Lisa A. Grupe
Lisa F. Huffman
Norman W. Bray, Ph.D.
University of Alabama at Birmingham
Presented at the 1997 Biennial Meeting of the Society for Research in Child Development in Indianapolis, Indiana.
Mailing address: Department of Psychology and Civitan International Research Center, SC 313, University of Alabama at Birmingham, Birmingham, AL 35294. Phone: (205) 934-0657, FAX: (205) 975-6330. Send Internet email to: bray@cis.uab.edu
When kindergartners are asked to solve simple addition problems, they often externally represent the addends by counting on their fingers or by using manipulatives (blocks, etc.) (Baroody, 1992; Bray, Huffman, Ward & Hawk, 1994; Siegler & Jenkins, 1989). Manipulatives have been widely used in early elementary mathematics education because they provide a concrete, external representation of otherwise abstract numbers, thereby possibly improving performance. Conflicting findings about the use of manipulatives have been demonstrated in many studies (Fennema,1972b; Moody, Abell & Bausell, 1971). Though these studies have focused mainly on accuracy with little or no examination of strategy use, no clear picture has emerged on how manipulatives influence accuracy or strategy use. Therefore, the present study investigated the effect of manipulatives on accuracy and children's use of strategies while solving addition problems.
The subjects were 8 kindergartners (Mage= 6.4 years) in public schools in Birmingham, Alabama. At the beginning of the study, all children were equivalent on basic number knowledge and accuracy for simple addition problems. Children were randomly split into two groups: four with manipulatives (WM) available (forty small plastic bears) to solve problems and four with no manipulatives (NM). Children were tested individually and given no instruction on strategy use or addition. Two sessions per week for 12 weeks were conducted between February and May of the children's kindergarten year. Each session consisted of 12 addition problems: six small addend problems (both addends 5), three large addend problems (one addend 5 and one between 6 and 9), and three challenge problems (one addend > 10, the other < 5). To examine change across sessions, the 24 sessions were broken down into six blocks of four sessions each.
Problems appeared on a computer monitor while the experimenter read the problem aloud ("What is 3 + 5"?). After each answer, the child was asked how s/he arrived at the answer. Using videotapes of the sessions, accuracy and 13 strategies were scored with reliability greater than .90. There were four finger-counting strategies and four corresponding manipulative-counting strategies [i.e., counting from one on fingers or with bears, count from an addend with fingers or bears], four counting strategies which involved no representation [i.e., counting aloud, counting from an addend
without fingers or bears], and one strategy, retrieval ("I knew it"), which involved no representation and no counting.
The presence of manipulatives did not have a significant effect on accuracy (MWM = 84% , MNM = 71%; F (1,6) = 1.43, p > .28). The amount of exposure the children have to addition (whether problems are in earlier or later blocks) and what type of problem the children are solving (small addend, large addend, challenge) appears to have more of an influence on accuracy. Across blocks, accuracy improved [F (5,30) = 3.65, p < .01] from 70% in Block 1 to 83% in Block 6. For problem type, accuracy decreased with problem difficulty [F(2,12) = 6.90, p <.01; Msmall = 94%, ; Mlarge = 70%, ; Mchallenge = 51%.
Were there differences across groups on strategy use? Only two of the four children with manipulatives chose to use them, and they did not do so exclusively; they also used other non-manipulative strategies. They often used the same counting strategy in one session but switched between using fingers and bears for representation. Manipulative use dropped out entirely by Block 4 (Session 15). Overall, the two groups (WM, NM) displayed remarkably similar patterns of strategy use; however, one child in each group chose never to use representational strategies with accuracy varying widely (one child achieved 90% (WM) and one achieved 71% (NM) accuracy). It is interesting to note that a contributing factor to the low (71%) accuracy achieved by the child with no manipulatives was due to the use of an "illegal strategy" on every challenge problem (e.g., adding "24 + 2" as "2+4+2" ).
Six of the eight children started out using strategies involving representation (fingers/bears) and moved toward strategies without representation (retrieval, count from an addend). By block 6, all eight children had moved away from representation and toward the use of retrieval (no counting, no representation) . More detailed individual case studies of these eight children will be presented in the poster.
Results from this study show that the presence of manipulatives did not influence accuracy in kindergartners solving addition problems. The type of problem and whether a problem occurs in earlier or later blocks seem to influence strategy use, whereas the presence of manipulatives does not.