講述式的數學教學活動與因疫情緊急的遠距教學的實施，對學生的學習動機及學習成效帶來許多限制。運用遊戲化學習輔助數學教學可以引起學習者的學習動機且降低學習焦慮，提高學習者對於數學學習的投入程度，達到心流。而導入多重表徵鷹架結合遊戲化，可望幫助學習者進行更高層次的思考以及問題解決能力，並降低學習焦慮，進而提高學習成效。
本研究探討三種教學活動(講述式教學活動、心智工具搭配鷹架教學活動與心智工具搭配鷹架遊戲化教學活動)對學生數學學習的影響。本研究運用所開發的線上遊戲「幾何建築師」結合線上心智工具與多表徵鷹架進行遊戲化教學，在教學活動中提供一故事情境，循序漸進地引導學生完成學習活動。心智工具中提供學習者多重表徵鷹架，再透過遊戲化的機制(例如:即時檢核積分、積分排行榜)來協助學生對數學立體圖形展開圖的概念有更多的瞭解，且加深其所學知識之印象。本研究之研究對象為50位台灣北部某高職學生，以不等組前後測設計探討三種教學活動下學習者的學習成效、學習動機、心流狀態、活動焦慮以及活動情緒。研究結果顯示，在學習成效上，心智工具搭配鷹架教學活動組學生的學習成效顯著的退步。在學習動機方面，心智工具搭配鷹架遊戲化教學活動組在實驗前後的學習動機有顯著上升，而講述式教學活動組的學習動機則是顯著下降。三組組間比較發現心智工具搭配鷹架教學活動組與心智工具搭配鷹架遊戲化教學活動組的學習動機顯著高於講述式教學活動組。心智工具搭配鷹架教學活動與心智工具搭配鷹架遊戲化教學活動兩組的心流狀態與其子維度及正向情緒方面皆高於中位數，活動焦慮接近中位數，而負面情緒方面則低於中位數。
另外，本研究也初步分析學習成效、心流狀態、學習動機、焦慮與活動情緒各維度間彼此的關聯，並提出相關的研究與教學實務的建議。

Due to the outbreak ofan epidemic, the lecture-based learning and distance learning of mathematics caused many restrictions on students' learning motivationand performance. Thegamification formathematics teaching can motivatestudents, reduce theiranxiety, increasetheirengagementin mathematics learning, and finally achieveflow. The learning activities, that combined multi-representational scaffold-based gamification, is expected to help studentsengage inhigher-level thinking and problem-solving skills, and reduce theirlearning anxiety, thereby improvinglearning effectiveness.
The aim of this study was to investigate the impact of three learning activities(lecture-based teaching activity, mind tool with scaffolding teaching activity, and mind tool with scaffold-basedgamification teaching activity) onmathematics learning.In the study, wedeveloped an online game "Geometric Architect"and integrated an online mind tooland multi-representational scaffold-basedgamification teaching.We provideda story situation and gradually guidedstudents to complete the learning activities.The mind tool with multi-representationalscaffold-based gamification mechanism (such as real-time ratingandranking) helped students to understandthethreedimensionsof drawingdiagrams.The participants of this study were fiftyvocationalhigh schoolstudentsfromnorthern Taiwan.A pre-test and post-test research design were used to explore the students’learning effectiveness, learning motivation, flow state,activity anxiety, and activity emotions under the three teaching activities.The results showed that the learning effectiveness of students in the group of mind tool with scaffolding has significantly degraded.In terms of learning motivation, the students in thegroup of mind tool with scaffold–basedgamification teachingsignificantly improved their learning motivation after the experiment. On the other hand, the students in the lecture-based group significantlydecreased their learning motivation.The comparisonbetweenthe three groupsrevealed that the learning motivations of themind tool with scaffolding group and mind tool with scaffold–basedgamificationgroupwere significantly higher than that of the lecture-based group.The flow state, sub-dimensions, and positive emotions of students in themind tool with scaffolding group and mind tool with scaffold–basedgamificationgroup are higher than the median.Their activity anxietiesare close to the median, and their negative emotions are lower than the median.
Furthermore, thisstudy also preliminarily analyzed the correlation among learning effectiveness, flow state, learning motivation, activity anxiety, and activity emotion.According to the results, we providedsome suggestions and implications for future research.

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