Introduction of myself. Experience teaching and modeling. Not the smartest person in the room, my expertise is more in pedagogy and science, still learning about the nature of mathematics.
Can do round robin introduction or activity or wait till tomorrow.
30 min - Engage participants in 1) share with a neighbor your professional goals 2) whiteboard student goals.
30 min - Make a master list of student goals with which to refer back to in the workshop. Discuss how these are goals “you as an educator value”.
30 - 60 min - Teacher led discussion on how main learning theories (behaviorist LT, constructivist LT dvelopmental LT, and Social LT) relate to the modeling cycle (paradigm lab, development of model, deployment, validation). How the modeling cycle relations to student goals which has to lead to student actions to develop those goals. Modeling activities encourage these actions and enable the teacher to make decisions to move the learner in the direction of understanding. See Big Ideas 2014 for more notes in this. NOS and how scientific thinking is not natural.
Break
Unit 1 Scientific Thinking
30 min - Introduce Paradigm Lab
“What can you measure about a circular object?” Encourage list on board by making dashes and giving “statue” wait time. (radius, circumference, area, arc,length… all acceptable responses)
“What relationship, if any, exists between circumference and diameter? (WRIAEB)
Things to consider before we start…
- How much data is enough data? (at least 3 to see a pattern, but at least 5 to evaluate possible
outliers)
- What range of data is sufficient to see a relationship (a variety of sizes, order of magnitude).
- How will we measure? (string, roll it, tape measure…)
- What assumptions are we making (circles are all perfectly round, we can find the center of the
circle)
20 min Data Collection
Until Lunch…. Interpreting Data
- Guide to use of a table
- look for patterns in changes in the table (make side calculations “>” between each progression
down the table, is it a 1 to 1? 1 to 2? etc..) Refrain from the verbiage up and down, use
increase and decrease, sidebar discussion to relate to Aarons regarding use of words that are
appropriate and specific to the nature of scientific thinking.
- guide to graphing by hand first,
- looking for a trendline with the computer and select a math code
- are there more meaningful variables you could put into your code than X and Y?
Tease out as D doubles….. ??? Leave it hangin’
After Lunch
1 Hr - whiteboard preparation and discussion of lab. Discussion can take on any form… all boards in front, circle, something simple. (may want to point out this is not a lab report, be clear and concise, use abbreviation and symbology where you can)
Make an example/direction board for the kids, possible WB quadrant entries 1) sketch of predictive graph 2) data table 3) Sketch of real graph 4) Slope Value? Slope Units? 5) Expected Y Int? Experimental y Int? Why are they different? Units for Int? 6) Math code/relationship 7) Procedure and materials. FIgure out what you want and that you feel has the best organization and flow.
Present possible WB discussion options 1) Circle with rules, 2) Put all boards up in front and question students in direction of points you want them to notice 3) Board presentations (talk about students’ initial attitudes during WB discussion, philosophies, modelers do this differently, refer to reading on managing discourse.
Discuss the purpose of the WBD from the teacher standpoint 1) have specific goals you want students to draw from the discussion and steer conversation with questioning to those goals 2) In this first unit goals you may want to address are a) patterns in the changes in the data tables, b) slope value and UNITS, c) differences in measuring techniques and effects on the data, d) establish norm for board presentations that will last for the rest of the course (look at paragraph above)
Data should show numbers for slope that range around the value of Pi.
- Evaluate how measuring methodology could effect this range. Points of discussion regarding the nature of scientific inquiry: Do we ever get exact data? How are constants established?
- What do the units for slope mean? Discuss the idea of a ratio or proportion (two ratios that would be equal to each other) vs. parts of the whole (Assign Aarons Chapter 1 for HW). in this lab you have teased out the units for the slope… what are the variables that make up the ratio? … length/length. Draw circle on the board cut into thirds and discuss the idea that this ratio
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