Personal Learning Path #6

Background

I am working from the New York State Teacher Certification Examinations (NYSTCE) standards, Field 005: Mathematics. This week, we will be discussing a topic from Competency 0006 - Statistics and Probability. Within this Competency, I have chosen the following performance indicator: "Summarizes and represents data on a single count or measurement variable (e.g., using number lines, dot plots, histograms, and box plots)."

Here are the NY State Common Core Learning Standards for Mathematics which align with my selected topic:

My goal is to create a multi-day class project which, while completed individually, requires students to collect and analyze data they obtain from their classmates. The project will require students to pick a topic, obtain data from their classmates (through an organized, collaborative class effort), and then complete the required tasks outlined below. This is an original activity, though I'm sure that other teachers have created similar activities in the past.

The Activity

This is an activity that can be implemented early in a Statistics/Probability class. Though it applies to data with a single variable, a similar activity could easily be created for other concepts in statistics as the class progresses.

Step 1: Students will be required to pick a question they would like to ask their classmates. It must be something with a single numerical response. Possible examples: (1) How many books have you read in the past year? (2) What is your ideal movie length in minutes? (3) How many pets have you had in your lifetime? (4) How tall are you in inches?

Step 2: The teacher will then collect the students' questions and place them into some sort of spreadsheet or Google form. The teacher will send this form out to everyone in the class, and the students will enter their responses to each of the questions from their peers. The teacher will then make the data available to the appropriate students.

Step 3: Once the students receive their data, they will be asked to submit an individual document with the following information:

• State the question you asked your classmates.
• State the number of responses you received.
• Calculate the following pieces of information about your data (no full sentences needed):
• Range
• Mean
• Standard deviation
• First quartile
• Third quartile
• Interquartile range
• Median
• Mode
• Outliers
• Display your data in the following three ways:
• A dot plot
• A histogram
• A box plot
• Answer the following questions in full sentences:
• Describe the shape of your data.
• Is it unimodal or bimodal?
• Is it symmetric or is it skewed to the left or right?
• Is it uniform?
• Interpret the mean, mode, and outliers of your data.
• For example, if you asked your classmates how many books they read in the past year, then you might write, "The mean was 4.3, which means that my classmates read an average of 4.3 books in the past year."
• Describe the spread of your data.
• Is your distribution broad or narrow?
• How would you interpret this spread based on the question you asked your classmates? 
• For example, if you asked your classmates how many books they read in the past year, then you might write, "The data spread was broad, which means that some of my classmates read very few books in the past year while others read a lot." Alternatively, you might write, "The data spread was narrow, which means that most of my classmates read a similar number of books in the past year."
• What can you conclude from the data you collected? What is your main takeaway?

Step 4: Once students submit a document with the responses to the above questions, they should prepare a 5-minute presentation of their data to share with the class.

Step 5 (optional): If the teacher is feeling particularly ambitious, they could also have students submit an 8x12 sized poster drawing of a graph of their choice (dot plot, histogram, or box plot) from their project. Each student's graph can be placed around the room once they present. The graph should state the student's question. These small posters can act as permanent classroom decorations.

Step 6 (optional): If the teacher is feeling super duper extra ambitions, after the presentations, the teacher could have all the students write down two compliments and suggestions for future research they have for their fellow classmates after their presentations (four post-it notes total). These could be pasted underneath each student's poster. For example, imagine that Student A presented on the question, "How many books did you read in the past year?" Student B could respond with a compliment, "I found it interesting that someone read 22 books in the past year." Student C could respond with the compliment, "I liked the way you color coded your box plot." Student D could respond with the future research suggestion, "You could also ask people how many TV shows they watched in the past year." Student E could respond with the future research suggestion, "You could ask people how many pages they read rather than how many books, since books have very different lengths." The teacher could then hand these questions/compliments back to the students and ask for any student volunteers to share a nice compliment or an interesting question they received.

Here is a document with instructions that the teacher can provide to the students:

Reflection

I think this activity is fantastic. I am quite pleased with how it turned out, and I will absolutely use this activity if I end up teaching statistics or probability. I like the collaborative element where students get to ask their classmates a question of interest to them. In other statistics classes, I know that teachers let students gather the data themselves by approaching every student individually, but I find that to be overly chaotic, so I think using a Google form or spreadsheet would be much more efficient while still encouraging that class collaboration. The questions asked in Step 3 are quite comprehensive and would work well as an end-of-unit project. I also think that the structure of this project would work well for future statistics projects in which students are collecting data based on two different variables, for example. I have included two potential additions above in Steps 5 and 6, and I think these would be wise to implement. They encourage students to communicate with and listen to one another, and hanging the students' graphs around the classroom will create a nice, collaborative, student-centered environment. One potential modification would be to make certain trickier questions extra credit, since this will be a time consuming project for some students. Alternatively, the teacher could add other more challenging questions regarding normal distribution and use those as extra credit questions instead. A second potential modification would be to allow students to create a short video to present their work instead of presenting in front of the class. The teacher could even help a student film a 5-minute presentation video after class one day if the student needs help.