IA Difference between Type 1 and Type 2

[i_need_help]

Does anyone know the difference between Type-1 and Type-2 math portfolios?

Does one require the use of technology and the other the use of algebraic and mathematical proof?

[Keel]

Ones a mathematical investigation (I) and the other is mathematical modelling (II). Thats how it is in HL maths, Im sure it applies for SL as well but I dont think its the same for studies. Both require algebra and technology. But assessment I requires more proving.

[i_need_help]

Ones a mathematical investigation (I) and the other is mathematical modelling (II). Thats how it is in HL maths, Im sure it applies for SL as well but I dont think its the same for studies. Both require algebra and technology. But assessment I requires more proving.

Okay that makes sense. Thanks so much!

[dessskris]

Type I — Mathematical Investigation

While many teachers incorporate a problem-solving approach into their classroom practice, students also should be given the opportunity formally to carry out investigative work. The mathematical investigation is intended to highlight that:

• the idea of investigation is fundamental to the study of mathematics
  
• investigation work often leads to an appreciation of how mathematics can be applied to solve problems in a broad range of fields
  
• the discovery aspect of investigation work deepens understanding and provides intrinsic motivation
  
• during the process of investigation, students acquire mathematical knowledge, problem-solving techniques, a knowledge of fundamental concepts and an increase in self-confidence.

All investigations develop from an initial problem, the starting point. The problem must be clearly stated and contain no ambiguity. In addition, the problem should:

• provide a challenge and the opportunity for creativity
  
• contain multi-solution paths, that is, contain the potential for students to choose different courses of action from a range of options.

Essential skills to be assessed

• Producing a strategy
  
• Generating data
  
• Recognizing patterns or structures
  
• Searching for further cases
  
• Forming a general statement
  
• Testing a general statement
  
• Justifying a general statement
  
• Appropriate use of technology

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Type II — Mathematical Modelling

Problem solving usually elicits a process-oriented approach, whereas mathematical modelling requires an experimental approach. By considering different alternatives, students can use modelling to arrive at a specific conclusion, from which the problem can be solved. To focus on the actual process of modelling, the assessment should concentrate on the appropriateness of the model selected in relation to the given situation, and on a critical interpretation of the results of the model in the real-world situation chosen.

Mathematical modelling involves the following skills:

• Translating the real-world problem into mathematics
  
• Constructing a model
  
• Solving the problem
  
• Interpreting the solution in the real-world situation (that is, by the modification or amplification of the problem)
  
• Recognizing that different models may be used to solve the same problem
  
• Comparing different models
  
• Identifying ranges of validity of the models
  
• Identifying the possible limits of technology
  
• Manipulating data

Essential skills to be assessed

• Identifying the problem variables
  
• Constructing relationships between these variables
  
• Manipulating data relevant to the problem
  
• Estimating the values of parameters within the model that cannot be measured or calculated from the data
  
• Evaluating the usefulness of the model
  
• Communicating the entire process
  
• Appropriate use of technology

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Criteria Assessed:

(Source: Math Portfolio Criteria, 2005, pp 2-4)