Formula - Revision history

Inna mik: (username removed) (log details removed)

2025-06-17T08:22:47Z

(username removed) (log details removed)

← Older revision

Revision as of 10:22, 17 June 2025

Inna mik: (username removed) (log details removed)

2025-06-17T08:14:11Z

(username removed) (log details removed)

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Revision as of 10:14, 17 June 2025

Inna mik: mental task example

2025-05-29T15:42:11Z

mental task example

← Older revision		Revision as of 17:42, 29 May 2025
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	===Step 1: Identification of [[bottleneck]]===		===Step 1: Identification of [[bottleneck]]===
	Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between ~~<math>~~e^(x^2)~~<math>~~ which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.		Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between e^(x^2) which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.

	Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.		Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.

	===Step 2: Description of [[Mental moves\|mental tasks]] needed to overcome the [[bottleneck]]===		===Step 2: Description of [[Mental moves\|mental tasks]] needed to overcome the [[bottleneck]]===
	The experts is able to see the structure by zooming in and out to blend out the details.		The experts is able to see the structure by zooming in and out into the formula to blend out the details.

	He ~~knows~~ the ~~order~~ of operation and ~~thinks of~~ results as		He encapsulates the result of one operation as an element which will be an input to the next operation. Thus he sees the operation sign as important ones e.g while reading "a+bs" he doesnt compare the letters a,b,s but the operation signs + and because he has to make a decision that the * goes first. This results in reading the formula as a sum of two elements.

	===[[Step 3 - Modeling Mental Operations\|Step 3: Modelling the tasks]]===		===[[Step 3 - Modeling Mental Operations\|Step 3: Modelling the tasks]]===

Inna mik at 15:05, 1 May 2025

2025-05-01T15:05:04Z

← Older revision		Revision as of 17:05, 1 May 2025
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	===Step 1: Identification of [[bottleneck]]===		===Step 1: Identification of [[bottleneck]]===
	Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between </math>e^(x^2)</math> which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.		Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between <math>e^(x^2)<math> which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.

	Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.		Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.

Inna mik at 15:04, 1 May 2025

2025-05-01T15:04:42Z

← Older revision		Revision as of 17:04, 1 May 2025
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	===Step 1: Identification of [[bottleneck]]===		===Step 1: Identification of [[bottleneck]]===
	Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between </math> e^(x^2) </math> which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.		Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between </math>e^(x^2)</math> which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.

	Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.		Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.

Inna mik at 15:04, 1 May 2025

2025-05-01T15:04:19Z

← Older revision		Revision as of 17:04, 1 May 2025
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	===Step 1: Identification of [[bottleneck]]===		===Step 1: Identification of [[bottleneck]]===
	Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between <math> e^(x^2) </math> ~~x^2 <math>~~ which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.		Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between </math> e^(x^2) </math> which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.

	Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.		Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.

Inna mik: try math again

2025-05-01T15:03:54Z

try math again

← Older revision		Revision as of 17:03, 1 May 2025
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	===Step 1: Identification of [[bottleneck]]===		===Step 1: Identification of [[bottleneck]]===
	Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between <math> e^(x^2) </math> which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.		Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between <math> e^(x^2) </math> x^2 <math> which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.

	Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.		Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.

Inna mik: try math mode

2025-05-01T15:03:07Z

try math mode

← Older revision		Revision as of 17:03, 1 May 2025
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	===Step 1: Identification of [[bottleneck]]===		===Step 1: Identification of [[bottleneck]]===
	Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between \(e^(x^2)\) which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.		Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between <math> e^(x^2) </math> which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.

	Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.		Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.

	===Step 2: Description of [[Mental moves\|mental tasks]] needed to overcome the [[bottleneck]]===		===Step 2: Description of [[Mental moves\|mental tasks]] needed to overcome the [[bottleneck]]===
			The experts is able to see the structure by zooming in and out to blend out the details.

	===Step 3: Modelling the tasks===		He knows the order of operation and thinks of results as

			===[[Step 3 - Modeling Mental Operations\|Step 3: Modelling the tasks]]===

	===[[Step 4: Give Students Practice and Feedback\|Step 4: Practice and Feedback]]===		===[[Step 4: Give Students Practice and Feedback\|Step 4: Practice and Feedback]]===

Inna mik: test Latex

2025-05-01T14:56:35Z

test Latex

← Older revision		Revision as of 16:56, 1 May 2025
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	===Step 1: Identification of [[bottleneck]]===		===Step 1: Identification of [[bottleneck]]===
	Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between e^(x^2) which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.		Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between \(e^(x^2)\) which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.

	Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.		Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.
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	===Step 3: Modelling the tasks===		===Step 3: Modelling the tasks===

	===Practice and Feedback===		===[[Step 4: Give Students Practice and Feedback\|Step 4: Practice and Feedback]]===

	===Anticipate and lessen resistance===		===Anticipate and lessen resistance===
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	==Available resources==		==Available resources==
			[https://youtu.be/p50Q3mx-VNg Interview Video]

	==See also==		==See also==

Inna mik: Categories

2025-04-24T15:18:12Z

← Older revision		Revision as of 17:18, 24 April 2025
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	[https://decodingthedisciplines.org/wp-content/uploads/2020/07/OF_V_Poster-Stank_170525_Endfassung-1.pdf Understanding Mathematics by Visualizing Structures], by Sabine Stank		[https://decodingthedisciplines.org/wp-content/uploads/2020/07/OF_V_Poster-Stank_170525_Endfassung-1.pdf Understanding Mathematics by Visualizing Structures], by Sabine Stank

	==~~Notes~~==		===People interested in this Bottleneck===
			Inna Mikhailova
	~~==References==~~		[[Category:Bottleneck]]
			[[Category:Mathematics]]
			[[Category:Algebra]]
	[[Category:Decoding work]]		[[Category:Decoding work]]
			[[Category:Decoding Interview]]