Defining and measuring conceptual knowledge in mathematics

Developmental Review

Volumn 34, Issue 4, 2014, Pages 344-377

  Crooks, Noelle M ^a   Alibali, Martha W ^b  

^a Broward Community College   (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Cardinality; Conceptual knowledge; Equivalence; Inversion; Mathematical thinking

Indexed keywords

EID: 84925943329     PISSN: 02732297     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dr.2014.10.001     Document Type: Review

References (216)

1. Alibali M.W. How children change their minds: Strategy change can be gradual or abrupt. Developmental Psychology 1999, 35:127-145.
2. G.
3. E.
4. G.
5. G.
6. Baroody A.J., Dowker A. The development of arithmetic concepts and skills: Constructing adaptive expertise. "Studies in Mathematics Thinking and Learning" series 2003, Lawrence Erlbaum Associates, Mahwah, NJ. A. Schoenfeld (Ed.).
7. E.
8. I.
9. I.
10. I.
11. G. A.J. Baroody, A. Dowker (Eds.).
12. Bermejo V., Morales S., Garcia deOsuna J. Supporting children's development of cardinality understanding. Learning and Instruction 2004, 14:381-398.
13. G.
14. C.
15. G. D.F. Bjorklund (Ed.).
16. I. J. Campbell (Ed.).
17. I.
18. G.
19. G.
20. G.
21. C.
22. Brownell W.A. When is arithmetic meaningful?. The Journal of Educational Research 1945, 38(7):481-498.
23. I.
24. G.
25. G.
26. G.
27. I.
28. I.
29. G.
30. E.
31. G. J. Hiebert (Ed.).
32. Carr M., Alexander J., Folds-Bennett T. Metacognition and mathematics strategy use. Applied Cognitive Psychology 1994, 8:583-595.
33. C.
34. Crooks, N. M., & Alibali, M. W. (2013). Equivalence problem strategy data from undergraduate participants. Unpublished raw data.
35. G. F.L. Rowley-Kelly, D.H. Reigel (Eds.).
36. G.
37. E.
38. E.
39. G.
40. I.
41. G.
42. G. L.D. English (Ed.).
43. E.
44. G.
45. C.
46. C.
47. C.
48. E.
49. Garofalo J., Lester F.K. Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education 1985, 16(3):163-176.
50. G.
51. C.
52. C.
53. C. J. Hiebert (Ed.).
54. I.
55. I.
56. Gilmore C.K., Papadatou-Pastou M. Patterns of individual differences in conceptual understanding and arithmetic skill: a meta-analysis. Mathematical Thinking and Learning 2009, 11:25-40.
57. G.
58. G.
59. G. L.A. Penner, G.M. Batsche, H.M. Knoff, D.L. Nelson (Eds.).
60. C.
61. G.
62. G.
63. G.
64. G.
65. G. H. Stevenson, H. Azuma, K. Hakuta (Eds.).
66. E.
67. G.
68. G.
69. Hiebert J. Conceptual and procedural knowledge: The case of mathematics 1986, Erlbaum, Hillsdale, NJ.
70. G. D.A. Grouws (Ed.).
71. G. J. Hiebert (Ed.).
72. G. J. Hiebert (Ed.).
73. G.
74. G.
75. G.
76. C.
77. G.
78. G. R. Zazkis, S.R. Campbell (Eds.).
79. G. T.P. Carpenter, E. Fennema, T.A. Romberg (Eds.).
80. G. J. Kilpatrick, J.O. Swafford, B. Findell (Eds.).
81. Knuth E.J., Alibali M.W., McNeil N.M., Weinberg A., Stephens A.C. Middle school students' understanding of core algebraic concepts: equality and variable. Zentralblatt für Didaktik der Mathematik / International Journal on Mathematics Education 2005, 37:68-76.
82. G.
83. G.
84. G.
85. G.
86. G. S.G. Paris, H.M. Wellman (Eds.).
87. C.
88. G.
89. G.
90. G.
91. G.
92. G.
93. G. B. Danny (Ed.).
94. G.
95. E.
96. G.
97. E.
98. McNeil N.M. U-shaped development in math: 7-year-olds outperform 9-year-olds on equivalence problems. Developmental Psychology 2007, 43(3):687-695.
99. E.
100. E.
101. E.
102. E.
103. E.
104. Medin D. Concepts and conceptual structure. American Psychologist 1989, 44(12):1469-1481.
105. G.
106. G.
107. G. K.R. Harris, S. Graham, D. Deshler (Eds.).
108. G.
109. National Council of Teachers of Mathematics Principles and standards for school mathematics http://www.nctm.org/standards/default.aspx?id=58.
110. National Governors Association Center for Best Practices, Council of Chief State School Officers Common core state standards for mathematics http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf.
111. G.
112. C.
113. G.
114. Pardhan H., Mohammad R.F. Teaching science and mathematics for conceptual understanding? A rising issue. Eurasia Journal of Mathematics, Science and Technology Education 2005, 1(1):1-20.
115. G.
116. G.
117. G.
118. G.
119. Prather R.W., Alibali M.W. The development of arithmetic principle knowledge: how do we know what learners know?. Developmental Review 2009, 29:221-248.
120. Reason M. Relational, instrumental and creative understanding. Mathematics Teaching 2003, 184:5-7.
121. G.
122. G.
123. E.
124. E.
125. G.
126. G.
127. E.
128. G. C. Donlan (Ed.).
129. G.
130. G.
131. G.
132. G.
133. G.
134. I.
135. I.
136. I.
137. Robinson K.M., LeFevre J. The inverse relation between multiplication and division: Concepts, procedures, and a cognitive framework. Educational Studies in Mathematics 2012, 79:409-428.
138. Rogers T.T., McClelland J.L. A parallel distributed processing approach to semantic cognition: applications to conceptual development. Building object categories in developmental time 2005, 335-387. Erlbaum, Hillsdale, NJ. L. Gershkoff-Stowe, D.H. Rakison (Eds.).
139. E.
140. Sarnecka B.W., Carey S. How counting represents number: What children must learn and when they learn it. Cognition 2008, 108:662-674.
141. C.
142. G.
143. G.
144. Schneider M., Rittle-Johnson B., Star J.R. Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge. Developmental Psychology 2011, 47(6):1525-1538.
145. I.
146. Schneider M., Stern E. The developmental relations between conceptual and procedural knowledge: A multimethod approach. Developmental Psychology 2010, 46(1):178-192.
147. G.
148. G.
149. C.
150. I.
151. G.
152. G.
153. C. J. Bideaud, C. Meljac, J.-P. Fischer (Eds.).
154. G.
155. Star J. Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education 2005, 36(5):404-411.
156. Steinberg R.M., Sleeman D.H., Ktorza D. Algebra students' knowledge of equivalence of equations. Journal for Research in Mathematics Education 1991, 22(2):112-121.
157. I.
158. Stigler J.W., Hiebert J. The teaching gap: Best ideas from the world's teachers for improving education in the classroom 1999, Free Press, New York, NY.
159. Stock P., Desoete A., Roeyers H. Mastery of the counting principles in toddlers: a crucial step in the development of budding arithmetic abilities?. Learning and Individual Differences 2009, 19:419-422.
160. G.
161. G.
162. G.
163. I.
164. G.
165. E. 10.1080/10986060701360910.
166. C.
167. C.
168. E.
169. C.
170. I.
171. I.
172. E.
173. E.
174. E.
175. C.
176. I.
177. I.
178. I.
179. C.
180. E.
181. E.
182. E. 10.1080/14794802.2012.756635.
183. E.
184. I.
185. E.
186. I.
187. C.
188. C.
189. E.
190. C.
191. E.
192. McNeil N.M. A change-resistance account of children's difficulties understanding mathematical equivalence. Child Development Perspectives 2014, 8(1):42-47.
193. E.
194. E.
195. C.
196. E.
197. C.
198. I. M. Marschark, P.C. Hauser (Eds.).
199. I.
200. C.
201. E. K. Tellez, J. Moschkovitch, M. Civil (Eds.).
202. E.
203. E.
204. C.
205. I.
206. E.
207. I.
208. I.
209. I.
210. E. A.J. Baroody, A. Dowker (Eds.).
211. I.
212. E.
213. C.
214. E.
215. C.
216. C.