Anticipating Student Responses to Improve Problem Solving

2007 ◽  
Vol 12 (9) ◽  
pp. 504-511
Author(s):  
Ann H. Wallace
Keyword(s):  
Problem Solving ◽  
Mathematics Teacher ◽  
Careful Planning ◽  
Actual Problem ◽  
Student Responses ◽  
The Difference ◽  
Problem Solve ◽  
Teaching Problem ◽  
Or Task ◽  
The Way

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.

scholarly journals German Teacher Educators' Conceptions About Teaching Problem Solving in Mathematics Classroom - an Obstalce to a Large-Scale Dissemination?!

2018 ◽  
Vol 12 (2) ◽  
pp. 77-97
Author(s):  
Ana Kuzle
Keyword(s):  
Professional Development ◽  
Problem Solving ◽  
Mathematics Teacher ◽  
Large Scale ◽  
Teacher Educators ◽  
Mathematics Classroom ◽  
Research Report ◽  
Mathematics Teacher Educators ◽  
Set Up ◽  
Teaching Problem

Problem solving in Germany has roots in mathematics and psychology but it found its way to schools and classrooms, especially through German Kultusministerkonferenz, which represents all government departments of education. For the problem solving standard to get implemented in schools, a large scale dissemination through continuous professional development is very much needed, as the current mathematics teachers are not qualified to do so. As a consequence, one organ in Germany focuses on setting up courses for teacher educators who can “multiply” what they have learned and set up their own professional development courses for teachers. However, before attaining to this work, it is crucial to have an understanding what conceptions about teaching problem solving in mathematics classroom mathematics teacher educators hold. In this research report, I focus on mathematics teacher educators’ conceptions about problem solving standard and their effects regarding a large-scale dissemination.

Technology Tips: Multiple Representations and Connections Using Technology

1998 ◽  
Vol 91 (1) ◽  
pp. 62-67
Author(s):  
Charles Vonder Embse ◽  
Vernon W. Yoder
Keyword(s):  
Problem Solving ◽  
Mathematics Teacher ◽  
Functional Relationship ◽  
Multiple Representations ◽  
Problem Situation ◽  
Dynamic Nature ◽  
Static Picture ◽  
Independent Variable ◽  
The Difference

George Polya's famous four-step problem-solving method begins with understanding the problem through various means, including identifying the unknown, establishing the conditions of the problem, separating the conditions into more convenient parts, and drawing a figure or picture (Polya 1945). As a mathematics teacher, the first question I often ask students when they seek help in doing a problem is “Did you draw a picture?” Many times, the answer to my questions is “Yes, but it didn't help.” The difficulty might be that the picture representing the problem, although correct, does not really represent the dynamic nature of the problem situation. Drawing a static picture representing one state of a functional relationship does not guarantee that students will “see” how changes in the independent variable produce corresponding changes in the dependent variable. A better situation would be to draw several pictures representing various stages of the problem. An even better situation would be to draw a dynamic picture in which the drawing changes as the independent variable changes. Like the difference between a videotape of a football play and a newspaper picture of the play, a dynamic picture can be used repeatedly as a tool to investigate in detail what really happens.

scholarly journals The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem-solving lesson

2022 ◽  
Author(s):  
Fay Baldry ◽  
Jacqueline Mann ◽  
Rachael Horsman ◽  
Dai Koiwa ◽  
Colin Foster
Keyword(s):  
Problem Solving ◽  
Teaching Practice ◽  
Careful Planning ◽  
Student Responses ◽  
Research And Teaching ◽  
Mathematical Discussions ◽  
Solution Methods ◽  
Multiple Alternative ◽  
Productive Discussion ◽  
Alternative Solutions

AbstractIn this paper, we analyse a grade 8 (age 13–14) Japanese problem-solving lesson involving angles associated with parallel lines, taught by a highly regarded, expert Japanese mathematics teacher. The focus of our observation was on how the teacher used carefully planned board work to support a rich and extensive plenary discussion (neriage) in which he shifted the focus from individual mathematical solutions to generalised properties. By comparing the teacher’s detailed prior planning of the board work (bansho) with that which he produced during the lesson, we distinguish between aspects of the lesson that he considered essential and those he treated as contingent. Our analysis reveals how the careful planning of the board work enabled the teacher to be free to explore with the students the multiple alternative solution methods that they had produced, while at the same time having a clear overall purpose relating to how angle properties can be used to find additional solution methods. We outline how these findings from within the strong tradition of the Japanese problem-solving lesson might inform research and teaching practice outside of Japan, where a deep heritage of bansho and neriage is not present. In particular, we highlight three prominent features of this teacher’s practice: the detailed lesson planning in which particular solutions were prioritised for discussion; the considerable amount of time given over to student generation and comparison of alternative solutions; and the ways in which the teacher’s use of the board was seen to support the richness of the mathematical discussions.

scholarly journals When Police Behave-A Transformation Program That Reshapes Police-Community Relationships Based on Problem Solving and Values

2020 ◽  
Vol 10 (3) ◽  
pp. 58
Author(s):  
Mohamed Buheji
Keyword(s):  
Problem Solving ◽  
Community Engagement ◽  
Police Culture ◽  
Development Programs ◽  
Global Pandemic ◽  
The Difference ◽  
The Government ◽  
The Way

The escalation of the global events that followed the death of George Floyd in USA Minneapolis, Minnesota on May 25th of 2020, and what followed from demonstrations in all over the world; despite the presence of a global pandemic, shows the importance and the complications of an event that started with police miss-behaviour. ‘I can’t breathe’ a slogan carried by Floyd and many others earlier, carries within it, lots of meaning, however, one of the most important of meanings is the police brutality and the way they behave in certain times. This paper reviews the modern policing and specifically the values expected to be embedded in the police culture and the way they behave even in challenging times.The literature review goes into exploiting the importance of police and community engagement through problem-solving programs and the accumulative collective impact on ‘empathetic policing’ that lead to ‘social dialogue’. The case study in this paper focuses on the ‘police inspiration labs’ and how it gave a chance for more police with community engagement towards solving essential society problems. Besides, the paper shows the difference between (systems-driven vs behaviours-driven) police development programs. The paper carries important implication for developing further the role of the police in the ‘quality of life’ and support the government to transform the budget of policing into grey areas, i.e. area where the police are encouraged to execute more efforts towards preventing and developing instead of correcting and reacting towards community incidences and challenges.

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

2003 ◽  
Vol 1 (03) ◽  
Author(s):  
M.A. Murray-Lasso
Keyword(s):  
Problem Solving ◽  
Current Interest ◽  
Educational Value ◽  
Solution Algorithms ◽  
Teaching Problem ◽  
The Right ◽  
The Way

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.

Klein with Lacan: A Study on the Reception of Lacanian Ideas in Uruguay and Its Effects on Clinical Practices (1955–82)

2020 ◽  
Vol 22 (3) ◽  
pp. 341-361
Author(s):  
Gonzalo Grau-Pérez ◽  
J. Guillermo Milán
Keyword(s):  
Clinical Practice ◽  
Clinical Material ◽  
Clinical Practices ◽  
Before And After ◽  
The Difference ◽  
The 1960S ◽  
The Relationship ◽  
Discursive Approach ◽  
The Way ◽  
Clinical Cases

In Uruguay, Lacanian ideas arrived in the 1960s, into a context of Kleinian hegemony. Adopting a discursive approach, this study researched the initial reception of these ideas and its effects on clinical practices. We gathered a corpus of discursive data from clinical cases and theoretical-doctrinal articles (from the 1960s, 1970s and 1980s). In order to examine the effects of Lacanian ideas, we analysed the difference in the way of interpreting the clinical material before and after Lacan's reception. The results of this research illuminate some epistemological problems of psychoanalysis, especially the relationship between theory and clinical practice.

Ragam Qiraat Al-Qur'an

SUHUF ◽  
2015 ◽  
Vol 2 (1) ◽  
pp. 53-72
Author(s):  
Ahmad Fathoni
Keyword(s):  
The Third ◽  
The Difference ◽  
The Way

The object of the study of the knowledge of the variety of the Quranic reading  is the  Qur'an itself. The focus is on the difference of the reading and its articulation. The method is based on the riwayat or narration which is originated from the Prophet (Rasulullah saw) and its use is to be one of the instruments to keep the originality of the Qur’an. The validity of the reading the Qur’an is to be judged based on the valid chain  (sanad ¡a¥ī¥)  in accord with the Rasm U£mānÄ« as well as with the  Arabic grammar. Whereas the qualification of its originality is divided into six stages as follow: the first is mutawātir, the second is masyhÅ«r, the third is āhād, the fourth is syaz, the fifth is maudū‘, and the six is mudraj. Of this six catagories, the readings which can be included in the catagory of mutawātir are Qiraat Sab‘ah (the seven readings) and Qiraat ‘Asyrah  (the ten readings). To study this knowledge of reading the Qur’an (ilmu qiraat), one is advised to know about special terms being used such as  qiraat  (readings), riwayat (narration), tarÄ«q (the way), wajh (aspect), mÄ«m jama‘, sukÅ«n mÄ«m jama‘ and many others.

Through the Lens of Gadamer’s Hermeneutics: In comparison between Amina Wadud’s and Mohammed Talbi’s Interpretations of Q. 4:34

SUHUF ◽  
2017 ◽  
Vol 9 (2) ◽  
pp. 193-214
Author(s):  
Afifur Rochman Sya'rani
Keyword(s):  
Gender Inequality ◽  
Married Couple ◽  
Contextual Approach ◽  
The Status ◽  
Similarities And Differences ◽  
The Difference ◽  
Muslim Scholars ◽  
The Way

Most of traditional Muslim exegetes interpret Q. 4:34 in terms of maintaining the superiority of men over women. Some progressive Muslim scholars then insist a contextual approach to the verse to criticize gender inequality. Among some progressive Muslim scholars, this article comparatively examines the interpretations of Amina Wadud and Mohammed Talbi of Q. 4:34. Although both of them propose a contextual reading of the verse, they have different intellectual background, approach and method in interpreting the Qur’ān. The questions are to what extent the similarities and differences of both Wadud’s and Talbi’s interpretation of Q. 4:34 and how far their interpretations reflect their respective intention and perspective? Applying Gadamer’s hermeneutical approach, the article concludes that [1] Both Wadud and Talbi argue that the verse does not establish the superiority of men over women, but acknowledges duties division among married couple; [2] the difference among their interpretations is on the status of relationship among married couple; [3] Wadud’s and Talbi’s interpretations represent their respective hermeneutical situations and the way they define ontologically the nature of  interpretation and Qur’anic hermeneutics affect on producing the meanings of the verse.

Ronald Coase and the Difference between Markets and Firms

2018 ◽  
Author(s):  
Abraham A. Singer
Keyword(s):  
Transaction Cost ◽  
Economic Activity ◽  
Transaction Cost Economics ◽  
Theory Of The Firm ◽  
Tabular Form ◽  
Specific Investment ◽  
The Difference ◽  
Marginal Revolution ◽  
The Way

This chapter reviews the development of transaction cost economics and unpacks its theory of the firm. The chapter begins with the marginal revolution in economics and how it altered the way economists understood the corporation. It then reviews the work of Ronald Coase and Oliver Williamson, explaining how they provided a novel account of firms. Transaction cost economics emphasizes how firms use hierarchy and bureaucracy to overcome problems of opportunism and asset-specific investment to coordinate some types of economic activity more efficiently than markets can. The transaction cost account of the corporation’s productivity component is shown in tabular form in comparison with its historical forerunners reviewed in the previous chapter.

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