Unit 1: Nature of Science, Measurement and Number, Symbol and Representation

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• Instructional Notes

The initial emphasis in this unit is on developing the communication and process skills and as well as revising behaviors and expectations to support the development of a functional learning community. This includes introductions to ambiguity in the meaning of words and questions, and the concept that for clear communication meaning needs to be negotiated within the community.
A second emphasis is on drawing the distinction between relation (number) and quantity, and the important but subtle point that number represents an abstraction, a whole part relation, that can only be represented symbolically. This leads into introductary discussions and applications of continuous and discrete variables, systems analysis, dimensional analysis, proportional analysis and reasoning.A third emphasis is on developing statistical reasoning and technigues for characterizing and describing the degree of uncertainty and variation in a set of measurements or a population.

• Topics of Investigation
  

• Norms for Collaborative work, Repectful, Effective and Open-Communication, and Concept-building and Sense-Making.

• The Nature of Science - and its Relation to Truth and Reality

• Measurement and its Underpinnings -Relations and Proportions
  

• Symbols and Representations -Negotiated meaning.

• Introduction to Mathematical Models - the Normal Distribution.

• Enduring Understandings

These are my understandings arrived at after some reflection on the class discussions, they present a more sophisticated take on these issues than it is reasonable to expect of students. However, these understandings shape my approach to teaching physics, and the jist of these ideas was addressed by the students in classroom discussions.

• Science is not reality. Science is the process and outcomes from a long-term collaborative human endeavor to make sense of "reality", i.e. form a shared and logically coherent consensus of understandings supported by evidence concerning the underlying relationships that govern our existance and experience.

• Aspect of our "personal" experience are outside the realm of science because we have no way to directly check or experience against anyone elses to arrive at consensus. For example, we could never get in someone elses head to determine whether they also experience the color blue, the size of the room, the flow of time or the amount of pressure of a touch in the exact same way that we do. This leds us to ask the question, "What are the aspects of reality about which we can agree?", and this led to the key question "Why can we be more definite about shape than color?"

• In investigating the shape/color question we arrived at the conclusion that those aspects of reality about which we can agree and be most "sure", (proportions, whole/part relations, number and symmetry), tend to be relations, i.e. things that "live in the space" between objects or not in the objects themselves. These kinds of relations must form the foundations of scientific understanding, but paradoxically since they are also abstractions, we can only represent them indirectly through example or symbol. Therefore hand and hand with the challenge of developing our understanding of science is the challenge of developing the shared language and symbols to represent and communicate our scientific ideas. However, just naming is not understanding, the idea must exist along with the name.

• Measurements of continuous variables are intrinsically uncertain.
  

• Distinctions to be drawn:

• Differences between science and reality.

• Differences between "outer reality" and personal experience.

• Difference between a scientific theory and a hypothesis.

• Difference between a scientific law and "the truth".

• Distinction between objects that are "visible" and "drawable" and concepts that are only exist through relationship and/or comparison and can only be represented symbolically.

• Differences between discrete and continuous relations, and how this distinction relates to certainty.

• Differences in the three processes that we traditionally all call "multiplication".
• scaling or replication - number by quantity
• combining conversion factors via the chain rule - number by number
• dimension changing definition of new quantities - quantity by quantity
  

• Difference between a measured value and the actual value.

• Differences between measurement uncertainty and variation within a population

• Instructional Objectives:

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• Specific skills to be developed include:
  
  Reasoning skills:
  •Listening and comparing the ideas of others to one's own.
  
  •Analyzing a system by identifying it parts and their relations.
  
  •Destinguishing between number and quantity.
  
  •Destinguishing quantities in terms of their dimension or base unit.
  
  •Distinguishing between continuous and discrete relations
  
  •Differentiating between quantitative and proportional relations
  
  •Expressing proportional relations algebraically
  
  •Interpreting algebraic expressions
  
  •Applying proportional reasoning and/or combining chains of whole/part relations
  to derive additional proportions or conversion factors.
  
  •Estimating and communicating uncertainty using +/- or () notation.
  
  Metacognitive skills:
  •Self-monitoring and self-evaluating individual contributions to the classroom and discussions (earns professional points through self-reporting)
  
  • Monitoring, evaluating and suggesting procedural improvements to classroom and group processes (earns professional points through self-reporting).
  
  •Moitoring the use of words, symbols and other representations that are ambiguous in meaning or have not been clearly defined (earns professional points through self-reporting)
  
  •Collaboratively managing the flow of the classroom discussion. (earns professional points through self-reporting)
  
  •Evaluating the work of others to identify criteria for best practice (nominations for whiteboard "hall of fame")
  
  Communicaiton skills:
  •Effectively communicating ideas using multiple representations (whiteboards).
  
  •Communicating understanding individually in writing with illustrations (journal entrees)
  
  •Summarizing group results and consensus verbally (whiteboard presentations).
  
  •Critical listening and respectful and open-minded evaluation of the results and ideas of others (whiteboard circle).
  
  •Building consensus through questioning, clarifying, comparing, contrasting, restating, reflecting, organizing and summarizing (whiteboard circle).
  
  Additional Skills for Honors:
  
  •Using algebraic subscripts and summation notation
  
  •Calcuating a standard deviation for a set of data
  
  •Applying statistical models (the normal distribution) to predict probabilities.
  

• Overview: Sequential narrative explaining how each activity/lesson is connected, along with general strategy notes. Please indicate each activity or lesson name in this narrative in boldface, so they are easy to distinguish. Be sure that the title of the activity or lesson is the same as the sub-page title.