# Solving Problems Using Problem Solving Concrete operational: - PDF document

## Piagetian Development: Solving Problems Using Problem Solving Concrete operational: Formal operational: classification control of variables Dr. David C. Stone conservation combinatorial reasoning Department of Chemistry decentering

1. Piagetian Development: Solving Problems Using Problem Solving Concrete operational: Formal operational: classification control of variables Dr. David C. Stone conservation combinatorial reasoning Department of Chemistry decentering correlational reasoning University of Toronto hypothetical-deductive TDSB Eureka Conference, February 2011 reversibility reasoning seriation probabilistic reasoning dstone@chem.utoronto.ca http://www.chem.utoronto.ca/~dstone/teachers/ transitivity proportional reasoning Dr. David C. Stone, Department of Chemistry, University of Toronto Dr. David C. Stone, Department of Chemistry, University of Toronto Friday, February 25, 2011 1 Friday, February 25, 2011 2 U. Guelph 1 st -year Self-Test: U of T 2 nd -Year Self-Test: • Given the expression A/B = When correctly expressed in SI units, a 2008 2007 2006 2005 X/Y, then B is equal to: density of 1.23 g/cm 3 is: a)XY/A 7.9% 6.9% Wrong units b)AY/X 68.4% 75.7% 76% 77% a) 1.23 x 10 -3 g/m 3 4.8% c)X/AY 18.4% 13.0% b) 1.23 x 10 -3 kg/m 3 28.6% Inverted d)Y/AX c) 1.23 g/m 3 5.3% 4.4% 4.8% conversion d) 1.23 x 10 3 kg/m 3 61.9% Courtesy of Prof. Lori Jones, U. Guelph Dr. David C. Stone, Department of Chemistry, University of Toronto Dr. David C. Stone, Department of Chemistry, University of Toronto Friday, February 25, 2011 3 Friday, February 25, 2011 4 U of T 2 nd -Year Self-Test: U of T 2 nd -Year Self-Test: Consider the following balanced chemical reaction: A solution of known iodine concentration may be prepared by mixing solutions of iodate and iodide under acidic conditions: 2 MnO 4– + 16 H + + 15 I – � 2 Mn 2+ + 5 I 3– + 8 H 2 O a IO 3– + b I – + c H + � p I 2 + q H 2 O What volume of 0.0525 M iodide would be required to When correctly balanced, the stoichiometric coefficients in exactly react with 20.0 ml of 0.0125 M permanganate? this reaction equation are: 7.0% � inverted coefficients a) 0.63 ml a) a = 1, b = 1, c = 6, p = 1, q = 3 51.2% � mass only 18.6% � forgot the coefficients b) 4.76 ml b) a = 1, b = 5, c = 6, p = 3, q = 3 41.9% 72.1% c) 35.7 ml c) a = 3, b = 3, c = 6, p = 3, q = 3 7.0% � charge only 2.3% � inverted concentrations d) 84.0 ml d) a = 5, b = 1, c = 6, p = 1, q = 5 0.0% Dr. David C. Stone, Department of Chemistry, University of Toronto Dr. David C. Stone, Department of Chemistry, University of Toronto Friday, February 25, 2011 5 Friday, February 25, 2011 6

2. U. Guelph 1 st -year Self-Test: U. Guelph 1 st -year Self-Test: • The geometry of a water • The geometry of molecule 2008 2007 2006 2005 in which the central atom is molecule is: bonded to 2 H atoms and 2008 2007 2006 2005 88.8% 85.2% 85% 85% a)angular or bent has 2 lone pairs is: 15.9% 16.4% b)linear 4.5% 5.7% a)tetrahedral c)pyramidal b)angular or bent 53.0% 52.8% 54% 54% 4.6% 5.9% d)tetrahedral c)linear 2.1% 3.2% 13.9% 12.8% d)pyramidal 17.2% 18.1% Courtesy of Prof. Lori Jones, U. Guelph Courtesy of Prof. Lori Jones, U. Guelph Dr. David C. Stone, Department of Chemistry, University of Toronto Dr. David C. Stone, Department of Chemistry, University of Toronto Friday, February 25, 2011 7 Friday, February 25, 2011 8 Threshold Concepts Equals vs. Equivalent? • Jan Meyer & Ray Land: There are six times as many students as professors at a particular university. This can be expressed “[Are] akin to a portal, opening up a new and mathematically as: previously inaccessible way of thinking ... a) 6S = P Equivalent “units” of students & professors without which the learner cannot progress ” Calculation of students from professors b) S = 6P in Overcoming Barriers to Student Learning , chapter 1, emphasis added At a particular university there are six times as many • moles & stoichiometry • molecular geometry students as professors. This fact is represented by • heat & temperature • particles & kinetic theory the equation S = 6 P . What does the letter S stand • atoms & properties • equilibrium processes for? • chemical bonds • reaction kinetics Dr. David C. Stone, Department of Chemistry, University of Toronto Dr. David C. Stone, Department of Chemistry, University of Toronto Friday, February 25, 2011 9 Friday, February 25, 2011 10 Equals vs. Equivalent? Alternate Concepts • Stoichiometry: • What do the following symbols indicate? a A + b B � c C + d D H �������� H 2 �������� H + • mass is conserved • compounds have definite proportions of elements � stoichiometric reaction requires definite ratios of compounds n A = a b � n A = n B � a moles of A n B b moles of B Dr. David C. Stone, Department of Chemistry, University of Toronto Dr. David C. Stone, Department of Chemistry, University of Toronto Friday, February 25, 2011 11 Friday, February 25, 2011 12

3. Alternate Concepts Alternate Concepts • Balance the following equation for the • A metallic wire has the following properties: production of ammonia: a)conducts electricity b)brown colour N 2 + H 2 � NH 3 c)density of 8.93 g/cm 3 • Represent the balanced reaction using circles d)malleable & ductile with letters in the centre to depict the atoms: e)expands on heating Suppose you could isolate one single atom from the N N H H H H H H metallic wire: which of the above properties would it have? N N H H H H H H Dr. David C. Stone, Department of Chemistry, University of Toronto Dr. David C. Stone, Department of Chemistry, University of Toronto Friday, February 25, 2011 13 Friday, February 25, 2011 14 Alternate Concepts Alternate Conceptions: • The wire is heated in an evacuated vessel until it • Bonding and Properties completely evaporates. The resulting gas has the – metallic bonding poorly understood following properties: All at sea... a)compressible b)expands on heating c)pungent odour d)yellow colour e)attacks plastics Suppose you could isolate one single atom from this gas: which of the above properties would it have? Keith S. Taber, Science Education , 2003 , 87(5) , 732-758 Dr. David C. Stone, Department of Chemistry, University of Toronto Dr. David C. Stone, Department of Chemistry, University of Toronto Friday, February 25, 2011 15 Friday, February 25, 2011 16 Conceptual Problems Conceptual Problems • Individual 0.200 g samples of each of the following • Four identical sealed containers are filled with a gases were placed in four separate 1.00 L stoppered different gas as indicated below until each contains flasks at 298 K. In which flask do you expect the exactly the same mass. If all four are held at the gas to exert more pressure? Explain your answer. same temperature, which flask contains gas at the greatest pressure? Flask: A B C D Flask: A B C D Gas: CH 4 Ne N 2 CO 2 Gas: CH 4 Ne N 2 CO 2 M m (g/mol) 16.0 20.2 28.0 44.0 M m (g/mol) 16.0 20.2 28.0 44.0 Dr. David C. Stone, Department of Chemistry, University of Toronto Dr. David C. Stone, Department of Chemistry, University of Toronto Friday, February 25, 2011 17 Friday, February 25, 2011 18

4. Algorithmic & Conceptual Problem-Solving • The following diagram represents a cross- • G. H. Wheatley: sectional view of a rigid sealed tank... “ What you do, when you don’t know what to do ” as cited by Bodner, U. Chem. Ed. 2003 Routine Novel exercise problem Algebraic/ Conceptual numeric (non-numeric) Dr. David C. Stone, Department of Chemistry, University of Toronto Dr. David C. Stone, Department of Chemistry, University of Toronto Friday, February 25, 2011 19 Friday, February 25, 2011 20 Problem-Solving Activities • Groups of ~ 3–4 people • Appoint an observer to record the process ! • Solve a problem (10 minutes): – The Waterfall Problem – The Pizza Problem – The Water and Wine Problem – The Xenon Fluoride Problem Dr. David C. Stone, Department of Chemistry, University of Toronto Friday, February 25, 2011 21

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