Learning Mathematics: Issues, theory and classroom practice, Third Edition

Learning Mathematics: Issues, Theory and Classroom Practice, Third Edition

Volumn , Issue , 2004, Pages 1-228

  Orton, Anthony ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85186977438     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (286)

1. Abreu, G., Bishop, A. J. and Pompeu, G. (1997) ‘What children and teachers count as mathematics’, in T. Nunes and P. Bryant (eds), Learning and Teaching Mathematics. Hove, East Sussex: Psychology Press, pp. 233–63.
2. Anderson, J. R. (1985) Cognitive Psychology and its Implications. New York: W. H. Freeman.
3. Askew, M. and Wiliam, D. (1995) Recent Research in Mathematics Education 5–16. London: HMSO.
4. Assessment of Performance Unit (1980) Mathematical Development: Primary Survey Report Number 1. London: HMSO.
5. Assessment of Performance Unit (1982a) Mathematical Development: Primary Survey Report Number 3. London: HMSO.
6. Assessment of Performance Unit (1982b) Mathematical Development: Secondary Survey Report Number 3. London: HMSO.
7. Assessment of Performance Unit (undated) Mathematical Development: A Review of Monitoring in Mathematics 1978 to 1982. Slough: NFER.
8. Aubrey, C. (1993) ‘An investigation of the mathematical knowledge and competencies which young children bring into school’, British Educational Research Journal, 19(1), 27–41.
9. Austin, J. L. and Howson, A. G. (1979) ‘Language and mathematical education‘, Educational Studies in Mathematics, 10, 161–97.
10. Ausubel, D. P. (1960) ‘The use of advance organizers in the learning and retention of meaningful verbal material’, Journal of Educational Psychology, 51, 267–72.
11. Ausubel, D. P. (1963) ‘Some psychological and educational limitations of learning by discovery‘, New York State Mathematics Teachers Journal, XIII, 90–108. (Also in The Arithmetic Teacher, 11(5), 290–302, 1964.)
12. Ausubel, D. P. (1968) Educational Psychology: A Cognitive View. New York: Holt, Rinehart & Winston.
13. Balacheff, N. (1991) ‘Treatment of refutations: Aspects of the complexity of a constructivist approach to mathematics learning‘, in E. von Glasersfeld (ed.), Radical Constructivism in Mathematics Education. Dordrecht: Kluwer, pp. 89–110.
14. Barnes, D. (1976) From Communication to Curriculum. Harmondsworth: Penguin.
15. Baroody, A. J. (1987) Children’s Mathematical Thinking. New York: Teachers College Press.
16. Bartlett, F. (1958) Thinking. London: George Allen & Unwin.
17. Bell, A. W, Costello, J. and Küchemann, D. (1983) Research on Learning and Teaching. Windsor: NFER-Nelson.
18. Bell, A., Swan, M., Onslow, B., Pratt, K. and Purdy, D. (1989) Diagnostic Teaching for Long Term Learning. Nottingham: Shell Centre for Mathematical Education.
19. Bell, P. (1970) Basic Teaching for Slow Learners. London: Muller.
20. Bereiter, C. (1997) ‘Situated cognition and how to overcome it’, in D. Kirshner and J. A. Whitson (eds), Situated Cognition: Social, Semiotic and Psychological Perspectives. Mahwah, NJ: Lawrence Erlbaum, pp. 281–300.
21. Berry, J. W. (1985) ‘Learning mathematics in a second language: Some cross-cultural issues’, For the Learning of Mathematics, 5(2), 18–23.
22. Bigge, M. L. (1976) Learning Theories for Teachers, 3rd edn. New York: Harper & Row.
23. Biggs, E. E. (1972) ‘Investigational methods’, in L. R. Chapman (ed.), The Process of Learning Mathematics. Oxford: Pergamon, pp. 216–40.
24. Biggs, E. and Shaw, J. (1985) Maths Alive! London: Cassell.
25. Bishop, A. J. (1973) ‘The use of structural apparatus and spatial ability – a possible relationship’, Research in Education, 9, 43–9.
26. Bishop, A. J. (1980) ‘Spatial abilities and mathematics education – a review’, Educational Studies in Mathematics, 11, 257–69.
27. Bishop, A. J. (1988a) ‘Mathematics education in its cultural context’, Educational Studies in Mathematics, 19, 179–91.
28. Bishop, A. J. (1988b) Mathematical Enculturation: A Cultural Perspective on Mathematics Education. Dordrecht: Kluwer.
29. Bishop, A. J. (1991) ‘Mathematics education in its cultural context’, in M. Harris (ed.), Schools, Mathematics and Work. London: The Falmer Press, pp. 29–41.
30. Bloom, B. S., Engelhart, M. D., Furst, E. J., Hill, W. H. and Krathwohl, D. R. (1956) Taxonomy of Educational Objectives: Cognitive Domain. London: Longman.
31. Boaler, J. (1997) Experiencing School Mathematics. Buckingham: Open University Press.
32. Booth, L. R. (1984) Algebra: Children’s Strategies and Errors. Windsor: NFER-Nelson.
33. Branford, B. (1921) A Study of Mathematical Education. Oxford: The Clarendon Press.
34. Brown, G. and Desforges, C. (1977) ‘Piagetian psychology and education: Time for revision’, British Journal of Educational Psychology, 47, 7–17.
35. Brown, M. (1978) ‘Cognitive development and the learning of mathematics’, in A. Floyd (ed.), Cognitive Development in the School Years. London: Croom Helm, pp. 351–73.
36. Brown, M. (1981a) ‘Number operations’, in K. M. Hart (ed.), Children’s Understanding of Mathematics: 11–16. London: John Murray, pp. 23–47.
37. Brown, M. (1981b) ‘Place value and decimals’, in K. M. Hart (ed.), Children’s Understanding of Mathematics: 11–16. London: John Murray, pp. 48–65.
38. Brown, S. I. and Walter, M. I. (1983) The Art of Problem Posing. Philadelphia: The Franklin Institute Press.
39. Bruner, J. S. (1960a) ‘On learning mathematics’, The Mathematics Teacher, 53, 610–19.
40. Bruner, J. S. (1960b) The Process of Education. Cambridge, MA: Harvard University Press.
41. Bruner, J. S. (1966) Toward a Theory of Instruction. Cambridge, MA: Harvard University Press.
42. Bruner, J. S. (1973) Beyond the Information Given. London: George Allen & Unwin.
43. Bruner, J. S. and Kenney, H. J. (1965) ‘Representation and mathematics learning’, in L. N. Morrisett and J. Vinsonhaler (eds), Mathematical Learning. Monograph of the Society for Research in Child Development, 30(1), pp. 50–9.
44. Bruner, J. S., Goodnow, J. J. and Austin, G. A. (1956) A Study of Thinking. New York: Wiley.
45. Bruner, J. S., Olver, R. R. and Greenfield, P. M. (1966) Studies in Cognitive Growth. New York: Wiley.
46. Bryant, P. (1974) Perception and Understanding in Young Children. London: Methuen.
47. Burger, W. F. and Shaughnessy, M. J. (1986) ‘Characterizing the van Hiele levels of develop ment in geometry’, Journal for Research in Mathematics Education, 17, 31–48.
48. Burton, L. (1984) Thinking Things Through. Oxford: Blackwell.
49. Buxton, L. (1981) Do You Panic About Maths? London: Heinemann.
50. Byers, V. and Erlwanger, S. (1985) ‘Memory in mathematical understanding’, Educational Studies in Mathematics, 16, 259–81.
51. Carpenter, T. P. and Moser, J. M. (1982) ‘The development of addition and subtraction problem-solving skills’, in T. P. Carpenter, J. M. Moser and T. A. Romberg (eds), Addition and Subtraction: A Cognitive Perspective. Hillsdale, NJ: Lawrence Erlbaum, pp. 9–24.
52. Carraher, T. N., Carraher, D. W. and Schliemann, A. D. (1987) ‘Written and oral mathematics’, Journal for Research in Mathematics Education, 18(2), 83–97.
53. Child, D. (1986) Psychology and the Teacher, 4th edn. London: Holt, Rinehart and Winston.
54. Chipman, S. F. and Mendelson, M. J. (1979) ‘Influence of six types of visual structure on complexity judgements in children and adults’, Journal of Experimental Psychology: Human Perception and Performance, 5(2), 365–78.
55. Cobb, P. (1987) ‘Information-processing psychology and mathematics education – a constructivist perspective’, Journal of Mathematical Behaviour, 6, 3–40.
56. Cobb, P., Wood, T. and Yackel, E. (1991) ‘A constructivist approach to second grade mathematics’, in E. von Glasersfeld (ed.), Radical Constructivism in Mathematics Education. Dordrecht: Kluwer, pp. 157–76.
57. Cockcroft, W. H. (1982) Mathematics Counts. London: HMSO.
58. Collis, K. F. (1975) A Study of Concrete and Formal Operations in School Mathematics: A Piagetian Viewpoint. Hawthorn, Victoria: Australian Council for Educational Research.
59. Copeland, R. W. (1979) How Children Learn Mathematics. New York: Macmillan.
60. Cormier, S. M. and Hagman, J. D. (1987) ‘Introduction’, in S. M. Cormier and J. D. Hagman (eds), Transfer of Learning: Contemporary Research and Applications. San Diego, CA: Academic Press, pp. 1–8.
61. d’Ambrosio, U. (1985) ‘Ethnomathematics and its place in the history and pedagogy of mathematics’, For the Learning of Mathematics, 5(1), 44–8.
62. d’Ambrosio, U. (1991) ‘Ethnomathematics and its place in the history and pedagogy of mathematics’, in M. Harris (ed.), Schools, Mathematics and Work. London: The Falmer Press, pp. 15–25.
63. Dasen, P. R. (1972) ‘Cross-cultural Piagetian research: A summary’, Journal of Cross-Cultural Psychology, 3(1), 23–39.
64. Dasen, P. R. (1977) ‘Introduction’, in P. R. Dasen (ed.), Piagetian Psychology: Cross-Cultural Contributions. New York: Gardner Press, pp. 1–25.
65. Davis, R. B. (1966) ‘Discovery in the teaching of mathematics’, in L. S. Shulman and E. R. Keislar (eds), Learning by Discovery: A Critical Appraisal. Chicago: Rand McNally, pp. 115–28.
66. Davis, R. B. (1984) Learning Mathematics: The Cognitive Science Approach to Mathematics Education. London: Croom Helm.
67. Dearden, R. F. (1967) ‘Instruction and learning by discovery’, in R. S. Peters (ed.), The Concept of Education. London: Routledge and Kegan Paul, pp. 135–55.
68. Department of Education and Science (1985) Mathematics from 5 to 16. London: HMSO.
69. Department of Education and Science/Welsh Office (1988) Mathematics for Ages 5 to 16. London: HMSO.
70. Dewey, J. (1910) How We Think. Boston, MA: Heath.
71. Dickson, L., Brown, M. and Gibson, O. (1984) Children Learning Mathematics. Eastbourne: Holt, Rinehart & Winston (Schools Council).
72. Dienes, Z. P. (1960) Building Up Mathematics. London: Hutchinson.
73. Dienes, Z. P., translated by P. Seaborne (1973) The Six Stages in the Process of Learning Mathematics. Windsor: NFER.
74. Donaldson, M. (1978) Children’s Minds. Glasgow: Fontana/Collins.
75. Durkin, K. and Shire, B. (eds) (1991) Language in Mathematical Education. Buckingham: Open University Press.
76. Eliot, J. and Smith, I. M. (1983) An International Directory of Spatial Tests. Windsor: NFER-Nelson.
77. Entrekin, V. S. (1992) ‘Mathematical mind mapping’, The Mathematics Teacher, 85(6), 444–5.
78. Esler, W. K. (1982) ‘Physiological studies of the brain: Implications for science teaching’, Journal of Research in Science Teaching, 19, 795–803.
79. Evans, J. (2000) Adults’ Mathematical Thinking and Emotions. London: Routledge/Falmer.
80. Fasheh, M. (1991) ‘Mathematics in a social context: math within education as praxis versus math within education as hegemony’, in M. Harris (ed.), Schools, Mathematics and Work. London: The Palmer Press, pp. 57–61.
81. Fennema, E. and Tartre, L. A. (1985) ‘The use of spatial visualization in mathematics by girls and boys’, Journal for Research in Mathematics Education, 16, 184–206.
82. Fitzgerald, A. and Rich, K. M. (1981) Mathematics in Employment (16–18). Bath: University of Bath.
83. Flanders, N. A. (1970) Analyzing Teaching Behaviour. Reading, MA: Addison-Wesley.
84. Fogelman, K. R. (1970) Piagetian Tests for the Primary School. Windsor: NFER.
85. Freudenthal, H. (1968) ‘Why to teach mathematics so as to be useful’, Educational Studies in Mathematics, 1, 3–8.
86. Frobisher, L. (1994) ‘Problems, investigations and an investigative approach’, in A. Orton and G. Wain (eds), Issues in Teaching Mathematics. London: Cassell, pp. 150–73.
87. Frobisher, L. (1999) ‘Primary schoolchildren’s knowledge of odd and even numbers’, in A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics. London: Cassell, pp. 31–48.
88. Frobisher, L., Monaghan, J., Orton, A., Orton, J., Roper, T. and Threlfall, J. (1999) Learning to Teach Number. Cheltenham: Stanley Thornes.
89. Furneaux, W. D. and Rees, R. (1978) ‘The structure of mathematical ability’, British Journal of Psychology, 69, 507–12.
90. Fuys, D., Geddes, D. and Tischler, R. (1988) The Van Hiele Model of Thinking in Geometry among Adolescents. Reston, VA: NCTM.
91. Gagné, R. M. (1975) Essentials of Learning for Instruction. Hinsdale, IL: The Dryden Press.
92. Gagné, R.M. (1985) The Conditions of Learning and Theory of Instruction, 4th edn. New York: Holt, Rinehart & Winston.
93. Gagné, R. M. and Briggs, L. J. (1974) Principles of Instructional Design. New York: Holt, Rinehart & Winston.
94. Gagné, R. M. and Brown, L. T. (1961) ‘Some factors in the programming of conceptual learning’, Journal of Experimental Psychology, 62, 313–21.
95. Gagne, R. M. and Smith, E. C. (1962) ‘A study of the effects of verbalization on problem-solving’, Journal of Experimental Psychology, 63, 12–18.
96. Garrick, R., Threlfall, J. and Orton, A. (1999) ‘Pattern in the nursery’, in A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics. London: Cassell, pp. 1–17.
97. Gattegno, C. (1960) Modern Mathematics with Numbers in Colour. Reading: Educational Explorers.
98. Gay, J. and Cole, M. (1967) The new mathematics and an old culture. New York: Holt, Rinehart & Winston.
99. Gerdes, P. (1985) ‘Conditions and strategies for emancipatory mathematics education in underdeveloped countries’, For the Learning of Mathematics, 5(1), 15–20.
100. Gerdes, P. (1988) ‘On culture, geometrical thinking and mathematics education’, Educational Studies in Mathematics, 19, 137–62.
101. Gerdes, P. (1994) ‘Reflections on ethnomathematics’, For the Learning of Mathematics, 14(2), 19–22.
102. Getzels, J. W. and Jackson, P. W. (1962) Creativity and Intelligence. New York: Wiley.
103. Ghent, L. (1956) ‘Perception of overlapping and embedded figures by children of different ages’, American Journal of Psychology, 69, 575–86.
104. Ginsburg, H. (1977) Children’s Arithmetic: The Learning Process. New York: Van Nostrand.
105. Ginsburg, H. P., Choi, Y. E., Lopez, L. S., Netley, R. and Chao-Huan, C. (1997) ‘Happy birthday to you: early mathematical thinking of Asian, South American, and U.S. children’, in T. Nunes and P. Bryant (eds), Learning and Teaching Mathematics. Hove, East Sussex: Psychology Press, pp. 163–201.
106. Goldin, G. A. (1989) ‘Constructivist epistemology and discovery learning in mathematics’, in G. Vergnaud, J. Rogalski and M. Artigue (eds), Proceedings of the Thirteenth Annual Conference for the Psychology of Mathematics Education, Volume 2. Paris, France: G. R. Didactique, CNRS, pp. 15–22.
107. Gray, E. M. (1991) ‘An analysis of diverging approaches to simple arithmetic: Preference and its consequences’, Educational Studies in Mathematics, 22, 551–74.
108. Gray, E. M. and Tall, D. O. (1994) ‘Duality, ambiguity and flexibility: A “proceptual” view of simple arithmetic’, journal for Research in Mathematics Education, 26(2), 116–40.
109. Grünbaum, B. and Shephard, G. (1986) Tilings and Patterns: An Introduction. San Francisco: Freeman.
110. Guilford, J. P. (1959) ‘Three faces of intellect’, The American Psychologist, 14, 469–79. (Also in Wiseman, S. (ed.) (1967) Intelligence and Ability. Harmondsworth: Penguin Books, pp. 218–37.)
111. Gura, P. (1992) Exploring Learning: Young Children and Block Play. London: Paul Chapman.
112. Hadamard, J. (1945) The Psychology of Invention in the Mathematical Field. Princeton, NJ: Princeton University Press.
113. Harris, M. (1997) Common Threads: Women, Mathematics and Work. Stoke on Trent: Trentham Books.
114. Hart, K. (1980) ‘A hierarchy of understanding in mathematics’, in W. F. Archenhold, R. H. Driver, A. Orton and C. Wood-Robinson (eds), Cognitive Development Research In Science and Mathematics. Leeds: University of Leeds Centre for Studies in Science Education, pp. 39–61.
115. Hart, K. M. (ed.) (1981) Children’s Understanding of Mathematics: 11–16. London: John Murray.
116. Hart, K. M. (1984) Ratio: Children’s Strategies and Errors. Windsor: NFER–Nelson.
117. Hart, K. M. (1989) ‘There is little connection’, in P. Ernest (ed.), Mathematics Teaching: The State of the Art. Lewes: The Palmer Press.
118. Hartley, J. R. (1980) Using the Computer to Study and Assist the Learning of Mathematics. Leeds: University of Leeds Computer–Based Learning Unit.
119. Harvey, R., Kerslake, D., Shuard, H. and Torbe, M. (1982) Language Teaching and Learning 6: Mathematics. London: Ward Lock.
120. Heim, A. W. (1970) AH4 Group Test of General Intelligence. Windsor: NFER.
121. Her Majesty’s Inspectorate (1985) Mathematics from 5 to 16. London: HMSO.
122. Her Majesty’s Inspectorate (1989) Aspects of Primary Education: the Teaching and Learning of Mathematics. London: HMSO.
123. Herscovics, N. (1989) ‘Cognitive obstacles encountered in the learning of algebra’, in S. Wagner and C. Kieran (eds), Research Issues in the Learning and Teaching of Algebra. Reston, VA: NCTM, pp. 60–86.
124. Hershkowitz, R. (1990) ‘Psychological aspects of learning geometry’, in P. Nesher and J. Kilpatrick (eds), Mathematics and Cognition. Cambridge: Cambridge University Press, pp. 70–95.
125. Hill, C. C. (1979) Problem-solving: Learning and Teaching. London: Frances Pinter.
126. Holt, J. (1964) How Children Fail. Harmondsworth: Penguin.
127. Hope, J. A. (1985) ‘Unravelling the mysteries of expert mental calculation’, Educational Studies in Mathematics, 16, 355–74.
128. Howard, R. W. (1987) Concepts and Schemata. London: Cassell.
129. Hoyles, C. and Sutherland, R. (1989) Logo Mathematics in the Classroom. London: Routledge.
130. Hoyles, C., Küchemann, D. and Foxman, D. (2003) ‘Comparing geometry curricula: Insights for policy and practice’, Mathematics in School, 32(3), 2–6.
131. Hudson, L. (1966) Contrary Imaginations. Harmondsworth: Penguin.
132. Hughes, E. R. (1980) ‘Should we check children?’, in W. F. Archenhold, R. H. Driver, A. Orton and C. Wood-Robinson (eds), Cognitive Development Research in Science and Mathematics. Leeds: University of Leeds Centre for Studies in Science Education, pp. 87–104.
133. Hughes, M. (1986) Children and Number. Oxford: Blackwell.
134. Hutt, C. (1972) Males and Females. Harmondsworth: Penguin.
135. Johnson, D. A. and Rising, G. R. (1967) Guidelines for Teaching Mathematics. Belmont, CA: Wadsworth.
136. Johnson-Laird, P. N. (1983) Mental Models. Cambridge: Cambridge University Press.
137. Joint Matriculation Board/Shell Centre for Mathematical Education (1984) Problems with Patterns and Numbers: An 0–level Module. Manchester: Joint Matriculation Board.
138. Kamii, C. K. with DeClark, G. (1985) Young Children Reinvent Arithmetic: Implications of Piaget’s Theory. New York: Teachers College Press.
139. Kane, R. B., Byrne, M. A. and Hater, M. A. (1974) Helping Children Read Mathematics. New York: American Book Co.
140. Karplus, R. and Peterson, R. W. (1970) ‘Intellectual development beyond elementary school II: Ratio, a survey’, School Science and Mathematics, 70, 813–20.
141. Katona, G. (1940) Organizing and Memorizing. New York: Columbia University Press.
142. Kirshner, D. and Whitson, J. A. (1997) ‘Editors‘ introduction’, in D. Kirshner and J. A. Whitson (eds), Situated Cognition: Social, Semiotic and Psychological Perspectives. Mahwah, NJ: Lawrence Erlbaum, pp. 1–16.
143. Kolinsky, R., Morais, J., Content, A. and Cary, L. (1987) ‘Finding parts within figures: A developmental study’, Perception, 16, 399–407.
144. Krathwohl, D. R., Bloom, B. S. and Masia, B. B. (1964) Taxonomy of Educational Objectives: Affective Domain. London: Longman.
145. Krutetskii, V. A. (1976) The Psychology of Mathematical Abilities in Schoolchildren. Chicago: University of Chicago Press.
146. Küchemann, D. (1980) ‘Children’s difficulties with single reflections and rotations’, Mathematics in School, 9(2), 12–13.
147. Küchemann, D. (1981) ‘Reflections and rotations’, in K. M. Hart (ed.), Children’s Understanding of Mathematics: 11–16. London: John Murray, pp. 137–57.
148. Laborde C. with Conroy, J., de Corte, E., Lee, L. and Pimm, D. (1990) ‘Language and mathematics’, in P. Nesher and J. Kilpatrick (eds), Mathematics and Cognition. Cambridge: Cambridge University Press, pp. 53–69.
149. Lancy, D. F. (1983) Cross-cultural Studies in Cognition and Mathematics. New York: Academic Press.
150. Larkin, J. H. (1989) ‘Eight reasons for explicit theories in mathematics education’, in S. Wagner and C. Kieran (eds), Research Issues in the Learning and Teaching of Algebra. Reston, VA: NCTM, pp. 275–7.
151. Lave, J. (1988) Cognition in Practice: Mind, Mathematics and Culture in Every day Life. Cambridge: Cambridge University Press.
152. Lave, J. (1997) “The culture of acquisition and the practice of understanding’, in D. Kirshner and J. A. Whitson (eds), Situated Cognition: Social, Semiotic, and Psychological Perspectives. Mahwah, NJ: Lawrence Erlbaum, pp. 17–36.
153. Leder, G. (1985) ‘Sex-related differences in mathematics: An overview’, Educational Studies in Mathematics, 16, 304–9.
154. Lee, L. and Wheeler, D. (1987) Algebraic Thinking in High School Students: Their Conceptions of Generalization and Justification. Montreal: Concordia University.
155. Lerman, S. (1989) ‘Constructivism, mathematics and mathematics education’, Educational Studies in Mathematics, 20(2), 211–23.
156. Lester, F. K. Jr. (1977) ‘Ideas about problem-solving: A look at some psychological research’, The Arithmetic Teacher, 25(2), 12–14.
157. Lester, F. K. Jr. (1989) ‘Mathematical problem-solving in and out of school’, The Arithmetic Teacher, 37(3), 33–5.
158. Lindsay, P. H. and Norman, D. A. (1977) Human Information Processing. New York: Academic Press.
159. Lochhead J. (1985) ‘New horizons in educational development’, Review of Research in Education, 12, 3–9.
160. Lochhead, J. (1991) ‘Making math mean’, in E. von Glasersfeld (ed.), Radical Constructivism in Mathematics Education. Dordrecht: Kluwer, pp. 75–87.
161. Lovell, K. (1971a) ‘Proportionality and probability’, in M. F. Rosskopf, L. P. Steffé and S. Taback (eds), Piagetian Cognitive-Development Research and Mathematical Education. Reston, VA:NCTM, pp. 136–48.
162. Lovell, K. (1971b) The Growth of Understanding in Mathematics: Kindergarten Through Grade Three. New York: Holt, Rinehart & Winston.
163. Lysaught, J. P. and Williams, C. M. (1963) A Guide to Programmed Instruction. New York: Wiley.
164. MacNamara, E. A. (1990) Subitizing and addition of number: A study of young children learning mathematics. Unpublished M.Ed, thesis, University of Leeds.
165. Magajna, Z. (2001) Geometric thinking in out-of-school contexts. Unpublished Ph.D. thesis, University of Leeds.
166. Mager, R. F. (1975) Preparing Instructional Objectives (issued 1962 as Preparing Objectives for Programmed Instruction). Belmont, CA: Fearon.
167. Masingila, J. O., Davidenko, S. and Prus-Wisniowska, E. (1996) ‘Mathematics learning and practice in and out of school: A framework for connecting these experiences’, Educational Studies in Mathematics, 31, 175–200.
168. Mason, J., Burton, L. and Stacey, K. (1985a) Thinking Mathematically (revised). Wokingham: Addison-Wesley.
169. Mason, J., Graham, A., Pimm, D. and Gowar, N. (1985b) Routes to/Roots of Algebra. Milton Keynes: Open University Press.
170. Mathematical Association (1923) The Teaching of Geometry in Schools. London: G. Bell & Sons.
171. Mathematical Association (1939) A Second Report on the Teaching of Geometry in Schools. London: G. Bell & Sons.
172. Mathematical Association (1970) Primary Mathematics – A Further Report. London: Mathematical Association.
173. Matthews, G. (1964) Matrices. London: Edward Arnold.
174. Midlands Mathematical Experiment (1964) Report 1962–63. London: Harrap.
175. Miller, G. A. (1956) ‘The magical number seven, plus or minus two: Some limits on our capacity for processing information’, Psychological Review, 63, 81–97.
176. Ministry of Education (1958) Teaching Mathematics in Secondary Schools. London: HMSO.
177. Mitchelmore, M. C. (1980) ‘Three-dimensional geometrical drawing in three cultures’, Educational Studies in Mathematics, 11, 205–16.
178. Mobley, M. (1987) Making Ourselves Clearer: Readability in the GCSE. London: Secondary Examinations Council.
179. Morgan, C. (1998) Writing Mathematically. London: The Palmer Press.
180. Morris, R. W. (1974) ‘Linguistic problems encountered by contemporary curriculum development projects in mathematics’, in Interactions Between Linguistics and Mathematical Education. Paris: UNESCO/CEDO/ICMI.
181. Newell, A. and Simon, H. A. (1972) Human Problem Solving. Englewood Cliffs, NJ: PrenticeHall.
182. Noss, R. and Hoyles, C. (1996) Windows on Mathematical Meanings: Learning Cultures and Computers. Dordrecht: Kluwer.
183. Novak, J. D. (1977) A Theory of Education. Ithaca, NY: Cornell University Press.
184. Novak, J. D. (1980) ‘Methodological issues in investigating meaningful learning’, in W. F. Archenhold, R. H. Driver, A. Orton and C. Wood-Robinson (eds), Cognitive Development Research in Science and Mathematics. Leeds: University of Leeds Centre for Studies in Science Education, pp. 129–55.
185. Novak, J. D. and Gowin, D. B. (1984) Learning How to Learn. Cambridge: Cambridge University Press.
186. Nuffield Mathematics Project (1967) I Do, and I Understand. Edinburgh, London, New York: Chambers/John Murray/Wiley.
187. Nuffield Mathematics Project (1969) Computation and Structure 4. Edinburgh, London, New York: Chambers/John Murray.
188. Nuffield Mathematics Project (1970, 1973) Checking Up I, II, III. Edinburgh, London, New York: Chambers/John Murray/Wiley.
189. Nuffield Maths 5–11 (1983) Nuffield Maths 6 Teacher’s Handbook. Harlow: Longman.
190. Nunes, T. and Bryant, P. (1996) Children Doing Mathematics. Oxford: Blackwell.
191. Nunes, T., Schliemann, A. D. and Carraher, D. W. (1993) Street Mathematics and School Mathematics. Cambridge: Cambridge University Press.
192. Orton, A. (1971) ‘Teaching about functions in the secondary school’, Mathematics Teaching, 57, 45–9.
193. Orton, A. (1983) ‘students’ understanding of differentiation’, Educational Studies in Mathematics, 14, 235–50.
194. Orton, A. (1994) ‘Learning mathematics: implications for teaching’, in A. Orton and G. Wain (eds), Issues in Teaching Mathematics. London: Cassell, pp. 35–57.
195. Orton, A. (2001) ‘Psychology of learning and instruction, overview’, in L. S. Grinstein and S. I. Lipsey (eds), Encyclopedia of Mathematics Education. New York: RoutledgeFalmer, pp. 594–602.
196. Orton, A. and Orton, J. (1999) ‘Pattern and the approach to algebra’, in A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics. London: Cassell, pp. 104–20.
197. Orton, J. (1997) ‘Matchsticks, pattern and generalization’, Education 3–13, 25(1), 61–5.
198. Orton, J. (1999) ‘Children’s perception of pattern in relation to shape’, in A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics. London: Cassell, pp. 149–67.
199. Orton, J. and Orton, A. (1996) ‘Making sense of children’s patterning’, in L. Puig and A. Guitierrez (eds), Proceedings of the Twentieth International Conference for the Psychology of Mathematics Education, Volume 4. Valencia, Spain: Universitat de Valencia, pp. 83–90.
200. Orton, J., Orton, A. and Roper, T. (1999) ‘Pictorial and practical contexts and the perception of pattern’, in A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics. London: Cassell, pp. 121–36.
201. Otterburn, M. K. and Nicholson, A. R. (1976) ‘The language of (CSE) mathematics’, Mathematics in School, 5(5), 18–20.
202. Papert, S. (1980) Mindstorms. Brighton: The Harvester Press.
203. Pegg, J. and Redden, E. (1990) ‘Procedures for, and experiences in, introducing algebra in New South Wales’, Mathematics Teacher, 83(5), 386–91.
204. Piaget, J. (1973) The Child’s Conception of the World. London: Paladin.
205. Picciotto, H. and Wah, A. (1993) ‘A new algebra: Tools, themes, concepts’, Journal of Mathematical Behavior, 12, 19–42.
206. Poincare, H. (1970) ‘Mathematical creation’, in P. E. Vernon (ed.), Creativity. Harmondsworth: Penguin, pp. 77–88.
207. Polya, G. (1954) Mathematics and Plausible Reasoning. Princeton, NJ: Princeton University Press.
208. Polya, G. (1957) How to Solve It. New York: Doubleday Anchor Books. (First published in 1945 by Princeton University Press.)
209. Polya, G. (1962) Mathematical Discovery. New York: Wiley.
210. Popper, K. R. (1972) Objective Knowledge: An Evolutionary Approach. Oxford: The Clarendon Press.
211. Presmeg, N. (1986) ‘Visualization in high school mathematics’, For the Learning of Mathematics 6(3), 42–6.
212. Reed, S. K. (1973) Psychological Processes in Pattern Recognition. New York: Academic Press.
213. Rees, R. (1974) ‘An investigation of some common mathematical difficulties experienced by students’, Mathematics in School, 3(1), 25–7.
214. Rees, R. (1981) ‘Mathematically gifted pupils: Some findings from exploratory studies of mathematical abilities’, Mathematics in School, 10(3), 20–3.
215. Renwick, E. M. (1935) The Case Against Arithmetic. London: Simpkin Marshall.
216. Resnick, L. B. and Ford, W. W. (1984) The Psychology of Mathematics for Instruction. Hillsdale, NJ: Lawrence Erlbaum.
217. Richards, J. (1991) ‘Mathematical discussions’, in E. von Glasersfeld (ed.), Radical Constructivism in Mathematics Education. Dordrecht: Kluwer, pp. 13–51.
218. Rosnick, P. and Clement, J. (1980) ‘Learning without understanding: The effect of tutoring strategies on algebra misconceptions’, Journal of Mathematical Behavior, 3(1), 3–27.
219. Rosskopf, M. E, Steffé, L. P. and Taback, S. (eds) (1971) Piagetian Cognitive-development Research and Mathematical Education. Reston, VA: NCTM.
220. Russell, S. (1983) Factors Influencing the Choice of Advanced Level Mathematics by Boys and Girls. Leeds: University of Leeds Centre for Studies in Science and Mathematics Education.
221. Sawyer, W. W. (1955) Prelude to Mathematics. Harmondsworth: Penguin.
222. Saxe, G. (1991) Culture and Cognitive Development: Studies in Mathematical Understanding. Hillsdale, NJ: Lawrence Erlbaum.
223. Saxe, G. B. and Posner, J. (1983) ‘The development of numerical cognition: Cross-cultural perspectives’, in H. P. Ginsburg (ed.), The Development of Mathematical Thinking. New York: Academic Press, pp. 292–317.
224. Scandura, J. M. and Wells, J. M. (1967) ‘Advance organizers in learning abstract mathematics’, American Educational Research Journal, 4, 295–301.
225. Scheerer, M. (1963) ‘Problem-solving‘. Scientific American Offprint 476. (From Scientific American, 208(4), 118–28).
226. Schliemann, A. (1984) ‘Mathematics among carpenters and apprentices’, in P. Damerow, M. W. Dunckley, B. F. Nebres and B. Werry (eds), Mathematics for All. Paris: UNESCO, pp. 92–5.
227. Schliemann, A. (1995) ‘Some concerns about bringing everyday mathematics to mathematics education’, in L. Meira, and D. Carraher, (eds), Proceedings of the 19th International Conference for the Psychology of Mathematics Education, Volume 1. Recife, Brazil: Universidade Federal de Pernambuco, pp. 45–60.
228. Schools Council (1965) Mathematics in Primary Schools. London: HMSO.
229. Scribner, S. (1984) ‘studying working intelligence’, in B. Rogoff and L. Lave (eds), Everyday Cognition: Its Development in Social Context. Cambridge, MA: Harvard University Press, pp. 9–40.
230. Seaborne, P. L. (1975) An Introduction to the Dienes Mathematics Programme. London: University of London Press.
231. Sewell, B. (1981) Use of Mathematics by Adults in Everyday Life. Leicester: ACACE.
232. Shuard, H. (1982a) ‘Differences in mathematical performance between girls and boys’, in W. H. Cockcroft, Mathematics Counts. London: HMSO, pp. 273–87.
233. Shuard, H. (1982b) ‘Reading and learning in mathematics’, in R. Harvey, D. Kerslake, H. Shuard and M. Torbe, Language Teaching and Learning 6: Mathematics. London: Ward Lock, pp. 84–121.
234. Shuard, H. and Rothery, A. (eds) (1984) Children Reading Mathematics. London: John Murray.
235. Shuard, H., Walsh, A., Goodwin, J. and Worcester, V. (1991) Calculators, Children and Mathematics. London: Simon and Schuster.
236. Shulman, L. S. (1970) ‘Psychology and mathematics education’, in E. G. Begle (ed.), Mathematics Education. Chicago: NSSE, pp. 23–71.
237. Skemp, R. R. (1964) Understanding Mathematics: Teacher’s Notes for Book I. London: University of London Press.
238. Skemp, R. R. (1971) The Psychology of Learning Mathematics. Harmondsworth: Penguin.
239. Skemp, R. R. (1976) ‘Relational understanding and instrumental understanding’, Mathematics Teaching, 77, 20–6.
240. Skemp, R. R. (1982) ‘Communicating mathematics: Surface structures and deep structures’, Visible Language, XVI, 281–8.
241. Skinner, B. F. (1961) ‘Teaching machines’. Scientific American Offprint 461. (From Scientific American, 205(5), 90–102).
242. Skinner, B. F. (1974) About Behaviourism. London: Jonathan Cape.
243. Smith, I. M. (1964) Spatial Ability: Its Educational and Social Significance. London: University of London Press.
244. Solomon, Y. (1989) The Practice of Mathematics. London: Routledge.
245. Springer, S. P. and Deutsch, G. (1981) Left Brain, Right Brain. San Francisco: Freeman.
246. Stacey, K. (1989) ‘Finding and using patterns in linear generalizing problems’, Educational Studies in Mathematics, 20, 147–64.
247. Stern, C. with Stern, M. B. (1953) Children Discover Arithmetic. London: Harrap.
248. Sternberg, R. J. (1989) ‘A componential approach to intellectual ability’, in R. J. Sternberg (ed.), Advances in the Psychology of Human Intelligence, Volume 1. Hillsdale, NJ: Lawrence Erlbaum, pp. 413–57.
249. Stewart, J. (1985) ‘Cognitive science and science education’, European Journal of Science Education, 7, 1–17.
250. Stewart, J. and Atkin, J. (1982) ‘Information processing psychology’, Journal of Research in Science Teaching, 19, 321–32.
251. Sutton, C. (ed.) (1981) Communicating in the Classroom. London: Hodder & Stoughton.
252. Suydam, M. N. and Weaver, J. F. (1977) ‘Research on problem-solving: Implications for elementary school classrooms’, The Arithmetic Teacher, 25(2), 40–2.
253. Tait, K., Hartley, J. R. and Anderson, R. C. (1973) ‘Feedback procedures in computer-assisted arithmetic instruction’, British Journal of Educational Psychology, 43, 161–71.
254. Thorndike, E. L. (1922) The Psychology of Arithmetic. New York: Macmillan.
255. Threlfall, J. (1996) ‘The role of practical apparatus in the teaching and learning of arithmetic’, Educational Review, 48(1), 3–12.
256. Threlfall, J. (1999) ‘Repeating patterns in the early primary years’, in A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics. London: Cassell, pp. 18–30.
257. Threlfall, J. and Frobisher, L. (1999) ‘Patterns in processing and learning addition facts’, in A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics. London: Cassell, pp. 49–66.
258. Torbe, M. and Shuard, H. (1982) ‘Mathematics and language’, in R. Harvey, D. Kerslake, H. Shuard and M. Torbe, Language Teaching and Learning 6: Mathematics. London: Ward Lock, pp. 1–21.
259. Underbill, R. G. (1991) ‘Two layers of constructivist curricular interaction’, in E. von Glasersfeld (ed.), Radical Constructivism in Mathematics Education. Dordrecht: Kluwer, pp. 229–48.
260. UNESCO (1974) Interactions Between Linguistics and Mathematical Education. Paris: UNESCO/CEDO/ICMI.
261. Ursini, S. (1991) ‘First steps in generalization processes in algebra’, in F. Furinghetti (ed.), Proceedings of the Fifteenth International Conference for the Psychology of Mathematics Education, Volume 3. Assisi, Italy: Università di Genova, pp. 316–23.
262. Vergnaud, G. (1982) ‘A classification of cognitive tasks and operations of thought involved in addition and subtraction problems’, in T. P. Carpenter, J. M. Moser and T A. Romberg (eds), Addition and Subtraction: A Cognitive Perspective. Hillsdale, NJ: Lawrence Erlbaum, pp. 39–59.
263. Vergnaud, G. (1990) ‘Epistemology and psychology of mathematics education’, in P. Nesher and J. Kilpatrick (eds), Mathematics and Cognition. Cambridge: Cambridge University Press, pp. 14–30.
264. Vernon, P. E. (1950) The Structure of Human Abilities. London: Methuen.
265. Verschaffel, L. and De Corte, E. (1997) ‘Word problems: A vehicle for promoting authentic mathematical understanding and problem-solving in the primary school’, in T. Nunes and P. Bryant (eds), Learning and Teaching Mathematics. Hove, East Sussex: Psychology Press, pp. 69–97.
266. Vithal, R. and Skovsmose, O. (1997) ‘The end of innocence: A critique of “ethnomathematics” ’, Educational Studies in Mathematics, 34, 131–57.
267. von Glasersfeld, E. (1987) ‘Learning as a constructive activity’, in C. Janvier (ed.), Problems of Representation in the Teaching and Learning of Mathematics. Hillsdale, NJ: Lawrence Erlbaum, pp. 3–17.
268. von Glasersfeld, E. (1991) ‘Introduction’, in E. von Glasersfeld (ed.), Radical Constructivism in Mathematics Education. Dordrecht: Kluwer, pp. xiii–xx.
269. Vygotsky, L. S. (1962) Thought and Language. New York: MIT Press/Wiley.
270. Walkup, L. E. (1965) ‘Creativity in science through visualization’, Perceptual and Motor Skills, 21(1) 35–41.
271. Wall, W. D. (1965) ‘Learning to think’, in W. R. Niblett (ed.), How and Why Do We Learn? London: Faber & Faber.
272. Waring, S., Orton, A. and Roper, T. (1999) ‘Pattern and proof, in A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics. London: Cassell, pp. 192–206.
273. Warren, E. (1992) ‘Beyond manipulating symbols’, in A. Baturo and T. Cooper (eds), New Directions in Algebra Education. Red Hill, Australia: Queensland University of Technology, pp. 252–8.
274. Wertheimer, M. (1961) Productive Thinking. London: Tavistock Publications.
275. Wickelgren, W. A. (1974) How to Solve Problems. San Francisco: Freeman.
276. Williams, E. and Shuard, H. (1982) Primary Mathematics Today, 3rd edn. Harlow: Longman.
277. Williams, J. S. (1985) ‘Using equipment in teaching mechanics’, in A. Orton (ed.), Studies in Mechanics Learning. Leeds: University of Leeds Centre for Studies in Science and Mathematics Education, pp. 55–86.
278. Wilson, B. (1981) Cultural Contexts in Science and Mathematics Education. Leeds: University of Leeds Centre for Studies in Science and Mathematics Education.
279. Winston, R. (2003) The Human Mind. London: British Broadcasting Corporation and Bantam Press.
280. Witkin, H. A., Moore, C. A., Goodenough, D. R. and Cox, P. W. (1977) ‘Field-dependent and field-independent cognitive styles and their educational implications’, Review of Educational Research, 47(1), 1–64.
281. Wood, D. (1988) How Children Think and Learn. Oxford: Blackwell.
282. Wood, R. (1977) ‘Cable’s comparison factor: Is this where girls‘ troubles start?’, Mathematics in School, 6(4), 18–21.
283. Wrigley, J. (1963) ‘some programmes for research’, in F. W. Land (ed.), New Approaches to Mathematics Teaching. London: Macmillan, pp. 30–9.
284. Young, R. G. (1966) Sets: A Programmed Course. London: Methuen.
285. Zachos, I. (1994) Problem-solving in Euclidean geometry in Greek schools. Unpublished Ph.D. thesis, University of Leeds.
286. Zaslavsky, C. (1973) Africa Counts. Boston, MA: Prindle, Weber & Schmidt.