Giving Students Experience with the Statistical Cycle
I recently had the opportunity to work with a class in which I taught the math, ELA, science, and social studies content.  I decided to invest a lot of energy early on talking about statistics and data, in hopes that this would lay a foundation for later work in social studies and science.

Frequently, math instruction in statistics focuses only on data analysis—that is, reading and creating graphs and learning how to calculate measures of central tendency, such as mean, median, and mode.  While these are certainly important, the scope needs to be much broader to help students become truly “statistically literate.” 

I started the unit by exploring the statistical cycle in its entirety: posing a question, deciding on and executing a plan to collect data, analyzing the data, and finally reflecting on the results to see if they do, in fact, answer the question, and with what degree of confidence.

We undertook our own survey project in which students designed a survey to collect data that they felt would be useful for the staff of our adult education program.  They debated different wordings of questions and discussed the best way to distribute and collect the surveys. 

After the surveys were collected, groups of students discussed ways to tabulate the data (while I encouraged them to come to a consensus about how they would deal with irregular or unexpected responses).  They then created several types of graphs and compared what impact each type of graph had on the impression the viewer had of the data.  Finally, they had to decide to what extent they had answered the original question.  

In many cases, they found that their original wording did not quite give them the answers they wanted (piloting questions first can be helpful in understanding how they will be interpreted!), or that they may have needed a larger sample to feel more confident. While my students may not have changed the world with this project, they certainly got an authentic experience of what data collection and analysis is really like.

While conducting the experiment, the messiness of real data collection showed up again: some of the airplanes hit people or objects, and they had to decide what to do with those trials. They discovered that two different people timing the same event on their phones will be off by a little bit—how do they deal with that?  Was it okay to open the window in the room, or would that affect the “flying conditions”?  My students had a lot of fun with this project and did a great job discussing and working through the challenges that arose.

The statistical method (and the classic “controlled experiment”) are a great place to explore data and statistics, but this is not the only way data is used in the sciences. 

In an upcoming unit on the human body, I am going to teach a lesson on vaccines.  Students will hear arguments on both sides of the childhood vaccine debate and will also look at data showing the rates of smallpox in different countries over time, comparing before and after vaccines were available as well as before and after they were made mandatory. 

Looking at data collection in the context of health care will be interesting, as controlled experiments are not always possible for ethical reasons. For example, we cannot ethically assign children to not receive vaccines, since there is evidence that unvaccinated children are at a higher risk of contracting certain diseases.

Later on, I will be teaching a unit on climate and climate change, which presents another challenge for data collection: how do you run a controlled experiment on a system as large and complicated as a planet, with changes that take place over a long period of time?  When we look at how climate scientists collect and interpret data, we will see them taking advantage of “natural experiments,” such as climate information before and after the Industrial Revolution, when human production of CO2 increased dramatically.

Data and Statistics in Social Studies
The study of history relies on a lot of quantitative data, but also presents its own set of challenges for statistical analysis.  We can’t go back in time to collect data that no one recorded, so historians sometimes have to use other types of data as a proxy. For example, a historian might use voter registration rates to make inferences about political participation, or school enrollment numbers to make inferences about education and literacy levels.

Raw historical data can also help generate questions.  In an upcoming unit on U.S. immigration, I will have students look at a graph of U.S. refugees over time, which shows not only the total numbers, but also breaks the total down by continent of origin.  Looking closely at the graph should generate some questions about what was happening in the world at different points in time, such as What was going on in Europe in the 90’s that led to so many refugees to the U.S.?  What happened in 1976, 2001, and 2017 to cause sudden drops in the number of refugees?  Looking at data can get students curious, since data never tell the full story.

Some Techniques for Presenting Data
When presenting data or statistics that students have not generated themselves, how the data are presented can make a different in student engagement. Two techniques I use a lot are notice/wonder and graph reveals.

When I find an interesting graph, I often combine notice/wonder with a graph reveal.  In a graph reveal, I create a slideshow that starts with a version of the graph without any labels or context.  I ask students what they notice and wonder, and what information they would like to have.  Each slide adds a little more to the graph (scales, axes labels, and last of all, a title).  At each stage we do a quick notice/wonder.  This works well for very complex, rich data displays since students don’t have to process all the elements at once, and creates a lot of interest because they want to know if their predictions are correct. (I originally encountered this idea on the blog Teaching to the Beat of a Different Drummer, in a post titled “Trick or Treat!”)

If you are interested in learning more about how to incorporate statistical literacy into your adult education classroom, check out the SABES website for some upcoming courses on data and statistics from the SABES Mathematics and Adult Numeracy Curriculum & Instruction PD Center.  This is a topic that deserves a place in every content area, not just the math classroom.

Be sure to read the earlier article by Melissa, "The Case for Statistical Literacy Across Subject Areas".

Melissa Braaten is an adult education instructor at Catholic Charities Haitian Multi-Services Center in Dorchester, MA. Melissa has taught ASE and pre-ASE math and reading, as well as ABE writing, computer skills, and health classes. Melissa also is a training and curriculum development specialist for the SABES Mathematics and Adult Numeracy Curriculum & Instruction PD Center at TERC. She has written several articles for Math Musings, the Adult Numeracy blog.

by Melissa Braaten

In the academic sphere, statistics can sometimes seem like the odd one out. Most of us associate statistics with math, although it is far more dependent on context for meaning than other domains of math.

For example, a graph of population data with the context removed is just a meaningless squiggle.

Now consider the same graph with its intended labels.

(For even more information, view the original chart.)

Different fields of study have different ways of collecting and interpreting data.  Physicists may run controlled experiments in a lab; climate scientists may compare historical and present day measurements; social scientists may collect surveys. These context-specific applications of statistics can be taught in content classes to enrich students' understanding of statistics, as well as the content matter. 

For example, while teaching a unit about the U.S. Civil Rights movement, my class looked at voter registration data before and after the Voting Rights Act of 1965. The dramatic (sometimes up to tenfold) increase in the rates of black registered voters in Southern states after this legislation helps to tell part of this country’s history. In addition, it demonstrates how data can be used to support inferences about historical realities, such as the effectiveness of voter suppression against African Americans before the Voting Rights Act.

In adult education, we want our students to be able to engage in their personal, professional, and civic lives in a deep and meaningful way. We want students to grapple with the big issues of the day and contributing to the conversation. This is one of the reasons for the instructional shifts in the College & Career Readiness Standards for Adult Education (CCRSAE) across content areas. When it comes to ELA, the shifts emphasize the use of textual evidence in reading, writing and speaking. Our adult students need to be able to analyze textual and academic arguments, and to cite evidence from those arguments to form their own. In the “content-rich nonfiction” texts that we are using to build knowledge, arguments based on data and statistics are common, and statistical literacy is a must.

It is hard enough to offer multimedia in a typical adult education setting. It is even tougher to offer multimedia to adult learners in a medium-security state prison, where I teach now.

Perhaps similar to yours, many of my students left school between the 7th and 9th grades due to learning disabilities, immigration issues, poor family support and complicated environments. Their lack of background knowledge is very apparent in many subjects. Add to that the prison restrictions on device and internet use within the classroom, and the general challenges of teaching inside the wall.

Still, it is possible. I would like to share how I have taught U.S. History in a memorable and easy-to-understand way, while addressing the College and Career Readiness Standards for Adult Education (CCRSAE).

I presented the evolution of our country through a multimedia timeline. This approach allowed me to show pertinent events, people, and documents through a variety of primary and secondary sources.

I tried to incorporate the strategies for Howard Gardner's theory of multiple intelligences and Webb’s Depth of Knowledge into my activity questions and used reading, writing, math, and science texts to expand the scope of learning. I incorporated technology by including video and audio files containing music, speeches, podcasts, documentaries, and more.

I found that presenting formative and cumulative assessment activities individually and as a group allowed me to effectively evaluate the needs and progress of my students, and that I could use a variety of assessment activities such as cloze reading, matching terms, and games presented through PowerPoint, PDFs, Word documents, and websites. The hardware I used included SMART Boards, LCD projectors, laptops, and an Elmo document projector.

Many of the activities I created from scratch, but there are hundreds of shared online educational resources. When teaching outside of prison, I’ve also used smartphones and QR codes.

Following is an example of how multimedia may be incorporated into teaching the Declaration of Independence.

(6) Analyze the Declaration as a primary source
The National Archives has a trove of resources for primary sources. I use the document worksheet pictured here.

I have also presented this U.S. History lesson online through a webinar to my adult educator peers in order to stress the usefulness of multimedia, and to show how it:

• appeals to a variety of learning styles
• provides a broad support for a variety of texts
• improves the accessibility of the learning environment by extending it to otherwise inaccessible places (this is especially important with the limitations placed on a prison environment).
  

There are numerous ways to incorporate multimedia in any subject, and yes, it may take a little more work, but I can assure you that it will create an engaging and memorable lesson!