本研究的目標為：在討論的學習環境下，探討國中生進行數樣式關係論證，為自己的觀點或結論說明理由時，表達能力之成長情形。
本研究為敘述性研究，採用質的研究方法。研究對象是以方便抽樣的方式，選取研究者任教的班級中四男二女共六位自願的國一學生。研究時以三人為一組的小組討論方式，進行三次教學訪談，分別要求學生寫下最好的理由、最能說服別人的理由以及最符合數學形式的理由。根據研究文獻與英國ＳＭＰ教材，設計四個論證數樣式規律的問題，將其中兩題讓學生重複作答，用以對照學生是否在表達理由的能力上有成長。紀錄學生的作答結果、學生間互動討論的過程、教師介入的結果以及隨後的再次作答，用詮釋性研究的方法進行分析。
研究結果發現，六位學生作答時說明理由的類型共有兩類：經驗論與敘述關鍵性質。而表達能力的發展，會有五個階段：理解起始資訊、經驗論、描述關鍵性質、批判經驗論證、形式化，而且是一種動態、折返的歷程。研究也觀察到在討論的學習環境中，教師與同儕對於學習有四種影響：提供不同的表達理由類型、演示關係、引發學習者使用文字符號、教師主導學生說明理由的信念。
根據這些結果，本研究對發展國中學生說明理由時的表達能力，提出了三點建議：小組討論有助於表達理由的能力之成長、批判經驗論證有助於學生發展形式化地表達理由的能力、教學上不能強求學生使用形式論證的方式

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