Project Abstract: Rock Star Autograph
Create and perfect the autograph that you will use when you become rich and famous. How long do you think it is? If you replaced the ink with a piece of string and pulled that string so it became a straight line, how long would it be?
This project explores the relationship of total length with complex lines and of ways to measure these complex lines. The student creates a way to measure something complex and discovers what it means to have errors associated with those measurements. Finally they should achieve an understanding of how accurately one can report their findings.
What did you teach and how did you teach it?
Standards curriculum covered was the following:
Students will be able to articulate how one type of measurement may suit a specific task better than another. This includes measuring the total line segment for one’s unique signature. The students tried different methods of measurement and created a table listing out potential error for each type of system of measurement. Ultimately, they will be able to address uncertainty with an original data set.
Probability and Statistics – taking an original data set, determining mean, variance and standard deviation of a normally distributed random variable. Understanding the nature and importance of uncertainty.
Methods of uncertainty: random and systematic. We will estimate the uncertainty associated with each measurement.
The methods of instruction included creating an original data set using our 'hands' to imagine the height of a 15 hand horse as an estimate for what we would expect to get compared to an 'industry standard'. We compared the differences between our class measurement to determine what an industry standard is and why relative error and uncertainty are important in the real world.
Then we considered many forms of measurement and came up with 5 types collecting data. The different types of measurements were taken at tables and we discussed at each table what random and systematic errors were associated with that type of measurement. We also determined how to reduce error and how to accurately represent the uncertainty associated with each measurement.
What concepts and skills did the students gain in this class through this project?
The students had to determine how to take a measurement where no specific way of taking that measurement was given. They had to use whatever means available with classroom and household materials to creatively address how to take meaningful estimates. Ultimately students took away the concept that though most calculations performed at school involve exact answers, real-world measurements must include consideration of what can go wrong and an understanding that any measurement will have some inherent uncertainty.
How is the curriculum for this project academically rich and grade-level challenging?
As the first project of the semester, the curriculum was developed to review geometry from last semester. Then, the application provided a more sophisticated application of that same knowledge. Additionally, new skills included writing a scientific paper and calculating uncertainty associated with real-world measurements.
To what extent was there integration across disciplines in your class through this project?
This project included a large writing component. They needed to clearly communicate how they created a method of measurement, how they took the measurements and what the error associated with each measurement was. For many students, it was the first time they submitted a piece of technical writing.
Which Habits of Heart and Mind (HoHM) and Design Principles were utilized in this project?
Perspective
This experiment required each student to examine multiple ways to measuring something complex. They had to weigh up advantages to each type of measurement and determine why their chosen method was the best for their unique signature.
Evidence
Each student generated their own data and relevant information. Ultimately, they had to find out for themselves why their method of measurement was the most appropriate.
Refinement
There were several opportunities to reflect on their own work and to provide critical feedback for other students. This process of refinement included looking for strengths and weaknesses and always making improvements where it is possible.
Perseverance
This opportunity was one that required each student to challenge themselves. For most students, the math was new, technical writing was new and the idea of looking deeply into measurement was perplexing. Those students had to persevere in order to overcome challenges associated with this large amount of new information.
How did you incorporate refinement through this project?
The first level of refinement came with a comparison to an 'imperfect' model assignment. They had a rubric in table format and a model that didn't include some statements and did include some incorrect statements but was representative of a 'final' product. We graded this together and determined what good about this model, what was missing and how they might want to improve on the presented model.
The second level of refinement was written peer review. Each student attached a feedback cover sheet with writing prompts about warm feedback. These included things like what do you like about this person's product? What would you want to incorporate in your work? The second step was a copy of the rubric and a preliminary grade based on which statements, data and conclusions were present. Finally, there was a writing prompt to include what the reader would have wanted to see in order to make this product excellent. Each draft was reviewed by 2-3 peers.