User:IssaRice/Tiers of learning in mathematics: Difference between revisions
No edit summary |
No edit summary |
||
| Line 5: | Line 5: | ||
| Computation-based || The material is taught, but proofs of the main results are not covered. Example: high school/freshman calculus courses, in most cases. | | Computation-based || The material is taught, but proofs of the main results are not covered. Example: high school/freshman calculus courses, in most cases. | ||
|- | |- | ||
| Proof-based, but focusing on exercises || The material is taught using proofs, but where the student is not expected to prove the main results themselves. Instead, the student is expected to be able to solve (often artificial) problems (including proof-based) that make use of the main results. Example: math 13X and math 33X at UW. | | Proof-based, but focusing on exercises || The material is taught using proofs, but where the student is not expected to prove the main results themselves. Instead, the student is expected to be able to solve (often artificial) problems (including proof-based problems) that make use of the main results. Example: math 13X and math 33X at UW. | ||
|- | |- | ||
| Building the theory from scratch || The material is taught using proofs, but the focus is on being able to prove the results oneself, where the exercises ''are'' the proofs of the main results. Example: Tao's ''Analysis''; reading a textbook that gives proofs of main results, but where one tries to prove the theorems oneself first. | | Building the theory from scratch || The material is taught using proofs, but the focus is on being able to prove the results oneself, where the exercises ''are'' the proofs of the main results. Example: Tao's ''Analysis''; reading a textbook that gives proofs of main results, but where one tries to prove the theorems oneself first. | ||
Revision as of 19:39, 7 December 2018
| Name | Description |
|---|---|
| Computation-based | The material is taught, but proofs of the main results are not covered. Example: high school/freshman calculus courses, in most cases. |
| Proof-based, but focusing on exercises | The material is taught using proofs, but where the student is not expected to prove the main results themselves. Instead, the student is expected to be able to solve (often artificial) problems (including proof-based problems) that make use of the main results. Example: math 13X and math 33X at UW. |
| Building the theory from scratch | The material is taught using proofs, but the focus is on being able to prove the results oneself, where the exercises are the proofs of the main results. Example: Tao's Analysis; reading a textbook that gives proofs of main results, but where one tries to prove the theorems oneself first. |
| Building the theory from scratch in parallel | The material is taught using proofs and the focus is on being able to prove the results oneself in multiple ways. Example: working through multiple analysis books in parallel and keeping a dependency graph of theorems in one's mind as one does this. |
| Reverse mathematics | Mathematics from a "logical strength" point of view, where one is building the theory from scratch in parallel but also tracking the strengths of various results. |