Lesson 3 - Inferences from Proxy Variables-Mock AFM

Course: Integrated Science, Physics, Biotechnology and/or STEM courses

Unit: Measurement, Scientific Process, and Instrumentation Design

Inferences from Proxy Variables-Mock AFM (atomic force microscope)

Objectives:
What students learn…

  • Observation is the skill of recognizing and noting some fact or occurrence in the natural world. Observation includes the act of measuring.
  • To infer is to arrive at a decision or logical conclusion by reasoning from evidence.
  • Scientists use observations to make inferences.
  • Additional information can improve the validity of inferences.
  • Proxy variables can be used to make observations.
  • An Atomic Force Microscope (AFM) uses repulsive force as a proxy variable to make observations of surfaces at the atomic scale. Processing the data with of visualization software, scientists infer surface structure from these observations.
  • Increased resolution can provide additional information.
  • Design solutions involve tradeoffs.

What students do…

  • Make observations and generate inferences about differing types of data.
  • Use “touch" data to draw an unknown object in a bag.
  • Make inferences about the identify of the object from the drawings.
  • Use a mock Atomic Force Microscope (AFM) to infer surface structure from “touch" data processed with Excel into a 3D graph.
  • Brainstorm ways to improve the design of their mock AFM & evaluate the trade-offs.
  • Evaluate the limitations of utilizing proxy variables to take measurements.
  • Evaluate the limitations of observation to infer patterns or make predictions.

*Access a short article on new techniques to measure brain activity.  This article specifically discusses brain neurology as a system and the need for novel ways to "see" into it.  Taken from the August 2011 HHMI Bulletin, vol. 24, No. 3.  "Let's Get Small" by Helen Fields.

Instructional Activities:

Please note: There are additional materials needed for this lesson. The paper bags with items for the warm up activity should be assembled and taped shut before class. The mock AFM boxes can be assembled ahead of time, or students could assemble them in class. If assembled during class, the surfaces should be inserted into the boxes without students seeing them so have students trade boxes or one class make them for use in another class. Students will also need computer access (one per group) to plot the mock AFM data on the premade Excel file.  See teacher directions.

Materials Not Included (for ~25 students, ~8 groups of ~3):
Vanilla for scent
-Paper lunch bags (per student)
-Collection of items of similar size and shape (pack of gum, eraser, used (EMPTY) lighter, USB drive, 9Vbattery). See powerpoint slide #10. (1 per student)
-Probe sticks (one per group) that have been marked in 0.2cm resolution (wooden skewers from the grocery store work well).
-Rulers (one per group)
-AFM box (1 per group)
-marking pen(1 per group)
-1cm x 1 cm graph paper (and somewhat smaller 0.5 cm x 0.5 cm if completing the 'fine' resolution data collection).
-box about the size of a shoe box (one per group)

  1. Warm-up: How does observation lead to inference?(There is a student worksheet that goes with these slides.)
    • What distinguishes an observation from an inference? (Power Point) Before students enter, have the classroom smelling of vanilla. Ask students to describe the smell [slide 2] using descriptive words (data) then ask them to make inferences about what the smell implies (cookies?, air freshener?).  Do the same for shadow [slides 3-7]. Encourage observations of the picture first, rather than inference (not “it’s a shadow from a man’s face," but “it’s a contoured region of low light surrounded by higher light intensity“). To assess their understanding of the difference between the two terms, slide 8 returns to the wind speed activity. Students are asked to identify the observations and inferences used to arrive at a wind speed value. Be sure they know the difference between observation and inference before they move on. Student groups could share in a whole class discussion or you could check in with each group as they discuss the trade-offs. The term “proxy variable(s)" is introduced to describe measuring/observing something we reasonably infer to be an indicator of something we cannot directly observe with our senses.
    • How can we use proxy variables to make observations? How does additional information help our inferences? (PowerPoint, Student Activity) (Slide 9) Hand out paper bags containing one of the items on the material list (pack of gum, flash drive, 9V battery, lighter, or eraser). Students should make a drawing based on their observations about the object, but cannot open the bag for direct visual observations.  Ask students what they think is in their bag (inference).(Slide 10) Discuss the different approaches to make observations (probably some form of touch data) used to make inferences. Once many have made guesses as to the object’s identity, show the possibilities and ask if they can make a stronger inference with the additional data.
    • If you could not rely on visual observations, how could you make inferences about your environment? (PowerPoint) (slide 11) Students are asked to consider how they could make observations about two different sidewalks without visual stimuli. Often we need to rely on other characteristics to “see" objects, such as a bat’s echolocation or a shark’s electroreception. Specifically, we can use touch to determine the shape of an object. Push students to specify details about the process: What would the edge feel like? How would you know if there’s a bump, an incline, or step up/down? Slide 12 illustrates the use of a cane to transmit the “touch" data through a probing process. Slide 13 illustrates tactile surface features built to aid the visually impaired in detecting boundaries such as sidewalk to street or transit crossings. Once students identify the purpose, questions can be posed concerning how notable the features need to be (this will set up a future signal to noise discussion) or how regular/large the pattern would need to be to distinguish the “touch" data from natural occurring variations in the surface.
  2. Mock Atomic Force Microscope
    • How can we use touch data to see things that are very small? (PowerPoint)

      Slides 14, 15, & 16 Introduce the concept of using “touch" data to make observations at scales too small to see with the human eye. Slide 17 introduces the Atomic Force Microscope. Since atoms repel each other, we could probe a surface with a very fine tip and record the feedback from the changing topography. Repulsion data from dragging a small ‘cane" across a surface is visualized with computer software so that inferences about atomic structure can be made. Slides 18 & 19 show examples of data used to visualize the hexagonal structure of carbon in graphite and the repeating “steps" in gold.

      Teacher background: Chemical analysis has shown that graphite is composed of carbon, but more analysis is needed to show the geometry of the atomic structure. . This is what an Atomic Force Microscope (AFM) does (http://virtual.itg.uiuc.edu/training/AFM_tutorial/ ). Basically, a fine tip is dragged along a sample surface while a laser reflects off the back of the tip to a light sensor. As the surface dips and bumps the tip moves in or out, changing the reflected angle of the laser. The light sensor uses this subtle change to determine how the tip must have moved and therefore the geometry of the sample surface. Displaying the bumps as bright regions and dips as dimmer regions, a pattern emerges. Noticing the periodicity, a structure can be deduced for graphite; hexagonal layers of carbon atoms. Similar instruments such as the Scanning Tunneling Microscope (STM) yield similar data (an STM does not measure touch, but the proximity to a surface by how much current flows from the tip to the surface). Notice how either method deduces a hexagonal layered structure for graphite. Gold, for example, appears smooth to the eye, but exhibits “steps" when viewed with an AFM on a relatively large scale of half of a micrometer. Upon magnification, “strips" appear on the formerly smooth surface. At maximum magnification, the actual atoms of gold can be seen on the surface of these strips. These are the hexagonally arranged bumps.

  3. Collecting Data with a mock Atomic Force Microscope
    • Gross Data Collection

      Handout mock AFM boxes (or have students assemble them in class) and marked probe sticks. The provided surfaces should be hidden inside (box opaque and lids taped down) (slide 20). Instruct student groups that they are NOT to open the box. Demonstrate how students will use proxy “touch" data collected as probe stick measurements to infer the surface structure. To help interpret the data visually, the measurements can be directly entered into the premade Excel File Lesson 3 3D Plot Mock AFM: using the Sheet named Student Data Gross.

      Guiding Questions for a whole class discussion regarding the processed data:

      1. Is there enough data to infer the structure of the surface?
      2. Is there enough data to infer a predictable pattern? Teacher Notes: The cast shapes intentionally vary so that how easily the structure can be inferred & the pattern predictability varies considerably from group to group. At this point, each group’s answers to these two questions should be ambiguous.
      3. How could we improve our data collection design to generate stronger inferences about your unknown surface? (slide 21)
        Teacher Notes: Student answers may vary. One key idea that students should recognize is that some means of achieving greater resolution could provide additional useful data. Ask students to extrapolate what new data could be revealed by shrinking the tip size of the probe stick within the grid they just used or conversely to use their current tip size to take measurements at smaller and smaller grid intervals (0.05 cm x 0.05cm, etc. ). Drawing out the extrapolations on whiteboards in groups can help them visualize the effect of the change.

        While students are discussing the effect of the changes, the teacher should be circulating to change out the screen (graph paper with smaller squares) for the fine data collection, ensuring that students do not see into the box.

    • Fine Data Collection  (optional)
      Have students repeat the process using the fine data collection screen (0.5 cm intervals) and the Sheet named Student Data Fine within the same Excel spreadsheet. Once the fine data collection & graphing is complete, collect the boxes and set out the surfaces for students to view.
    • Students should then complete the Post Mock AFM Worksheet.

      Assessment:

      How will I know they know…… Review students identified observations & inferences for the wind speed challenge.
      Review students suggestions to improve the mock AFM.
      Review students mock AFM worksheets.  Use example graphs (slides 22-27) to see if students can identify the structures they describe.

      Resources:

      PowerPoint: Mock AFM

      Excel 3D Plot Mock AFM

      Student Worksheets Mock AFM Student Worksheet for ppt, Post AFM activity questions

       Teacher information Directions for making the AFM box, Answer Key: Post Mock AFM Student Worksheet, Answer Key: PPT worksheet

    • Accommodations:
      Extension Activities:
    • The NanoEd website has lesson plans to build & test a more rigorous Macro AFM simulator utilizing tapping, contact, or magnetic modes.
    • Students who do not visualize graphs well may benefit from additional or introductory work.   This activity requires 2 odd shaped bottles (obtain at vintage shops), a plastic champagne glass, and a plastic 'party' glass, ruler, graduated cylinder and container for water. It generally takes 80 minutes to complete and gives students an understanding of slope and y-intercept...and the importance of looking at axes labels.