In this paper, I have described lessons on velocity, which stand on the ground of a graphical schema (Dorfler, W., 1991, p.74) of the process of generalization. This model proposed by Dorfler, W. is as follows.

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　　 I have subdivided child's knowledge on velocity into conceptual knowledge and procedural knowledge. Simultaneous activation of these knowledge has been my task since I have grappled with a study of child's knowledge on velocity. Hence I considered to try to make advantage of this model.
　　To connect one item with another item on this model, I have make use of views of Toda, K. and Mach, E..
　　Toda, K. suggested the following differentiation of stages of problem solving in 1954.: When one is confronted with a personal task, which is appropriate for the mathematical thinking and the mathematical process, one (1) perceives it as one's task, (2) makes a problem out of it, (3) gives the mathematical presentation to this, (4) recons out it, (5) interprets the result as the answer of the problem, and (6) considers it as the answer of the task. When I consider these six stages, Stage (1)and Stage (6) are concerned with competence analyzing tasks, Stage (2) is related to problem making ability, and Stage (3)〜(5) are related to word problem solving ability, I think. Also I considered the process of the thinking experiment of Mach, E. and thought the following process of the thinking experiment about the elementary school.: (1) Establishment of ideal/abstract conditions (Establishment of the precondition), (2) Establishment of factors (constant and variable) (Establishment of observational conditions), and (3) Establishment of the changeable method of factors. And after (1)〜(3), the following process follows.: (4) Establishment of the hypothesis and (5) real experiments. Moreover lessons were going well under these two views.

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　　In this paper, I have described findings in investigations after lessons on velocity, which stand on the ground of a graphical schema (Dorfler, W., 1991, p.74) of processes of generalization.
　　For connecting an item with another item on this model, I have made use of 6 stages on problem solving of Toda, K. (1954) and processes of the thinking experiment of Mach, E. (1971).

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　　By the way, I have set up the following 3 hypotheses and examined to verify them. The participants in examinations include 170 pupils of 3 elementary schools' grade 6 in Kobe. "
If I carry out lessons on velocity as planned which raise task-analyzation power on velocity and are based on the general model proposed by Dorfler, W.
Hypothesis (1)
　　For task-analyzation power, there maybe exist meaningful differences between pupils whom I taught and ones whom another teachers taught.
Hypothesis (2)
　　For emotional aspects, there maybe exist meaningful differences between pupils whom I taught and ones whom another teachers taught.
Hypothesis (3)
　　For pupils whom I taught, there maybe exist correlation between task-analyzation power and emotional aspects, but there unlikely do for pupils whom another teachers taught.
　　As the result of the examination on task-analyzation power, F-test and t-test verified "Hypothesis (1)" (i.e. F (34, 134)≒44.423 > F (30, 120), t≒6.33^* (^*p≦.05)).
　　As the result of the examination on emotional aspects, F-test and t-test verified "Hypothesis (2)" (i.e. F (34, 134)≒1.175 < F (30, 120), t≒3.48^* (^*p≦.05)).
　　Also Pearson's product-moment correlation coefficient was 0.746 in pupils whom I taught, and was 0.051 in pupils whom another teachers taught, so that this verified "Hypothesis (3)".

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