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STUDENTS' CONCEPTIONS OF THE THREE DIMENSIONS
OF THE QUANTITY OF MATTER (MASS, VOLUME AND PARTICLES)
AND ITS IMPLICATION FOR 9TH GRADE CHEMISTRY
Tikva Rager (Goldman)
The purpose of this study is to examine how students in the 9th grade understand the concept of quantity of matter which is represented by three dimensions: mass, volume and particles. The study will examine how the students differentiate between these dimensions, how they can connect between them and how they convert one dimension into another.
The three dimensions derive from three characteristics of matter: mass, volume and particularity. Unlike mass and volume, which are concrete dimensions that are sensed and grasped intuitively, the particulate dimension cannot be directly measured. Mass and volume are macroscopic phenomena whereas the particulate dimension is microscopic.
Mass is measured in gram and kilogram units, volume is measured in liter (decimeter) units, whereas the particulate dimension, which was scientifically defined later (1971), is measured in Mole units. The notion of Mole originated in ancient Latin, in which the word means a pile (of particles).
The chemist measures a quantity of matter by weighing its mass or by defining its volume, but because the chemical formulas of substances and the reactions between them are expressed in particles, the chemist should know how to convert from one dimension to the other.
Experience in the field of teaching as well as in research shows that students find it difficult to grasp the concept of the particulate dimension ("particulate" amount) and the calculation of quantities in chemistry (stoichiometry).
A pilot research was conducted among 66 students (9th and 10th graders). The 9th graders had not studied chemistry and the 10th graders had. A questionnaire was prepared to tap participants' ability to differentiate between the three dimensions. The test was done by presenting them with different substances, using two kinds of tasks:
1. Tasks involving static systems in which there is no change in the material. Here students were presented with different materials which were equal in one of their dimensions. Students were asked whether those materials were equal (or different) in the other dimensions.
2. Tasks involving dynamic systems in which changes take place in the material. Here students were asked about conservation (or change) of mass, volume and particulate amount of a certain material which was presented to them, and which then was changed due to a process of heating.
The materials presented were of different states of matter.
The results of the pilot research yielded assumptions concerning cognitive skills and knowledge factors that influence the ability to differentiate between the three dimensions of a quantity of matter. These assumptions were examined in an additional study, in which a written questionnaire was presented to 297 9th grade students. This population was divided into two groups: an experimental group, which studied chemistry according to a program based on the results of the pilot research, and a control group, which did not study chemistry. The questions were analogous to those given in the pilot research.
The research was based on the following assumptions:
1. Quantity of matter is an essential concept in chemistry.
2. Quantity of matter is represented by three different dimensions.
3. In order to understand quantitative subjects in chemistry, a student must be able to differentiate between the three dimensions of quantity of matter.
4. The dimension of particles ('particularity'), and its unit, do not have the same status as the other dimensions which measure the quantity of matter, and they are not yet completely acknowledged by the scientific community as analogous to mass and volume. The dimension of particularity is a relatively late concept (accepted by the scientific community as a scientific dimension only from the second half of the 20th century and finally defined in 1971).
5. The difficulties in learning and teaching the quantitative aspects in chemistry are eminently related to the problem of differentiating between the dimensions of a quantity of matter. These difficulties are also known from the history of the development of these concepts in science.
6. Understanding and differentiating the particulate dimension is difficult because it is abstract and not subject to direct measurement. Therefore it cannot be intuitively grasped in every day life but must be acquired only through learning.
7. The ability to differentiate between the three dimensions of the quantity of matter depends on:
i) The content of the tasks: whether they are static or dynamic tasks, tasks concerning different states of matter, tasks in which the differentiation is between different pairs of dimensions: mass/volume; mass/particulate amount; volume/particulate amount.
ii) The cognitive skills required to differentiate between the different pairs of dimensions: conversion which requires direct-ratio thinking and conversion in inverse-ratio thinking.
iii) Students' level of knowledge and the correct internalization of the content and concepts which are essential to the ability to differentiate between dimensions (conservation of matter and basic concepts in the particulate theory).
8. It is possible to improve students' ability to differentiate between the dimensions of the quantity of matter with appropriate instruction based on the findings from the pilot research.
The research hypotheses were:
1. Differences in students' performance will be according to different tasks and to the different cognitive skills required by these tasks.
Assumption 1 was divided into five sub-hypotheses which expected differences in performance between: static/dynamic tasks; direct-ratio thinking/inverse-ratio thinking tasks; tasks in pairs of different dimensions; conservation of mass and conservation of particles tasks in dynamic systems.
2. Differences will occur in student performance between the experimental group and the control group: the experimental group was expected to improve its performance in the tasks. This would mean an improvement in the ability to differentiate between the dimensions.
The results indicate that the average percentage of correct answers for all the questions in the control group (those who did not study chemistry) is low (60%). This average consists of values between 75% in some tasks and 28% in other tasks.
All the hypotheses except one were confirmed:
1. The ability to differentiate between the dimensions in static tasks is lower than the ability to differentiate in dynamic tasks.
2. Performance in direct-ratio tasks differs from performance in inverse-ratio tasks but there is a strong interaction between the kind of ratio and the state of matter, while it was found in both the pilot research and in the experimental group that the inverse-ratio tasks are more difficult than the direct-ratio tasks, in gas tasks (where performance is very low) success rates in inverse-ratio tasks are higher than in direct-ratio tasks.
3. Performance in gaseous tasks is lower than in liquid and solid tasks.
4. Performance in tasks in which the differentiation is between volume and particles was the lowest due to the low performance in the gaseous state.
5. The experimental group improved its performance significantly in all the tasks, except in inverse-ratio conversion tasks between mass and particles in the static system, where improvement was only small.
In summary:
1. Students' difficulties in differentiating between the three dimensions of the quantity of matter are mainly connected with difficulties in conversion between the dimensions of volume and particles in the gaseous state in static systems.
2. Differentiation difficulties are connected with the content of the tasks and with the proportional cognitive skill (direct-ratio/inverse ratio) needed to perform those tasks.
3. Improvement in the ability to differentiate between the dimensions of the quantity of matter may be achieved by appropriate instruction.
The results indicate the need to be aware of the specidifficulties associatedwith the knowledge and cognitive skills needed in order to understand conversions between the dimensions of the quantity of matter, in general, and more specifically, in stoichiometry.
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