1. Final Exam Preparation CI 319 Fall 2007 Mara Alagic

2. Case-based scenarios: Conjecture/speculate how a child might attempt to solve the problem dependent on child’s age. Generate at least three ways a child may solve the problem. Each way of solving should reflect a different level of child development. You do not have to give exact age of a child (you will learn more about that in your methods classes) but sort your answers, starting from what the youngest child might do and going up slowly to older children.

3. Scenario 1 Assume that you have an opportunity to give a shoe-box and lots of small cubes to a child of an unknown age. Ask the following question: How many cubes can you fit in this shoe-box?

4. Scenario 2 Fold a piece of paper horizontally into a cylinder (“hamburger” fold) so that edges perfectly touch (you can tape it). Fold another piece of paper of the exactly same size into a cylinder, but now vertically (“hotdog” fold). You have two cylinders. Which one can hold more (rice, water …)? Make a prediction, write it down and write why you think that.

5. Problem Sets Describe what you think you are getting from experiences of designing problem sets in terms of understanding how prek-6 students learn.

6. Process Standards Describe what you think you are getting from learning about process standards in terms of understanding how prek-6 students learn.

7. Process Standards Problem Solving Reasoning and proof Communication Connections – other curriculum; within math; real-life Representations -

8. Content Standards Number sense and operations Geometry Measurement Algebra Data Analysis and probability

9. Final Presentation (5-7min) A selected ‘challenging problem’ (any PS) Interactive ICT integration (any PS) Metacognitive reflection strategies Artifact that you made to support your presentation (poster, manipulatives, game,...) - include an explanation on ppt See the Presentation grading rubric (syllabus) for further details

10. Strategies for Designing Problem Sets (1) Include ‘common knowledge’; list all steps; be specific Start early Vocabulary – age appropriate Scaffolding – different designs Reliable websites Creativity, excitement and appropriateness There is always place for improvement

11. Strategies for Designing Problem Sets (2) Know the content – workshops, learn, learn, collaborate, share Developing the formula before using it Focus on problems (design and solution) to solve, not lesson plans Scaffolding breaking it down Better time management: do 1-2 problems per day

12. PS 4: Ratio, Permutations Combinations Select one of these three concepts Design only 3 problems: challenge, middle, lowest Reflection: Very detailed, about designing PS in general + about designing PS4