In a secondary school in a southeastern state a large number of overage students who are at least 2 grade levels behind where they should be in academic terms, have struggled with academic performance and have often dropped out of school. Educational researchers have found that the implementation of instructional interventions is important in meeting the learning needs of these students. The purpose of this bounded case study was to determine educators' perspectives of possible intervention strategies to improve the academic performance of overage students in grades 9 and 10 at the school. Constructivism was used as the conceptual framework. The research questions were focused on what teachers, counselors, and administrators viewed as the best possible intervention for improving the academic performance of overage students at the school. Interviews were conducted with 4 classroom teachers, 2 counselors, and 2 administrators who had worked with overage students at the school. Interview data were coded and analyzed for common themes. Participants identified small group instruction as the best possible instructional intervention to support constructivist learning for overage students. Using study findings, a policy white paper was created for local school officials and administrators, which included the recommendation that small group instruction be used for overage students along monitoring student progress by a school leadership team. Implementation of the recommendations may help overage students at the study site improve their critical thinking, problem-solving, and decision making skills which may result in positive social change as they experience academic success and become productive members of the school and larger surrounding community.

在生態學、生物學、和比較文學的研究中，物種個數通常是評估生物多樣性的重要指標，單一群落物種數的估計已有非常豐富的相關研究。較為知名者包括Good (1953)提出未出現物種的機率，作為估計物種數的參考，往後Good的想法被大量延伸，推演出不少新的估計方法，像是Burnham and Overton (1978)的Jackknife估計法，Chao and Lee (1992)利用涵蓋機率的估計。相對而言，兩群落共有物種數的研究較少，現有研究中較為知名的有Chao et al. (2000)的估計式。 本研究延伸Good想法，探討Jackknife估計法在兩群落的應用，以出現一次的共有物種（一階Jackknife估計），推估未出現共有物種機率，並且仿造Burnham and Overton的想法，建立共有物種數的估計值及變異數。本文除了以電腦模擬，也使用實例（包括：金庸武俠小說、台灣野生水鳥、巴拿馬螃蟹和巴洛科羅拉多森林）檢驗本文的Jackknife估計法，利用涵蓋機率角度發現抽出某特定比例樣本時，估計值涵蓋母體共有物種數之機率值達到九成以上，且也與Chao提出的估計值比較。 / The number of species is frequently used to measure the biodiversity of a population in ecology, biology, and comparative literature. There are quite a lot of studies related to estimating the number of species. Among these studies, Good (1953) proposed a famous estimate (Turing’s estimate) for the probability of unseen species. Subsequently, many methods have been proposed for estimating the number of species based on Good’s idea. For example, the Jackknife estimator by Burnham and Overton (1978) and sample coverage probability by Chao and Lee (1992) are two famous estimates for the number of species. In contrast, there are not many studies for the number of shared species in two communities, and Chao et al. (2000) is probably the only one. This article extends Good’s idea and the Jackknife method to estimate the number of shared species in two communities. Similar to Burnham and Overton, we establish the estimate and its estimated variance, based on the number of species appearing exactly once. We also use computer simulation and real data sets (Jin-Yong martial arts novels, Taiwan wild birds, Panama crustacean, and Barro Colorado Island forest) to evaluate the proposed method. We found that the coverage probability for confidence interval covering the true number of shared species is more than 90%. In addition, we compare the proposed method with Chao’s method.