放聲思考法融入形成性評量對提升國中生數學概念理解能力之探究

Abstract

本研究旨在探討數學教師改變教學評量模式，以放聲思考法融入形成性評量後，是否對於提升國中學生數學概念理解能力造成影響。其研究目的有三：探討放聲思考法融入形成性評量之評量模式的實施歷程與調整方向；探討放聲思考法融入形成性評量對學生數學概念理解能力之影響；探討放聲思考法融入形成性評量對教師專業成長之影響。 本研究採取行動研究法，以研究者所任教國中的七年級一個班級，共32位學生為研究對象，並且將學生分為高、中、低三種成就組別進行分組分流的探究。配合試探期與實踐期的課程教學進度，形成性評量的試題範圍定錨於「一元一次方程式」與「二元一次聯立方程式」兩個單元。行動規劃有課堂概念教學、課前形成性評量、書面解題篩選、兩階段學生解題回溯放聲思考、評量回饋討論等歷程，用以擴展學生對於新概念學習的理解層面，進而提升對數學概念的理解能力。 將研究過程中所蒐集之質性與量化資料進行彙整與分析後發現：一、在評量次數、題數的精簡與學生的分組分流後，方案實施可以不影響教學，不增加進度壓力；二、不同學習成就學生對數學概念的理解有層面上的落差，透過口述解題與評量回饋能幫助學生提升對於概念的「能說明」、「能應用」與「自我認識」，進而發展「能詮釋」、「有觀點」與「有同理心」的能力，並且提升學習成效；三、行動方案可以幫助教師提升學生學習問題診斷能力，學習評量運用能力與抽象概念的教學能力，並且促使教師在教學態度上產生開放、公平、關懷與包容的正向轉變。 根據研究發現提出的建議有：一、教師以放聲思考法融入形成性評量前，需引領學生進行放聲思考練習，並且營造班級的安全學習氣氛。因應學生學習程度與學習現況，適性地從不同理解層面來培養學生對數學概念的理解能力；二、未來研究者可在不同學科或不同學習階段進行評量與概念理解能力的相關探究。This study aimed at enhancing students’ understanding of mathematical concepts through using Thinking Aloud Method to conduct formative assessment instead of using traditional ways in junior high school. By conducting mixed-methods research, the study addressed three research objectives: (1) to explore how courses of Thinking Aloud Method with formative assessment are conducted and adjusted (2) to explore how Thinking Aloud Method with formative assessment influences students’ understanding of mathematical concepts and (3) to explore how Thinking Aloud Method with formative assessment influences Teacher Professional Development. The study is an action research of an actual classroom in the junior high school that the teacher-researcher is at. A total of 32 seventh graders were invited to participate in this study and they were divided into three groups by different proficiency levels which are high, intermediate and low. There are two phases of Thinking Aloud Method with formative assessment, which are Development and Enactment. The study focused on One-variable Linear Equation and Two-Dimensional Linear Systems of Equations. The teaching process contains concepts teaching, following by formative assessment, choice of participants, two-phase orally problem solution and feedback discussion. Through these steps, the facets of students’ understanding were broaden and at the same time students’ abilities of understanding concepts were enhanced. The data of the study were collected qualitatively and quantitatively. The findings of the study are discussed in three sections. Firstly, after decreasing the number of math problems and assessment frequency as well as grouping students, Thinking Aloud Method with formative assessment didn’t affect the original teaching method and process. Secondly, students in different levels behaved differently in facets of understanding mathematical concepts. Through orally math problem solution, students enhanced their abilities of Explanation, Application and Self-Knowledge. Meanwhile, feedback discussion helped students improve their Interpretation, Perspective and Empathy abilities. Lastly, the study enhanced teachers’ professional abilities of diagnosing students’ learning problems, applying assessments, and teaching abstract concepts. Additionally, the study positively changed teachers’ teaching attitudes to a more open, fair, caring and concerning status. Two suggestions for teachers and future research were provided. For teachers, they should create a safe environment for students, guide students to practice thinking aloud before conducting Thinking Aloud Method and cultivate students’ understanding of mathematical concepts from different facets based on students’ current learning stage and proficiency. For researchers, they can use Thinking Aloud Method with formative assessment in different subjects and different learning stages in the near future.