1. Helping students to build problem-solving skills
Problem: Whenever there is a gap between where you are now and where you want to be, and you don’t know how to find a way to cross that gap you have a problem.
Problem-solving: What you do, when you don’t know what to do.
Problem solving is a complex process that is affected by many variables.

2. Experts and Novices Routine exercises Problems
This strongly depends on the level of student education.
Ex.
‘Robinson annulation reactions involve two steps: Michael addition and aldol condensation. Assume that Michael addition leads to the following intermediate. What would be produced when this intermediate undergoes aldol condensation?’
Experts and Novices

3. Modelling problem solving
Polya’s model (1946):
understand the problem
devise a plan
carry out the plan
look back
Dewey’s model:
A state of doubt or awareness of difficulty
Attempt to identify the problem
Transforming problem-setting propositions or hypotheses
Successive testing of hypotheses and reformulation of the problem as necessary
Understanding the successful solution and applying it both to the problem at hand and other examples of the problem.

4. The real pathway (Wheatley, 1984)
Read the problem
Now read the problem again
Write down what you hope is the relevant information
Draw a picture, make a list, or write an equation or formula to help you begin to understand the problem
Try something
Try something else
See where this gets you
Read the problem again
Test intemediate results to see whether you are making progress toward an answer.

5. Read the problem again
When appropriate, strike your forehead and say (son of a …)
Write down an answer (not necessarily the answer)
Test the answer to see if it makes sense
Start over if you have to, celebrate if you don’t.

6. Lee & Fensham Model (1996)
Reading and understanding the problem statements as a whole, rephrasing or simplifying the problem statements, using symbols or diagrams to visualise the problem
Translating the parts of the problem statement into statements that had meaning to themselves
Setting goals and subgoals
Selcting the important information from the translation statements
Retrieving facts or rules from memory
Achieving goals or subgoals by explicit linking of the last two steps
Cheching the paths of the solution or the answers.

7. Expert/Novice dichotomy
Experts classified problems according to the principles governing the solution to the problem; novices categorised problems by their surface structure.
- Compare Expert vs. Novice students
- Expert/novice is not a dichotomy, but a continuum.

8. Successful/Unsuccessful solvers
Successful problem solvers:
Have a good command of basic facts and principles
Construct appropriate representations
Have general reasoning strategies, that permit logical connections among elements of the problem
Apply a number of verification strategies concerning the consistent representation of the problem, the logical soundness of the solution, error-free computations.

9. Conceptual vs. algorithm
Even the best numerical problem solvers can perform poorly on conceptual questions.
Students can answer an algebraic question but cannot answer a conceptual question dealing with the same topic.
On a class:
50% high on both algorithmic and conceptual questions
30% high on algorithmic, low on conceptual
10% low on algorithmic, high in conceptual
10% low in both algorithmic and conceptual questions.

10. Conceptual understanding
Solving a problem does not guarantee by itself conceptual understanding.
Student’s performance on exam questions doesn’t accurately reflect their understanding of the concept.
Conventional multiple choice tests don’t adequately assess student understanding.
‘Rule learner’ : memorising rules and algorithms and practising until they could be applied flawlessy.
The major reason why students have difficulty solving chemistry problems is because they don’t understand the underlying chemical concepts.

11. Understanding thermodynamic concepts
Use of everyday language instead of precise scientific meaning
Confused thermodynamic concepts
Use informal (prior) knowledge
Generalise thermodynamic principles beyond specific conditions
Use concepts from kinetics to explain thermodynamics of chemical phenomena.
Tendency to treat chemical changes as physical changes.
Confuse the molecular and macroscopic level.

12. Representations
The internal or mental representation of a problem changes as the problem is worked.
Ex. Solving a synthetic organic problem (graduate student level)
The choice of a represenational system is a strategic decision (i.e. symbolic vs. propositional representations).
Tactical decisions are made within the representational system.
Successful probelm solvers constructed significantly more representations than those who were unsuccessul.

13. Cognitive variables Spatial ability Reasoning ability
Restructuring/disembedding ability
Working memory capacity
Prior knowledge
‘Idea association’ and ‘problem translating’ skills are important predictors of success for solving unfamiliar problems.

14. Teaching problem solving
Explicit problem-solving instruction improved the quality of students’ representation, but has no effect on conceptual understanding.
Students seem to approach exercisess and problems the same way, i.e. looking for an algorithm that fits their interpretaion of the question.
Solve problems with the students, instead of for them!

15. Cooperative learning ‘Think aloud pair’ Working in groups
Discussion in class
- Development of interpersonal and communication skills

16. Selected readings
Bodner, G.M. (1987). The role of algorithms in teaching problem-solving. Journal of Chemical Education, 64,
Bodner, G.M. & Domin, D.S. (2000). Mental models: The role of representations in problem-solving in chemistry. University Chemistry Education, 4,
Bunce, D.M., Gabel, D.L. & Samuael, J.V. (1991). Enhancing chemistry problem solving achievement using problem categorization. Journal of Research in Science Teaching, 28,
Camacho, M., & Good R. (1989). Problem-solving and chemical equilibrium: successful versus unsuccessful performance. Journal of Research in Science Teaching, 26,
Carter, C.S., LaRussa, M.A., Bodner, G.M. (1987). A study of two measures of spatial ability as predictors of success in different levels of general chemistry. Journal of Research in Science Teaching, 24,

17. de Astudillo, L. R. , & Niaz, M. (1996)
de Astudillo, L.R., & Niaz, M. (1996). Reasoning strategies used by students to solve stoichiometry problems and its relationship to alternative conceptions prior knowledge and cognitive variables. Journal of Science Education Technology, 5,
Fasching, J.L., & Erickson, B.L. (1985). Group discussions in the chemistry classroom and the problem-solving skills of students. Journal of Chemical Education, 62,
Gabel, D.L., & Sherwood R.D. (1983). Facilitating problem-solving in high school chemistry. Journal of Research in Science Teaching, 20,
Gabel, D.L., Sherwood, R.D., & Enochs L. (1984). Problem-solving skills of high school chemistry students. Journal of Research in Science Teaching, 21,
Heyworth, R.M. (1999). Procedural and conceptual knowledge of expert and novice students for the solving of a basic problem in chemistry. International Journal of Science Education, 21,

18. Lee, K. L. , Goh, N. K. , Chia, L. S. , & Chin, C. (1996)
Lee, K.L., Goh, N.K., Chia, L.S., & Chin, C. (1996). Cognitive variables in problem solving in chemistry: A revisited study. Science Education, 80,
Lythcott, J. (1990). Problem-solving and requisite knowledge of chemistry. Journal of Chemical Education, 67,
Nakhleh, M.B. (1993). Are our students conceptual thinkers or algorithmic problem solvers? Journal of Chemical Education, 70,
Nakhleh, M.B., & Mitchell R.C. (1993). Concept learning versus problem-solving: there is a difference. Journal of Chemical Education, 70,
Niaz, M., Robinson W.R. (1992). Manipulation of logical structure of chemistry problems and its effect on student performance. Journal of Research in Science Teaching, 29:

19. Niaz, M. (1995). Progressive transitions from algorithmic to conceptual understanding in student ability to solve chemistry problems: A Lakatosian interpretation. Science Education, 79,
Niaz, M. (1995). Cognitive conflict as a teaching strategy in solving chemistry problems: A dialectic-constructivist perspective. Journal of Research in Science Teaching, 32,
Nurrenbern, S.C., & Pickering, M. (1987). Conceptual learning versus problem solving: is there a difference? Journal of Chemical Education, 64,
Pendley, B.D., Bretz ,R.L., & Novak, J.D. (1994). Concept maps as a tool to assess learning in chemistry. Journal of Chemical Education, 71, 9-15.
Phelps, A. J.(1996). Teaching to enhance problem-solving: It's more than the numbers. Journal of Chemical Education, 73,
Pickering, M. (1990). Further studies on concept learning versus problem-solving. Journal of Chemical Education, 67,

20. Sawrey, B.A. (1990). Concept learning versus problem-solving: revisited. Journal of Chemical Education, 67,
Shibley, I.A. Jr., & Zimmaro, D.M. (2002). The influence of collaborative learning on student attitude and performance in an introductory chemistry lab. Journal of Chemical Education, 79,
Smith, C.A., Powell, S.C. & Wood, E.J. (1995). Problem based learning and problem-solving skills. Biochemical Education, 23,
Smith, K.J. & Metz, P.A. (1996). Evaluating student understanding of solution chemistry through microscopic representations. Journal of Chemical Education, 73,
Staver, J.R. & Lumpe, A.T. (1995). Two investigations of students’ understanding of the mole concept and its use in problem-solving. Journal of Research in Science Teaching, 32, ,

21. Tingle, J.B., & Good, R. Effects of cooperative grouping on stoichiometric problemsolving in high school chemistry. Journal of Research in Science Teaching, 27,
Towns, M., & Grant, E. (1998). 'I believe I will go out of this class actually knowing something:' Cooperative learning activities in physical chemistry. Journal of Research in Science Teaching, 34,
Treagust, D.F. (1988). The development and use of diagnostic instruments to evaluate students' misconceptions in science. International Journal of Science Education, 10,
Woods, D.R. (1989a). Developing students’ problem-solving skills. Journal of College Science Teaching, 19,
Woods, D.R. (1989b). Developing students’ problem-solving skills. Journal of College Science Teaching, 19,
Yarroch, W.L. (1985). Students' understanding of chemical equation balancing. Journal of Research in Science Teaching, 22,