# 6th Grade Statistics: Separating the Music from the Noise.

At the end of last year, I mentioned the need to create a clearer and more unified progression for the statistics unit in my 6th grade general classes.  Throughout this year, I’ve been looking forward to teaching statistics more and more.  I talked with teachers at my building about my plans for the unit.  I intentionally picked out sessions at the ICTM conference (the Illinois affiliate of NCTM) that were about middle school stats.  I read parts of the thorough (and compact!) Developing Essential Understanding of Statistics Grades 6-8 to get a richer understanding of the themes throughout the CCSSM standards for this content.

Essentially, I was ready to make statistics more than the jumble of topics that it was during my first year of teaching.  When I say jumble, I mean the topics seemed disconnected and my students never really seemed to see the power of what we were doing with data. Here’s a breakdown of my progression from last year:

1. Recognizing and Writing Statistical Questions
2. Measures of Variation and Central Tendency (Range, Mode, Median, Mean)
1. Work with lists of data
2. Work with Frequency Tables
3. Constructing Dot Plots (Review from 5th grade)
4. Revisit Measures of Variation and Central Tendency
1. Find using data from dot plots
2. MARS Mean, Median, Mode Lesson
5. Histograms
6. Mean Absolute Deviation
7. Skew of Data
1. Overall Shape of Data
2. Impact of Outliers on the Mean
8. Box Plots and IQR
9. Review and Assessment

My progression wasn’t the worst, but I felt like a lot of the struggles I saw throughout the unit were the product of students failing to connect the ideas.  I explained the connections between topics, but I felt like the progression prevented the connections from appearing naturally in discussions and activities.  I also felt like too much of this unit was analyzing random strings of data.

The more I thought about the content and read about statistics throughout this school year, the more I found that my planned tweaks were really just getting back to heart of statistics and getting students to recognize the need for the subject.  Statistics helps people make music (sense) out of what can seem like random noise (unorganized data).  Beyond this framework for descriptive statistics, I could extend the metaphor further by saying that statistics helps people compose music of their own design (framing questions, collecting samples, and interpreting sample data).

In order to make my vision a reality, I decided that the best course of action for this unit would involve collecting data for a handful of statistical questions and constantly revisiting the data as my classes learn each new idea.  This cycle will help students see how different concepts in statistics can help us use data to better answer questions.

Armed with my introspection and resources, here’s the revised progression I made for this school year:

1. Recognizing and Writing Statistical Questions
2. Collecting and Organizing Data from Statistical Questions
1. Why collect and organize data?
2. Lists (from least to greatest), Frequency Tables, Dot Plots.
3. Grouping Data using Frequency Tables and Histograms.
3. Analyzing Data for Variability (occurs during work with dot plots and histograms)
1. Mode – What’s the most common/frequent data point?
2. Range – How large is the spread of the data?
3. Clusters- Where is the data grouped?
4. Outliers – What data points are far away from most values?
5. Compare Mode and Range for Data Sets
1. Collect data from multiple classes for the same questions.
2. Compare using lists, tables, and graphs
4. Analyzing Data for Central Tendency
1. Median
1. Where’s the middle value in this set of data? What does this value tell us about the data?
2. Refer to dot plots initially, then frequency tables and lists of data.
2. Mean
1. What’s an average?  What does this value tell us?
2. How do outliers affect the mean?
3. Revisit Variability and Deepen Central Tendency concepts using MARS Lesson.
4. How does the median compare the mean?
1. Use computations and graphs to answer this question.
2. Identify skew in data
5. Analyzing Variability from Center
1. Variability from Median (Box Plots and IQR)
2. Variability from Mean (Mean Absolute Deviation)
3. Comparing Variability from Median and Variability from Mean for sets of Data
6. Formulating Detailed Answers to Statistical Questions (Summarizing Findings for the Unit).
7. Assessment

I’m part way through this progression as I write this post and I’ve been liking the results so far.  The start of the progression (questions and organizing data) were a low entry for students and I was able to leverage prior knowledge in a more powerful way than last year.  Students shared reasons and methods for organizing data, then I was able to steer their thinking towards variability and developing an understanding of the concept using graphs. Instead of histograms being a random detour in the unit, this graph became another way of displaying data to identify the most frequent data points, shape of data, clustering of values, and potential outliers.  I’m really interested in seeing how students comprehend median and mean this year since I will be grounding the concepts in an understanding of the center of a display of data.  I’m also hoping to have students work on some sort of culminating project after the assessment to have them use all of the concepts to answer a statistical question.

What do you think of my new progression for 6th grade statistics?  How can I improve this progression?  I’d like some feedback and how other teachers are approaching statistics in middle school.