This lab is part of a curriculum from the AMTA (American Modeling Teachers Association) that starts out each unit with a paradigm lab. This lab involves students being exposed to identifying independent and dependent variables, collecting data, and creating and analyzing a graph. I do this specific lab to help students get used to the process of coming up with their own variables, data collection methods, data analysis, and summarizing results written and verbally.
During the pre-lab discussion, I show students the Lab Set-up and ask them what things that they think they could measure about the bridge or change about the set-up to be different than the current set-up. I record all suggestions from students. Then I categorize them into bridge design factors (things that affect how the bridge looks) and measures of bridge strength (things that affect how much the bridge can hold). I tell students they must choose a design factor which is the independent variable. I help them narrow down all the design factors and guide them to focus on number of spaghetti strands. Students then identify the dependent variable, the strength of the bridge, and I help them narrow down all strength factors and guide them to the number of marbles that can be supported. Finally, I ask students to record values of the other factors and make sure they remain constant or the controlled variables.
I do this pre-lab discussion so that students come up with variables that they think are important for the lab like in this Pre-Lab Student Generated List. This is part of a guided inquiry process where they come up with as many variables as possible and then I guide them to variables to focus on. My goal for students in the activity is to think of anything that could be a variable within an experiment. I want them to be able to come up with the independent, dependent and all of the controlled variables. Each paradigm lab that I have my students do is to have them determine the equations that they will use themselves from their data.
Prior to the data collection, I assign roles to students based on the number desk they are sitting in at their table. The roles are: (1) Marble Catcher (2) Bridge Handler (3) Data Recorder and (4) Spaghetti Cleaner. I discuss with students that each person must fulfill his or her role in order for the lab to work smoothly. To determine what roles students have, they look at the number on their table, at their individual seat (numbers 1-4 at each table), and whatever their number is will correspond the the number job they have (shown with the numbers above). I give the students roles to help give them provide positive interdependence and individual accountability within the group.
As students get ready to collect data I remind them of a few things for this lab. I tell them:
(1) Don’t move tables too far apart. You want the spaghetti to have at least one inch or so on each table.
(2) Increase the number of marble for each case of spaghetti strands until it breaks and record the last number supported.
(3) Make sure the Data Recorder types every piece of data into a Google spreadsheet shared with your entire group.
As the groups collect data, I walk around the room to facilitate their data collection by making sure that they have the correct set-up and are adding marbles and spaghetti strands appropriately.
After students have collected the data, I show students how to go through Plotly. I have students use Plotly because it is an easy way to input data and create trendlines on graphs. As I demonstrate on the screen students will be following along with a copy of the instructions on their Chromebooks. I go through the steps in the Plotly Data and Graphing Instructions so they can see how to input data, create a graph and get an equation from a best fit line. I do this so students can have a visual representation of actually going through the process in addition to the written instructions. I want to make sure that students can physically go through the process of creating a data table and graph in Plotly so that don't have as many questions later on.
When we have gone through the demonstration, I refer students to the Lab Summary Template on their Chromebooks where they will put all of their graphical, mathematical and written results. Similar to when I go over the Plotly instructions, I expect my students to be following along on their Chromebooks or on the screen. This lab they will do a practice group summary, but in future labs they will be either graded group summaries or graded individual summaries depending on the lab.
As I go through the sections I use a sample set of data and write exactly what I expect in the Google Doc. In the Graphical Representation section, I screen shot my graph and crop the screen shot so just the graph is showing so that students know that is what I want to see. Then I answer the question about slope in the format of "For every 1 x, there are ___ y's." Next is the y-intercept in the format of "When x=0, y is ____." The mathematical representation is where I tell students that I want them to replace x and y with the variables in words. I also make sure to tell them that only the slope and y-intercept receive units. Finally the written representation is where I refer them to the Graphing Reading Packet where the last page lists all of the types of graphs and the format to write the written expressions.
I go through both of these demonstrations to help my students to understand exactly what they are expected to do since we use both of these tools frequently throughout the year.
When the students have gone through the demonstration, they work with their groups to complete the data analysis and the lab summary together. For me, this is an important time for me to be walking around and correcting things that I don't want to see in the lab summary and praising things that students are doing well.
I have each group share a copy of the Google Doc with me. In this case, I tell students that the Bridge Handler and Spaghetti Cleaner are to be typing in the document but everyone must contribute their ideas. I also tell students that the Data Recorder and the Marble Catcher are in charge of creating the graph of the data. Each student is working on their own Chromebook but they are working on a shared Google Doc.
When students are done with the summary, they use this information for their whiteboards and turn this in to me by sharing the document with me.
Students create a whiteboard for the discussion that includes the graph and the equation (with units!) on the whiteboard. I have students sit in a circle with whiteboards facing each other. Below is a list of questions that I ask students. I start with the experimental procedure and then to the graph and the equation. I want to make sure that students are getting used to comparing graphs and data and pulling out similarities and differences while still understanding how the procedure fits into their results. I also ask my groups to make sure that if one person speaks from their group that they do not speak again until everyone in their group has spoken.
I run the discussion by asking questions verbally. I try to guide them to see the important parts of the data collection process, the data itself, and the data analysis. When students want to answer they raise their hands and I call on them. Since this is our first discussion like this, students typically are talking to me but as we continue to have these discussions students start to talk to each other. Once I feel that we have covered the answer as a class we move on to the next question. Here are the questions I use to lead the discussion:
- Experimental Procedure:
What was your independent variable? Dependent variable?
What does it mean that we controlled variables?
How did you control your variables?
How do you know if you collected enough data?
- Graph and Equation:
What do we see in common with all of our graphs? (focus on axis labels, units, variables in the right place, etc.)
What does the straight-line graph tell you about the bridge?
What does the y-intercept mean in terms of the bridge?
What does the slope mean in terms of the bridge? (Use units to help)
Why do different groups have different values for their slopes?
What would a larger slope look like if it were added to your board?
What parts of your equation should have units and which shouldn’t?
I do this discussion so that students can take time to really analyze their own data and draw conclusions from multiple data sets. I also do this to help students express their results verbally in addition to written in the lab summary.
I provide students with a Graphing Reading Packet of the graphing basics for homework. I have them highlight 10 of the most important things to keep in mind when from the packet as they read. I give them this homework so that students have a first look at the important aspects of graphing and can bring several ideas that they think are important to the discussion that we have the next day on graphing. I expect that students are able to answer my questions in the next day's discussion where I focus on what they picked out of the reading instead of me lecturing to them about the important aspects of graphing. I do not collect this homework but I have students take it out during the discussion and as I walk around I check to see who has it done and who does not for an idea of who has completed his or her homework.