1 / 36

Summary ? Discourse

Summary ? Discourse. 聯結學說 E.L. Thorndike(1874-1949). 完形心理學 德國 20’s M. Wertheimer (1880-1943) W. Kohler (1887-1967) K. Koffka (1886-1941). 行為主義 ( 美國 ) 20’s – 30’s J. Watson (1878-1958) 「在一個行為主義者看來的心理學」 (1913) I. Pavlov (1849-1936). 認知心理學 20’s – 50’s J.Piaget (1896-1980)

susannah-short
Download Presentation

Summary ? Discourse

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Summary ? Discourse

  2. 聯結學說 E.L. Thorndike(1874-1949) 完形心理學 德國20’s M. Wertheimer (1880-1943) W. Kohler (1887-1967) K. Koffka (1886-1941) 行為主義(美國) 20’s – 30’s J. Watson (1878-1958) 「在一個行為主義者看來的心理學」(1913) I. Pavlov (1849-1936) 認知心理學 20’s – 50’s J.Piaget (1896-1980) J.S. Bruner (1915-) D.P.Ausubel 新行為主義 30’s – 50’s B.F. Skinner (1904-1990) 折衷學派 60’s – 80’s R.M. Gagné (1916-) R.Glaser(1915-) BASICS

  3. ※Reinforcement & classroom/ social setting ※ S-R-K ※ Intrinsic & external motivation ※ Locus of control ※ Attribution ※“cause” and “effect”

  4. A fable reported by Ausubel (1948) The following day, when the little hoodlums came to jeer at him, he came to the door and said to them, “From today on any boy who calls me ‘Jew’ will get a dime from me.” Then he put his hand in his pocket and gave each boy a dime. Delighted with their booty, the boys came back the following day and began to shrill, “Jew! Jew!” The tailor came out smiling. He put his hand in his picket and gave each of the boys a nickel, saying, “A dime is too much-I can only afford a nickel today.” The boys went away satisfied because, after all, a nickel was money, too. However, when they returned the next day to hoot at him, the tailor gave them only a penny each. “Why do we get only a penny today?” they yelled. “That’s all I can afford.” “But two days ago you gave us a dime, and yesterday we got a nickel. It’s not fair, mister. ” “Take it or leave it, That’s all you’re going to get!” “Do you think we’re going to call you ‘Jew’ for one lousy penny?” “So don’t” And they didn’t. Human Motivation (Bernard Weiner)

  5. conscious CONCEPTION VIEW unconscious PRIMITIVE BELIEF affect (100%) cognition (100%) CONCEPTION OF MATH: DEFINITION N

  6. CONSCIOUS affect. (100%) view expectation preconception stereotype image conception primitive beliefs cognitive (100%) UNCONSCIOUS

  7. ghosts practice ( beliefs in action) process of adaptation to the context ( type of school, location of the school, principal, parents, …) conception of mathematics teaching ( set of conscious and beliefs) subject matter personal experience knowledge educational theories Teachers’ belief on mathematics teaching: ghosts unconscious or repressed

  8. Expert judgment

  9. COMMON BELIEFS (Lim, 1999) • Mathematics is a difficult subject • Mathematics is only for the clever ones • Mathematics as a male domain • Other Myths: Kogelman & Warren, 1978; • Paulos, 1992)

  10. Instrumental view • Platonic view • Problem solving view (Ernest, 1991) • Vies of mathematics teaching • - learner-focused • - content-focused, emphasis on conceptual understanding • - content-focused, emphasis on performance • - classroom-focused • (Thompson, 1992)

  11. DIMENSIONS • - Epistemological (how can math be acquired) • Ontological (what is math ?) • (Furinghetti, 1998)

  12. “What do you think mathematics is ?” FRAGMENTED COHESIVE “How do you usually go about learning math ?” Those who hold a fragmented view incline to go about surface learning and those who hold a cohesive view incline to go about deep learning Crawford et al (1994)

  13. Five common views of the UK sample • Utilitarian • Symbolic • Problem solving • Enigmatic (mystic) • Absolutist • Dualistic view

  14. Categories and subcategories of images of mathematics and frequency of corresponding responses Images of mathematics (F=797) Attitude Beliefs Process of learning Nature of mathematics Values/goals (feelings) (about own mathematical ability) (teaching/learning) (in mathematics/education) (f=346 or 43.4%) (f=39 or 4.9%) (f=110 or 13.8%) (f=237 or 29.7%) (f=65 or 8.2%) Frequency (f) = number of responses corresponding to the categories or subcategories.

  15. Categories and subcategories of images of mathematics and frequency of corresponding responses Images of mathematics (F=727) Attitude Beliefs Process of learning Nature of mathematics Values/goals (feelings) (about own mathematical ability) (teaching/learning) (in mathematics/education) ( f=272 or 37.4%) (f=62 or 8.5%) (f=227 or 31.2%) (f=93 or 12.8%) (f=73 or 10.1%) Frequency (f) = number of responses corresponding to the categories or subcategories.

  16. CONCEPTION & PHENOMENOGRAPHY • Outcome space & critical aspects • “Can you tell me something you’ve learned?” • learning to do • learning to know • learning to understand • Pramling (1983)

  17. Learning • - increasing one’s knowledge • - memorising and reproducing • - applying what has been learned • - understanding • - seeing something in a different way • changing as a person • Marton, Dall’Alba, & Beaty (1993)

  18. Understanding - existential understanding (that something is the case, what really is the case, the meaning of something) - hermeneutic understanding (what things look like for another, what an expression means) - phenomenological understanding (how something works, why something is the case, inherent regularity or structure) Helmstad & Marton (1991)

  19. Deep and surface learning Quantitative Surface Multistructural and lower Qualitative Deep Relational and higher • Pedagogy of variation • - Discernment • - Awareness • Simultaneity • Lived space

  20. SOURCE Collective Anschauuang Lim’s model

  21. CONSEQUENCES ※ Student ※ Intended belief  implemented belief  attained belief  achieved belief ※ Teacher ※ Self-monitoring

  22. METHODOLOGY “Mathematics is …” “Mathematics learning is …” ※ “Math is a game played according to certain simple rules with meaningless marks on paper” (D. Hilbert) ※ “Mathematics may be defined as the subject in which we never know what are talking about, nor whether what we are saying is true” (B. Russell) ※ “Mathematics has nothing do with logic” (K. Kodaira) ※ “The moving power of mathematical invention is not reasoning but imagination” (A. DeMorgan)

  23. Zimmermann Pehkonen questionnaire Good mathematics teaching includes: 1. doing calculations mentally 2. the idea that getting the right answer is always more important than the way of solving the problem 3. doing computations with paper and pencil 4. the idea that the pupil can sometimes make guesses and use trial and error 5. the idea that everything ought to be expressed always as exactly as possible 6. drawing figures 7. the idea that one ought to get always the right answer very quickly 8. strict discipline 9. doing word problems 10. the idea that there is always some procedure which one ought to exactly follow in order to get the result 11. the idea that all pupils understand 12. the idea that much will be learned by memorising rules 13. the idea that pupils can put forward their own questions and problems for the class to consider 14. the use of calculators 15. the idea that the teacher helps as soon as possible when there are difficulties 16. the idea that everything will always be reasoned exactly

  24. 17. the idea that different topics, such as calculation of percentages, geometry, algebra, will taught and learned separately; they have nothing to do with each other 18. the idea that there will be as much repetition as possible 19. the idea that studying mathematics has practical benefits 20. the idea that only the mathematical talented pupils can solve most of the problem 21. the idea that studying mathematics can only always be fun 22. calculations of areas and volumes (e.g. the area of a rectangular and the volume of a cube) 23. the idea that studying mathematics requires a lot of effort by pupils 24. the idea that there are usually more than one way to solve problem 25. the idea that games can be used to help pupils learn mathematics 26. the idea that when solving problems, the teacher explains every stage exactly 27. the idea that pupils are led to solve problems on their own without help from the teacher 28. the constructing of different concrete objects (e.g. a box or a prism) and working with them 29. the idea that there will be as much practice as possible 30. the idea that all or as much as the pupil is capable of will be understood 31. the idea that also sometimes pupils are working in small group 32. the idea that the teacher always tells the pupils exactly what they ought to do.

  25. Conceptions of Mathematics Questionnaire 1. For me, mathematics is the study of numbers 2. Mathematics is a lot of rules and equations 3. By using mathematics we can generate new knowledge 4. Mathematics is imply an over-complication of addition and subtraction 5. Mathematics is about calculation 6. Mathematics is a set of logical systems which have been developed to explain the world and relationships in it. 7. What mathematics is about finding answers through the use of numbers and formulae 8. I think mathematics provides an insight into the complexities of our reality. 9. Mathematics is figuring out problems involving numbers 10.Mathematics is a theoretical framework describing reality with the aim of helping us understand the world

  26. 11. Mathematics is like a universal language which allows people to communicate and understand the universe 12. The subject of mathematics deals with numbers, figures and formulae 13. Mathematics is about playing around with numbers and working out numerical problems 14. Mathematics uses logical structures to solve and explain real life problems 15. What mathematics is about is formulae and applying them to everyday life and situations 16. Mathematics is a subject where you manipulate numbers to solve problems 17. Mathematics is logical system which helps explain the things around us 18. Mathematics is the study of the number system and solving numerical problems 19. Mathematics is models which have been devised over years to help explain, answer and investigate matters in the world • Fragmented: 1, 2, 4, 5, 7, 9, 12, 13, 16, 18 • Cohesive: 3, 6, 8, 10, 11, 14, 15, 17, 19

  27. Conception of Mathematics Learning Scale 1. Mathematics is computation 2. Mathematics problems given to students should be quickly solvable in a few steps 3. Mathematics is the dynamic searching for order and pattern in the learner’s environment 4. Mathematics is a beautiful, creative and useful human endeavour that is both a way of knowing and a way of thinking 5. Right answers are much more important in mathematics than the ways in which you get them 6. Mathematics knowledge is the result of the learner interpreting and organising the information gained from experiences 7. Students are rational decision makers capable of determining for themselves what is right and wrong 8. Mathematics learning is being able to get the right answers quickly 9. Periods of uncertainty, conflict, confusion, surprise are a significant part of the mathematics learning process 10. Young students are capable of much higher levels of mathematical thought than has been suggested traditionally 11. Being able to memorise facts is critical in mathematics learning 12. Mathematics learning is enhanced by activities which build upon and respect students’ experiences 13. Mathematics learning is enhanced by challenge within a supportive environment 14. Teachers should provide instructional activities which result in problematic situations for learners 15. Teachers or the textbook – not the student - are the authorities for what is right or wrong 16. The role of the mathematics teacher is to transmit mathematical knowledge and to verify that learners have received this knowledge 17. Teachers should recognise that what seem like errors and confusions from an adult point of view are students’ expressions of their current understanding 18. Teachers should negotiate social norms with the students in order to develop a co-operative learning environment in which students can construct their knowledge

  28. OTHERS Conceptions of professors Mathematicians’ way of knowing What do we do when we do math Image of mathematician View of adults

More Related