2. Thinking ‘Behind’ the Steps Engaging Students in Thinking ‘Behind’ the Steps

3. Objectives of this workshop series cognitive development needs 1.Identify the cognitive development needs of students educational theories 2.Introduce some educational theories which can help us address the developmental needs easy methods for teaching / assessment 3.Propose easy methods for teaching / assessment for helping with these cognitive development needs adopting / adapting 4.Explore ways for adopting / adapting some of the methods in your course

4. Adopting / adapting the methods in your specific context The facilitators provide generic ideas The participants adopt / adapt the ideas in specific subjects Designed generic worksheets Directly use / modify the worksheets for specific subjects Suggested ways for implementing the ideas in teaching and assessment Brain storm how to adopt / adapt the ideas in your own courses

5. Focus of this session Fostering students' abilities in solving problems Objective: Fostering students' abilities in solving problems conceptual problems, numerical problems, scientific and technical problems, laboratory investigation, etc. Think 'behind' the steps Strategy proposed: Think 'behind' the steps

6. 2 Levels Developing Problem Solving Abilities at 2 Levels Cognitive strategies for problem solving Metacognitive strategies w.r.t. problem solving What are they? How to develop them? What are they? How to develop them?

7. Metacognition What is metacognition? A.Awareness / knowledge of what cognition (learning) is B.Abilities to control cognition (learning), i.e. the disposition & habits that support and drives learning Key operations in metacognition (control of learning) 1.Planning 1.Planning your learning 2.Monitoring 2.Monitoring your learning 3.Assessing 3.Assessing your learning

8. Elaborated approaches to develop problem solving abilities The literature contains different models of problem solving, e.g. Representing the problem Formulating possible subproblems Formulating a plan Testing feasibility of alternative plans Seeking relevant information, tools Using information, tools to solve the subproblem/ problem Justifying the reasoning behind one's conclusion … There are extended courses for training problem solving.

9. In search of Easy methods for teaching & assessment Easy methods for teaching & assessment to enhance problem solving abilities

10. What students say about problem solving tasks Will these give us some clues ? What students say about problem solving tasks “For example, “A + B = ?” is what we usually work on, and if he suddenly gives us a different one “A*B = ?”, then I will not know how to solve it.” “Some subjects just give us a manual, we just follow it. … We may do that by following the procedures. But after that, if you ask me how to do it, I won’t know.” “…the focus should not be on drawing an apple. It should rather be focusing on how to draw an apple and the process of thinking in-between…” What is causing problems in learning about problem solving?

11. A common obstacle for problem solving abilities – The 'algorithm  solution' A common obstacle for problem solving abilities – The 'algorithm  solution' routine without For some 'problems' students could arrive at an answer by blindly carrying out the algorithm / procedural routines without understanding the concept / logic behind the steps, e.g. Apply formulae of physical laws to solve scientific problems Following mathematical algorithm to solve mathematic problems Following manuals in computing, technical operations Carrying out recipe type laboratory experiments

12. algorithm / procedures thinking and reasoning Following the algorithm / procedures VS Focusing on the thinking and reasoning “…the focus should not be on drawing an apple. It should rather be focusing on how to draw an apple and the process of thinking in-between…”

13. Thinking 'Behind' the Steps Modeling the problem solving process by teacher Think aloud during teaching Engaging students in articulating their problem solving process Think-of-Your-Thinking Worksheet Two-person instruction O heuristic for experiments Vee Diagram for research investigation

14. Think-of-your-thinking Worksheet A tool to encourage students to actively seek of gaps in their thinking and understanding Components of the worksheet: Instructions First Aid Kit Left Column Right Column

15. Think-of-your-thinking in Teaching and Assessment Teaching: 1. As a compare-with-the-expert assignment follow-up 2. Demonstration in lecture / tutorial Assessment: 1. Use it as a continuous assessment

16. Two Persons’ Instructions What is Two Persons’ Instructions? The Two Persons’ Instructions is a method designed to awaken the awareness of reasons behind procedures by creating a situation where students can experience the gaps in their knowledge. Rationale The differences between two plans for the same objective also strike curiosity in one’s mind By examining the differences one finds out about the reasons behind the steps, which in turn become a stimulus for reflection on one’s own plan

17. Using the Two Persons’ Instructions How to use? Plan, exchange, clarify Examples In practical class For assignment

18. O diagram What is an O diagram? The O diagram is a powerful tool that can be used in all sorts of experiments and investigations. It effectively bridges the gap between procedures and the reasons behind them, and the gap between the question and the answer of an investigation. Rationale Unlike the V diagram, the O diagram shows no gap between conceptual and practical issues The O shape joins the cause and the end of an experiment Through stating the reasons behind each step, they understand the procedure better, and become aware of what they do not understand about the procedure

19. Using O diagram for laboratory How to use? Before the laboratory class, write inside the circle all theories and key concepts that you can think of that are relevant to the experiment going to be carried out during the class. Work anti-clockwise through the circle, from hypothesis to conclusion. As you carry out the experiment, record on the outside of the circle the steps you’ve taken and write the reason for each step inside the circle, adjacent to the steps. If a reason is already in the circle (e.g. a theory you’ve written down before the experiment), draw a line to link the step to it.

20. The V diagram for Research What is a V diagram? A heuristic for research, or discovery learning in general; a powerful tool for balancing the theory side and the practical side of a topic Structure of V It has 2 sides, representing conceptual and methodological issues of the topic respectively Sub-headings Focus question and events/objects

21. V diagram in 1984 - Gowin Why use? To bridge theory and practice To show that knowledge is constructed over time How to use? Begin with concepts, objects, events Introduce the idea of records and focus question Record transformation and knowledge claims Principles and theories Value claims

22. V diagram in 1984 - Gowin You’re calling this a ‘simple’ method?

23. Visualising the V The focus question is like the sun, to which all face – i.e. items on either side are all about the question, or, about answering the question and solving the problem. The conceptual side of the V is like a tree; it grows over time. On the right are the immediate actions taken, which contribute to the growth of the conceptual side. The thinking side and the doing side are closely intertwined – and only through the marriage of theory and practice would the highest level of knowledge be achieved. side. The observation of event/object is like a pond at the bottom of a mountain; it is the source of all that grow above.

24. Why is it so powerful? Rationale The diagram provides a visual structure for students to organize information, so as to reduce their mental overload. In particular, the V-shape helps students to focus their attention to the observation and question under construction, thus narrowing the gap between methodologies and theories

25. Materials for the V diagram A briefing for student The V diagram for research worksheet

26. One thing I would like to try is

27. Thinking 'behind' the steps Fostering problem solving abilities by Thinking 'behind' the steps Developing problem solving abilities at 2 levels Cognitive development Metacognitive development Teacher-modeling by thinking aloud during teaching Students articulating their own thinking process during problem solving