本研究先探究數學問題解決及核心能力內涵理論，以工程問題的數學解題能力為核心，從理論面建立此能力指標之構面及要素。其次以專家訪談及諮詢修正指標。並以德懷術方法建構出此能力指標架構，完成具有普遍性原則的指標。接著以鷹架學習理論ZPD 概念，編製引導式回答題及其相關文件，對學生進行半結構式試探性評量及提出答題的看法，來修正與驗證能力指標之可行性。所得結論：1.建立四個層級架構與四項轉銜能力的構面與向度。2.建立工程問題數學解題能力43 項指標。3.「引導式回答題」之比對及作答方式，可評量電子工程問題的數學解題能力的強弱。4.能力指標具有連續且不可分割邏輯及權重值的差異。
This research will first examine the problem-solving theories in mathematics and the core competence theory to establish competence indicators with dimensions and elements. And then, the indicators established based on the theories will be modified after interviews and consultations with experts and the structure will be built upon Delphi Technique to comply with the universal principle. Next, ZPD (the Zone of Proximal Development) theory will be applied to compile a list of leading questions and relative documents. Semi-structural testing evaluations will be proceeded on students and their views on how they answer questions will be collected, so as to modify and verify the feasibility of these competence indicators. The conclusions of this research include: 1. A structure of 4 tiers and 4 dimensions and aspects of transforming and connecting abilities; 2. 43 indicators of applying math problem-solving abilities to engineering problems; 3. an evaluation of the capability of applying math problem-solving abilities to engineering problems through comparing the "leading questions" and the nature of answering questions; 4. the continuous and inseparable logic nature of the competence indicators and the differences between the weight values.