The decision to make a drawing, we

The decision to make a drawing, we think, depends primarily on the assessment that doing so will make the solution easier to find. The perceived benefits might be that a drawing mitigates working memory, presents a concrete model on which to act, eases the search for related information, or makes problem characteristics more explicit. Those benefits do not apply (or occur) to young children trying to solve simple word problems. For fifth graders, the benefits of making drawings of the kind of problems we presented were much more apparent. How these benefits are perceived, however, depends on the problem. A drawing of a quantified three-term series problem, for instance, relieves working memory and visualizes the unknown relationship that needs to be quantified. The benefit of a drawing of an (a-1).b problem is that it serves to make explicit that the number of intervals between adjacent objects is one less than the number of objects. In the case of fifth graders, the utility of a drawing also is more readily perceived because many of the concepts in complex word problems have been taught with the help of drawings (e.g., area, volume, and fractions). This cues the making of a drawing in the solution process, especially when nonroutine problems are concerned. In all those cases, however, the decision to make a drawing depends on the benefits perceived by the pupil. We sometimes observed that pupils decided not to make a drawing because they had immediate access to a solution procedure, even though this procedure was incorrect (and could be corrected when a drawing was made). This situation often occurred when pupils were confronted with an (a-1).b problem. The belief in the correctness of the chosen solution procedure sometimes was so strong that, when asked to make a drawing of the situation, the drawing was adapted to fit the solution procedure.

結果 (繁體中文) 1:

使繪圖的決定，我們認為，主要取決於評估，認為這樣做會使得解決方案更容易找到。
感知的好處可能是繪圖減輕工作記憶，禮物上採取行動的具體模式，簡化了相關信息的搜索，或者使問題的特徵更加明確。
這些好處不適用（或發生）幼兒試圖解決簡單題。對於五年級學生，使那種我們提出問題的圖紙的好處是更明顯。
這些好處是如何看待，但是，取決於問題。
量化三項系列問題的圖紙，例如，緩解工作記憶和可視化的關係不明，需要加以量化。
的（A-1）.B問題的圖的好處是，它用於使明確的相鄰對象之間的間隔的數量是一個小於對象的數量。
在第五年級學生的情況下，一個圖還的效用更容易察覺，因為許多在複雜字的問題的概念被教導與附圖（例如，面積，體積，和分數）的幫助。
在求解過程繪製的該線索的製作，尤其是在非常規問題的關注。
在所有這些情況下，然而，使繪圖的決定取決於由學生感知的好處。
我們有時會發現，學生決定不做出圖紙，因為他們不得不解決程序的即時訪問，即使這個過程是不正確的（和圖紙是何時可修正）。
當學生用的（A-1）.B問題面臨這種情況常發生。
在選擇的解決方案程序的正確性的想法有時是如此強烈，當要求做的情況繪製，繪圖被調整以適應解決方案的過程。

結果 (繁體中文) 3:

我們認為，作圖的决定主要取決於這樣做會使解決方案更容易找到的評估。
感知到的好處可能是，繪圖可以減輕工作記憶，提供一個具體的行動模型，簡化對相關資訊的蒐索，或者使問題特徵更加明確。
這些好處不適用於（或發生在）試圖解决簡單單詞問題的幼兒。對於五年級的學生來說，畫出我們提出的那種問題的圖畫的好處要明顯得多。
然而，如何看待這些好處取決於這個問題。
例如，繪製一個量化的三項序列問題，可以釋放工作記憶，並視覺化需要量化的未知關係。
繪製（a-1.b）問題圖的好處是，它可以明確表示相鄰對象之間的間隔數比對象數少一個。
對於五年級的學生來說，繪畫的實用性也更容易被感知，因為複雜單詞問題中的許多概念都是通過繪畫（例如面積、體積和分數）來教授的。
這提示在解决過程中繪製圖形，特別是在涉及非常規問題時。
然而，在所有這些情况下，作畫的决定取決於學生所感受到的好處。
我們有時觀察到，學生們决定不作畫，因為他們可以立即使用解決方案程式，即使這個程式不正確（作畫時可以糾正）。
這種情況經常發生在學生遇到a-1.b問題時。
有時人們對所選擇的解決方案程式的正確性的信念是如此强烈，以至於當要求繪製一張情况圖時，該圖被調整為適合解決方案程式。