Thinking: What counts as understanding?

Chinese version: /zh-hant/thinking/understanding/

• Date: 2026-09-10
• Related goal: Current Goal
• Status: Raw learner reasoning captured from a guided diagnostic. Preserve wording; interpretation is recorded separately.

Questions and my current answers (before critique)

1. Formula recall versus understanding

If a person can recite Newton’s second law, F = ma, but cannot judge a new situation, do they know it or understand it?

My answer:

不知道

2. Two shopping carts, same applied force

Cart A is empty and cart B is full. Which has the greater acceleration?

My answer:

A. F=ma > a = F/m, F 一定，m 越小 a 越大

3. B has twice A’s mass, same net force

What is B’s acceleration relative to A’s?

My answer:

一半，因為成反比

4. “A heavier object is harder to push, so it must receive less force.”

My answer:

不對。難推是因為同樣的力推，質量大的加速度更小，動得更慢，看上去更難推。而更重的想推得同樣快可以施加更多的力，這樣反而收到更多力

5. Supply and demand

A says they understand supply and demand because “when supply is low, price is high,” but cannot answer what happens when demand also drops sharply.

My answer:

2 . 其它規則沒有了解到

6. Prediction versus explanation

One person predicts correctly but cannot explain why. Another explains but predicts incorrectly in a new situation. Who understands?

My answer:

2個都不算是理解

7. “The longer one studies, the better their grades will certainly be.”

My answer:

成績的好壞受極多因素影響，時間只是其中一個

8. Conditional causal claim: study time and grades

Rewrite “讀書時間越長，成績一定越好” more precisely, and give a situation where extra time would not be expected to help.

My answer:

用錯學習方法，不顧身體情況，不做規劃，不做復盤反思，這樣下來不管時間增加多少成績不見到改善

當學習方法有效、身體狀況足以專注、並有規劃和復盤時，學習成績才能有所提升。

用論文的實驗報告來驗證。

9. Cognitive ability versus understanding ability

A can concentrate and remember well but only recites definitions. B has ordinary memory but explains causal relations and applies concepts to new examples. Who has stronger understanding and cognitive ability?

My answer:

不知道

Tutor summary given:

B shows stronger demonstrated understanding of the topic because B explains causal relations and applies the concept to new examples. A demonstrates the named cognitive supports—concentration and memory—but definition recall alone does not demonstrate understanding. The short description does not justify ranking either person’s overall cognitive ability or intelligence.

10. Ability and understanding ability

什麼是能力，什麼又是理解能力？

Tutor summary given:

Ability is a reliable capacity to perform a type of task under relevant conditions. Understanding ability is a topic-specific capacity to build and use a model: explain why, predict what changes, apply the idea in a new case, and revise assumptions after counterevidence. Memory and attention can support this performance but are not the same as understanding.

What I am uncertain about

• How cognitive abilities such as attention and working memory differ from understanding ability, and how the two interact.
• How to state a precise, general definition of understanding.
• How to convert a broad causal claim into a fully conditional, testable version rather than only identifying boundary cases.

LLM critique request

Challenge the reasoning without replacing it. Identify missing assumptions, the earliest invalid inference, counterexamples, and one stronger way to test or explain the idea. Ask one question if evidence is insufficient.

Follow-up action

• Create a drill
• Add feedback
• Write a reflection
• Distil a reusable note
• Complete the next drill response