development of Spatial abilities
Hartwig Meissner
Westf. Wilhelms-Univ. Muenster, Germany
Abstract:How does the teaching unit „We Build a Village” further the development of spatial abilities? We report on research results from an investigation in eight primary schools with 376 pupils.
Design
"Begreifen" is a German word with a double meaning. On the one hand "begreifen" means to touch or to feel physically (with your hands), on the other hand it means "understanding" (in your head). Thus "begreifen" is one of the keys to develop spatial thinking, it is a synonym for Piaget's "thinking is internalized action". With regard to this view we developed the teaching unit "We Build a Village" to introduce geometry concepts of plane and three dimensional geometry in primary schools (8 lessons, age 8-10). The children work with about 35 different geometric solids. Many activities form the lessons: Sorting and classifying, folding, drawing, cutting, constructing developments, using plasticine, building solids and houses by their developments.
In the research project we wanted to measure via pre- and post-test how the teaching unit furthers the development of spatial abilities. To cover the three factors from Thurstone (Spatial Relations, Visualisation, Spatial Orientation) we choose and/or constructed 9 tasks with altogether 31 items. Control classes got the same tests with a regular teaching.
Results
task / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / allpre-test / ,527 / ,739 / ,548 / ,652 / ,476 / ,601 / ,503 / ,261 / ,307 / ,513
posttest / ,665 / ,799 / ,652 / ,785 / ,584 / ,732 / ,590 / ,453 / ,313 / ,619
signif. / ,000 / ,051 / ,000 / ,000 / ,001 / ,000 / ,000 / ,000 / ,868 / ,000
Table 1: Test results experimental group (N = 184)
Comparing the pre-test results the control group showed a higher performance than the experimental group (means 0,548 vs. 0,513, p=0,025). But in the post-test there were no more significant differences. A t-test also indicates that there are gender differences, although small for most of the test items. For more details see "Reference".
Reference
Meissner, H. (2006): Projekt “DORF” – Raumvorstellungen verbessern. In press: Journal fuer Mathematikdidaktik 27, Teubner Stuttgart, Germany - Summary in English see via:
Handout “Development of Spatial Abilities”PME 30, Praha (2006)
Abstract:How does the teaching unit „We Build a Village” further the development of spatial abilities? Results from an investigation in eight German primary schools with 376 pupils.
Design
"Begreifen" is a German word with a double meaning. On the one hand "begreifen" means to touch or to feel physically (with your hands), on the other hand it means "understanding" (in your head). Thus "begreifen" is one of the keys to develop spatial thinking, it is a synonym for Piaget's "thinking is internalized action". With regard to this view we developed the teaching unit "We Build a Village" to introduce geometry concepts of plane and three dimensional geometry in primary schools (details see Meissner/Mueller-Philipp 1997 or Meissner 1992).The children work with about 35 different geometric solids, made by styroform, by wood, by paper developments, or by plastics (details see fig. 1 on page 4 of this paper). Many activities form the lessons: Sorting and classifying, folding, drawing, cutting, constructing developments, using plasticine, building solids and houses by their developments. At the end of the course the children build their own village with a grocery store, a church, a school, and other houses, including a creek, streets, and parking areas.
In the research project we wanted to measure via pretest and posttest how the teaching unit (8 lessons, age about 9 years) furthers the development of spatial abilities. Control classes got the same tests with a regular teaching.
The Test
Task 1: Where was the photographer?
/(a) in boat ___ (b) in boat ___ (c) in boat___
Task 2: Through which window do you see the chair?
/(a) window ____ (b) window ____ (c) window ____
Task 3: How many small cubes?
(a) ___ cubes (b) ___ cubes (c) ___ cubes (d) ___ cubes
Task 4: Which hand?
hand A hand B /
(a) hand___ (b) hand___ (c) hand___ (d) hand__
Task 5: A box with a Smily on top and a Growi below will be turned around in front of the class along a given sequence of movements. (But then to work on the test items the students do not get a real box) - Question: Which will be on top, Smily or Growi?
(a)(b)
Task 6: The same box?
/Yes No Yes No Yes No Yes No
(a) (b) (c) (d)
Task 7: Correct development?
Yes No Yes No Yes No(a) (b) (c)
/ Yes No Yes No Yes No
(d) (e) (f)
Task 8: Color the edge which belongs to the black edge when you construct the cube:
(a) (b)(c)
Task 9:Which symbol? Draw the symbol:
/(a) (b)
Results
The pretest gives a survey on spatial abilities of 351 third graders in Northern Germany:
Task / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 1 - 9boys / ,546 / ,736 / ,638 / ,698 / ,615 / ,657 / ,513 / ,251 / ,310 / ,552
girls / ,531 / ,738 / ,541 / ,679 / ,390 / ,599 / ,513 / ,267 / ,308 / ,507
all / ,539 / ,737 / ,589 / ,689 / ,501 / ,628 / ,513 / ,259 / ,309 / ,529
Tab. 1. Pretest results for tasks 1-9, mean values for boys (N=174) and girls (N=177)
Comparing the different mean values we find significant differences (t-test) between boys and girls for the whole test (p=0,004), but in detail only for task 3 (p=0,005) and task 5 (p<0,001). The effect of the teaching unit is presented in table 2.
Item / pre / post / signif.1a / ,429 / ,587 / ,002
1b / ,685 / ,766 / ,043
1c / ,467 / ,641 / ,000
2a / ,658 / ,745 / ,032
2b / ,669 / ,739 / ,080
2c / ,891 / ,913 / ,494
3a / ,777 / ,859 / ,032
3b / ,641 / ,766 / ,001
3c / ,473 / ,565 / ,043
3d / ,299 / ,419 / ,004
4a / ,750 / ,880 / ,001
4b / ,739 / ,859 / ,004
4c / ,511 / ,685 / ,000
4d / ,609 / ,717 / ,016
5a / ,364 / ,440 / ,071
5b / ,587 / ,728 / ,002
Item / pre / post / signif.
6a / ,745 / ,821 / ,061
6b / ,609 / ,745 / ,007
6c / ,533 / ,669 / ,002
6d / ,516 / ,696 / ,000
7a / ,679 / ,794 / ,014
7b / ,261 / ,484 / ,000
7c / ,620 / ,685 / ,164
7d / ,636 / ,560 / ,122
7e / ,636 / ,674 / ,394
7f / ,185 / ,342 / ,000
8a / ,391 / ,549 / ,000
8b / ,272 / ,565 / ,000
8c / ,120 / ,245 / ,000
9a / ,283 / ,288 / ,897
9b / ,332 / ,337 / ,911
Tab. 2. Pre-test vs. post-test, all items (experimental group, N=184)
Fig. 1: The set of solids
References
Meissner, H. (2006): Projekt “DORF” – Raumvorstellungen verbessern. Journal fuer Mathematikdidaktik 27 (1), p. 28-51. Teubner Stuttgart, Germany - Summary in English via
Meissner, H., Mueller-Philipp, S.(1997): Wir bauen ein Dorf. Grundschulunterricht 44 (6), p. 40-44. Paedagogischer Zeitschriftenverlag, Berlin Germany
Meissner, H. (1992): Geometry - We build a village. The Student Confronted by Mathematics, Proceedings of ICSIMT 44, p. 241-252. University of Illinois, Chicago USA