在這裡使用 IR 的一個題目,來討論一個 CR 的觀念 - 樣本客觀:
建議先花 2 mins 做完題目: http://goo.gl/FkDCwP
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In an experiment, researchers posed simple questions in geometry to children from varied backgrounds. One group consisted of 7-to-13-year-old children of the Mundurucu, an isolated indigenous group in the Amazon basin. The Mundurucu children, who had no formal training in geometry, answered the questions just as quickly and accurately as did French chidlren of the same ages who did have formal training in geometry. In contrast, 5-year-old North American children had much more trouble answering the questions. The researchers concluded that some basic geometric knowledge is innate, but this innate knowledge typically develops only after age 5.
In the table, select the statement that would, if true, most strengthen the researchers' conclusion and most weaken it, respectively. Make only two selections, one in each column.
(A) North American children 7 to 13 years old had much more trouble answering the questions than did the Mundurucu of the same ages
(B) None of the 5-year-old North American children had ever studied any geometry.
(C) Mundurucu children who were 5 years old had just as much trouble answering the questions as did the 5-year-old North American children.
(D) The researchers posed the same questions to 5-year-old French and Mundurucu children as they posed to the 7-to-13-year-old children.
(E) Most of the children studied answered one or more of the questions incorrectly.
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題目大意: 研究人員發現,在 Amazon 的一個原住民部落 Munduruc’u,7 - 13 歲的小孩沒受過幾何的正式訓練,回答問題和法國同年紀的小孩 (受過正式的幾何訓練) 一樣快。相反的, 5 歲的北美小孩無法很順利的回答這些問題。研究專家得出結論,認為基本的幾何知識是天生的,但這樣天生的知識通常在五歲之後才會開始發展。
而 two - part analysis 要在選項中分別回答兩個問題 (簡介在此: http://ndxica.pixnet.net/blog/post/40130233),一個問題選一個答案 (兩個答案可重複選同一個選項)。在此題要回答 "Most Strength" 和 "Most Weaken" (所以必然是不可能選擇同一個答案)。
在此題,題目的論點有著明顯的一個落差 - 樣本不一致。5 歲的北美小孩對幾何問題有障礙 (受過正式幾何訓練) + 7 - 13 歲的 Munduruc’u 小孩可順利回答幾何問題 (沒受過正式幾何訓練) -> 推得幾何知識是天生,且在 5 歲之後開始發展。
看似很 ok,但其實樣本並不一致 - 樣本為北美小孩和 Munduruc’u 小孩,雖然題目已經交代了樣本的教育程度,但不同的樣本可能還有其他客觀條件有所不同。
答案 (A) North American children 7 to 13 years old had much more trouble answering the questions than did the Mundurucu of the same ages
我們把此答案放入同一個樣本 (北美小孩) 來比較: 5 歲的北美小孩回答幾何問題有障礙 (題目資訊),而 7 - 13 歲的北美小孩回答幾何問題比起 7 - 13 歲 Munduruc’u 小孩來說有更多的障礙 (答案資訊)。證明了北美小孩並沒有如研究人員所說的,隨著年紀增長 (超過 5歲),而發展出天生的幾何知識。所以 Weaken 了此題目。
答案 (C) Mundurucu children who were 5 years old had just as much trouble answering the questions as did the 5-year-old North American children.
我們把此答案放入同一個樣本 (Amazon 原住民) 來比較: 5 歲的 Munduruc’u 小孩回答問題比起 5 歲北美小孩來說,回答幾何問題有更多的障礙 (答案資訊)。而 7 - 13 Munduruc’u 小孩回答幾何問題沒有太多障礙 (題目資訊)。證明了Munduruc’u 小孩如研究人員所說的,隨著年紀增長 (超過 13歲),而發展出天生的幾何知識。所以 Strengthen了此題目。
示意圖如下:
題目:
答案 (A):
答案 (C):
當然,其他答案可能多少會影響題目,但並沒有此兩個答案直接討論樣本一致性來的大,在此為了強調重點,以討論此兩個正確答案為主。
Two-Part Analysis 的題目類型,必須同時選出兩個答案,而此題目出得相當漂亮,正好可以用樣本一致性同時討論一個題目的加分 (Strengthen) 和扣分 (Weaken),在此分享給各位。
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