Cognitively Guided Instruction - Revision history

imported>Michael Pershan: /* Influence and Criticism */

2015-07-05T01:49:01Z

Influence and Criticism

← Older revision		Revision as of 01:49, 5 July 2015
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	Some reviewers have also noted (http://www.promisingpractices.net/program.asp?programid=114) that student performance on the Iowa Test of Basic Skills did not differ significantly between control and CGI groups in [[Carpenter, Fennema, Peterson, Chiang, & Loef (1989)]].		Some reviewers have also noted (http://www.promisingpractices.net/program.asp?programid=114) that student performance on the Iowa Test of Basic Skills did not differ significantly between control and CGI groups in [[Carpenter, Fennema, Peterson, Chiang, & Loef (1989)]].

	The initial CGI research took place with students drawn from "predominantly white, middle-class to upper-middle class neighborhoods" in Madison, Wisconsin ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]). However, more recent work has begun to study the impact of CGI on groups of special education ([http://eric.ed.gov/?id=EJ668770 \| Behrend (2003)]) ESL, (Celedon-Pattichis & Turner, (2012)) and economically and racially diverse students ([[Jacobs, Franke, Carpenter, Levi & Battey, (2007)]]).		The initial CGI research took place with students drawn from "predominantly white, middle-class to upper-middle class neighborhoods" in Madison, Wisconsin ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]). However, more recent work has begun to study the impact of CGI on groups of special education ([http://eric.ed.gov/?id=EJ668770 Behrend (2003)]) ESL, (Celedon-Pattichis & Turner, (2012)) and economically and racially diverse students ([[Jacobs, Franke, Carpenter, Levi & Battey, (2007)]]).

	=Publications=		=Publications=

imported>Michael Pershan: /* Research on Student Thinking */

2015-07-02T18:08:22Z

Research on Student Thinking

← Older revision		Revision as of 18:08, 2 July 2015
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	From 1979 to 1981, Carpenter, Hiebert and Moser conducted a study of the mathematical thinking of approximately 100 first, second and third grade students in Madison, Wisconsin. They interviewed each student three times each year, observing them solve addition and subtraction word problems. Their aim was to investigate "the development of children's abilities to solve verbal addition and subtraction problems and particularly in the processes and strategies used by children." ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)])		From 1979 to 1981, Carpenter, Hiebert and Moser conducted a study of the mathematical thinking of approximately 100 first, second and third grade students in Madison, Wisconsin. They interviewed each student three times each year, observing them solve addition and subtraction word problems. Their aim was to investigate "the development of children's abilities to solve verbal addition and subtraction problems and particularly in the processes and strategies used by children." ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)])
	[[File:Problemtypes.png\|500px\|thumb\|right\|Problem Types, from [http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]]]		[[File:Problemtypes.png\|500px\|thumb\|right\|Problem Types, from [http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]]]
	Their earliest work identified a taxonomy of addition and subtraction word problem types. Different problem within this taxonomy are differently difficult for children even when the "arithmetic" remains constant. For example, "Tom had 11 apples, and then lost 3 of them, how many does he have left?" might be easier for a student to represent than "Tom has 11 apples and 3 of them are spoiled, how many are no spoiled?" as the former problem has an action that a student can act out using counters, paper or some other representation.		Their earliest work identified a taxonomy of addition and subtraction word problem types. Different problem within this taxonomy are differently difficult for children even when the "arithmetic" remains constant. For example, "Tom had 11 apples, and then lost 3 of them, how many does he have left?" might be easier for a student to represent than "Tom has 11 apples and 3 of them are spoiled, how many are not spoiled?" as the former problem has an action that a student can act out using counters, paper or some other representation.

	Another major result of this early study was the identification of a learning progression that children pass through on their way to more advanced procedures for solving addition/subtraction word problems. At early stages, they found that children solve word problems by directly representing the action in a problem, with counters or any other available physical object. (For this reason, word problems without clearly presented actions tend to be more difficult at these early stages.) Students then develop various counting strategies to make their work more efficient, and eventually come to abstract the structure of the word problem and use memorized facts to solve problems.		Another major result of this early study was the identification of a learning progression that children pass through on their way to more advanced procedures for solving addition/subtraction word problems. At early stages, they found that children solve word problems by directly representing the action in a problem, with counters or any other available physical object. (For this reason, word problems without clearly presented actions tend to be more difficult at these early stages.) Students then develop various counting strategies to make their work more efficient, and eventually come to abstract the structure of the word problem and use memorized facts to solve problems.

imported>Michael Pershan: /* Research on Student Thinking */

2015-07-02T18:06:40Z

Research on Student Thinking

← Older revision		Revision as of 18:06, 2 July 2015
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	=Research on Student Thinking=		=Research on Student Thinking=

	From 1979 to 1981, Carpenter, Hiebert and Moser conducted a study of the mathematical ~~development~~ approximately 100 first, second and third grade students in Madison, Wisconsin. They interviewed each student three times each year, observing them solve addition and subtraction word problems. Their aim was to investigate "the development of children's abilities to solve verbal addition and subtraction problems and particularly in the processes and strategies used by children." ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)])		From 1979 to 1981, Carpenter, Hiebert and Moser conducted a study of the mathematical thinking of approximately 100 first, second and third grade students in Madison, Wisconsin. They interviewed each student three times each year, observing them solve addition and subtraction word problems. Their aim was to investigate "the development of children's abilities to solve verbal addition and subtraction problems and particularly in the processes and strategies used by children." ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)])
	[[File:Problemtypes.png\|500px\|thumb\|right\|Problem Types, from [http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]]]		[[File:Problemtypes.png\|500px\|thumb\|right\|Problem Types, from [http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]]]
	Their earliest work identified a taxonomy of addition and subtraction word problem types. Different problem within this taxonomy are differently difficult for children even when the "arithmetic" remains constant. For example, "Tom had 11 apples, and then lost 3 of them, how many does he have left?" might be easier for a student to represent than "Tom has 11 apples and 3 of them are spoiled, how many are no spoiled?" as the former problem has an action that a student can act out using counters, paper or some other representation.		Their earliest work identified a taxonomy of addition and subtraction word problem types. Different problem within this taxonomy are differently difficult for children even when the "arithmetic" remains constant. For example, "Tom had 11 apples, and then lost 3 of them, how many does he have left?" might be easier for a student to represent than "Tom has 11 apples and 3 of them are spoiled, how many are no spoiled?" as the former problem has an action that a student can act out using counters, paper or some other representation.

imported>Michael Pershan: /* Research on Student Thinking */

2015-07-02T18:06:30Z

Research on Student Thinking

← Older revision		Revision as of 18:06, 2 July 2015
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	=Research on Student Thinking=		=Research on Student Thinking=

	From 1979 to 1981, Carpenter, Hiebert and Moser conducted a study of approximately 100 first, second and third grade students in Madison, Wisconsin. They interviewed each student three times each year, observing them solve addition and subtraction word problems. Their aim was to investigate "the development of children's abilities to solve verbal addition and subtraction problems and particularly in the processes and strategies used by children." ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)])		From 1979 to 1981, Carpenter, Hiebert and Moser conducted a study of the mathematical development approximately 100 first, second and third grade students in Madison, Wisconsin. They interviewed each student three times each year, observing them solve addition and subtraction word problems. Their aim was to investigate "the development of children's abilities to solve verbal addition and subtraction problems and particularly in the processes and strategies used by children." ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)])
	[[File:Problemtypes.png\|500px\|thumb\|right\|Problem Types, from [http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]]]		[[File:Problemtypes.png\|500px\|thumb\|right\|Problem Types, from [http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]]]
	Their earliest work identified a taxonomy of addition and subtraction word problem types. Different problem within this taxonomy are differently difficult for children even when the "arithmetic" remains constant. For example, "Tom had 11 apples, and then lost 3 of them, how many does he have left?" might be easier for a student to represent than "Tom has 11 apples and 3 of them are spoiled, how many are no spoiled?" as the former problem has an action that a student can act out using counters, paper or some other representation.		Their earliest work identified a taxonomy of addition and subtraction word problem types. Different problem within this taxonomy are differently difficult for children even when the "arithmetic" remains constant. For example, "Tom had 11 apples, and then lost 3 of them, how many does he have left?" might be easier for a student to represent than "Tom has 11 apples and 3 of them are spoiled, how many are no spoiled?" as the former problem has an action that a student can act out using counters, paper or some other representation.
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	Another major result of this early study was the identification of a learning progression that children pass through on their way to more advanced procedures for solving addition/subtraction word problems. At early stages, they found that children solve word problems by directly representing the action in a problem, with counters or any other available physical object. (For this reason, word problems without clearly presented actions tend to be more difficult at these early stages.) Students then develop various counting strategies to make their work more efficient, and eventually come to abstract the structure of the word problem and use memorized facts to solve problems.		Another major result of this early study was the identification of a learning progression that children pass through on their way to more advanced procedures for solving addition/subtraction word problems. At early stages, they found that children solve word problems by directly representing the action in a problem, with counters or any other available physical object. (For this reason, word problems without clearly presented actions tend to be more difficult at these early stages.) Students then develop various counting strategies to make their work more efficient, and eventually come to abstract the structure of the word problem and use memorized facts to solve problems.

	Further research detailed problem types and student thinking about multiplication/division problems (Carpenter et al. (1993)), multi-digit arithmetic strategies (Carpenter et al. (1998)), and fraction concepts (Empson, (1999)).		Further research detailed problem types and student thinking about multiplication/division problems (Carpenter et al. (1993)), multi-digit arithmetic strategies (Carpenter et al. (1998)), and fraction concepts (Empson, (1999)).

	=Research on Teacher Knowledge of Student Thinking=		=Research on Teacher Knowledge of Student Thinking=

imported>Michael Pershan: /* Influence and Criticism */

2015-07-02T18:00:19Z

Influence and Criticism

← Older revision		Revision as of 18:00, 2 July 2015
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	Some reviewers have also noted (http://www.promisingpractices.net/program.asp?programid=114) that student performance on the Iowa Test of Basic Skills did not differ significantly between control and CGI groups in [[Carpenter, Fennema, Peterson, Chiang, & Loef (1989)]].		Some reviewers have also noted (http://www.promisingpractices.net/program.asp?programid=114) that student performance on the Iowa Test of Basic Skills did not differ significantly between control and CGI groups in [[Carpenter, Fennema, Peterson, Chiang, & Loef (1989)]].

	The initial CGI research took place with students drawn from "predominantly white, middle-class to upper-middle class neighborhoods" in Madison, Wisconsin ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]). However, more recent work has begun to study the impact of CGI on groups of special education ([http://eric.ed.gov/?id=EJ668770 \| Behrend (2003)]) ESL, (Celedon-Pattichis & Turner, (2012)) and economically and racially diverse students ([[Jacobs, Franke, Carpenter, Levi & Battey, 2007]]).		The initial CGI research took place with students drawn from "predominantly white, middle-class to upper-middle class neighborhoods" in Madison, Wisconsin ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]). However, more recent work has begun to study the impact of CGI on groups of special education ([http://eric.ed.gov/?id=EJ668770 \| Behrend (2003)]) ESL, (Celedon-Pattichis & Turner, (2012)) and economically and racially diverse students ([[Jacobs, Franke, Carpenter, Levi & Battey, (2007)]]).

	=Publications=		=Publications=

imported>Michael Pershan: /* Research on Teacher Knowledge of Student Thinking */

2015-07-02T18:00:16Z

Research on Teacher Knowledge of Student Thinking

← Older revision		Revision as of 18:00, 2 July 2015
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	In a series of studies of the teachers subsequent to the workshop, the CGI team documented connections between teacher decision-making and the CGI knowledge base. Teachers who had participated in their workshop gave their students more opportunities to solve problems, expected multiple strategies and knew more about student thinking. In addition, student achievement on mathematical tasks improved. ([[Fennema, Carpenter, Franke, Levi, Jacobs, & Empson (1996)]])		In a series of studies of the teachers subsequent to the workshop, the CGI team documented connections between teacher decision-making and the CGI knowledge base. Teachers who had participated in their workshop gave their students more opportunities to solve problems, expected multiple strategies and knew more about student thinking. In addition, student achievement on mathematical tasks improved. ([[Fennema, Carpenter, Franke, Levi, Jacobs, & Empson (1996)]])

			In further work, the CGI research team documented their work with teachers in fraction/decimal and algebra workshops (e.g. [[Jacobs, Franke, Carpenter, Levi & Battey, (2007)]]).

	=''Children's Mathematics'' and Other Publications=		=''Children's Mathematics'' and Other Publications=

imported>Michael Pershan: /* Influence and Criticism */

2015-07-02T17:57:13Z

Influence and Criticism

← Older revision		Revision as of 17:57, 2 July 2015
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	Some reviewers have also noted (http://www.promisingpractices.net/program.asp?programid=114) that student performance on the Iowa Test of Basic Skills did not differ significantly between control and CGI groups in [[Carpenter, Fennema, Peterson, Chiang, & Loef (1989)]].		Some reviewers have also noted (http://www.promisingpractices.net/program.asp?programid=114) that student performance on the Iowa Test of Basic Skills did not differ significantly between control and CGI groups in [[Carpenter, Fennema, Peterson, Chiang, & Loef (1989)]].

	The initial CGI research took place with students drawn from "predominantly white, middle-class to upper-middle class neighborhoods" in Madison, Wisconsin ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]). ~~More~~ recent work has begun to study the impact of CGI on groups of special education ([http://eric.ed.gov/?id=EJ668770 \| Behrend (2003)]) ESL, (Celedon-Pattichis & Turner, (2012)) and economically and racially diverse students (~~http://ies.ed.gov/funding/grantsearch/details.asp?ID=1295~~).		The initial CGI research took place with students drawn from "predominantly white, middle-class to upper-middle class neighborhoods" in Madison, Wisconsin ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]). However, more recent work has begun to study the impact of CGI on groups of special education ([http://eric.ed.gov/?id=EJ668770 \| Behrend (2003)]) ESL, (Celedon-Pattichis & Turner, (2012)) and economically and racially diverse students ([[Jacobs, Franke, Carpenter, Levi & Battey, 2007]]).

	=Publications=		=Publications=

imported>Michael Pershan: /* Influence and Criticism */

2015-07-02T17:52:59Z

Influence and Criticism

← Older revision		Revision as of 17:52, 2 July 2015
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	Some reviewers have also noted (http://www.promisingpractices.net/program.asp?programid=114) that student performance on the Iowa Test of Basic Skills did not differ significantly between control and CGI groups in [[Carpenter, Fennema, Peterson, Chiang, & Loef (1989)]].		Some reviewers have also noted (http://www.promisingpractices.net/program.asp?programid=114) that student performance on the Iowa Test of Basic Skills did not differ significantly between control and CGI groups in [[Carpenter, Fennema, Peterson, Chiang, & Loef (1989)]].

	~~While the~~ initial CGI research took place with students drawn from "predominantly white, middle-class to upper-middle class neighborhoods" in Madison, Wisconsin ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)])~~, there are research efforts~~ to ~~replicate~~ the ~~affects~~ of CGI ~~with more~~ economically and racially diverse ~~student populations.~~ (http://ies.ed.gov/funding/grantsearch/details.asp?ID=1295)		The initial CGI research took place with students drawn from "predominantly white, middle-class to upper-middle class neighborhoods" in Madison, Wisconsin ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]). More recent work has begun to study the impact of CGI on groups of special education ([http://eric.ed.gov/?id=EJ668770 \| Behrend (2003)]) ESL, (Celedon-Pattichis & Turner, (2012)) and economically and racially diverse students (http://ies.ed.gov/funding/grantsearch/details.asp?ID=1295).

	=Publications=		=Publications=

imported>Michael Pershan: /* Influence and Criticism */

2015-07-02T15:52:38Z

Influence and Criticism

← Older revision		Revision as of 15:52, 2 July 2015
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	The CGI work has been limited to the primary school grades. Some researchers have argued that a CGI program would be ill-suited for instructing teachers in student thinking in higher grades, due to the complexity of student conceptual knowledge in more advanced topics. [[Lesh & Doerr (2003)]] make this criticism, and propose an approach that encourages teachers to directly observe and develop their own models for student thinking in higher grades. (See, [[Models and Modeling Perspective]].)		The CGI work has been limited to the primary school grades. Some researchers have argued that a CGI program would be ill-suited for instructing teachers in student thinking in higher grades, due to the complexity of student conceptual knowledge in more advanced topics. [[Lesh & Doerr (2003)]] make this criticism, and propose an approach that encourages teachers to directly observe and develop their own models for student thinking in higher grades. (See, [[Models and Modeling Perspective]].)

	Some reviewers have also noted (http://www.promisingpractices.net/program.asp?programid=114) that student performance on the Iowa Test of Basic Skills did not differ significantly between control and CGI groups in [[Carpenter, Fennema, Peterson, Chiang, & Loef (1989)].		Some reviewers have also noted (http://www.promisingpractices.net/program.asp?programid=114) that student performance on the Iowa Test of Basic Skills did not differ significantly between control and CGI groups in [[Carpenter, Fennema, Peterson, Chiang, & Loef (1989)]].

	While the initial CGI research took place with students drawn from "predominantly white, middle-class to upper-middle class neighborhoods" in Madison, Wisconsin ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]), there are research efforts to replicate the affects of CGI with more economically and racially diverse student populations. (http://ies.ed.gov/funding/grantsearch/details.asp?ID=1295)		While the initial CGI research took place with students drawn from "predominantly white, middle-class to upper-middle class neighborhoods" in Madison, Wisconsin ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]), there are research efforts to replicate the affects of CGI with more economically and racially diverse student populations. (http://ies.ed.gov/funding/grantsearch/details.asp?ID=1295)

imported>Michael Pershan at 15:51, 2 July 2015

2015-07-02T15:51:59Z

← Older revision		Revision as of 15:51, 2 July 2015
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	While the initial CGI research took place with students drawn from "predominantly white, middle-class to upper-middle class neighborhoods" in Madison, Wisconsin ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]), there are research efforts to replicate the affects of CGI with more economically and racially diverse student populations. (http://ies.ed.gov/funding/grantsearch/details.asp?ID=1295)		While the initial CGI research took place with students drawn from "predominantly white, middle-class to upper-middle class neighborhoods" in Madison, Wisconsin ([http://eric.ed.gov/?id=ED188892 Carpenter & Moser, (1979)]), there are research efforts to replicate the affects of CGI with more economically and racially diverse student populations. (http://ies.ed.gov/funding/grantsearch/details.asp?ID=1295)

	=~~Research~~=		=Publications=
	*[[Carpenter & Moser (1984)]]		*[[Carpenter & Moser (1984)]]
	*[[Carpenter, Fennema, Peterson, Chiang, & Loef (1989)]]		*[[Carpenter, Fennema, Peterson, Chiang, & Loef (1989)]]