(Description) |
(Öinks added) |
||
| Line 7: | Line 7: | ||
==Decoding work done== | ==Decoding work done== | ||
===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. | ||
===Step 2: Description of mental tasks needed to overcome the bottleneck=== | ===Step 2: Description of [[Mental moves|mental tasks]] needed to overcome the [[bottleneck]]=== | ||
===Modelling the tasks=== | ===Step 3: Modelling the tasks=== | ||
===Practice and Feedback=== | ===Practice and Feedback=== | ||
| Line 29: | Line 29: | ||
==See also== | ==See also== | ||
[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== | ==Notes== | ||
Revision as of 17:12, 24 April 2025
Difficulties often emerge while students have to recognize a structure of a complex formula. In particular, it is difficult for students to
- use the brackets to parse the formula from handwritten form to one line form, e.g. for programming ;
- see the steps that should be done first while rearranging a formula;
- use substitutions in chain rule or while solving equations.
Decoding work done
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.
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 tasks needed to overcome the bottleneck
Step 3: Modelling the tasks
Practice and Feedback
Anticipate and lessen resistance
Assessment of student mastery
Sharing
Researchers involved
Available resources
See also
Understanding Mathematics by Visualizing Structures, by Sabine Stank
