The Mole Concept

Developing an Instrument To Assess Conceptual Understanding

Shanthi R. Krishnan 8001Chend Coltina Trail, austin, TX 78749

Ann C. Howe Department of Curriculum and Instruction, University of Maryland, College Park, MD 20742

Research on students' alternative frameworks in science and the recent advances in cognitive psychology have em- phasized that leaming takes place within the context of already acquired knowledge. This realization has caused science educators increasingly to be concerned about the knowledge held by the students prior to instruction (14) . When these prior conceptions are misconceptions, then they prove to have a detrimental effect in problem solving (5) and course performance (6).

One of the most important aspects of research in science education is directed toward gaining a better under- standing of the difficnlties that students have in learning science. Research indicates that students' difficulties in learning science wnmpts is due in part to the teachers' lack ofknowledge regarding students'prior understanding of wncepts under study (1, 4).

Students'conceptions that are different from those held by the scientific community have been labeled as "miscon- ceptions", "preconceptions", "alternative frameworks", or "children's science". One way of understanding students' conceptions tha t has been employed widely is the Piagetian individual interview method. Osborne and Frey- berg(7) and Watts (8) have described a variety ofinterview formats or procedures for conducting these interviews. Though shown to be effective, this method still is not ac- ce~ted readilv bv teachers. because. in addition to being - . extremely time-consuming, it also de- mands expertise in order to interpret and analyze the results.

Individual instruction also has beenused successfully as a method for correcting mis- conceptions by Lavie and Novak (91, but it has the same disadvantages as the inter- view method. One tool that would be read- ily used by the teachers would be a paper- pencil test specifically designed for the purpose of identifying misconceptions. Such a test then could be used as a diagnos- tic tool to guide the teacher toward ad- dressing students' misconceptions revealed through instructions specifically designed for the purpose. Such diagnostic tests have been developed by Peterson (10) in cova- lent bonding in chemistry, Haslam (11) in biology, and Treagust (12) in both covalent bonding and structure in chemistry and in photosynthesis and respiration of plants in biology These tests contain two-tier multi- ple-choice items that are not suitable for all concepts in science, particularly those in physical science that require formal appli- cation of concepts in problems.

describes a method for developing a paper and pencil test to evaluate students' understanding of the mole concept" in chemistry. The development of this instrument was based on research regarding students' understanding of the mole concept and was revised upon piloting and Fur- ther reviewing. The development of this instrument was based upon Treagust's (12) work, with modifications incor- porated to accommodate for the scope and nature of the topic under study.

Research Method The development of the diagnostic test wnsisted of four

main stages that are explained in a greater detail in the following sections.

Stage 1. Defining the Content

This stage involved the identification and careful study of the defmition of the mole concept as defined in popular chemistry textbooks. Then the mole concept was redefined as statements, each statement involving only one variable. The next stage was to identify the way in which each of these derived definitions of sub-concepts may be used in problem solving involving the mole. The concept map pre- sented as Figure 1 developed by Gower, Daniels, and Lloyd (13) was used to validate these derived definitions. This concept map is composed of such related concepts as

MOLE CONCEPT 1 1

I Shorthand I representation

of pure substances

Treagnst (12) gives a detailed description of the method he used for developing a test for diagnosing misconceptions. This paper Figure 1. Mole wncept map.

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npe 2. no-Tier Pue-False Questions with Reasons atomic mass and molecular mass, as well as the applica- tion concepts of molecular formula and svmbols. therebv indicating'the relationships between theauhsunkn(: cm- cepts and the unilWna mole concern. The identified defini- tions also were vaiid&d by science educators and chemis- t ry instructors in regard to scientific accuracy and contextual limitations of the mole concept used in this study.

Stage 2. Defining Learning Objectives

The next s t e ~ was to redefme the definitions in the form of learning objectives so that the test items may he devel- oped in order to test these obiectives. The overall definition o? the mole concept was first stated as five sukoncepts. Each of these subconcepts was then restated as a learning objective. These objectives were then reviewed and revised and the final statements of the objectives are as follows.

Objectiue I . The student will know that the male is a count- ing unit and that one mole of any substance wntains the same number of units as one mole of any other substance. . Objwrrue 2. The atudent will know that the male is defined as the amount ofsubstancr containing Avogadro's number uf units or particles of that substance. Obiective 3. The student will be able to recwnize that the - atomic ratios in the formula of a molecule is also the molar ratio of atoms in that molecule. . Obieetiue 4. The student will be able to calculate the atomic or &oleeular masses in grams fmm the molai masses of the respective atoms or molecules, and vice-versa. Objective 5. The student will be able to relate the molecular emrdinates in the balanced equation with the molar ratios of the molecules of reactants and products.

Stage 3. Research on Students' Misconceptions in the Mole Concepl

This stage involved a detailed review of previous re- search studies that focused on students'mismnceptions in the mole concept. Considerable work has been done re- eardine students' understandine of the mole concent (14- - 19). K e misconceptions identged in these stud& were compiled in a list to be used in developing items in the di- agnostic test. The prepared list of misconceptions were presented to experienced chemistry instructors who vali- dated them as true misconceptions if held by students.

Stage 4. Developing the Test Items

The next step was to develop test items for the learning objectives that were defined in stage 2. I t was realized that anv one tme of question would not cover the entire scope of ;he moi~concr~t under study. Hence, it wasdecided thst four types of test Items would be used and that the identi- fied misconceptions would be used as distracters or as oth- envise appropriate in the test items. The four types of test -. items used are as follows.

o p e I . Simple Multiple-choice Questions

These items tested the basic definition of the mole con- cept. The distracters used in these multiple-choice items wire based on the list of misconceptions.

Emmple 1 . A mole of HzO and a mole of O2

(a) have the same mass (b) contain one molecule each (c) have a mass of 1 g each (d) contain the same number of molecules

There were three items in this test that fell under this category of questions.

These questions consisted of a simple statement with a multiple-choice of four answers for each statement. The four answers began as true or false followed by a reason. Students are not only required to take a stand on whether the statement is true or false but also to explain their rea- sons for saying so. That way one can understand the rea- soning of the students.

Example 2 . One mole of oxygen molecules contain more inde- pendent units ( 0~) than one mole of oxygen atoms (0).

(a) True, because there are two atoms of 0 far every molecule of Oz.

(b) True, because one mole of OZ weighs more than one mole of 0 .

(c) False, because both of them have the same number of par- ticles.

(d) False, because one male of 0 has the same mass as one mole of 02.

Here again the distracters in the choice of answers were developed based on the list of misconce~tions. There were two such items in the test.

npe 3. %o-Tier Multiple-choice Items In this cateaow, the students were asked a auestion and - -.

given a choice of four answers to pick from. 1; addition to this they were also asked to state reasons for their answer choice in their own words.

Erample 3. Circle the letter corresponding with the best" an- swer for each of the fallowing questions and give reasons for your choice.

One molecule of sulfur contains 8 S atoms. Then one mole of sulfur malecules will wntain

(a) 8 g of sulfur (b) 8 moles of sulfur atoms (c) 6.02 x loz3 sulfur atoms (d) 8 sulfur atoms Reason:

There were five such items in the final instrument.

Ope 4. Problems In this category, the students were presented with a

problem that required mathematical calculations to arrive at an answer. The students were required to illustrate clearly their calculations and circle the answer.

Example 4. Each carbon atom wntains 6 electrons. How many carbon atoms will contain one mole of electrons?

Answer:- Calculation:

There were 10 such questions in the final version of the test. In these questions, the teacher is encouraged to pay attention to the students' methods of calculations rather than their answers in order to understand their trains of thought. This also enables the teacher to determine whether the students have difficulty in combining two sim- ple steps in a complex problem. Example 4 is an example of a simple problem. Example 5 is an examole of a more complex~roblem.

Example 5 . How many grams of NaHC03 will react to form 10.0 g of Con in the following reaction?

NaHC03 + HCI + NaCl+ HZO + COz

The final version of this diagnostic instrument, which consisted of 20 items was arranged as represented in Fig- ure 2. This version along with a copy of Figure 2 was pre- sented individually to an expert committee consisting of two university chemistry professors, four high school

654 Journal of Chemical Education

SUB-CONCEPTS -) t GJ

I

LEARNING -ID OBJECTNES I I

TESTITEMS (4 itemsforeach learning objective)

List of misconce~tions identified in each item.

Figure 2. Distribution of the test items in the Mole Concept Test.

Students' Selection of Answers to Example 2

Class Students' Choice of Answers in %

a b ca d

Chemistry Majors(A) 15 5 70 10

Introductory Chemistry (6) 25 5 50 20

?3atands for the correct answer.

chemistry teachers, four graduate science education stu- dents. and two chemistrv laboratom instructors. Their suggestions and comments were analyzed and incorpo- rated in the revised version of the instrument. This revised version of the instrument was administered to a group of 20 chemistm maiors in their so~homore vear in wlleee. The data t l k s obtained were used to an item analysis on the instrument. An estimate of the reliability of the instrument was determined by calculating the Kuder-Richardson's reliability coefficient that was found to be r = 0.81. The difficulty anddiscrimination indices and the point biserial coefficient also were determined for each item in the instrument. They were found to fall within the acceptable range of O.PO.8 for difficulty index, 0.46- 0.86 for discrimination index, and 0.22-0.68 for point biserial coefficient.

This final version of the Mole Concept Test (MCT) also was administered to 20 volunteers from an introductory university chemistry course.

Analysis of an Example

The performance of these students in Example 2 (given above) is presented in the Table and discussed in order to illustrate how the instrument and the resulting data can be used by chemistry teachers.

If this had been a simple truefalse item, it can be noted that 80% of studentsfiom class Aand 70% of students from class B had the correct answer because the answer would then be "false". Upon the introduction of the reason state- ment, it was possible to see that only 70% of students from class A and 50% of students from class B had the correct response.

C O N C E P ~ The students' choice of (a) indicates that students have an incomplete un-

7 derstanding of what the term "inde-

7 P pendent units" in the definition of "mole", stands for, as opposed to the number of atoms in a multi-atomic molecules. This misunderstanding is prevalent even in sophomore chemis- try majors. The students'choice of an- & & swer (b) is consistent with literature available on students' misconceptions stating that students often believe "mole" to be an exclusive property of the molecules and not the atoms. This misconception is similar to that re- ported by Novick and Menis (14) and Cervellati, et al. (161, which states that students considered that one "mole" of any substance always re- lated to a certain number of "mole- eules" of that substance.

Choice (dl, apart from differentiating those students who have acquired the concept of mole as being a counting unit from those who have not, also serves the second purpose of identifying the misconception that students commonly have regarding the confusion of the term "quantity" in the definition of mole as meaning a "wnstant mass" rather than a "constant number". It must be noted that these mis- conceptions, although found com~arativelv less often. are quite-prevalent even in sophomore chemistry majors, thereby substantiating the difficulty of c h a n h g these - - misconceptions through regular instrktion.

The instrument thus developed is ready to be used in classroom in order to diagnose students'eo&eptual under- standing of the mole. Then this will enable the teachers to ~ l a n and desien their instructions in order to address the - ~ ~ ~ ~~~~- ~ ~ ~ ~ - - -

inconsistencies in students' conceptions in mole concept. Through this article, we have not only presented a pa-

per-pencil test instrument for diagnosing misconceptions in Mole Conce~t. but also we have ~rovided a detailed de- scription of th l method used in thCpreparation of this in- strument. This will enable future researchers and teachers in order to prepare a similar paper-pencil test that could be used to diagnose miswnceptions in other concepts. A copy of the instrument "Mole Concept Test" is available from the one of the authors (SRK).

Literature Cited IDriver, R.; Easlqv. J. Stud. Sci. Edur 1978.5, 61-84. 2. Driver R.: Erickson. G.Stud &i. Edue 1988.10 8 7 a

6. Champ~ne,A.B.:I(lopfopf,L.E.:Anderm, J.H.Am. JPhys. 1880,48,107P1019. 7. Osbome, R.; Freyberg, P Learning in Science The Implimfions of ChildrPnS Sci-

on-; Heinernan" Publishers: New Hampshire, 1980. 8. Watts, M. Ropmsmlotion ofPhysics and Chemistry Knomledgo. Ludwigsburg West

Germany, 1981,365-386, 9. Navak, J. DP~ocPPdingsoflhelnfomotionolSeminar on Miiiicepfians in Mothe-

mol&andSckn~% Ithaen, New Yark, 1983. 10. Peterson, J. Unpublished masters thesis, Curtin University of Pchnology. Perth,

Australia, 1986. 11. Haslam, F Unpublished masters theis. Cvrtin University ofl!echnology. Perth,

Australia, 1987. 12. Reaguof,D. E in,. J.Sci. Educ. 1988,10(2J, 159-169. 13. Gower, D. M.; Daniels, D. J.; Llqvd, B. Sch. Ser. Mu. 1977,58,667. 14. Novlck,S.;Meni% J. J. Chom.Educ. I976,53I11J, 72G727. 15. VincentA.Edue. Chem. 1981,18. 114. 16. Ceruellati. A. JCham. Educ. 1882,59(101,852856. 17. Howe, A. C.; D m , B. P. J Ilrs Sci. Tpoeh. 1982,109(3), 217-224. 18. ME M a n s , F. REdm. Chem. 1983.20.6. 19. Morris, J. E.; Waddin8ton.D. J.Edue. Chom. 1982, July,37.

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