國內針對數學學習障礙學童（MLD）的教學介入之素材多偏重數學學科內容，本研究則聚焦在計算核心能力，整合「數感」、「數學事實提取」和「分解與重組」等三項能力之計算核心課程作為教學素材，據以對應MLD學童的認知核心能力缺陷，亦結合國內外實徵證據支持有效的教學方法與原則，實施教學介入成效與相關議題之研究。另考量小樣本研究若僅採取傳統統計考驗，有可能因違反統計假設而造成偏誤，故本研究利用自助法和線性混合效果模式等統計技術和傳統的重覆量數變異數分析一起分析，期應用三種統計的分析，解決小樣本研究的問題。本研究分兩階段探討本課程之成效，先用前驅研究試行本課程並探討其成效之趨勢，經過前驅研究調整課程後，以準實驗研究繼續探討三項研究問題，(1) 計算核心課程對MLD高危險群學童之成效，（2）本課程作為鑑定MLD之教學反應（RTI）之可行性，（3）自助法和線性混合效果模式，相較於重覆量數變異數分析，在小樣本重覆量數研究之優勢。
本研究之準實驗研究樣本篩選自北區一所國小全體一年級合計217位學童參與本研究，經過兩學期之數學能力表現篩選，符合MLD高危險群之實驗組學童共計10位，接受總時數400分鐘之計算核心課程。經智力配對且數學核心能力表現等資料控制選出對照學童計11位，該組學童未接受教學介入。兩組在前測和後測均實施「看數」、「數學事實提取」、「進階數學事實提取」和「分解與重組」等四項計算核心能力測驗。
本研究發現如下：（一）計算核心課程對MLD高危險群學童具備教學介入成效；（二）MLD高危險群學童在教學介入後，初步發現「成長速率無反應」和「最終表現水準無反應」雙低個案，綜合評估可肯定本課程在MLD鑑定的RTI鑑定實施有其可行性；（三）應用自助法和線性混合效果模式之統計技術進行資料分析，對小樣本教學介入研究有助益。
基於上述研究結果，本研究對於MLD之未來研究與補救教學之實務提出相關看法及建議。

The materials of intervention for students with mathematical learning disabilities (MLD) have been placed particular emphasis on curriculum content for years in Taiwan. However, the arithmetic core competences, including abilities of “number sense”, “math fact retrieval”, and “decomposition and regrouping” were neglected, which could correspond to the core deficits in students with MLD. Therefore, the study aimed to investigate the effect of the intverention based on the the arithmetic core competences. However, the small-sample study might confront the problem of violating statistical assumptions, but small-sample is common in the intervention of MLD. Therefore, the statistical methods of “bootstrap” and “linear mixed effect model” are applied to deal with the assumption-violating issues of the small-size. Additionally, after the intervention is approved as effective in the above purposes, the feasibility of this intervention as a pre-referral stage of MLD identification when using dual discrepancy criteria of response to intervention (RTI).
The second-grade students from one primary school in the northern Taiwan participated in the study. The students were screened by the measurement in two semesters. Those met the high-risk criteria of MLD and had parents’ consent were recruited in the experimental group. Ten students participated in the intervention and 11 high-risk MLD students without having parents’ consent were in the control group. They were compatible with the intelligent quotient and screen test of arithemetic competence. Both group were admininstrated pretest and posttest, including “subtizing”, “math fact retrieval”, “advanced math fact retrieval”, and “decomposition and regrouping.”
The main findings of this study were concluded as follows:
1. The arithmetic core competence intervention was approved to significantly improve the arithemetic competence of students with high-risk MLD by comprehensive analysis of three statistical methods.
2. The students with non-responder both of growth and final status could be identified after the intervention. As a result, this intervention program seemed to be feasible as a pre-referral stage of MLD identification.
3. The small-sample study would get benefit from the statistical methods of “bootstrap” and “linear mixed effect model”.

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