［教育時評］什麼是批判性思考？
Surely we have all heard business executives, policy makers, civic leaders, and educators talking about the term “critical thinking.” But what exactly is it? Why is it considered so useful and important?
我們一定都聽過企業領導者、政策制定者、公民領袖以及教育工作者談論批判性思考。 但這到底是什麼？為何它被認為有效且重要呢？
To a certain extent we all know what “critical thinking” means — it means high-quality thinking. Some might say that is the opposite of illogical or irrational thinking, but this definition still seems vague. Is critical thinking the same as analytical thinking? What about creative thinking?
在某種程度上，我們都知道「批判性思考」的意思——意即優質的思考。也許有些人會說此異於不合邏輯或非理性的思考。但這樣的定義似乎還是很模糊。批判性思考是否與分析性思考一樣？那創造性思考呢？
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Let’s explore the concept further through examples, and use our critical thinking skills together. To come up with a more concrete definition, let us answer the following questions:
讓我們從幾個面向進一步探討這個問題，並一起運用批判性思考。為了提出更具體的定義，就讓我們回答下列問題：
1. What would happen if we did not have critical thinking?
若我們不具備批判性思考會有什麼影響？
2. When do we use critical thinking?
我們何時該使用批判性思考？
3. Can you think of examples of critical thinking?
你能想到有關批判性思考的例子嗎？
4. How do we assess critical thinking?
我們該如何評價批判性思考？
5. Does critical thinking involve working with other people? Why or why not?
批判性思考是否需要與他人合作？為什麼？
By answering these questions, our definition of critical should be becoming more tangible.
藉由回答這些問題，我們對批判的定義應會變得更加明確。
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From experience, most now know that critical thinking is thinking that has a purpose (proving a point, interpreting what something means, solving a problem), and critical thinking can be a collaborative process. Without it, we wouldn't be able to solve complex problems without definite answers in and outside the classroom.
We are bombarded with information and problems on a daily basis in our society today. We need critical thinking to help us process information and solve these problems.
從經驗中，多數人現在知道批判性思考是帶有「目的」的思考（證明觀點、解決問題、詮釋某一事物的意涵），而批判性思考可以是一個協作的過程。沒有它，我們將會遭遇極大的麻煩，因為無論是在課內或課外，當我們在解決複雜的問題時必會遇到困難。在當今的社會中，我們每天都會遭受各種資訊與問題的轟炸。我們需要批判性思考來幫助我們處理資訊並解決這些問題。
If you would like to know the skills involved in critical thinking and listen to a podcast on the topic, leave “What are critical thinking skills?” in the comments. I will post another article on the topic next week if there's enough interest.
若同學想更深入了解批判性思考到底涵蓋了哪些技能，並收聽相關的podcast，歡迎在留言區回覆「What are critical thinking skills?」。若有相當數量的人感興趣，我將於下星期分享第二篇文章～
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參考文獻：
Facione, P. A. (2011). Critical thinking: What it is and why it counts. Insight assessment, 2007(1), 1-23.
McPeck, J. E. (2016). Critical thinking and education. Routledge.
圖片出處：Me thinking about dinner.
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critical point意思 在 [微積] 找critical point - 看板Math - 批踢踢實業坊 的推薦與評價
題目:f(x)= sqrt(x^2-4),求f(x)的critical point
書上定義critical point是導數為0或導數不存在的點
首先我分析這函數的定義域,得到Dom(f)=R\(-2,2)
x
顯然對x < -2 及 x > 2 ,f(x)均可導,導數為 f'(x)=------------
sqrt(x^2-4)
此時導數均存在
接著再看端點x=-2與x=2
f(x) - f(-2) sqrt(x^2-4) - 0
考慮左導數 f' (-2) = lim -------------- = lim ----------------
- x-> -2 x - (-2) x -> -2 x + 2
sqrt(x-2)
= lim ----------- = -infty
x -> -2 sqrt(x+2)
類似地,右導數 f' (2) = +infty
+
因此f在x=-2,2 均不可導,所以f的critical point有-2,2
不過書上給的答案是"沒有critical point",這讓我很疑惑,麻煩大家幫忙,謝謝
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