本研究針對工程類科系共同必修工程數學科目以認知心理學角度設計出一套教學新構思，雙層式教學，並配合合作學習及開放式學習等配套措施實際進行教學，最後再以訪談方式進行質的研究。經過三年的教學及訪查，同學們對工程數學 O.D.E.（常微分方程）, Laplace transform, Fourier series, Matrix 等章節內容的學習成效反應為：學習較為完整，且較有效率；比較有整體性概念，易進入狀況，循序漸進，使細部知識健全；能夠延伸至工程問題，較能了解物理意義，且具連貫性；直接切入重點，不浪費時間；先建立印象，概念易理解，再聽一遍時較易掌握重點，對於深層函義之數學理論於學習時較不吃力；以廣角度的方式進行了解學習，有助於擴充思維角度；有目標的學習，自己較易掌握學習進度；有系統的唸書，不會死讀書；比較懂得抓住重點；對自己的邏輯思考較具幫助；由於開放式學習過程中經常互相討論使學習更能加深印像；考試亦可學習，而且會以學懂為目標，並非只以想拿高分或只求及格為目的。本研究除文中所提之限制外，經調查訪談後發現於教學過程中小組討論時，某些同學因對工程數學實在沒有興趣而學習成就低且造成同學間互動不佳的情形發生；某些少部分成績較強的同學由於比較自私所以討論時不太願意教導有疑問的同學；一般同學大多不認為考試次數越多學習效果會越佳，即使老師會當學生，只要被當人數多的話當下大家也不會怕；適當的考試次數大約是一學期4~7次；同組的同學若居住的距離相去太遠則非常影響相互間的互動頻率，間接地也會影響評鑑的結果。綜合觀之，本研究值得未來再加入老師評量方式及學生學習策略等其他因子一並研究，近一步配合交叉統計分析與回歸分析，並推廣到其他同質型科目繼續做全方位研究討論。

An instruction design for engineering mathematics course from cognitive psychology point was employed and the effect was investigated in this study. The instruction, double-layer teaching, equipped with open learning as well as cooperate learning was implemented practically and quality results were analyzed by interview. After three years’ instruction and investigation, the reactions of students learning engineering mathematics in topics of O.D.E., Laplace, Fourier series, and Matrix are completion of learning and more effective, easy to get whole picture and to involve more detail gradually, able to extend to practical engineering problems to know the physical meaning without losing continuity of the concepts, strait forward touching the key point wasting no time, general concepts been erected after first time to teach then easier to learn other theorem through deeply thinking in the second times, helpful to extend thinking range wide while learning, making learning target obviously and easy to hold the learning schedule, systematically learning in stead of awkward reading, good for germane thinking, improving ability of logical thinking, impressing learner with what have learned through open-learning discussing, and learning attitude varying from just pass or getting higher score to real understand what learnt. Except for the restrictions of this research, after the investigation we found some negative points and they are some students still getting low achievement and the interaction of the students being poor for lack of learning interesting, small part of high achievement students reluctant to teach others who has question, the more the times of test the better the consequences of learning being unacceptable for most of the students, and the proper times of test around 4 to 7 in a semester. In addition to the above, even though the teacher requests students seriously, they are unawareness if most of students are not pass. The last point we found that some students didn’t want to discuss each other just because the distance they lived is too far to talk. In short, some further studies are worth to do such as the ways of teacher assessment, learning strategy, and other factors. This study can also implement to other courses in a wide variety ways by using statistic and regression applications.