:::

詳目顯示

回上一頁
題名:國小四年級學生數常識反應類型共同性錯誤分析與迷思概念成因之探究
作者:陳霈頡
校院名稱:國立嘉義大學
系所名稱:國民教育研究所
指導教授:楊德清
李茂能
學位類別:博士
出版日期:2009
主題關鍵詞:數常識錯誤類型迷思概念混合模式number senseerror patternmisconceptionmixture SEM
原始連結:連回原系統網址new window
相關次數:
  • 被引用次數被引用次數:期刊(2) 博士論文(0) 專書(0) 專書論文(0)
  • 排除自我引用排除自我引用:2
  • 共同引用共同引用:0
  • 點閱點閱:88
本研究採用調查法蒐集嘉義、雲林與彰化地區國小四年級學生數常識電腦化診斷
測驗之資料,透過混合模式、Rasch模式以及訪談,分析學生在數常識測驗四個建構
(瞭解數與運算的基本意義、數字的分解與合成、運算結果之合理性的判斷、比較數
字相對大小)中答題反應類型的共同性錯誤以及迷思概念。
本研究主要結果摘要如下:
一、相對於「比較數字相對大小」建構,學生在其它三個建構上較無法有效的運用數
常識去解題。
二、學生習慣透過傳統算則,回答「數字的分解與合成」的問題。
三、學生在「具備運算結果之合理性的判斷」上較其它三個建構,習慣運用猜測反應
答題。
四、學生在「瞭解數與運算的基本意義」與「數字的分解與合成」建構上的迷思概念
較其它二個建構嚴重。
五、學生在各建構上運用「數常識」答題的比率不會因為「性別」而異。
六、學生在「運算結果之合理性的判斷」運用「傳統算則」答題反應類型的比率會因
為「性別」而異。
七、在「瞭解數與運算的基本意義」上,普遍存在關於「分數基本概念」的迷思概念。
八、在「數字的分解與合成」上,普遍存在關於「乘法相關運算」的迷思概念。
九、學生在「運算結果之合理性的判斷」上的迷思概念,普遍源自缺乏數感與量感。
The study using survey collected the online test data from fourth grade students in
Chiayi, Yunlin and Changhua county, Taiwan, to analyze the common error patterns of
their response types and misconceptions in four main components of number sense
(“Understanding the meanings of numbers, operations and their relationships”, “Being
able to compose and decompose numbers flexibly”, “Judging the reasonableness of a
computational result via different strategies”, “Recognizing the relative magnitude of
numbers”) using mixture modeling, Rasch analysis and interview. The main research
findings are shown below:
1. As compared to “Recognizing the relative magnitude of numbers”, the students tended
to not effectively use “number sense response” to reply to a question on the other three
subscales.
2. In “Being able to compose and decompose numbers flexibly”, the students tended to
reply to a question through regular four arithmetic operations.
3. As compared to the other three subscales, the students tended to reply to a question by
guessing on “Judging the reasonableness of a computational result via different
strategies”.
4. The students appeared to have more serious misconceptions in “Understanding the
meanings of numbers, operations and their relationships” and “Being able to compose
and decompose numbers flexibly”.
5. The rates of the students’ uses in “number sense” between sexes were not significantly
different.
6. Merely in “Judging the reasonableness of a computational result via different
strategies”, there was significant difference between sexes on the rates of the students’
“rule-based response”.
7. There were widespread misconceptions about fraction in “Understanding the meanings
of numbers, operations and their relationships”.
8. There were widespread misconceptions about multiplication-related operations in
“Being able to compose and decompose numbers flexibly”.
9. The misconceptions in “Judging the reasonableness of a computational result via
different strategies” generally came from the lack of number sense and quantity sense.
中文部份
王文中(1996)。幾個有關Rasch測量模式的爭議,教育與心理研究,19,1-26。new window
王文中(2004)。Rasch測量理論與其在教育和心理之應用。教育與心理研究,27,new window
637-694。
王曉璿、林朝清、周建宏、蔡松男、王怡萱(2009)。不同電腦輔助學習策略輔助數學
分數概念課程學習效益之研究。數位學習科技期刊,1(4),326-346。
王寶庸(1995)。現代測驗理論。台北:心理出版社。
尤燕翎、張麗麗(2009)。實作評量對數學解題及問題解決態度之影響─以Rasch模式結合效度及成效之檢核。論文發表於心理學會年會,台北。
江秉叡、李茂能、楊德清(2007)。國小第一階段數常識電腦診斷測驗評量。論文發表於2007數常識電腦化診斷測驗系統之成果發表會,嘉義。
吳心馨、楊德清(2006)。國一學生在情境與純數字問題之估算策略的研究。論文發表
於中華民國第22屆科學教育學術研討會,台北。
李茂能(1997)。評分者信度:Aiken和諧係數之應用。嘉義師院學報,11,77-88。
李茂能(2002)。 量化研究的品管:統計考驗力與效果值分析。國民教育研究學報,8,1-24。new window
李茂能(2003)。「圖解式結構方程模式軟體AMOS之簡介與應用」,國民教育研究學報,11,1-39。new window
李茂能(2006)。結構方程模式軟體AMOS之簡介及其在測驗編製上之應用。台北:心
理。
李茂能(2009)。圖解AMOS在學術研究之運用。台北:五南。
李威進、李茂能、楊德清(2005)。完成九年一貫第一階段學童數常識表現之研究。科學教育研究與發展季刊,38,61-78。(NSC-92-2521-S-415-002)
吳明隆(2007)。以使用者學習角度詳細而有系統的介紹AMOS的操作與其在SEM上的應用。台北:五南。
吳毓瑩、呂玉琴 (1997)。潛在類別分析對兒童等值分數概念結構之解析(國科會專題研究計畫成果報告編號:NSC85-2511-S-152-007)。台北:中華民國行政院國家科學委員會。
林怡君(2007)。以Rasch模式探討國小五年級學童在客觀型式及開放型式數學分數試題上之表現。論文發表於「國小數學認知與評量」研討會,屏東。
林原宏(2007)。模糊理論在社會科學研究的方法論之回顧。量化研究學刊,1(1),53-85。
林素微、洪碧霞、林世華(2004)。國小高年級電腦化數感動態評量發展之探討。收錄於台南師範學院主編,科技化測驗與能力指標評量國際學術研討會論文集(頁57-99)。台南:台南師範學院。new window
林福來、黃敏晃、呂玉琴(1996)。分數啟蒙的教與學。論文發表於國立中
正大學認知與學習研討會,嘉義。
邱皓政(2007)。斷裂時代中的量化研究:統計方法學的興起與未來。αβγ量化研究學刊,1(1)。1-34。
邱皓政(2008)。潛在類別模式:原理與技術。台北:五南。new window
姚漢禱(2002)。以Rasch測量有效的等化分組循環賽的成績表現(國科會專題研究計畫成果報告編號:NSC90- 2413-H-179–003)。台北:中華民國行政院國家科學委員會。new window
姚漢禱(2004)。以Rasch測量有效的等化分組循環賽的成績表現。體育學報,37,275-287。new window
洪素敏、楊德清(2002)。創意教學~分數的補救教學。科學教育研究與發展季刊,29,33-52。
洪藹鈺、林原宏(2007)。國小五年級學童小數概念結構之潛在類別分析。論文發表於2007第四屆測量統計方法學學術研討會暨臺灣統計方法學學會年會,臺北。
高耀琮、張英傑(2003) 。兒童幾何圖形概念之探究。論文發表於九十二學年度師範
學院教育學術論文發表會,台南。
教育部(2003)。國民中小學九年一貫課程綱要。台北:教育部。new window
張育綾、林原宏(2007,9月)。國小五年級學童四則運算解題表現探討及其潛在類別分析。論文發表於2007第四屆測量統計方法學學術研討會暨臺灣統計方法學學會年會,臺北。
陳和貴(2002)。國小五年級學童分數概念學習表現及易犯錯誤類型之比較研究~以屏東縣多元文化族群為例。未出版之碩士論文,國立屏東教育大學數理教育研究所,屏東。
陳怡琴、張麗麗(2009)。Rasch模式探討數學分數實作評量之學習機會DIF。論文發表於心理學會年會,台北。
陳霈頡、楊德清(2006)。從解題中探究數常識的重要。國立編譯館館刊,34(2),83-94。
張育萍、劉祥通(2005)。一位國小五年級學生對比值問題的解題表現。科學教育研究
與發展季刊,39,39-59。
甯自強(2004)。中年級兒童數概念類型研究(3/3)(國科會專題研究計畫
成果報告編號:NSC 93-2521-S-142 -001)。台北:中華民國行政院國
家科學委員會。
游政雄、呂玉琴(2002)。台灣北部地區國小中年級學童分數概念之研究。國立台北師new window
範學院學報,15,37-68。
游政雄、呂玉琴、吳宏毅、劉世能(2003)。台灣北部地區國小學童的分數單位量概念
之研究。南師學報,37(1),19-40。
黃財尉(2008)。不同資料結構下異常作答指標決斷值的探討。輔導與諮商學報,30, 1-16。new window
黃登月、王文中(2005)。青少年約會衝突因應策略量表之發展。教育與心理研究,28,468-494。new window
葉建德、劉祥通(2005)。一位七年級學生的比率構念—從解速率問題表現的觀點。科
學教育月刊,279,2-20。
詹婉華、呂玉琴(2004)。國小高年級學童分數概念量表之設計研究。科學教育學刊,12(2),241-263。new window
楊政樺、陳光華、李佳如(2007)。休閒暨觀光產業研究,2(1),1-26。
楊德清(2000)。國小六年級學生回答數字常識問題所使用之方法。科學教育學刊,8(4),379-394。new window
楊德清(2002):從教學活動中幫助國小六年級學生發展數字常識能力之研究,科學教育學刊,10(3),233-260。new window
楊德清、李茂能(2005)。九年一貫數學領域新能力指標—電腦化數字常識評定量表之
設計與編製(第二階段)(國科會專題研究計畫成果報告編號:
NSC-93-2521-S-415-002)。台北:中華民國行政院國家科學委員會。
楊德清(2006)。從兒童迷思概念談數常識之教學經驗分享。台灣數學教師電子期刊,7,3-10。
楊德清、李茂能(2006)。九年一貫國小階段數常識電腦化診斷測驗系統之開發與應
用(1/3)(國科會專題研究計畫成果報告編號:NSC 94-2521-S-415-003)。
台北:中華民國行政院國家科學委員會。
楊德清、李茂能(2007)。九年一貫國小階段數常識電腦化診斷測驗系統之開發與應用
(2/3)(國科會專題研究計畫成果報告編號:NSC-94-2521-S-415-003)。
台北:中華民國行政院國家科學委員會。
楊德清、吳宛儒(2007)。數常識情境教學活動融入國小三年級數學科教學之研究。科學教育學刊,10(3),647-669。new window
楊德清、洪素敏(2003)。比較分數大小~從具體、半具體、至抽象符號表徵之教學行動研究。南師學報,37(2),75-103。
劉若男、林原宏(2008)。原住民學生在數學閱讀表現之潛在類別探討。論文發表於2008年原住民學生數理教育學術研討會,臺東市。
劉曼麗(2001)。國小學童的小數知識研究。屏東師院學報,14,823-858。new window
劉曼麗(2002)。台灣地區國小學童小數概念研究(II):國小學童「小數與小數運算」概
念之調查研究(國科會專題研究計畫成果報告編號:
NSC90-2521-S-153-003)。台北:中華民國行政院國家科學委員會。
劉曼麗(2003)。從小數符號的問題探討學生之小數概念。屏東師院學報,18,459-494。new window
鄭中平、翁儷禎(2002)。結構方程模式之遺漏值處理—潛在變項組型混合模式。調查研究,12,5-27。new window
滕發祥(2004)。數感及其教育價值。課程‧教材‧教法,12,47。
錢才瑋、王文中、陳承德、張文信、林宏榮、劉歐(2006)。Rasch分析在醫療界之應用。台南:閒道。
錢才瑋、邱千芳、王文中、蘇世斌(2007)。Rasch分析協助醫師篩選勞工健檢異常值之應用研究。中華職業醫學雜誌,14(1),29-42。
錢才瑋、黃建元、羅培德、許森彥、蘇世斌(2009)。醫院勞工對作業環境之感受度調
查研究:邁向健康促進醫院。中華職業醫學雜誌,16(2),93-108。
錢才瑋、劉歐、王文中(2009)。以Rasch分析來決定測驗同分時之錄取順序。測驗學new window
刊,56(2),129-151。
盧志明、黃財尉、方將任(2007)。Guttman型異常作答指標偵測力之比較。測驗學刊, 54, 147-174。new window
盧雪梅、毛國楠(2008)。國中基本學力測驗數學科之性別差異與差別試題功能(DIF)new window
分析。教育實踐與研究,21(2),95-126。
謝堅(1997)。實驗課程對四則運算教材的處理。國民小學數學新課程概說(中年級)。
台灣省國民學校教師研習會編印。
戴妏純(2007)。Rasch模式在分數診斷測驗難度及向度檢視上之應用。論文發表於「國小數學認知與評量」研討會,屏東。
Davis, R. E. (1990)。數學學習(劉秋木譯)。台北:五南圖書出版公司。
Patton, M. Q. (1995)。質的評鑑與研究(吳芝儀、李奉儒譯)。台北:桂冠圖書公司。
Schwarzenberger(1984)。錯誤的重要性。數學圈,21,73-80。
外文部份
Alajmi, A. H., & Reys, R. (2010). Examing eighth grade Kuwaiti students’ recognition and
interpretation of reasonable answers. International Journal of Science and Mathematics Education, 8(2), 117-139.
Amato, S. A. (2005). Developing students’ understanding of the concept of fractions as
numbers. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th PME
Conference, vol. 2 (pp.49-56). Melbourne: University of Melbourne.
Anderson, J. R., & Jeffries. (1985). Novice Lisp errors: Undetected losses of information
from working memory. Human-Computer Interaction, 1, 107-131.
Anghileri, J. (2006). Teaching number sense. Trowbridge, Wiltshire: Cromwell Press Ltd.
Arbuckle, J. L., & Wothke, W. (1999). AMOS users’ guide, Version 4.0. Chicago: SmallWaters.
Arbuckle, J. L. (2009). AMOS 18.0 user’s guide. Chicago, IL: SPSS, AMOS Development Corporation.
Arminger, G., & Stein, P. (1997). Finite mixture of covariance structure models with
regressors: loglikehood function, distance estimation, fit indices, and a complex example. Sociological Methods and Research, 26, 148-182.
Ashlock, R. B. (1986) . Error patterns in computation:A semi-programmed Approach (4th ed.). Columbus, OH: Merrill.
Ashlock, R. B. (2002). Error patterns in computation: Using error patterns to improve instruction. NJ: Pearson Education, Inc.
Aunio, P., Niemivirta, M., Hautamäki, J., Van Luit, J. E. H., Shi, J. & Zhang, M. (2006). Young Children's Number Sense in China and Finland. Scandinavian Journal of Educational Research, 50(5), 483-502.
Aunola, K., Leskinen, E., & Lerkkanen, M. K. (2004). Developmental dynamics of math performance from preschool to grade 2. Journal of Educational Psychology, 96, 699-713.
Australian Education Council. (1991). A national statement on mathematics for Australian schools. Melbourne: Curriculum Corporation.
Bagozzi, R. P., & Yi, Y. (1988). On the evaluation of structural equation models, Journal of
Academy of Marketing Science, 16(1), 74-94.
Ball, D. L. (1990). Prospective elementary and secondary teachers' understanding of
division. Journal for Research in Mathematics Education, 21, 132-144.
Ball, D. L. (2004). Mathematical proficiency for all students: Toward a strategic research
and development program in mathematics education. RAND Mathematics Study
Panel. Retrieved January 1, 2009 from
http://Fwww.rand.org/pubs/monograph_reports/MR1643/MR1643.pref.pdf
Baroody, A. J. (1987). The development of counting strategies for single-digit
addition. Journal for Research in Mathematics Education, 18(2), 141−157.
Bartholomew, D. (1987). Latent variable models and factor analysis. London: Charles Griffin and Company Limited.
Bednarz, N., & Janvier, B. (1982). The understanding of numeration in primary school. Educational Studies in Mathematics, 13, 33-57.
Behr, M., Lesh, R., Post, T., & Silver E. (1983). Rational Number Concepts. In R. Lesh &
M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes (pp. 91-125).
New York: Academic Press.
Behr, M. J., Wachsmuth, I., Post, T. R. & Lesh, R. (1984). Order and equivalence of
rational numbers, a clinical teaching experiment. Journal for Research in Mathematics Education, 15, 323-341.
Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disability. Journal of Learning Disabilities, 38(4), 333-339.
Bergeron, M. J., & Herscovics, H. (1987). Unit Fractions of a Continuous Whole. The
11th International Conference for the Psychology of Mathematics Education.
Beswick, K. (2004). Why does 0.999… = 1? A perennial question and number sense. Amt, 60(4), 7-9.
Billings, J. R. (2009). The relationship between fifth grade number sense and ninth grade algebra. Unpublished doctoral dissertation, Minnesota, U.S.A.
Bobis, J. (1996). Visualisation and the development of number sense with kindergarten children. In Mulligan, J. & Mitchelmore, M (Eds.). Children's number learning : A research monograph of the mathematics education group of Australasia and the Australian Association of Mathematics Teachers. Adelaide: AAMT.
Bright, G. W., Behr, M. J., Post, T. R. & Wachsmuth, I. (1988). Identifying fractions on
number lines. Journal for Research in Mathematics Education, 19, 215-232.
Brown, G., Quinn, R. J. (2006). Algebra students' difficulty with fractions: An error analysis. Australian Mathematics Teacher, 62(4), 28-40.
Burns, M. (1994). Arithmetic: The last holdout. Phi Delta Kappen, 1, 471-476.
Burton, G. M. (1993). Number sense and operations: Addenda series, grades K-6. Reston, VA: National Council of Teachers of Mathematics.
Butterworth, B., & Reigosa, V. (2007). Information processing deficits in dyscalculia. In D. B. Berch & M. M. M. Mazzocco (Eds.), Why is math so hard for some children?: The nature and origins of mathematical learning difficulties and disabilities (pp. 65-81). Baltimore, MD: Paul H. Brookes Publishing.
Carboni, L. (2008). Number sense everyday. Retrieved September 29, 2009, from: http://www.learnnc.org/lp/pages/numsense0402-1.
Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
Case, R. (1998). A psychological model of number sense and its development. Annual
meeting of the American Educational Research Association, San Diego, CA.
Charalambous, C., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study
students’ understandings of fractions. Educational Studies in Mathematics, 64(3),
293-316.
Clement, J. (1982). Students’ preconceptions in introductory mechanics. American Journal of Physics, 50, 66-71.
Cockburn, A. D., & Littler, G. H. (2008). Mathematical misconceptions : a guide for primary teachers. Los Angeles; London: SAGE.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences. New York: Academic Press.
Cohen, J., Chan, T., Jiang, T., & Seburn, M. (2008). Consistent estimation of Rasch item parameters and their standard errors under complex sample designs. Applied Psychological Measurement, 32(4), 289-310.
Cramer, K. A., Post, T. R. & delMas, R. C. (2002). Initial fraction learning by forth-and
fifith-grade students: A comparison for the effects of using commercial curricula with
the effects of using the rational number project curriculum. Journal for Research in
Mathematics Education, 33(2), 111-144.
Cutler, J. A. (2000). An analysis of the development of number sense by sixth-grade students during an intervention emphasizing systematic mental computation. Unpublished doctoral dissertation, Massachusetts Lowell, U.S.A.
Davis, R. B. (1984). Learning mathematics: The cognitive science approach to mathematics education. Norwood, N. J.: Ablex Publishing Corporation.
Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York: Oxford University Press.
Dehaene, S. (2001). Precis of the number sense. Mind and Language, 16, 16 – 36.
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39, 1-38.
Diamantopoulos, A., & Siguaw, J. A. (2000). Introducing LISREL: A guide for the uninitiated. New Delhi: Sage.
Diezmann, C., & Lowrie, T. (2007). The development of primary students’ knowledge of
the structured number line. In Woo, J. H., Lew, H. C., Park, K. S. & Seo, D. Y. (Eds.),
Proceedings of the 31st Conference of the International Group for the Psychology of
Mathematics Education, Vol. 2 (pp. 201-208). Seoul: PME.
Dolan, C. V., & Van der Maas, H. L. J. (1997). Fitting multivariate normal finite mixtures
subject to structural equation modeling. Psychometrika, 63, 227-253.
Dougherty, B. J., & Crites, T. (1989). Applying number sense to problem solving. Arithmetic Teacher, 36(6), 22-25.
Dunphy, E. (2007). The primary mathematics curriculum: enhancing its potential for developing young children’s number sense in the early years at school. Irish Educational Studies, 26(1), 5-25.
Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Lawrence Erlbaum Associates.
Empson, S. (2002). Organizing diversity in early fraction thinking. In B. Litwiller, & G. Bright (Eds.), Making Sense of Fractions, Ratios, and Proportions (2002 Yearbook) (pp.29-40). Reston, VA: National Council of Teachers of Mathematics.
Faulkner, V. N. (2009). The components of number sense: A brief outline. Teaching Exceptional Children, 41(5), 24-30.
Feigenson, L., & Carey, S. (2003). Tracking individuals via object-files: Evidence from infants' manual search. Developmental Science, 6, 568−584.
Figueras, O. (1989). Two different view of fraction: Fractionating and operating. Proceedings
of the 13th Conference of International Group for PME, Paris, France.
Fornell, C., & Larker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18, 39-50.
Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht,
Holland: D. Reidel Publishing Co.
Frobisher, L., Monaghan, J., Orton, A., Orton, J., Roper, T., & Therlfall, J. (2002). Learning to teach number. A handbook for students and teachers in the primary school. Cheltenham, United Kingdom: Nelson Thornes Ltd.
Gagné, E. D., Yekovich, C. W., & Yekovich, F. R. (1993). The cognitive psychology of
school learning (3rd ed.). New York, NY: Harper Collins College Publisher.
Geary, D. C., Bow-Thomas, C. C., & Yao, Y. (1992). Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically disabled children. Journal of Experimental Child Psychology, 54, 372-391.
Geary, D. C., & Hoard, M. K. (2005). Learning disabilities in arithmetic and mathematics: Theoretical and empirical perspectives. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 253-268). New York: Psychology Press.
Gersten, R., & Chard, D. (1999). Number sense: Rethinking mathematics instruction for students with mathematical disabilities. Journal of Special Education, 33, 19-28.
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and intervention for
students with mathematics difficulties. Journal of Learning Disabilities, 38(4),
293-304.
Giaquinto, M. (2007). Visual thinking in mathematics: an epistemological study. New
York: Oxford University Press.
Gould, P. (2005). Year 6 student's methods of comparing the size of fractions. In P.
Clarkson, Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche
(Eds.), Building connections: research, theory and practice (Proceedings of the Annual conference of the Mathematics Education Research Group of Australasia (pp.
393-400). Sydney: MERGA.
Grady, M.T., & Hutcherson, L. R. ( 1981 ) .Error analysis: An item analytic investigation of diagnostic tests. Research reports from the fourth and fifth national conference and prescriptive mathematics. 1980 research monograph. Revised third edition, 129-138. Kent, OH: Research council for diagnostic and prescriptive mathematics. (ERIC Document Reproduction Service. No. ED. 243708).
Greer, B. (1987). Nonconservation of multiplication and division involving decimals.
Journal for Research in Mathematics Education, 18(1), 37-45.
Griffin, M. M. (1995). You can't get there from here: situated learning, transfer, and map skills. Contemporary Educational Psychology, 20, 65-87.
Griffin, S. (2004). Building number sense with number worlds: A mathematics program for young children. Early Childhood Research Quarterly, 19, 173–180.
Guzman, JIN, Villagran, MA, Sedeno, MG, Jimenez, IM, Consejero, EM, & Cuevas, CA. (2010). Early math skills differences in 4-8 year old boys and girls. Revista española de pedagogía, 68(245), 85-98.
Halberda, J., Mazzocco, M. & Feigenson, L. (2008). Individual differences in nonverbal number acuity predict maths achievement. Nature, 455, 665-668.
Hannula, M. S. (2003). Locating fraction on a number line. In N. A. Pateman, B. J.
Dougherty, & J. Zilliox, Proceedings of the 2003 joint meeting of PME &
PMENA. Hawaii.
Hanson, S. A., & Hogan, T. P. (2000). Computional estimation skill of college students.
Journal for Research in Mathematics Education, 31(4), 483-499.
Hedrén, R. (1999). The teaching of traditional standard algorithms for the four arithmetic operations versus the use of pupils' own methods. In I. Schwank (Ed.), European research in Mathematics Education I. Proceedings of the First Conference of European Society for Mathematics Education (pp. 233-244). Osnabrueck: Forschungsinstitut fuer Mathematikditaktik.
Heineke, W. F., Blasi, L. (2001). Methods of evaluating educational technology. Greenwich: Information Age Publishing Inc.
Hsu, C. Y., Yang, D. C., & Li, M. N. (2001). The design of “the fifth and sixth grade
number sense rating scale. Chinese Journal of Science Education, 9(4), 351-374.
Hiebert, J. (1999). Relationships between research and the NCTM Standards. Journal for Research in Mathematics Education, 30, 3-19.
Hogan, T. P., & Brezinski, K. L. (2003). Quantitative estimation: One, two, or three
abilities? Mathematical Thinking and Learning, 5(4), 259 – 280.
Hoijtink, H. (1986). Detecting aberrant response patterns in the unidimensional scaling
model of Rasch. Groningen: R. U. Groningen.
Hoshino, T. (2001). Bayesian inference for finite mixtures in confirmatory factor analysis.
Behaviormetrika, 28(1), 37-63.
Howden, H. (1989). Teaching number sense. Arithmetic Teacher, 36 (6), 6-11.
Huang, W. L., Liu, Y. C., & Shiu, C. Y. (2008). Construction of an online learning system for decimal numbers through the use of cognitive conflict strategy. Computers and Education, 50 (1), 61-76.
Irwin, K. C. (2001). Using everyday knowledge of decimal to enhance understanding. Journal for Research in Mathematics Education, 32(4), 399-420.
Jansen, B. R. J., & Van der Maas, H. L. J. (2002). The development of children's rule
use on the balance scale task. Journal of Experimental Child Psychology, 81(4),
383-416.
Jasra, A., Holmes, C. C., & Stephens, D. A. (2005). Markov chain monte carlo methods
and the label switching problem in bayesian mixture modeling. Institute of Mathematical Statistics, 20(1), 50-67.
Jedidi, K., Jagpal, H.S., & DeSarbo, W.S. (1997). Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity. Marketing Science, 16, 39-59. Statistical Science, 20(1), 50–67.
Jordan, N. C., Kaplan, D., Ola’h, L. N., & Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153-175.
Jordan, N.C., Kaplan, D., Locuniak, M.N., & Ramineni, C. (2007). Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research & Practice, 22(1), 36-46.
Jordan, N.C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 20, 82-88.
Kalchman, M., Moss, J., & Case, R. (2001). Psychological models for the development of mathematical understanding: Rational numbers and functions. In S. Carver & D. Klahr (Eds.), Cognition and instruction (pp. 1–38). Mahwah, NJ: Erlbaum.
Kaminski, E. (2002). Promoting mathematical understanding: number sense in action. Mathematics Education Research Journal, 14(2), 133-149.
Karabatsos, G. (2003). Comparing the aberrant response detection performance of thirty-six person-fit statistics. Applied Measurement in Education, 16(4), 277–298.
Kathlen, T. T. (1987). Error Reduction Strategies for whole number operations in grade four. Unpublished doctoral dissertation, Brigham Young, U.S.A.
Keijzer, R., & Terwel, J. (2004). A low-achiever’s learning process in mathematics:
Shirley’s fraction learning. Journal of Classroom Interaction, 39(2), 10-23.
Klibanoff, R. S., Levine, S. C., Huttenlocher, J., Vasilyeva, M., & Hedges, L. V. (2006). Preschool children’s mathematical knowledge: The effect of teacher “Math Talk”. Developmental Psychology, 42(1), 59–69.
Kline, T. J. B. (2005). Psychological testing: A practical approach to design and evaluation. Thousand Oaks, CA: Sage.
Kuhn, D. (2000). Metacognitive development. Psychological Science, 9(5), 178-181.
Lachance, A., & Confrey, J. (2001). Helping students build a path of understanding from ratio and proportion to decimal notation. The Journal of Mathematical Behavior, 20(4), 503-526.
Lamon, S. J. (2002). Part – whole comparisons with utilizing. In B. Litweller, & G. Bright
(Eds.), Making sense of fractions, and ratio, and proportions (pp.162-175). Reston, VA: NCTM.
Lazarsfeld, P. F., & Henry, N. W. (1968). Latent Structure Analysis. New York: Houghton-Mifflin.
Lee, S. Y. (2007). Structural equation modeling: A Bayesian approach. Chichester, UK: John Wiley and Sons.
LeFevre, J. A. (2007, September). Verbal and nonverbal pathways: Mathematical development from Kindergarten to Grade 1. Paper presented at NUMBRA: A Summer School on Numeracy and Brain Development: Progress and Prospects, Santorini, Greece.
Li. M. N., & Yang, D. C. (2010). Development and validation of a computer-administered number sense scale for fifth-grade children in Taiwan. School Science and Mathematics, 110(4), 220-230.
Li, X., & Li, Y. (2008). Research on students' misconceptions to improve teaching and learning in school mathematics and science. School Science and Mathematics, 108 (1), 4.
Lincoln, Y., & Guba, E. (1985). Naturalistic inquiry. New York: Sage.
Loken, E. (2004). Using latent class analysis to model temperament types. Multivariate Behavioral Research, 39(4), 625-652.
Lord, F. M. (1980). Applications of item response theory to practional testing problems. Hillsdale, NJ: Lawrence Erlbawn Associates.
Mack, N. K. (2001). Building on informal knowledge through instruction in a complex content domain: Partitioning, units, and understanding multiplication of fractions. Journal for Research in Mathematics Education, 32(3), 267-295.
Malofeeva, E., Day, J., Saco, X., Young, L., & Ciancio, D. (2004). Construction and evaluation of a number sense test with Head Start children. Journal of Educational Psychology, 96, 648-259.new window
Markovits, Z., & Sowder J. T. (1994). Developing number sense: An Intervention study in
grade 7. Journal for Research in Mathematics Education, 25(1), 4-29.
Mastropieri, M. A., & Scruggs, T. E. (2002). Effective instruction for special education (3rd ed.). Austin, TX: Pro-Ed.
Maurer, S.B. (1987). New knowledge about errors and new biews about learners: What they mean to educations and more educators would like to know. In A.H. Schoenfeld(Ed.), Cognitive Science and mathematics Education (pp. 165-187). N .J.: LEA.
Mazzocco, M. M. M., & Thompson, R. E. (2005). Kindergarten predictors of math
learning disability. Learning Disabilities Research and Practice, 20(3), 142-155.
McCutcheon, A. L. (1987). Latent class analysis. Quantitative Applications in the Social Sciences Series No. 64. Thousand Oaks, California: Sage Publications.
McDermott, L. (1984). Research on conceptual understanding of physics. Physics Today, 37, 24-32.
McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12(3), 2-8.
McIntosh, A., Reys, B. J., & Reys, R. E. (1997). Number sense grades 6-8. Palo Alto: Dale
Seymour Publications.
McIntosh, A., Reys, B. J. & Reys, R. E., Bana, J., & Farrel, B. (1997). Number sense in
school mathematics: Student performance in four countries. MASTEC: Mathematics,
Science & Technology Education Centre.
McLaughlin, G. (2003). Effect of modeling instruction on development of proportional
reasoning II: theoretical background. Retrieved January 31, 2009 from
http://modeling.asu.edu/modeling-hs.html
McNeil, N. M., & Alibali, M. W. (2005). Why won't you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development, 76, 883-899.
McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297–312.
Meijer, R. R., & Sijtsma, K. (1995). Dection of aberrant item score pattern: A review of
recent developments. Applied Measurement in Education, 8, 261-272.
Menon, R. (2004). Elementary school children’s number sense. International Journal for Mathematics Teaching and Learning. Retrieved December 3, 2009, from http://www.exeter.ac.uk/cimt/ijmtl/ijmenu.htm
Mestre, J.(1989). Hispanic and Anglo students’ misconceptions in Mathematics. ERIC document Reproduction Service No. ED313192.
Misailidou, C., & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. Mathematical Behavior, 22(3), 335-368.
Mitchell, A. (2005). Measuring Fractions. Retrieved January 22, 2009 from
http://www.merga.net.au/documents/RP612005.pdf
Mix, K. S., Huttenlocher, J., & Levine, S. C. (2002). Quantitative development in infancy and early childhood. Oxford, UK: Oxford University Press.
Moskal, B. M., & Magone, M. E. (2000). Making sense of what students know: Examining the referents, relationships and modes students displayed in response to a decimal task. Educational Studies in Mathematics, 43(3), 313-335.
National Research Council (1989). Everybody Counts. A report to the nation on the future of mathematics education. Washington, DC: National Academy Press.
National Council of Teachers of Mathematics (2000). The principles and standards for
school mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics (2008). Curriculum focal points for mathematics in prekindergarten through Grade 8. Retrieved November 15, 2009, from http://www.nctm.org/standards/focalpoints.aspx?id=298
Newman, M. A. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks. Mathematics Education in Australia, 1, 239-258.
Pearson, K. (1894). Contributions to the mathematical theory of evolution, Philosophical Transactions of the Royal Society of London, Series A, 185, 71-110.
Pitkethly, A., & Hunting, R. P. (1996). A review of recent research in the area of initial
fraction concepts. Educational Studies in Mathematics, 30, 5-38.
Plemons, Marie &Annette Stern (1995). The effect of number sense instruction on prekindergarten children's understanding of the mathematics concept of more or less. Ed.D. dissertation, University of Houston, United States -- Texas. Retrieved January 29, 2010, from Dissertations & Theses: A&I.(Publication No. AAT 9528800).
Post, T. R., & Cramer, K. (1987). Children's strategies when ordering rational numbers.
Arithmetic Teacher, 35(2), 33-35.
Resnick, L. (1983). Mathematics and science learning: A new conception. Science, 220, 477-478.
Resnick, L.B. (1989). Defining, assessing, and teaching number sense. In J. T. Sowder & B. P. Schappelle(Eds.), Establishing foundations for research on number sense and related topics: report of a conference(pp.35-39). San Diego: San Diego University, Center for Research in Mathematics and Science Education.
Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989).
Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for
Research in Mathematics Education, 20(1), 8-27.
Resnick, L. B., & Omanson, S. F. (1987). Learning to understand arithmetic. In R. Glaser(Ed), Advances In Instructional psychology(Vol. 3) (pp.41-95). Hillsdale, NJ: Lawrence Erlbaum.
Reuterberg, S. E., & Gustafsson, J. E. (1992). Confirmatory factor analysis and reliability:
Testing measurement model assumptions. Educational and Psychological Measurement, 52, 795-811.
Reys, B. J. (1994). Promoting number sense in middle grades. Teaching Mathematics in the Middle School, 1(2), 114–120.
Reys, R. E. (1996). Helping children learn mathematics. Boston: Allyn and Bacon.
Reys, R. E., & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth- and eighth-grade students in Taiwan, Journal for Research in Mathematics Education, 29, 225-237.
Reys, R., Reys, B., McIntosh, A., Emanuelsson, G., Johansson, B., & Yang, D. C. (1999). Assessing number sense of students in Australia, Sweden, Taiwan, and the United States. School Science and Mathematics, 99(2), 61-70.
Riccomini, P. J. (2005). Identification and remediation of systematic error patterns in subtraction. Learning Disability Quarterly, 28(3), 233-242.
Rose, C. M., Arline, C. B. (2009). Uncovering student thinking in mathematics, grade 6-12. Thousand Oaks, Calif.: Corwin Press.
Salvia, J., & Ysseldyke, J. E. (2004). Assessment in special and inclusive education (9th ed.). Boston: Houghton Mifflin.
Scheuermann, A., & van Garderen, D. (2008). Analyzing students' use of graphic representations to determine misconceptions and error patterns for instruction. Mathematics Teaching in the Middle School, 13(8), 471-477.
Schneider, M., Grabner, R. H., & Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement: Their interrelations in grades 5 and 6. Journal of Educational Psychology, 101(2), 359-372.
Scott, M. S. M.(1987). The impact of a number sense program on mathematics achievement test scores and attitudes toward mathematics of eighth-grade students. Ph.D. dissertation, New Mexico State University, United States -- New Mexico. Retrieved January 29, 2010, from Dissertations & Theses: A&I.(Publication No. AAT 8719795).new window
Scruggs, T. E., & Mastropieri, M. A. (2002). On babies and bathwater: Addressing the problems of identification of learning disabilities, Learning Disability Quarterly, 25, 155-168.
Shih, M. Y. (2005). Effects of number sense intervention on second-grade students with mathematics learning disabilities. Unpublished doctoral dissertation, Texas, U.S.A.
Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444.
Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237-243.
Skwarchuk, S. L. (2008). Look who's counting! The 123s of children's mathematical development during the early school years. Encyclopedia of Language and Literacy Development (pp. 1-9). London, ON: Canadian Language and Literacy Research Network. Retrieved November 27, 2009, from http://www.literacyencyclopedia.ca/pdfs/topic.php?topId=243
Smith, R. M. (1996). Polytomous mean-square fit statistics. Rasch Measurement Transactions, 10(3), 516-517.
Smith, R. M., Schumacker, R. E., & Bush, M. J. (1998). Using item mean squares to evaluate fit to the Rasch model. Journal of outcome measurement, 2, 66-78.
Sowder, J. (1989). Introduction. In J. Sowder & B. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a conference (pp. 1-5). San Diego, CA: San Diego State University.
Sowder, J. T. (1992), Making sense of numbers in school mathematics. In G. Leinhardt, & R. Hattrup (Eds.), Analysis of Arithmetic for Mathematics Teaching (pp. 1-51). Hillsdale, NJ: Erlbaum.
Spelke, E. S. (2005). Sex differences in intrinsic aptitude for mathematics and science?: A critical review. American Psychologist. l 60(9), 950-958.
Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the
numerical value of fractions. Learning and Instruction, 14, 503–518.
Steinthorsdottir, O. B. (2005). Girls journey toward proportional reasoning. In Chick, H. L. & Vincent, J. L. (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 225-232). Melbourne: PME.
Sturdevant, R. J. (1992). Investigating the use of number sense by elementary students in grades 4, 6, and 8. (University of Missouri - Columbia, 1991). Dissertation Abstracts International, 53A, 748. DA9220845.
Tabachnica, B. G., & Fidel, L. S. (2007). Using multivariate statistics. Needham Heights, MA: Allyn and Bacon.
Tatsuoka, K. K. (1990). Toward an integration of item response theory and cognitive error disgnosis. In N. Frederiksen, R. Glaser, A. Lesgold, & M. Shafto (Eds.), Diagnositic monitor of skill and knowledge acquisition (pp. 453-488). Hillsdale, NJ: Lawrence Erlbaum.
Thornton, C. A., & Tucker, S. C. (1989), Lesson planning: the key to developing number sense. The Arithmetic Teacher, 36(6), 18-21.
Trafton, P. R., & Thiessen, D. (1999). Learning through problems: Number sense and computational strategies : a resource for primary teachers. Heinemann: Portsmouth, NH.
Treffers, A. (1991). Meeting innumeracy at primary school. Educational Studies in Mathematics, 26(1), 333-352.
Uebersax(1994). Latent Class Analysis of Substance Abuse Patterns. In L. M. Collins, & L. A. Seitz, Advances in Data Analysis for Prevention Intervention Research (pp. 64-80). USA, Bethesda: NIDA Research Monograph Press.
Uebersax, J. (2003). Latent Class Analysis. Retrieved September, 3, 2009, from
http://ourworld.compuserve.com/homepages/jsuebersax/
Vermunt, J. K., & Magidson, J. (2005). Structural equation models: Mixture models. In B. Everitt & D. Howell (Eds.), Encyclopedia of statistics in behavioral science (pp. 1922-1927). Chichester, UK: Wiley.
Wagner, D., & Davis, B. (2010). Feeling number: grounding number sense in a sense of quantity. Educational Studies in Mathematics, 74(1), 39-51.
Way, J. (2005). Number sense series: Developing early number sense. Retrieved December, 13, 2009, from
http://nrich.maths.org/2477
Wearne, D., & Hiebert J. (1988). Constructing and using meaning for mathematical symbols: The case of decimal fractions. In J. Hieber & M. Behr ( Eds.), Number concepts and operations in the middle grades (pp. 220-235). Reston, VA: NCTM.
Wilson, A. J., Revkin1, S. K., Cohen, D., Cohen, L., & Dehaene, S. (2006). An open trial assessment of "The Number Race", an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(20).
Wood, F. (1999). Gentle Introduction to Infinite Gaussian Mixture Modeling. . Retrieved June 26, 2010, from
http://www.cs.toronto.edu/~vnair/ciar/frank_wood.ppt
Woodward, J., & Howard, L. (1994). The misconceptions of youth: Errors and their mathematical meaning. Exceptional Children, 61(2), 126 - 36.
Wright, B. D. (1998). Who is awarded first prize? RaschMeasurement Transactions, 12(2),
629.
Wright, B. D., & Stone, M. H. (1979). Best test design. Chicago: MESA Press.new window
Wright, B. D., & Masters, G. N. (1982). Rating scale analysis. Chicago: MESA Press.
Wright, B. D., & Linacre, J. M. (1994). Reasonable mean-square fit values. Rasch Measurement Transactions, 8(3), 370.
Wright, B. D., & Mok, M. (2000). Rasch models overview. Journal of Applied Measurement, 1, 83-106.
Yang, D. C., & Reys, R. E. (2001). Developing number Sense. Mathematics Teaching, 176, 39-41. (NSC 89-2511-S-415-001).
Yang, D. C. (2002). Teaching and Learning number sense: one successful process-oriented activity with six grade students in Taiwan. School Science and Mathematics Journal, 102(4), 152-157.(NSC 89-2511-S-415-001)
Yang, D. C., & Reys, R. E. (2002). Fractional number sense strategies possessed by sixth grade students in Taiwan. Hiroshima Journal of Mathematics Education, 10(December), 53-70.
Yang, D. C. (2003). Teaching and learning number sense—An intervention study of fifth grade students in Taiwan. International Journal of Science and Mathematics Education, 1(1), 115-134. (NSC 90-2521-S-415-001)
Yang, D. C., Hsu, C. J., & Huang, M. C. (2004). A Study of teaching and learning number sense for six grade students in Taiwan. International Journal of Science and Mathematics Education, 2, 407-430.
Yang, D. C. (2005). Number sense strategies used by sixth grade students in Taiwan, Educational Studies, 31(3), 317-334.
Yang, D. C. (2007). Investigating the strategies used by pre-service teachers in Taiwan when responding to number sense questions. School Science and Mathematics, 107(7), 293-301.
Yang, D. C., & Hsu, C. J. (2009). Teaching number sense for 6th graders in Taiwan. International Electronic Journal of Mathematics Education, 4(2), 92-109.
Yang, D. C. & Li, M. N (2008). An investigation of 3rd grade Taiwanese students’ performance in number sense, Educational Studies, 34(5), 443–455.
Yang, D. C., Li, M. N., & Lin, C. I. (2008). A Study of the Performance of 5th Graders in Number Sense and its Relationship to Achievement in Mathematics. International Journal of Science and Mathematics Education, 6(4), 789-807.
Yang, D. C. & Wu, W. R. (Accepted). The study of number sense realistic activities integrated into third-grade math classes in Taiwan. The Journal of Educational Research.
Zhu, W. (1996). Should total scores from a rating scale be used directly ? Research Quarterly for Exercise and Sport, 67(3), 363-372.
Zhu, H. T., & Lee, S. Y. (2001). A Bayesian analysis of finite mixtures in the LISREL model. Psychometrika, 66(1), 133-152.



 
 
 
 
第一頁 上一頁 下一頁 最後一頁 top
:::
無相關著作
 
QR Code
QRCODE