從眼動與手寫角度來探討幾何問題解決時圖形轉換的性別差異

Abstract

數學教學的主要目標就是培養學生擁有解決各種複雜問題的能力(Wilson, Fernandez,& Hadaway, 1993)。數學問題的解題策略有好多種，但學生總是能在意想不到的地方被困惑著，可能受到先備知識、幾何變換、策略規劃等影響，沒有適當的修正輔導，學生很難建立正確的問題解決能力。傳統診斷方式只能透過學生的動作表現、作答狀況來推斷學生的可能問題點，這十分考驗教學經驗、時間成本以及專注度。本研究希望能在不影響學生的生態校度下，能夠有效率地找出學生問題解決的困難點，以便教師能對症下藥。 為瞭解學生在幾何圖形變換(如平移、旋轉、鏡射等性質)時的認知歷程，以及幾何變換對學生造成的認知負荷。從過去認知心理學的研究中發現，分析眼動儀與數位手寫板的指標能有效地觀察學生問題解決的歷程，尤其是專注於閱讀題目時在特定的AOI的表現以及在為了特定書寫目的下的書寫情況。本研究在解題歷程觀察訊息讀取(輸入)的過程，透過分析閱讀題目時的凝視時間(DT)、凝視次數(FC)、掃視路徑(SL)都能顯著反應認知負荷(吳昭容, 2019; 陳學志, 賴惠德, & 邱發忠, 2010; 黎佩芬 & 賴建都, 2011)。在數學解題中會需要大量的手寫來幫助思考與作答，紀錄並分析問題解決時的過程與結果(輸出)資訊，研究發現手寫筆跡中最大壓力(MaxP)、平均壓力(MeanP)、筆尖停頓次數(SPC)、停頓時間比例(RAT)、平均書寫速度(MeanV) 、平均X軸書寫速度(MeanVx) 、平均Y軸書寫速度(MeanVy)與認知負荷有相關(T. Lin, Xie, Chen,& Tang, 2013; G. Luria & Rosenblum, 2010)。 本研究選取110學年度臺灣北部某國中八年級學生，男性39名、女性22名，設計幾何試題讓學生解題，同時以眼動儀紀錄視覺關注的位置以及數位手寫板紀錄手寫作答時的書寫歷程，觀察幾何問題解決的歷程並探討解題表現以及性別造成的影響。為深入了解幾何變換試題的作答狀況，透過數學學習目標分段給分並標注學生手寫書寫的區域，運用二因子混合設計變異數分析及斯皮爾曼等級相關係數，討論解題表現學生以及性別對於不同幾何問題解決策略上的異同與相關性，提供教師在輔導學生問題解決困難時能有所依據，並期望透過本實驗進一步探索問題解決時眼動數據及手寫數據在輸入與輸出間的相關性。The primary goal of teaching mathematics is to foster students’ abilities to solve various complex problems. Several problem solvig strategies could be employed to solve a mathematical problem, however students usually encounter difficuities which beyond our expection. Several factors might lead to unsuccessfully solve the problem. Such as applying incorrect knowledge, unable to perform proper geometric transformation, or insufficiently planning. Without correct scaffolding or intervention, it would be uneasy for students to learn problem-solving skills. Traditionally, teachers diagnose solvers’ difficulties by observing the procedure and answers they write. Such diagnoses are time consuming and hard to help solvers simultaneously. To address the issue, the present study aims to observe solvers cognitive processes and find out indicators that could be used to detect solvers’ levels of cognitive load while solving problems.In this regard, goals of the present study is to explorer the cognitive processes and cognitive loads while solving geometry problems. The mathematical problems adopted in the present study require mental transformation of geometry, such as translations, rotations, or mirrors. Previous studies indicated that employing eye tracking and analyzing hadnwriting can effectively observe students' problem-solving processes, especially when they watch and write on specific AOIs. Such operations could be regarded as the input processes. Several eye movement measures, including the dwell time (DT), fixation count(FC) and saccade length(SL) were used due to thedetect are linked to cognitive load(Wu Zhaorong, 2019; Chen Xuezhi et al., 2010; Li Peifen & Lai Jiandu, 2011). In addition, based on the characteristics of mathematics learning, students need handwriting to help thinking and answering. Therefore, digital handwriting records provided teachers with information of problem solving on the processes and results(output). Regarding handwriting measures, studies suggested that the local handwriting’s maxPressure(MaxP), avgPressure(MeanP), Sensible Pause Count(SPC), Ratio Air Total(RAT), avgVelocity(MeanV), avgXVelocity(MeanVx) and avgYVelocity(MeanVy) are highly correlated with cognitive load (Lin et al., 2013; Luria& Rosenblum, 2010). Participants were recruited from a high school in northern Taiwan at the 110 academic year. A total of 39 males and 22 females were recruited. Participants were asked to solve geometry problems in which translations, rotations, and mirroring were necessary to successfully solve the problesms. Eye movements and handwriting were recorded simultaneously. The study aims to explore the impact of mental transformations and gender on the eye movement, and cognitive load by employing two-way analysis of variance. It is expected that the correlation between the input of eye-tracking data and output of handwriting data during problem-solving can be observed.