Thank you for visiting our site! You landed on this page because you entered a search term similar to this:

__7th grade level variables and equations explanations Equations Substitution variables__.We have an extensive database of resources on

*7th grade level variables and equations explanations Equations Substitution variables*. Below is one of them. If you need further help, please take a look at our software "Algebrator", a software program that can solve any algebra problem you enter!

| |||||

THE EFFECT OF STRUCTURAL VARIABLES ON THE LEVEL OF DIFFICULTY OF MISSING VALUE PROPORTION PROBLEMS | |||||

Gina Conner, Guershon Harel and Merlyn BehrNorthern Illinois University | |||||

Tournaire and Pulos (1985) listed two categories of variables which have been identified as influencing the difficulty level of proportion problems: student centered (e.g., age and gender) and task centered. The task centered variables are of two types: contextual (e.g., mixture versus rate) and structural. The structural variables include integer ratio, order of the unknown and numerical complexity. Harel and Behr (in press) defined an additional structural variable, the coordination of measure spaces. In their analysis of missing value proportion (MVP) problems. In this paper we will propose a MVP problem difficultly hierarchy, with respect to order and measure spaces coordination.
Careful consideration was taken to hold the other structural variables constant. These include integer ratio (none, one or two), the number of measure spaces (one or two), the number of dimensions of the measure space (one or two) and the partitionability of the measure space (yes or no). For further explanation of these variables see Harel and Behr (in press). The problems used in this study had no integer ratios, two measure spaces, one dimension in each measure space and partitionable measure spaces. The contextual variables were also held constant. The problems used continuous quantities, were of the rate type, were familiar and involved no use of manipulatives.
In order to hypothesize a difficulty order for all 8 problem types, it is necessary to decide whether the coordination of the measure space or the order of the missing value is more salient. At this time there is no indication which that would be, therefore the order of difficulty will be between pairs of problems only. That is, the comparison will be between the coordinated and the uncoordinated problems which have the some order of the missing value. It is likely that the coordinated problems will be easier than the uncoordinated problems because when solving a coordinated MVP problem, the equation formed by the solver for the closed per statement has the same structure as the equation for the open per statement, this reasoning suggests the following order of difficulty: BL
Due to the small sample size, the results indicate the trends identified in the percentage of students who correctly answered the problems. For the coordinated measure space problem types, the results are as follows: TR Since the results do not match the proposed order of difficulty, it is necessary to identify the error in the assumptions made. Harel and Behr (in press) stated that when solving MVP problems in which the open per statement appears first, it is necessary to change the problem presentation so that the closed per statement appears first. This process is accomplished through problem transformations and results in a problem representation, the solver's conceptualization of the problem. Since the percentage of correct answers for the problems were relatively high, we can assume that the students were able to change the order of the per statements with little difficulty. Therefore, the order of the per statements may be eliminated when considering problem difficulty in MVP problem presentation. When this is taken into consideration we can combine the results of TR with BR and TL with BL which gives the following results: R This indicates that if the measure spaces are coordinated the problems are easier when the order of the missing value is on the right than when it is on the left, Rc < Lc. This agrees with the hypothesis. Though, when the measure spaces are uncoordinated the hypothesis appears not to be supported by the data when the missing value was on the left the problems are easier than when it was on the right, L When solving MVP problems which have uncoordinated measure spaces, it may be necessary as a first step to use a transformation on the problem in order to change the uncoordinated problem presentation into a coordinated problem representation. There are a couple of ways this could be accomplished. For instance, if the student changes the problem so that the unknown is always on the right then TL The analysis of the results reveals that the most salient variable, with respect to percentage correct on MVP problems, is the order of the missing value within the open per statement. This variable not only influences the percentage correct, but also the type of transformation that the student uses on MVP problems with uncoordinated measure spaces. It is also true that once students are able to solve MVP problems, the order of the per statements and the coordination of the measure spaces has little or no affect on problem difficulty.
The results indicate that the order of the missing value and the coordination of the measure spaces may effect problem difficulty for pre-service teachers. A similar study indicates that the coordination of the measure spaces do effect problem difficulty for seventh grade students (Bezuk, 1986). It is doubtful that these issues are addressed in the classroom. It seems that making students aware of these slight variations In MVP problems would be an easy task for the teacher and may improve performance on MVP problems. It will also help students to realize that the MVP problems have many representations and therefore give them more flexibility in their solution strategies. Teachers can easily manipulate the problem presentation with respect to the structural variables and teach the students the possible transformations that can be applied to the problem presentation to make the problem more easy to solve. There are eight types of transformations, which form a mathematical group under the composition operation. For more information refer to Harel and Behr (in press). In general, since the percentage correct for all these MVP problems was not impressively high (the highest being 66%) and the subjects were preservice elementary teachers, this signals a need to educate these preservice teachers about MVP problems, their representations, the variables which affect problem difficulty and the various solution strategies which are appropriate. A larger study of this design should be pursued in order to validate the findings of this study. Further research should systematically consider all of the variables which have been described in Harel and Behr (in press).
Bezuk, N. B. (1986). Harel, G. & Behr., M. (In press). Structure and Hierarchy of Missing Value Proportion Problems and Their Representations. Tournaire, F., & Pulos, S. (1985). Proportional reasoning: A review of the literature. | |||||