The test consisted o f two 32-item subtests containing identical items. The items in each subtest were in random order. Students’responses to each subtest were compared with respect to the identified underlying rules o f operation used to solve each problem set. The results indicated that inconsistent rule application was common among students who had not mastered signed-number arithmetic operations. In contrast, mastery level students, those who use the right rules, show a stable pattern o f rule application in signed-number arithmetic. These results are discussed in light of the hypothesis testing approach to the learning process.

The normative model of leadership, proposed in earlier Technical Reports, is extended to include 'individual' problems (i.e., decision situations affecting only one subordinate) in addition to previously studied 'group' problems (i.e., decision situations affecting more than one subordinate). Descriptive models of leadership behavior are developed using subject responses to a problem set containing 24 group and 24 individual decision-making scenarios (case descriptions systematically varied on the eight attributes used in the normative model). Each of 98 leaders, including high ranking military officers from each branch of the service, was asked to specify the leadership process he would employ if confronted with each of the 48 cases. The results suggest that some findings supported by previous work can be generalized to individual situations. Comparison of the descriptive models, however, points to certain critical differences in the behavior of leaders faced with group versus individual problems. Evidence is presented to show the nature and implications of these differences. (Author)

The man trying to find a fault may make mistakes unless he asks effective diagnostic questions and verifies the answers. General principles for verifying indications in petroleum refineries are presented; some are easy to apply, others require instruction, practice or experience. Simple scores for verification or checking, C, and for effective diagnostic questioning, D, are proposed and their calculation is illustrated in the context of fault-finding in a crude distillation unit. C and D probably measure different fault-finding skills. The C score is improved by training, but comparisons are complicated by an apparent influence of the proportion of instrument faults in the problem set. Men may check instrument readings more often as their estimate of instrument unreliability increases. The D score is also sensitive to the effects of training and reflects differences in experience between novices and experienced men. D may over-estimate effective diagnostic strategy, but only in a small percentage of cases for men with refinery operating experience or new entrants after training.