high-school students’ problems learning the concept of...

High-school students’problems learning the concept of mole: A study to eventually get it right?

Nancy Brousseau, Collège Mont-Saint-Louis and Université de Montréal

Jesús Vázquez-Abad, Université de Montréal

Plan of the Presentation

Obstacles in chemistry learningCausesMole conceptProblem statementSituation in QuébecInstructional analysis of the conceptQuestionnaireInstructional suggestionsReferences

Obstacles in Chemistry Learning

Formulas EquationsVocabulary Atomic model Particulate nature of matter Comprehension of chemical principlesSymbolic Representation of chemical principles

Overall perspectiveBasic chemical conceptsRelationships between concepts and phenomena Memorisation

Causes

Abstract nature of conceptsStudents’ cognitive developmental stageSymbolic and representational nature of chemistryThree different levels of learning :

Sensorial (macroscopic), Atomic and molecular (microscopic) Symbolic (formula and algorithm)

Use of maths Information overflow Complexity of learning tasks in terms of information treatmentCommunication and language Lack of lab workLack of discussion Student’s and teacher’s misunderstanding of some fundamental concepts

Mole Concept

Seventh unit of the IS (mol)Unit of “amount of substance”Main function : means to pass from the microscopic level (atomic or molecular: number of particles) to the macroscopic level (sensorial: mass and volume)

Example: one mole of molecules of CO2 contains 6,02x1023 molecules of CO2, has a mass of 44g and occupies 22,4L of space at STP.

Molar Mass,

M (g/mol)

Avogadro’s Number ,

NA (particles/

mol)

Molar Volume,

Vm (L/mol)

Amount of substance

n (mol)

Massm (g)

Number of particlesN

(particles)

VolumeV

(L)

Problem Statement

Learning difficultiesTeaching difficulties (teacher/textbook)Low potential to pursue chemistry studiesIncomplete understanding of the conceptConfusion with units and quantities

Difficulties solving problems needing the concept of moleDifficulties solving stoichiometry problemsDifficulties solving concentration problemsDifficulties with the macro-microscopic relation

Situation in Québec

Context in which the concept is introduced: Physical science course

10th grade, enriched course only Module: Ionic phenomenaUnit: Solutions and concentrations Context: to change units of concentration from g/L to mol/L

Introduced with lots of problematic notions at the same time Only “a parenthesis”Immediate demand of applicationLack of time spent on the notionEmphasis on arithmetic


Ulterior use :Same course :

pH and indicators Chemical Reactions Stoichiometry

Chemistry, 11th grade


Analysis of 11 “official” textbooks availableVery few references to the conceptDeficient introduction

No historical references No references to its utility

Lack of clarity in definitions No imagesAnalogies often badly chosenRapid introduction of other related conceptsNotion sometimes divided in different unitsVery few examples Very few exercises

Instructional Analysis of the Concept

Typical challenges of teaching / learning the concept of mole

Concept’s definitionConcept’s difficultyUse of maths EtymologyTeaching Prerequisites

Concept’s Definition

Challenges of 18th century chemistryFinding the composition of compounds through the mass of the substances combining in chemical reactions Establishing an equivalence between mass, volume and number of particles

End of 19th, beginning of 20th century: two visions colliding

Macroscopic (mass and volume : Ostwald) Microscopic (atoms et molecules : Dalton, Avogadro)


Ostwald (1900): “The normal or molecular weight of a substance expressed in grams shall be called mole from now on.”

Adoption of the theory on atomic nature of matter

IUPAP (1957): “1 mole (symbol : mol) is the quantity of substance which contains the same number of molecules (or ions, or atoms, or electrons, as the case may be) as there are atoms in exactly 16 gramsof pure oxygen isotope O-16.”


IUPAP (1961): “The mole is defined as the amount of substance, which contains the same number of molecules (or ions, or atoms, or electrons, as the case may be), as there are atoms in exactly 12 gramsof the pure carbon nuclide C-12.”

IUPAC (1965): “A mole is an amount of substance of specified chemical formula, containing the same number of formula units (atoms, molecules, ions, electrons, quanta, or other entities) as there are in 12 grams (exactly) of the pure nuclide C-12.”


IUPAC (1967) :“The mole is the amount of substance of a system which contains as many elementary entities as there are carbon atoms in 0.012kg of C-12. The elementary entities must be specified.”

14th general conference on weight and measures (GCWM, 1971): “The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012kg of C-12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.”


Confusion of students and teachers over the mole and:

Mass Number of particles Avogadro’s number, NA

VolumeMolar massPropriety of matter

Problems of understanding the relation between “amount of substance” (the quantity) and “mole”(the unit)


Confusion of textbooks over the mole and:MassNumber of particles Avogadro’s number, NA

No historical comments on the evolution of the definition Almost no sign of “amount of substance”No relation made between “amount of substance”(the quantity) and “mole” (the unit)

Concept’s Difficulty

Concept’s level of abstraction vs. cognitive developmental stage of the students

Concept: theoretical or formal operational Requires formal operational stageCognitive level not achieved by a large proportion of studentsStudents’ difficulties representing such great numbers and such small particles

Information treatmentM-demand greater than the students’ capacity

Use of Maths

Problems with equations and proportional thinkingDifficulty linking operations needed to solve problems with more than one stepMath anxiety regarding numerical problemsMemorizing arithmetic rules

Etymology

New vocabularySimilar phonetics

MoleculeMoleMolar volume Molar massMolar molecular massMolar atomic mass Atomic massAtometc.

Teaching

Teachers’ inadequate and insufficient understanding of the conceptWrong definitions of the termsDeficient teacher trainingInconsistencies between textbook instructional approach and teacher’s strategyInconsistencies between teacher’s, textbook and scientific definitionInadequate teaching strategyNo historical perspective No discussion of its utilityNo qualitative approachAbstract unit defined as a concrete entity

Teaching

No distinction nor relation between “amount of substance” and “mole”Textbook inadequate contentsCurricular inadequate contentsInadequate learning sequenceMany notions concurrently seen that must be related (V, m, n, N, M, NA, Vm )Mathematical relations not all coveredImmediate Demand of ApplicationLack of practice in problem solvingLack of timePrerequisites (chemistry/maths) not acquired

Prerequisites

Vocabulary usedQuantities and units involvedRelation of proportionalityAtomic mass vs. relative mass vs. massChemical combination lawsChemical formulasMicroscopic vs. macroscopic levelAtomic theoryParticulate nature of matter

Questionnaire

36 questions divided into two parts:Qualitative

Concept of mole : definition, utility, history (8, mc)Relations with other concepts (3, multiple responses) Dalton’s Theory (7, mc)Particulate nature of matter (10, mc)

QuantitativeRelations with other concepts (3, multiple responses, open answers)Stoichiometry (5, mc)

Questionnaire

Spring 2004: 120 grade-10 students, after covering the unitOverall reliability (Chronbach’s alpha) > 0,92Answers to the concept section were more dispersed than othersCorrelations among sections:

Questionnaire

Sample response:Parmi les définitions suivantes, laquelle est celle du concept de mole?

a. L’unité de mesure de la quantité de substance d’un système contenant autant de particules élémentaires (atomes, ions, électrons, etc,) qu’il y a d’atomes dans 0.012 kg de carbone-12.

b. La masse de 6,02 x 1023 molécules d’une substance donnée.

c. L’espace occupé par 6,02 x 1023 molécules de gaz d’une substance donnée à température et pression normales.

d. Un nombre déterminé de particules soit 6,02 x 1023.

Questionnaire

Sample response:Parmi les définitions suivantes, laquelle est celle du concept de mole?

Instructional Suggestions

Assess understanding of prerequisites (chemistry/maths)Develop a conceptual understanding, qualitative before quantitative Make its utility explicit by linking the mole to the problem it is meant to solveDefine “amount of substance” and “mole”Define all terms used before relating themUse a historical approachWork in the zone of proximal developmentDecrease problems M-demand


Organise the tasks and questions involved into a hierarchyTeach students all the mathematical relations involved as well as the conversion factors with diagramsSolve quantitative problems using the factor-label methodAvoid solving problems using proportionsDo a great number of exercisesAsk questions clearlySolve stoichiometry problems


Use new teaching strategies and new learning environments

Laboratories Demonstrations Discussions Collaborative activities and projectsAnalogies Physical models and objectsVisual representationsUse of ICT (CAL, simulators, interactive multimedia)

References

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References

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References

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