| 研究 | 科技部專題計畫 | Research | MOST Project |
個人近五年專注於探究數學論證學習與教學、數學建模教學與評量、以及數學教師的統計知識與信念等三大主軸的研究。
在數學論證學習方面，形成幾何證明閱讀理解的內涵，以及理論化幾何證明理解的發展模式；並有國外學者來函表明作為tutorial
system理論參考。接著，延伸探討幾何證明閱讀策略對其閱讀理解的影響之結構模式，研究發現後設認知閱讀策略經由認知閱讀策略對幾何證明的閱讀理解產生影響，幾何證明閱讀理解表現佳的學生比差的學生自覺採用較多的規劃和監控的後設認知閱讀策略與理解深入意義的認知閱讀策略，研究成果已被接受發表予Educational
Studies in Mathematics，此期刊為屬於SSCI的三本數學教育期刊之一。就論證教學的部分，也以類比策略設計臆測活動，探討個案學生形成與檢驗猜想的認知行為與主動性之間的關係，並奠定此策略作為數學臆測教學設計的實徵基礎。進一步地，提出擬證明題的任務作為促進學生理解證明的策略，並論述此策略潛在的功能。
在數學建模教學方面，除了編製機率學習態度問卷外，也基於對數學建模的研究經驗，擔任建國高中向國科會科教處提出的高瞻計畫：「以建模與認知師徒制開發新興科技融入高中課程之研究」之諮詢者；受邀擔任宜蘭縣97學年度上學期數學領域精進教師課堂教學能力計畫－教學疑難工作坊研習的講師，推廣數學建模的教學設計；並至不同的高中講述關於數學建模的意義、評量方式與教學活動類型。
在數學教師統計知識與信念方面，部分研究成果有：
(1)分析數學教師在比較兩資料分配情境中，造反例的策略主要為簡化類別、固定頻率、調整類別，數學造反例不同之處在於未有明顯的命題；
(2)
擬定信賴區間的子概念測驗目標：「辨識信賴區間圖形表徵內的轉換」、「知道抽樣誤差較小不表示比較可信」、「能辨識樣本數與抽樣誤差、信賴區間、樣本比率、信心水準、標準差之間的關聯性」、「計算95%信心水準之信賴區間、樣本數、樣本比率或抽樣誤差」、「推論樣本比例」、「推論母體比例」、「以抽樣誤差計算信賴區間長度」、「解讀95%信心水準」和「誤以樣本分配推論信賴區間」；
(3)
焦點團體的數學老師認為統計教學時所遇到的困難或困境有：知識與經驗不足、對輔助工具的使用不熟悉或不易取得輔助教具、不易協調理論與經驗的觀點、考試不用計算機的限制、統計公式的定義不一致。
上述結果，有利於用來設計發展中學數學教師統計教學知能的專業成長活動。
科技部專題計畫
總計畫：設計為本的就是要學好數學之研究暨子計畫一：創新的課前奠基與課中建築活動模組之發展性研究
(2016/07~2018/06)
計畫主持人：楊凱琳教授
整合閱讀與建模的高中學生統計素養培育活動探討
(提升臺灣K-12學生數學素養之研究－子計畫六，2015/08~2018/07)
計畫主持人：楊凱琳教授
中學生閱讀幾何圖文的學習研究-閱讀理解與策略使用
(建構利於中學生閱讀理解與策略使用的幾何圖文之設計原則與評鑑指標－子計畫二，2013/08~2016/07)
計畫主持人：楊凱琳副教授
基於抽象化分析教科書並探討數學教師對教科書的觀點與評析：以幾何為內容
(2012/08~2015/07)
計畫主持人：楊凱琳副教授
基於抽象化概念發展分析數學教材的架構
(2011/08~2012/07)
計畫主持人：楊凱琳副教授
探討中學數學教師的統計教學知能
(統計教育研究:人才培育與資訊整合－子計畫五，2009/08~2012/07)
計畫主持人：楊凱琳副教授
發展數學臆測活動的支撐策略與學習評量
(數學臆測活動的設計、教學與評量－子計畫六，2007/08~2010/07)
計畫主持人：楊凱琳副教授
數學建模的評量與教學之研究
(2006/08~2009/07)
計畫主持人：楊凱琳副教授
Research
Kai-Lin Yang is the Professor in the Department of Mathematics, National Taiwan Normal University. She has served as a Mathematics Teacher Educator for 9 years. Her research interests include reading comprehension of geometry proof and reading strategies for comprehending geometry proof, the assessments of statistical concepts and mathematical modeling, teachers’ conceptions of the differences between statistics and mathematics, as well as mathematics textbook analysis based on abstraction.
She has published numerous papers in internationally prestigious journals, such as Educational Studies in Mathematics, For the Learning of Mathematics, International Journal of Science and Mathematics education, Mathematical Education Research Journal, and ZDM.
Dr. Yang’s current research deals with students’ reading comprehension of geometric construction, the interaction between reading comprehension and problem solving, and teachers’ professional development through the integration of reading comprehension and mathematics learning. She also devotes herself to planning and implementing teacher education courses for pre-service mathematics teachers and professional programs for in-service mathematics teachers.
MOST Project
Developmental research on innovative modules of
just-do-math
activities and construction activities
which is a project led by Kai-Lin Yang, from
July 2016
to June 2018.
Exploring Educational Approaches to Advancing High
School
Students’ Statistical Literacy from the Integration of Reading
Comprehension and Modeling Processes
which is a project led by Kai-Lin Yang and as a
sub-project led by Tai-Yi Tso, from
August 2015 to July 2018.
Study on Junior
High School Students’
Reading to Learn Geometry: Reading Comprehension and Strategy Use
which is a project led by Kai-Lin Yang and as a sub-project of
“Developing design principles and evaluation rubrics of geometry text to
facilitate junior high school students' reading comprehension and
strategy use” led by Fou-Lai Lin, from August 2013 to July 2016.
Study on textbook analysis and secondary mathematics teachers’
conceptions and evaluations of
textbooks based on the lens of abstraction: Geometry as content
which is a project led by Kai-Lin Yang, from August 2012 to July 2015.
Developing a framework for analysing
mathematical didactical materials based on the conception of abstraction
which is a project led by Kai-Lin Yang, from August 2011 to
August 2012.
The
application,
discovery and cultivation of statistics for mathematics teachers
which is a project led by Kai-Lin Yang and as a sub-project of “Research
on statistical education: professional cultivation and information
integration” led by Fou-Lai Lin, from August 2009 to July 2012.
The development of scaffolding strategies and
learning assessment for mathematics conjecturing activities
which is a
project led by Kai-Lin Yang and as a sub-project of “Design, teaching
and assessment of conjecturing activities in Mathematic” led by Fou-Lai
Lin, from August 2007 to July 2010.
Research on the assessment and instruction of mathematical modeling which is a project led by Kai-Lin Yang, from August 2006 to July 2009.