Please fill in the questionnaire (18 questions on perceptions of the course) NOW and hand them in immediately after you have completed. Thank you ! J
※Only English, Chinese and Mathematics were tested in JSEA (Junior Secondary Educational Assessment) - performance in other subjects showed high correlations with these three as found by multiple regression analyses.
※A certain school found that there is a high correlation between the banding of intake students with their CE results. Thus streaming is justified.
※In a panel meeting, a teacher boasted that the scores of his/her class have increased during the year.
※A panel chairperson wishes to purchase some teaching aids/computer software packages. S/He would like to know which of these commercially available teaching aids are proven to be effective.
※Is teaching with IT (teaching mathematics incorporating its history, teaching with games, etc. alike) better than conventional ways of teaching ?
※Why we make 300 the full mark for Chinese and English in some schools and that of Mathematics 200 ? How was the full mark of public examinations set (e.g. 90 marks for Additional Mathematics) ?
※Is it fair to compare the scores of Arts/Science students (Arts/Science oriented students for lower grades) since it is easier to score full mark in mathematics (as compared with composition) while some argued that it is difficult to score good marks in mathematics as the questions involved are always non-routine.
“Given the same topics and curriculum, mainland teachers can make 70 % of students understand mathematics concepts taught while our teachers can only ensure 30 % of students comprehend them.”
※Compare the following methodologies: (a) number of germs in a litre of water, (b) the number of tons of garbage collected in a seashore, (c) the rating of the performance of the Chief Executive.
Basic questions:
(1) After a topic is taught, with the use of a particular teaching method (i.e. a curriculum is implemented), how can we judge if it is effective ?
(2) What is the “cause” of such effects ?
Use of history on mathematics teaching: Design of the capsule
Inadequate material depicting the cultural aspect of mathematics / 1. Introduce the Chinese, Egyptian, Greek and Babylonian origins of the Pythagorean Proposition.
2. Introduce the Chinese “water weed problem” and the Indian “lotus problem”.
3. Passages from original classics given to the students for reference.
Rely too much on drilling / Multiple perspective to a single problem by introducing methods from various cultures.
Rely too much on algebraic treatment / Diagrammatic proofs from ancient Chinese mathematics introduced.
No connections between the Pythagorean Proposition and irrational numbers / A story on the discovery of incommensurable magnitude leading to a crisis in mathematics introduced.
Lack readily available activities / Activities adopted from historical stories introduced, such as making a right-angled triangle from a string with 11 knots (dividing the string in 12 = 3+4+5 equal parts) and deciphering the Babylonian tablet known as Plimpton 322.
Rare use of manipulatives / Let students make a right-angled triangle with the above string and let them prove the Pythagorean proposition themselves by geometrical dissection.
合格?
及格?
“In simplest terms, higher order thinking measures include all intellectual tasks that call for more than information retrieval. Any transformation of information is definitionally ‘higher order’ thinking. Early writers who took the approach of detailing intellectual processes and illustrative tasks included Bloom (1956) and Gagné (1985). … Other formulations of higher order thinking derive from the general problem-solving literature and emphasize such task components as problem identification and solution testing. … Higher order thinking can also take the form of metacognitive skills, such as planning and self-checking.”
Baker E.L. (1990). Developing comprehensive assessments of higher order thinking, Section 1: How is higher order thinking conceived and measured ? In G. Kulm (Ed.). Assessing Higher Order Thinking in Mathematics. Washington, D.C.: American Association for the Advancement of Science.
(a) Problems with irrelevant information
(b) “Problematic word problems”
(c) Problems which allow more than one solution
(d) Problems which allow multiple methods
(e) Problems with different interpretations possible
(f) Problems which ask for communication
(g) Problems which need judgement
(h) Problems that involve decision making
※ “Do you think you will graduate from college”
Billy, Brookover & Erickson, 1972
※ “I am able to do things as well as most other people”
Rosenberg, 1965
※ “I have a low opinion of myself”
Coopersmith, 1967
※ //
Marsh, 1992
One factor congeneric model
F
F'
Exp(Response)
= Exp(Response∣F)×P(F) + Exp(Response∣F')×P(F')
= Exp(#Child∣F)×+ Exp(#Taxi∣F')×
Randomised response technique
※ General positive view
※ Math education needs wider objective
※ Maintain interest important
※ Curriculum should be designed with strong theoretical basis
※ Post-basic: curriculum differentiation
※ Secure continuation at all levels
※ Explore foundation-extension model
※ Safeguard backwash effect
※ Guidelines & exemplars should be provided for teachers and writers
※ Support teachers with IT, enhancement of abilities and curriculum tailoring
※ Teacher education and collegiate exchange important
※ Stakeholders should be well-informed
※ Reduce non-teaching duties, upgrade social recognition
※ 屬於數學科的檢討
※ 過程與內容整合
※ 避免統一化
※ 處理「定態+間歇改動」之流弊
※ 強化教師
成績單
※ 課程理清精簡
※ 非官定課程的貢獻
※ 以單元選修作基調
※ 基礎+增潤
※ 預留備用教節
※ 不是所有都可即測
※ 預備知識評估
※ 先諮詢後定稿
※ 教學建議抽作附件
“You see, really and truly, apart from the things anyone can pick up (the dressing and the proper way of speaking, and so on), the difference between a lady and a flower girl is not how she behaves, but how she’s treated. I shall always be a flower girl to Professor Higgins, because always treats me as a flower girl, and always will; but I know I can be a lady to you, because you always treat me as a lady, and always will”.
Eliza doolittle to Colonel Pickering
George Bernard Shaw Pygmalion (1912).
29/1/01 Assessing affective, cognitive, social, psycho-social and other learning outcomes
Introduction
※ Starter questions {no plug in}
{test questionnaires}
Discussion on two cases
※ 鄭和黃 (1991a, 1991b)。
※ Wong (1992)
Research frameworks
※IEA curriculum framework (Robitaille, & Garden, 1996)
※History of mathematics research (Lit, Siu, & Wong, 2001)
※Holistic review research
※ 3P model
Getting started
※ Research question (Example of holistic review of the mathematics curriculum: Wong, Lam, Leung, Mok, & Wong, 1999, 2000)
※ Conceptualisation (ditto)
※ Identification of construct and measurement factors
※ Operationalisation/instrumentation of constructs (e.g. Robinson & Shaver, 1973) {McLeod, SDQ, Coopersmith}{brief here}
Conceptions of cognitive outcomes
※ Attainment
※ Asking for something more {Dispute of the 1999 // M&S question}, “transfer”
※ NRT & CRT (Biggs, 1996; Burstein et al., 1995; Stimpson & Morris, 1998)
※ Aptitude, performance prediction and preparatory knowledge (Ebel, & Frisbie, 1965)
Assessment of cognitive levels
※ Bloom’s taxonomy, Pittsburgh’s verb list (Cheng, 1977), TIMSS framework (Robitaille & Garden, 1996)
※ Bands of performance
※ Van Hiele levels (Van Hiele, 1986; Wilson, 1985)
※ SOLO tests (Collis & Romberg, 1992; Biggs Collis, 1989; Collis, Romberg, & Jurdak, 1986), Chelsea tests (Brown, Hart, & Küchemann, 1984)
※ HOTs (Kulm, 1990) and open-ended problems (Cai, Lane, & Jakabcsin, 1996)
Alternative assessments
※ Authentic assessment, task-based assessments (Wong, 1997; 黃，1997, 1998)
※ Performance assessment (Brown, Shavelson, 1996; Ni, 1997)
“Content-free” Abilities
※ Contest problems
※ Problem solving (Ki, //; Feldhusen, Houtz, & Ringenbach, 1972), problem posing (Leung, 1996) and process abilities (Lee, 1980) (intermediate assessment ?)
※ I.Q. and spatial ability
Other considerations
※ The PE issue and gender bias
※ Male norm ? (Fennema, Carpenter, Jacobs, Franke, & Levi, 1998; Leder, 1996)
Biggs, J.B. (1996) (ed.). Testing: to educate or to select. Hong Kong: Hong Kong Educational Publishing co.
Biggs, J.B., Collis, K.F. (1989). Towards a model of school-based curriculum development and assessment: Using the SOLO taxonomy. Australian Journal of Education, 33, 149-161.
Brown, J.H., Shavelson, R.J. (1996). Assessing hands-on science: A teacher’s guide to performance assessment. Thousand Oaks, CA: Crown.
Brown, M., Hart, K., & Küchemann, D. (1984). Chelsea Diagnostic Mathematics Tests. Berkshire: NFEF-Nelson.
Burstein, L., Koretz, D., Linn, R., Sugrue, B., Nowak, J., Baker, E.L., & Harris, E.L. (1995). Describing performance standards: Validity of the 1992 National Assessment of Educational Progress Achievement level descriptors as characterizations of mathematics performance. Educational Assessment, 3(1), 9-51.
Cai, J., Lane, S., & Jakabcsin, M.S. (1996). The role of open-ended tasks and holistic scoring rubrics: Assessing students’ mathematical reasoning and communication. In P.C. Elliott (Ed.), Communication in Mathematics: K-12 and Beyond (NCTM 1996 Yearbook), 137-145. Reston, VA: National Council of Teachers of Mathematics.
Cheng, S.C. (1977). An analysis of the cognitive level in mathematics instruction. Education Journal, 6, 187-195.
Collis, K., & Romberg, T. (1992). Collis-Romberg Mathematical Problem Solving Profiles. Hawthorn, Vic.: Australian Council for Educational Research.
Collis, K.F., Romberg, T.A., & Jurdak, M.E. (1986). A technique for assessing mathematical problem-solving ability. Journal for Research in Mathematics Education, 17(3), 206-221.
Ebel, R.L., & Frisbie, D.A. (1965). Essentials of educational measurement, Chapter 6: Validity: interpretation and use, 100-113. New Jersey: Prentice Hall.
Feldhusen, J.F., Houtz, J.C., & Ringenbach, S.E. (1972). The Purdue Elementary Problem-solving Inventory. Psychology Reports, //, 891-901.
Fennema, E., Carpenter, T.P., Jacobs, V.R., Franke, M.L., & Levi, L.W. (1998). A longitudinal study of gender differences in young children’s mathematical thinking (features). Educational Researcher, 27(5), 6-11. Together with “Introduction” (Fennema, E, & Carpenter, T.P., pp. 4-5), “Perspectives from mathematics education” (Sowder, J.T., pp. 12-13), “Perspectives from social and feminist psychology” (Hyde, J.S., & Faffee, S., pp. 14-16), “Perspectives from feminist philosophy” (Noddings, N., pp. 17-18) and “new Perspectives on gender differences in mathematics: A reprise” (Fennema, E., Carpenter, T.P., Jacobs, V.R., Franke, M.L., & Levi, L.W., pp. 19-21).
Kulm, G. (1990) (Ed.). Assessing Higher Order Thinking in Mathematics. Washington, D.C.: American Association for the Advancement of Science.
Leder, G.C. (1996). Mathematics and gender: A question of social shaping. Lecture presented at the 8th International Congress on Mathematical Education. Seville, Span, 14-21 July.
Lee, F.L. (1980). Analysis of cognitive strategies of problem solving process in mathematics and physics. Unpublished M.A. (Ed.) thesis. Hong Kong: The Chinese University of Hong Kong.
Leung, S. K. (1996). Problem posing as assessment: Reflections and Re-constructions. The Mathematics Educator, 1(2), 159-171.
Lit, C.K., Siu, M.K., & Wong, N.Y. (2001). The use of history in the teaching of mathematics: Theory, practice, and evaluation of effectiveness. Education Journal. In press.
Ni, Y. (1997). Performance-based assessment: Problems and design strategies. Education Journal, 23(2), 137-157.
Robinson, J.R., & Shaver, P.R. (1973). Measures of social psychological attitudes. Ann Arbor, Michigan: Survey Research Center, Institute for Social Research.
Robitaille, D.F., & Garden, R.A. (1996). Research Questions and Study Design (TIMSS Monograph No.2). Vancouver, B.C.: Pacific Educational Press. Q181.R47 1996 (CC)
Stimpson, P., & Morris, P. (1998) (Eds.). Curriculum and assessment for Hong Kong: Two components, one system. Hong Kong : Open University of Hong Kong Press.
Van Hiele, P.M. (1986). Structure and insight: A theory of mathematics education. Orlando, FL: Academic Press.
Wilson, M. (1985). Measuring a van Hiele geometry sequence: A reanalysis. //.
Wong. K.M.P. (1997). Do real-world situations necessarily constitute “authentic”mathematical tasks in the mathematics classroom ? Curriculum Form, 6(2), 1-15.
Wong, N.Y., Lam, C.C., Leung, F.K.S., Mok, I.A.C., & Wong, K.M. (1999). An Analysis of the Views of Various Sectors on the Mathematics Curriculum. Final report of a research commissioned by the Education Department, Hong Kong. [www.cdccdi.hk.linkage.net/ cdi/maths/document/Research2.htm]
Wong, N.Y., Lam, C.C., Leung, F.K.S., Mok, I.A.C., & Wong, K.M.P. (2000). Holistic reform of the mathematics curriculum - the Hong Kong experience. Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 3(2), 69-88. [www.fed.cuhk.edu.hk/~nywong]
黃家鳴(1997)。生活情境中的數學與學校的數學學習。《基礎教育學報》7卷12期，161-167。
黃家鳴(1998)。數學文字題及課業的處境應該有多真實？《數學教育》7期，44-54。
Case study:
Wong, N.Y. (1992). The relationship among mathematics achievement, affective variables and home background. Mathematics Education Research Journal, 4(3), 32-42.
鄭肇楨、黃毅英(1991a)。香港中學生的數學學習態度。《香港中文大學校育學報》19期，13-18。
鄭肇楨、黃毅英(1991b)。數學學習習慣和成績，父母學歷，居住面積及父母期望及學生期望的關係。《教學研究學報》6期，86-92。
5/2/01 Measuring instrument: identification of constructs, development and validation
Where do the instruments come from ?
※ Theories (Fraser, 1998)
※ Grounded research (Wong, 1996)
※ Adaptation of instruments
※ Cultural difference
※ Direct/indirect, perception/consquential behaviour, low and high inference tests
What are you measuring ?
※ What are they measuring ? (Biggs, 1993)
※ Social desirability: randomised response technique
Implementation
※ Sampling and pilot
※ Administration of questionnaire
Analysis
※ Reliability (addable ?)
※ EFA, CFA, weighting
※ Validity (Fraser, 1998)
※ Unit of analysis
Social factors
※Classroom environment and psychosocial environment (Fraser, 1998)
◎ antecedents
◎ mediating factor (Fraser, Williamson, & Tobin, 1987)
◎ measurement criterion
※Social economic status (TIMSS/IEA CE studies/ECA studies)
※Home background
Biggs, J. (1993). What do inventories of students’ learning processes really measure ? A theoretical review and clarification. British Journal of Educational Psychology, 63, 3-19.
Fraser, B.J., Williamson, J.C., & Tobin, K.G. (1987). Use of classroom and school climate scales in evaluating alternative high schools. Teaching and Teacher Education, 3, 219-231.
Case study:
Fraser, J.B. // (1998). Science learning environments: assessment, effects and determinants. In. B.J. Fraser, & K.G. Tobin (eds.), International handbook of science education, Vol. 1, 527-564. Dordrecht: Kluwer Academic Publishers.
Wong, N.Y. (1996). Students’ perceptions of the mathematics classroom in Hong Kong. Hiroshima Journal of Mathematics Education, 4, 89-107.
Readings for next lecture
Wong, N.Y., Lam, C.C., Leung, F.K.S., Mok, I.A.C., & Wong, K.M. (1999). An Analysis of the Views of Various Sectors on the Mathematics Curriculum. Final report of a research commissioned by the Education Department, Hong Kong. [www.cdccdi.hk.linkage.net/ cdi/maths/document/Research2.htm]
Wong, N.Y., Lam, C.C., Leung, F.K.S., Mok, I.A.C., & Wong, K.M.P. (2000). Holistic reform of the mathematics curriculum - the Hong Kong experience. Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 3(2), 69-88. [www.fed.cuhk.edu.hk/~nywong]
黃毅英、林智中、黃家鳴、莫雅慈、梁貫成(1999)。香港數學課程全面檢討。《數學教育》8期，2-9。[http://www.fed.cuhk.edu.hk/~fllee/mathfor/edumath/9906/ 02wong_etal.html]
黃毅英(2000)。香港數學教育另類報告2000 ─ 山仍是山的課程改革。載梁興強(2000)。《香港數學教育研討會2000論文集》，90-99。[www.fed.cuhk.edu.hk/ ~nywong]
12/2/01 Needs assessment I
The case of holistic review