這篇文章的目的是利用離散型年齡結構人口模型（discrete age-structured population models)分別建立國小學生及國小教師的人口模型，並模擬分析各種解決國小師資過剩問 題（即俗稱流浪教師問題）的方法。電腦模擬顯示這幾年新生人數遽減使得結果出現兩 難：如要控制生師比（student-teacher ratio，代表教育經費支出）在合理範圍內，則這幾 年無法聘新教師，師資過剩問題將愈來愈嚴重；如果聘新教師，則師資過剩問題可以稍 解，但生師比將會降到不合理的低點。六種方法中，逐年降低師培生人數再加上每年新聘 略高於師培生人數的新教師人數是最佳策略。日後面對少子化的衝撃，年齡結構模型可以 用來預測問題的發生，如人口數目陡降將在數年後讓大學過剩問題惡化，用此模型可以及 早發現問題，早日因應；此模型也可以在電腦上模擬各種策略，快速預見後果並從中找出 最佳策略。

In this paper, two discrete age-structured population models of the numbers of elementary school students and teachers are established, and overpopulation of qualified teachers of elementary schools are analyzed with these models. In recent years, the steep decline of the newborn population causes the dilemma: keeping the student-teacher ratio above the reasonable level or employing more teachers to soothe the overpopulation of the unemployed teachers. We find that reducing the number of newly qualified teachers year by year then employing a little more teachers than newly qualified ones is the best policy among six strategies. Facing the strike of birth rate decline in recent years, there are two benefits to use age-structured models. First, some problems can be foreseen before they cause serious results. For example, overpopulation of college teachers will worsen in the near future. Age-structured models can be used to acquire useful quantities. Secondly, instead of executing the strategies without considering their results, we may rapidly simulate the possible strategies for the problems and choose the best one among them.