分析學生如何利用二維拋體軌跡圖解題
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2015
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本研究以國立臺灣師範大學103學年度入學的大一新生，且修習普通物理實驗的理學院學生作為主要研究對象，共計257人，並配合物理系77名大二學生作對照，主要在探討學生在二維拋體拋體運動測驗，題目提供5條拋體軌跡的數據圖，讓學生運用數據圖中的資訊進行解題。題型由兩個小題組成，其中第1小題是探究學生高度與飛行時間的概念，幾乎不太需要計算。第2小題以計算題的方式呈現，探討學生如何利用圖中資訊，求得5條軌跡的初始速率大小關係。上述試測的結果並與2014年11月9日物理奧林匹亞初選考試的結果進行交叉比對答案類型。此次初選考試共2435名學生參加，其第1小題答對率接近90%，第二小題答對率約為1/3。
根據研究結果發現，學生的解題過程類型可分為七個類型，其中最常使用的類型為「使用運動學概念並直接代入數值計算」及「使用兩兩比較法」解題，各有五分之一的受試者。歸納其錯誤原因為（一）有數據計算過程的解題過程：「另有概念」、「列出錯誤的速度關係式」、「無法由數據圖資料判讀三角函數」、「忽略x、y軸單位長度的比值」及「計算錯誤」。（二）使用兩兩比較法的解題過程：「相同水平射程變因的軌跡線判斷錯誤」、「無法列出足夠的關係式」及「粗心而列錯關係式」。
受試者主要的錯誤為：由二維拋體數據圖欲解答物體的發射初速度時，對於相同水平射程的軌跡，疏忽初始發射仰角的因素，造成錯誤；因此我們建議於教學時加以檢視水平射程和仰角的關聯。雖然學生知道45o角拋射時，水平射程最遠，但是反過來就不是很清楚，也就是當水平射程相同、仰角為45o時，初速率為最小的概念。
This work is focused on student learning of two-dimension projectile motion. A data graph with five trajectories mimics the trace of 5 projectiles by varying the initial launch angle, vertical height and horizontal range. However, the vertical scale of the data graph is in unit of 100 m, while the horizontal scale is in unit of 1000 m. The freshman of Department of Mathematics, Physics, Chemistry, Life-science, Earth Sciences, and Industrial Education of National Taiwan Normal University participated the 30-minitue test on their very first class of General Physics Laboratory. A total of 257 freshmen took the exam. Seventy-seven sophomores of Department of Physics were also taken the same exam to serve as a reference for comparison. The main purpose of this study is to examine how students solve problems using the information given in a plot diagram of projectile motion. There are two parts of the test question. The first part is to write down the flight-time ordering of the 5 projectiles, and the second part is to find the magnitude ordering of initial speeds. Roughly, around 84% students got the correct answer for the first part, while 15% students for the second part. It is not necessary to compute the flight time nor the initial speed to get the correct answer, however, we do find the higher correct rate for student using formula for the second part. These results were cross-compared with the results of International Physics Olympiad on 9th of November, 2014. 2435 students participated in the exam, and the correct rate of the first part was 90%, that of the second part was 33%. We find that over 50% students do not know the effect of initial launch angle on the initial speed when two trajectories have the same horizontal range, though most of them know that the horizontal range is maximum for a launch angle of 45°for the same initial speeds. Students were trained to know the initial launch angle of 45° gives a maximum horizontal range, they do not know the projectiles having the same horizontal range is the 45 one possess a minimum initial speed.
This work is focused on student learning of two-dimension projectile motion. A data graph with five trajectories mimics the trace of 5 projectiles by varying the initial launch angle, vertical height and horizontal range. However, the vertical scale of the data graph is in unit of 100 m, while the horizontal scale is in unit of 1000 m. The freshman of Department of Mathematics, Physics, Chemistry, Life-science, Earth Sciences, and Industrial Education of National Taiwan Normal University participated the 30-minitue test on their very first class of General Physics Laboratory. A total of 257 freshmen took the exam. Seventy-seven sophomores of Department of Physics were also taken the same exam to serve as a reference for comparison. The main purpose of this study is to examine how students solve problems using the information given in a plot diagram of projectile motion. There are two parts of the test question. The first part is to write down the flight-time ordering of the 5 projectiles, and the second part is to find the magnitude ordering of initial speeds. Roughly, around 84% students got the correct answer for the first part, while 15% students for the second part. It is not necessary to compute the flight time nor the initial speed to get the correct answer, however, we do find the higher correct rate for student using formula for the second part. These results were cross-compared with the results of International Physics Olympiad on 9th of November, 2014. 2435 students participated in the exam, and the correct rate of the first part was 90%, that of the second part was 33%. We find that over 50% students do not know the effect of initial launch angle on the initial speed when two trajectories have the same horizontal range, though most of them know that the horizontal range is maximum for a launch angle of 45°for the same initial speeds. Students were trained to know the initial launch angle of 45° gives a maximum horizontal range, they do not know the projectiles having the same horizontal range is the 45 one possess a minimum initial speed.
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拋體運動, 初始發射角, 鉛直高度, 水平射程, 物理奧林匹亞, Projectile Motion, Initial Launch Angle, Vertical Height, Horizontal Range, Physics Olympiad