Timeline for Natural origins or learned habit: Why do students skip concepts before applications?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| S Oct 26, 2023 at 20:09 | history | suggested | Greg Martin | CC BY-SA 4.0 |
changed to inclusive language
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| Oct 22, 2023 at 1:55 | comment | added | Mahdi Majidi-Zolbanin | @AlexanderWoo very true. | |
| Oct 22, 2023 at 1:25 | comment | added | Alexander Woo | @MahdiMajidi-Zolbanin - they have this perception of learning in general, also complaining when their history professor expects them to have their own insight into the historical situations they are studying rather than just repeating what's in their readings and their lectures. Fundamentally, these students (and people like them who have given up on school) are obsolete in the age of AI, they realize if only subconsciously that society has cruelly left them with no future, and this realization accounts for much of the brokenness of politics all over the world. | |
| Oct 21, 2023 at 2:28 | comment | added | user103496 | To respond to your (deleted) comment (about why I don't write an answer here): Comments and answers here can simply be deleted without explanation if the mod doesn't like it. So I think I'd rather not waste my time. | |
| Oct 20, 2023 at 21:06 | review | Suggested edits | |||
| S Oct 26, 2023 at 20:09 | |||||
| Oct 19, 2023 at 17:33 | comment | added | Mahdi Majidi-Zolbanin | @AlexanderWoo ... the same type of example. It is more than that. But it is interesting that they have this inaccurate perception of learning mathematics. | |
| Oct 19, 2023 at 17:32 | comment | added | Mahdi Majidi-Zolbanin | @AlexanderWoo That is interesting. To be clear, a new problem that they haven't seen before, but have the required knowledge to solve it, right? For instance, they know the definition of continuity, they have seen, practiced and solved examples on this topic, and now they are given a new problem that they haven't seen before? Well, that's what learning mathematics is about, to be able to start from the definitions that they know, and apply it to solve a new problem that they haven't seen before. Learning mathematics is not just being able to repeat the solution of one example to solve ... | |
| Oct 19, 2023 at 17:11 | comment | added | Alexander Woo | @MahdiMajidi-Zolbanin: Many of my students believe that solving new problems they haven't seen before is a superhuman ability reserved for extraordinary people, and that asking students to do this is fundamentally unfair. | |
| Oct 19, 2023 at 14:49 | comment | added | user1815 | @breversa I disagree (kindly) with the linear ordering implied in your comment. A conceptual understanding is a complex of ideas and cognitive skills. Its inherent nonlinear structure is a challenge for teaching, which happens in time and is thus linearly ordered. One student may learn facts (such as the definition) and skills each at a different rate than another student learns those things. This differentiation probably would occur if two students had the same prior knowledge and same experience of the same learning activities — a hypothesis that is, I believe, impossible anyway. | |
| Oct 19, 2023 at 14:48 | comment | added | Mahdi Majidi-Zolbanin | @breversa That may be true. But how can someone verify whether a function is continuous at a given point, if they don't know what needs to be verified? Unless they memorized steps from previous solved examples, which may not be useful to a new problem that they have not seen before? | |
| Oct 19, 2023 at 13:39 | comment | added | breversa | @MahdiMajidi-Zolbanin: I came to the conclusion that definitions don’t help to understand, they help to remember… but only AFTER you’ve understood. They are the smallest amount of words needed to describe a concept, but definitely not to explain it. | |
| Oct 19, 2023 at 10:29 | comment | added | Mahdi Majidi-Zolbanin | limit of $f(x)$ as $x$ approaches $a$ is equal to $f(a)$, with no reference to $\epsilon$ and $\delta$. This definition is explained in different ways, various types of examples are solved, demonstrating how the solution to each example is obtained by referring back to the definition. Then if a new problem is given to students, which they have not seen before, the majority of them attempt to solve it by searching their inventory of solved examples, rather than using the definition. Where is this tendency stemming from? | |
| Oct 19, 2023 at 10:25 | comment | added | Mahdi Majidi-Zolbanin | The act of referring back to the definitions must occur prior to the realization that the definitions are difficult to understand. This referring back doesn't seem to be occurring. Even with simple definitions it doesn't occur. It is not always because the definitions are difficult to understand, it seems that either the need for doing this is not grasped by students, or they resist doing it. I almost never use the $\epsilon$-$\delta$ definition of limit or continuity in calculus. The definition of continuity in calculus is that (continued) | |
| Oct 19, 2023 at 4:05 | history | answered | fedja | CC BY-SA 4.0 |