Lesh & Zawojewski (2007) - Revision history

imported>Michael Pershan: /* Summary */

2015-07-01T19:04:23Z

Summary

← Older revision		Revision as of 19:04, 1 July 2015
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	==Summary==		==Summary==

	This chapter of the [[NCTM]] research handbook summarizes the existing research on problem solving and points to promising directions for future research. In general, it argues for the insufficiency of past attempts to find (and instruct students in) globally applicable problem solving strategies or heuristics. The piece advocates for a "Models and Modeling" approach to research on learning and teaching, a perspective that Lesh elaborates on in this piece and his other publications.		This chapter of the [[NCTM]] research handbook summarizes the existing research on problem solving and points to promising directions for future research. In general, it argues for the insufficiency of past attempts to find (and instruct students in) globally applicable problem solving strategies or heuristics. The piece advocates for a "Models and Modeling" approach to research on learning and teaching, a perspective that Lesh elaborates on in this piece and his other publications. (See, for example, [[Lesh & Lehrer (2003)]].)

	==Outline of Headings==		==Outline of Headings==

imported>Michael Pershan: /* Summary */

2015-07-01T19:03:27Z

Summary

← Older revision		Revision as of 19:03, 1 July 2015
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	==Summary==		==Summary==

	This chapter of the [[NCTM]] research handbook summarizes the existing research on problem solving and points to promising directions for future research.		This chapter of the [[NCTM]] research handbook summarizes the existing research on problem solving and points to promising directions for future research. In general, it argues for the insufficiency of past attempts to find (and instruct students in) globally applicable problem solving strategies or heuristics. The piece advocates for a "Models and Modeling" approach to research on learning and teaching, a perspective that Lesh elaborates on in this piece and his other publications.

	==Outline of Headings==		==Outline of Headings==

imported>Michael Pershan at 19:01, 1 July 2015

2015-07-01T19:01:06Z

← Older revision		Revision as of 19:01, 1 July 2015
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	* Year: 2007		* Year: 2007
	* Source: http://www.infoagepub.com/products/Second-Handbook-Research-Mathematics-Teaching-Learning		* Source: http://www.infoagepub.com/products/Second-Handbook-Research-Mathematics-Teaching-Learning

			==Summary==

	This chapter of the [[NCTM]] research handbook summarizes the existing research on problem solving and points to promising directions for future research.		This chapter of the [[NCTM]] research handbook summarizes the existing research on problem solving and points to promising directions for future research.

imported>Raymond Johnson: added outline of headings

2015-05-27T18:40:51Z

added outline of headings

← Older revision		Revision as of 18:40, 27 May 2015
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	This chapter of the [[NCTM]] research handbook summarizes the existing research on problem solving and points to promising directions for future research.		This chapter of the [[NCTM]] research handbook summarizes the existing research on problem solving and points to promising directions for future research.

			==Outline of Headings==
			* An Overview of Past Research on Mathematical Problem Solving
			** Early Problem-Solving Research
			*** Task Variables and Problem Difficulty
			*** Expert/Novice Problem-Solver Studies
			*** Instruction in Problem-Solving Strategies
			** Research on Higher-Order Thinking
			*** Metacognition
			*** Habits of Mind
			*** Beliefs and Dispositions
			*** Summary and Reflections on Research in Higher-Order Thinking
			* New Directions and Perspectives for Research in Mathematical Problem Solving
			** A Fresh Perspective on Problem Solving
			*** Beyond School Mathematics
			*** A Definition for Problem Solving
			*** Learning Problem Solving and Learning Mathematics
			*** Model-Eliciting Activities
			*** An Evolving View of Problem Solving
			** Promising Lines of Research on Mathematics Learning
			*** Research on Situated Cognition
			*** Research on Communities of Practice
			*** Research on Representational Fluency
			** Directions for Future Research
			** The Need for New Research Tools and Methodologies
			** An Illustration: The Evolving Models-and-Modeling Perspective

	==Quotes==		==Quotes==

imported>Raymond Johnson: Formatting, reference info

2015-05-27T18:33:10Z

Formatting, reference info

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-This chapter, by [[Richard Lesh]] and [[Judith Zawojewski]], from [[NCTM]]'s [[Second Handbook of Research on Mathematics Teaching and Learning]] summarizes the existing research on problem solving and points to promising directions for future research.
+{{Title|Problem Solving and Modeling}}
 ==Quotes==
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 <blockquote>"We propose the following definition: a task...becomes a problem (or problematic) when the "problem solver" (which may be a collaborating group of specialists) needs to develop a more productive way of thinking about the given situation."</blockquote>

imported>Michael Pershan at 11:19, 27 May 2015

2015-05-27T11:19:59Z

← Older revision		Revision as of 11:19, 27 May 2015
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	==Quotes==		==Quotes==

	<blockquote>"Begle (1979) reviewed early stages of this research. He concluded that "no clear-cut directions for mathematics education are provided by the findings of these studies...Similarly, Schoenfeld in his 1992 [[Schoenfeld 1992\|review of the literature]] concluded that attempts to teach students to use general problem-solving strategies (e.g. draw a picture, identify the givens and goals, consider a similar problem) generally had not been successful...In fact, even a decade later when Lester and Kehle (2003) compared a current list of issues to those described by Lester in 1994, they concluded that, still, little progress had been made in problem-solving research and that the literature on problem solving had little to offer to school practice."</blockquote>		<blockquote>"Begle (1979) reviewed early stages of this research. He concluded that "no clear-cut directions for mathematics education are provided by the findings of these studies...Similarly, Schoenfeld in his 1992 [[Schoenfeld (1992)\|review of the literature]] concluded that attempts to teach students to use general problem-solving strategies (e.g. draw a picture, identify the givens and goals, consider a similar problem) generally had not been successful...In fact, even a decade later when Lester and Kehle (2003) compared a current list of issues to those described by Lester in 1994, they concluded that, still, little progress had been made in problem-solving research and that the literature on problem solving had little to offer to school practice."</blockquote>

	<blockquote>"Krutetskii found that gifted students tend to perceive the underlying mathematical structure of problem situations very rapidly, whereas others tend to notice and remember relatively superficial problem characteristics. Notice that the characteristics of expert problem solvers identified by Krutetskii cannot be directly taught to the nonexperts. One cannot directly teach novice problem solvers to "generalize broadly," "identify the underlying structure," or "look ahead to skip steps," -- especially assuming that novices often view mathematical problem solving as keeping track of and carefully processing pieces of information."</blockquote>		<blockquote>"Krutetskii found that gifted students tend to perceive the underlying mathematical structure of problem situations very rapidly, whereas others tend to notice and remember relatively superficial problem characteristics. Notice that the characteristics of expert problem solvers identified by Krutetskii cannot be directly taught to the nonexperts. One cannot directly teach novice problem solvers to "generalize broadly," "identify the underlying structure," or "look ahead to skip steps," -- especially assuming that novices often view mathematical problem solving as keeping track of and carefully processing pieces of information."</blockquote>

imported>Michael Pershan at 11:19, 27 May 2015

2015-05-27T11:19:40Z

← Older revision		Revision as of 11:19, 27 May 2015
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	==Quotes==		==Quotes==

	<blockquote>"Begle (1979) reviewed early stages of this research. He concluded that "no clear-cut directions for mathematics education are provided by the findings of these studies...Similarly, Schoenfeld in his 1992 review of the literature concluded that attempts to teach students to use general problem-solving strategies (e.g. draw a picture, identify the givens and goals, consider a similar problem) generally had not been successful...In fact, even a decade later when Lester and Kehle (2003) compared a current list of issues to those described by Lester in 1994, they concluded that, still, little progress had been made in problem-solving research and that the literature on problem solving had little to offer to school practice."</blockquote>		<blockquote>"Begle (1979) reviewed early stages of this research. He concluded that "no clear-cut directions for mathematics education are provided by the findings of these studies...Similarly, Schoenfeld in his 1992 [[Schoenfeld 1992\|review of the literature]] concluded that attempts to teach students to use general problem-solving strategies (e.g. draw a picture, identify the givens and goals, consider a similar problem) generally had not been successful...In fact, even a decade later when Lester and Kehle (2003) compared a current list of issues to those described by Lester in 1994, they concluded that, still, little progress had been made in problem-solving research and that the literature on problem solving had little to offer to school practice."</blockquote>

	<blockquote>"Krutetskii found that gifted students tend to perceive the underlying mathematical structure of problem situations very rapidly, whereas others tend to notice and remember relatively superficial problem characteristics. Notice that the characteristics of expert problem solvers identified by Krutetskii cannot be directly taught to the nonexperts. One cannot directly teach novice problem solvers to "generalize broadly," "identify the underlying structure," or "look ahead to skip steps," -- especially assuming that novices often view mathematical problem solving as keeping track of and carefully processing pieces of information."</blockquote>		<blockquote>"Krutetskii found that gifted students tend to perceive the underlying mathematical structure of problem situations very rapidly, whereas others tend to notice and remember relatively superficial problem characteristics. Notice that the characteristics of expert problem solvers identified by Krutetskii cannot be directly taught to the nonexperts. One cannot directly teach novice problem solvers to "generalize broadly," "identify the underlying structure," or "look ahead to skip steps," -- especially assuming that novices often view mathematical problem solving as keeping track of and carefully processing pieces of information."</blockquote>

imported>Michael Pershan at 10:22, 27 May 2015

2015-05-27T10:22:13Z

← Older revision		Revision as of 10:22, 27 May 2015
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	<blockquote>"Krutetskii found that gifted students tend to perceive the underlying mathematical structure of problem situations very rapidly, whereas others tend to notice and remember relatively superficial problem characteristics. Notice that the characteristics of expert problem solvers identified by Krutetskii cannot be directly taught to the nonexperts. One cannot directly teach novice problem solvers to "generalize broadly," "identify the underlying structure," or "look ahead to skip steps," -- especially assuming that novices often view mathematical problem solving as keeping track of and carefully processing pieces of information."</blockquote>		<blockquote>"Krutetskii found that gifted students tend to perceive the underlying mathematical structure of problem situations very rapidly, whereas others tend to notice and remember relatively superficial problem characteristics. Notice that the characteristics of expert problem solvers identified by Krutetskii cannot be directly taught to the nonexperts. One cannot directly teach novice problem solvers to "generalize broadly," "identify the underlying structure," or "look ahead to skip steps," -- especially assuming that novices often view mathematical problem solving as keeping track of and carefully processing pieces of information."</blockquote>

	<blockquote>Why do after-the-fact descriptions of past activities not necessarily provide guidelines for next steps during future problem-solving activities? Perhaps one reason is because using a strategy, such as <i>draw a picture</i> assumes that a student would know what pictures to draw when, under what circumstances, and for which type of problems. Therefore, mastering <i>draw a picture</i> (in general) depends on the interpretation abilities--not just execution abilities. Thus, developing systems for interpreting problem situations is as important, if not more important, than developing processes for doing particular strategies.</blockquote>		<blockquote>"Why do after-the-fact descriptions of past activities not necessarily provide guidelines for next steps during future problem-solving activities? Perhaps one reason is because using a strategy, such as <i>draw a picture</i> assumes that a student would know what pictures to draw when, under what circumstances, and for which type of problems. Therefore, mastering <i>draw a picture</i> (in general) depends on the interpretation abilities--not just execution abilities. Thus, developing systems for interpreting problem situations is as important, if not more important, than developing processes for doing particular strategies."</blockquote>

	<blockquote>"Our interpretation of Polya's heuristics is that the strategies are intended to help problem solvers think about, reflect on, and interpret problem situations, more than they are intended to help them decide what to <i>do</i> when "stuck" during a problem attempt."</blockquote>		<blockquote>"Our interpretation of Polya's heuristics is that the strategies are intended to help problem solvers think about, reflect on, and interpret problem situations, more than they are intended to help them decide what to <i>do</i> when "stuck" during a problem attempt."</blockquote>

imported>Michael Pershan at 09:58, 27 May 2015

2015-05-27T09:58:38Z

← Older revision		Revision as of 09:58, 27 May 2015
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	This chapter, from [[NCTM]]'s [[Second Handbook of Research on Mathematics Teaching and Learning]] summarizes the existing research on problem solving and points to promising directions for future research.		This chapter, by [[Richard Lesh]] and [[Judith Zawojewski]], from [[NCTM]]'s [[Second Handbook of Research on Mathematics Teaching and Learning]] summarizes the existing research on problem solving and points to promising directions for future research.

	==Quotes==		==Quotes==

imported>Michael Pershan at 09:58, 27 May 2015

2015-05-27T09:58:09Z

← Older revision		Revision as of 09:58, 27 May 2015
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	This chapter, from [[NCTM]]'s[[Second Handbook of Research on Mathematics Teaching]] summarizes the existing research on problem solving and points to promising directions for future research.		This chapter, from [[NCTM]]'s [[Second Handbook of Research on Mathematics Teaching and Learning]] summarizes the existing research on problem solving and points to promising directions for future research.

	==Quotes==		==Quotes==