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國中教甄|數學數學109 年第 81 題單選題

David Tall conducted a study to investigate 16 year old students’ concept image and concept definition. The students were asked to draw the tangent to the following graph at the origin. Some students did not cope with the task and asserted that “...because the tangent should touch the line at one specific point but this tangent would touch it constantly." Which of the following best describes the cause of the students’ answer?

題目圖片
AAlmost always the concept definition will be evoked by students when solving problems
BAlmost always the concept image will be evoked by students when solving problems正確答案
CThe concept definition includes a form of words used to specify the concept, however, the students were asked to draw a tangent in this case
DThe concept image includes a form ofwords used to specify the concept, however, the students were asked to draw a tangent in this case
答案與詳解
B
正確答案
學生以切線只能碰一點的既有切線概念意象來判斷,無法接受切線與曲線在左側整段重合,因此最佳解釋是解題時主要喚起 concept image。

逐選項解析

AAlmost always the concept definition will be evoked by students when solving problems✕ 易錯陷阱
此選項與本題現象相反。學生並非依切線的正式定義進行推理,而是被過去形成的切線印象限制,因此不是幾乎總是喚起 concept definition。
BAlmost always the concept image will be evoked by students when solving problems✓ 正確
學生認為切線只能在特定點接觸曲線,這是先前經驗形成的概念意象。當原點左側的切線與曲線重合時,便與原有切線意象衝突,導致無法接受,符合 concept image 在解題時常被喚起的觀點。
CThe concept definition includes a form of words used to specify the concept, however, the students were asked to draw a tangent in this case✕ 錯誤
DThe concept image includes a form ofwords used to specify the concept, however, the students were asked to draw a tangent in this case✕ 錯誤

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