外文翻译---视觉-空间表征的类型和数学问题解决(编辑修改稿)

外文翻译---视觉-空间表征的类型和数学问题解决(编辑修改稿)内容摘要：

missing cell. The figures in each row and column differ by some rule or set of rules. The task is to induce these rules and apply them to choose the missing figure from a set of eight choices. 4. Spatial ability was measured by two tests, the Block Design subtest of the Wechsler Intelligence Scale for Children— Revised (WISCR。 Wechsler, 1976) and the Space subtest of the Primary Mental Abilities Test (PMA Space。 Thurstone amp。 Thurstone, 1947), which are characteristic of two different spatial abilities factors. In the Block Design test, participants are presented with a set of blocks that are white on some sides, red on some sides, and half redhalf white on others. They are then presented with a picture of a twodimensional red and white design. Their task is to arrange the blocks so that the design is shown. This test is characteristic of the spatial visualization factor (Carroll, 1993。 Lohman, 1988). The PMA Space test is a mental rotation test. On each trial, participants are shown a standard figure on the lefthand side of the page and six parison figures on the righthand side of the page. Their task is to indicate whether each of six parison figures is a planar rotation of the target figure (as opposed to its mirror image) as quickly and accurately as possible. This test is a measure of the spatial relations factor, also referred to as speeded rotation (Carroll, 1993。 Lohman, 1988). Procedure The measures were administered in two group sessions and one session in which students were tested individually. In the group sessions, all students were tested at once in their classroom. In the first group session, the DVRT was administered, and in the second group session, the Ravens Progressive Matrices and the PMA Space subtest were administered, according to the standard instructions for these instruments. Each session took approximately 1 hr. In the individual session, each student was first administered the MPI. The 15 problems were printed on cards and presented in different orders, such that no more than 6 students received the problems in any order. When each problem was presented, the student was first allowed up to 3 min to solve the problem, although students often gave an answer in less than this time. During this time the experimenter did not speak except to encourage a student to attempt a problem, but the experimenter did note any diagrams the student drew or gestures the student made. When the student had answered the problem (or after 3 minutes, if the student did not plete the problem), the student was asked the strategy questions about that problem (samples presented in Appendix B). Following the interviews, which were audiotaped, the students were administered the Block Design subtest of the WISCR. Scoring of Mathematical Processing Instrument Four different measures were scored from responses on the MPI. The first score was the number of problems solved correctly. The second score was a measure of the extent to which the student used visualspatial representations in solving the problems. Each student was given a score of 1 on each problem for which they reported use of a visualspatial representation and 0 for each problem on which there was no evidence that they used such a representation. The third and fourth scores measured the extent to which students39。 visualspatial representations were schematic or pictorial. For each problem on which a person used a visualspatial representation, the representation was scored as either primarily schematic or primarily pictorial. A visualspatial representation was scored as primarily schematic if the student drew a diagram, used gestures showing the spatial relations between objects in a problem in explaining their solution strategy, or reported a spatial image of the relations expressed in the problem. For example, consider the responses to the following problems: Problem 1: At each of the two ends of a straight path, a man planted a tree, and then every 5 meters along the path he planted another tree. The length of the path is 15 meters. How many trees were planted? Problem 11: A hitchhiker set out on a journey of 60 miles. He walked the first 5 miles and then got a lift from a lorry [truck] driver. When the driver dropped him [off], he still had half of his journey to travel. How far had he traveled in the lorry? The following protocols for Problems 1 and 11, respectively, were scored as indicating primarily schematic imagery because the solver reported representing the essential spatial relations relevant to solving the problem (., the distances between the trees or the length of the journey) and not the specific objects described in the problem: I had a [mental] picture of the path, not the trees, and it had something 5 meters along, not trees, just something. No, I didn39。 t see the lorry driver either. I just pictured 60 miles, it could have been 60 feet, 60 anything. Diagrams always showed the spatial relations between objects in a problem. Sample diagrams drawn for Problem 1 are shown in Figure 1. A visualspatial representation was scored as primarily pictorial if the student reported an image of the objects or persons referred to in a problem, rather than the relations between these objects. For example, the following imagery reported in Problems 1 and 11, respectively, was scored as primarily pictorial: I just saw the man going along planting trees. No, I just imagined him outside his house with his hand out, hitchhiking. If there was no evidence in the protocols that the relations between objects in a problem had been represented in an image, the representation was scored as pictorial. It was difficult to classify imagery of Problem 14 as either pictorial or schematic— most participants who reported imagery on this problem imaged a pass, which se。