Problem Sets: Requirements CI 319 Mathematics Investigations MOTO: Collaborative Learning

Mara Alagic: Mathematics Investigations - Problem Sets Requirements2 Challenge problem selection  Open-ended problem=More than one answer  Example: I have 0.7m 2 piece of cardboard and I am making a box for some of my scrap. What are some possible volumes for this box?  Real-life related  Significant mathematical idea addressed (e.g., volume for the first problem set)  Each step of the solution identified and justified in a table format  

Mara Alagic: Mathematics Investigations - Problem Sets Requirements3 Challenge problem: Quality of its solution SolutionJustification Solve the problem on this side without any explanations On this side, parallel with the step on the left, describe why and how every step is correct; Make sure to describe how is your Challenge open-ended

Mara Alagic: Mathematics Investigations - Problem Sets Requirements4 Scaffolding through word problems - representations leading to the main concept  At least 7 problems in addition to the Challenge  They all have to be word problems  They all have to be real-life related  They have to lead step-by-step (by difficulty) to the challenge  Ask: What do I need to know so that I can solve the challenge problem?  NOT calculational (plug and calculate) problems

Mara Alagic: Mathematics Investigations - Problem Sets Requirements5 Quality of the solutions  All solution steps are included  Corresponding justification details are included  Two-column solution format for each problem, as illustrated on the slide 3

Mara Alagic: Mathematics Investigations - Problem Sets Requirements6 Vocabulary  Concepts clearly introduced after an experience provided with a problem  Introduce new words precisely, as much as possible appropriate to the level of the problem after which you are introducing them  Precise connections to other concepts, if other concepts are used

Mara Alagic: Mathematics Investigations - Problem Sets Requirements7 ICT tools/virtual manipulatives  ICT (Information and Communication Technology) representation included  ICT may be part of any problem in the problem set  Problem has to be clearly stated and solved as all other problems  Interactivity clearly described  Reference to the ICT tool included

Mara Alagic: Mathematics Investigations - Problem Sets Requirements8 Metacognitive Reflection  Describe your own thinking during the design of the problem set  What did you learn in terms of  Mathematics content  Yourself; your thinking and learning habits?  What is the main quality of this set?  What is the main quality of this set?  How are problems connected?  Support your statements  Reflect, reflect, reflect, …

Mara Alagic: Mathematics Investigations - Problem Sets Requirements9 Please if you have any questions or suggestions: