scholarly journals Math puzzles, powerful ideas, algorithms and computers in teaching problem-solving

Author(s):  
M.A. Murray-Lasso

With the current interest in teaching problem-solving, it is important that the example problems that are presented to students have important educational value. Many mathematical puzzles, while requiring little specific background to be posed and remembered, are paradigms of important practical problems. If the teacher chooses the right puzzles, he/she not only will have motivated the student's interest, but will also have the opportunity of teaching powerful ideas that can be applied in a multitude of similar problems. Moreover the teacher will also be able to teach the corresponding solution algorithms and the way computers can be used as tools in problem-solving. The article presents these topics through an extensive example based on a well-known, apparently simple, wine-pouring puzzle that is intimately related to the concepts of state, shortest-routes and many management, engineering and industrial problems.

2007 ◽  
Vol 12 (9) ◽  
pp. 504-511
Author(s):  
Ann H. Wallace

I have been a Mathematics Teacher and Educator throughout all four publications of the Standards documents (NCTM 1991, 1995, 1989, and 2000). Over the years, while concentrating on improving various aspects of my teaching, specifically, improving my students' ability to problem solve, I have been perplexed to see students pick numbers out of a problem and perform an operation with no regard for the context. To address this issue by teaching problem-solving lessons made me realize that I did not know the difference between students solving a problem and actual problem solving. A lesson beginning with a problem or task does not make it a problem-solving lesson, especially when students would inevitably solve it the way I had intended. Instead of problem solving, my students were trying to figure out what I was thinking. To prevent the temptation of leading students in this way of thinking required careful planning of problem-solving lessons.


2010 ◽  
Vol 20 (4) ◽  
pp. 820-824
Author(s):  
Tigon Woline ◽  
Ann Marie VanDerZanden

Problem-based learning has become a popular pedagogical strategy for teaching problem-solving skills as well as subject content. However, implementation of this strategy is time-consuming. Use of the Internet and computer software could aide the creation, use, and maintenance of these teaching tools, encouraging more educators to use them. This study focused on 45 Iowa State University students enrolled in Horticulture 342, Landscape Installation and Maintenance. Students were assigned a series of four online, ill-structured case study problems based in a realistic residential landscape. Results indicated students understood the need for developing problem-solving skills, especially as they relate to future employment opportunities. However, students were concerned with obtaining the right answer, not with developing a strategy for solving problems. Students rated the statement about determining the best solution highest in importance (4.75 in 2007, 4.90 in 2008). Conversely, they rated a statement about determining what standards and judgment criteria should be used to evaluate possible solutions of least importance (3.75 in 2007, 4.20 in 2008). Students identified the value of the solution to the customer/client (4.63 in 2007, 4.80 in 2008), how well the cause of the problem was addressed by the solution (4.46 in 2007, 4.30 in 2008), and any potential negative consequences (4.33 in 2007, 4.40 in 2008) as the important factors that influence decision-making on the job. Students rated the online learning environment as adequate and they rated the overall experience as 3.94. Frustrations were primarily technical, including problems connecting to the system. Students liked the variety of resources available and that case information was consolidated in a single location.


2018 ◽  
Vol 68 (2) ◽  
pp. 498-516
Author(s):  
Neil O'Sullivan

Of the hundreds of Greek common nouns and adjectives preserved in our MSS of Cicero, about three dozen are found written in the Latin alphabet as well as in the Greek. So we find, alongside συμπάθεια, also sympathia, and ἱστορικός as well as historicus. This sort of variation has been termed alphabet-switching; it has received little attention in connection with Cicero, even though it is relevant to subjects of current interest such as his bilingualism and the role of code-switching and loanwords in his works. Rather than addressing these issues directly, this discussion sets out information about the way in which the words are written in our surviving MSS of Cicero and takes further some recent work on the presentation of Greek words in Latin texts. It argues that, for the most part, coherent patterns and explanations can be found in the alphabetic choices exhibited by them, or at least by the earliest of them when there is conflict in the paradosis, and that this coherence is evidence for a generally reliable transmission of Cicero's original choices. While a lack of coherence might indicate unreliable transmission, or even an indifference on Cicero's part, a consistent pattern can only really be explained as an accurate record of coherent alphabet choice made by Cicero when writing Greek words.


Author(s):  
Linda MEIJER-WASSENAAR ◽  
Diny VAN EST

How can a supreme audit institution (SAI) use design thinking in auditing? SAIs audit the way taxpayers’ money is collected and spent. Adding design thinking to their activities is not to be taken lightly. SAIs independently check whether public organizations have done the right things in the right way, but the organizations might not be willing to act upon a SAI’s recommendations. Can you imagine the role of design in audits? In this paper we share our experiences of some design approaches in the work of one SAI: the Netherlands Court of Audit (NCA). Design thinking needs to be adapted (Dorst, 2015a) before it can be used by SAIs such as the NCA in order to reflect their independent, autonomous status. To dive deeper into design thinking, Buchanan’s design framework (2015) and different ways of reasoning (Dorst, 2015b) are used to explore how design thinking can be adapted for audits.


2017 ◽  
Vol 16 (2) ◽  
pp. 177-192 ◽  
Author(s):  
Anaheed Al-Hardan

The 1948 Nakba has, in light of the 1993 Oslo Accords and Palestinian refugee activists' mobilisation around the right of return, taken on a new-found centrality and importance in Palestinian refugee communities. Closely-related to this, members of the ‘Generation of Palestine’, the only individuals who can recollect Nakba memories, have come to be seen as the guardians of memories that are eventually to reclaim the homeland. These historical, social and political realities are deeply rooted in the ways in which the few remaining members of the generation of Palestine recollect 1948. Moreover, as members of communities that were destroyed in Palestine, and whose common and temporal and spatial frameworks were non-linearly constituted anew in Syria, one of the multiples meanings of the Nakba today can be found in the way the refugee communities perceive and define this generation.


Author(s):  
Shai Dothan

There is a consensus about the existence of an international right to vote in democratic elections. Yet states disagree about the limits of this right when it comes to the case of prisoners’ disenfranchisement. Some states allow all prisoners to vote, some disenfranchise all prisoners, and others allow only some prisoners to vote. This chapter argues that national courts view the international right to vote in three fundamentally different ways: some view it as an inalienable right that cannot be taken away, some view it merely as a privilege that doesn’t belong to the citizens, and others view it as a revocable right that can be taken away under certain conditions. The differences in the way states conceive the right to vote imply that attempts by the European Court of Human Rights to follow the policies of the majority of European states by using the Emerging Consensus doctrine are problematic.


Author(s):  
Matti Eklund

What is it for a concept to be normative? Some possible answers are explored and rejected, among them that a concept is normative if it ascribes a normative property. The positive answer defended is that a concept is normative if it is in the right way associated with a normative use. Among issues discussed along the way are the nature of analyticity, and there being a notion of analyticity—what I call semantic analyticity—such that a statement can be analytic in this sense while failing to be true. Considerations regarding thick concepts and slurs are brought to bear on the issues that come up.


Author(s):  
Lisa Rodgers

‘Ordinary’ employment contracts—including those of domestic servants—have been deemed to attract diplomatic immunity because they fall within the scope of diplomatic functions. This chapter highlights the potential for conflict between these forms of immunity and the rights of the employees, and reflects on cases in which personal servants of diplomatic agents have challenged both the existence of immunity and the scope of its application. The chapter examines claims that the exercise of diplomatic immunity might violate the right to a fair trial under Article 6 of the European Convention on Human Rights and the way in which courts have dealt with these issues. The chapter analyses diplomats’ own employment claims and notes that they are usually blocked by the assertion of immunity, but also reflects on more recent developments in which claims had been considered which were incidental to diplomatic employment (eg Nigeria v Ogbonna [2012]).


2021 ◽  
pp. 1-16
Author(s):  
Nils Franzén

Abstract This article discusses why it is the case that we refuse to accept strange evaluative claims as being true in fictions, even though we are happy to go along with other types of absurdities in such contexts. For instance, we would refuse to accept the following statement as true, even in the context of a fiction: (i) In killing her baby, Giselda did the right thing; after all, it was a girl. This article offers a sensibilist diagnosis of this puzzle, inspired by an observation first made by David Hume. According to sensibilism, the way we feel about things settles their evaluative properties. Thus, when confronted with a fictional scenario where the configuration of non-evaluative facts and properties is relevantly similar to the actual world, we refuse to go along with evaluative properties being instantiated according to a different pattern. It is the attitudes we hold in the actual world that fix the extension of evaluative terms, even in nonactual worlds. When engaging with a fiction, we (to some extent) leave our beliefs about what the world is like behind, while taking our emotional attitudes with us into the fiction. To substantiate this diagnosis, this paper outlines a sensibilist semantics for evaluative terms based on recent discussion regarding predicates of personal taste, and explains how, together with standard assumptions about the nature of fictional discourse, it makes the relevant predictions with respect to engagement with fictions.


Author(s):  
Helen Ray-Jones ◽  
Mikhail Spivakov

AbstractTranscriptional enhancers play a key role in the initiation and maintenance of gene expression programmes, particularly in metazoa. How these elements control their target genes in the right place and time is one of the most pertinent questions in functional genomics, with wide implications for most areas of biology. Here, we synthesise classic and recent evidence on the regulatory logic of enhancers, including the principles of enhancer organisation, factors that facilitate and delimit enhancer–promoter communication, and the joint effects of multiple enhancers. We show how modern approaches building on classic insights have begun to unravel the complexity of enhancer–promoter relationships, paving the way towards a quantitative understanding of gene control.


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