Supporting Teachers in Reading and Writing the World with Data
Travis Weiland, Caitlin Ireland, Constant Segbefia
Goals and Conjectures
Project Goal: Investigating how to support secondary mathematics teachers in developing their own statistical literacy through data investigations of sociopolitical issues and translating that literacy into classroom practice
Research Conjecture 1: To develop a critical statistical literacy, people need to be situated in authentic praxis of multiple communities of practice (i.e., mathematics education, statistics education, statistics, & critical pedagogy) investigating meaningful issues to their communities.
Research Conjecture 2: If explicitly supported for an extended period of time, teachers can translate learning from a professional learning community (PLC) situated at the intersection of multiple communities of practice (CoP) to their classroom practice.
Research Questions
Critical Statistical Literacy
Change Theory
Change Theory
Change Theory
Designed Generative Themes
Issues in Data Investigations
Central Ideas
Culture & Norms
Culture/Norms
Agency | Belonging | Competence |
Openness – willingness to ask questions and understand without judgement. | Providing a Safe Space: Respect, listen, do unto others as you would have them do unto you. | When someone asks you to clarify – take it with good intentions. Don’t gloss over it. |
Willingness to Learn – participation. Step up and step back – consider airtime. | You and everyone belong. Confidence that we will support each other. | Recognize the distributed expertise |
Be willing to share your resources! | Clarify when needed: Uncover intentionality behind statements. Recognize differences of experiences. | Acknowledge by listening and ASK THE QUESTION. |
Feeling comfortable seeking alternative channels to voice thoughts/opinions (e.g., through facilitators) | Know when to pause and come back – table it and come back to it later | Give and receive constructive feedback – assume positive intent. |
Pedagogy
Goal is move toward critical pedagogy
Rubel’s (2017) work describe equity-driven mathematics instruction as including:
Berry et al. (2020) describe a developmental trajectory
Authentic Practice: Data Investigation Process
Critical Statistical
Literacy
Technology Tools
CODAP
Design Principles/Embodiments
Intervention Overview:
Professional Learning Community
Participants
Overview
Year 1
Summer 1 PLC (2023)
School Year 1 PLC (2023-2024)
Year 2
Summer 2 PLC (2024)
School Year 2 PLC (2024-2025)
Year 3
Summer 3 PLC (2025)
School Year 3 PLC (2025-2026)
Year 4
Summer 4 PLC (2026)
School Year 4 PLC (2026-2027)
Reading Data Visualization Activity
What do you notice?
What do you wonder?
Going Beyond Notice and Wonder
There are different ways you can read a data visualization
Reading
the Data
Reading the Data
Reading Between
the Data
Reading Between the Data
Reading Beyond
the Data
Reading Beyond the Data
Reading Behind
the Data
Reading Behind the Data
Reading Behind the Data
Reflection
Turn and talk with a neighbor
How can we do this for our classes?
Step 1: Consider your Learning Objective
Step 2: Select a Data Visualization
Levels of Relevance
Global
National
Regional
State
City
Neighborhood
Home
Where to Find Data Visualizations
Step 3: Select the data visualization practices you want to focus on.
Step 4: Choose purposeful questions to guide the reading data visualization discussion.
Step 4: Choose purposeful questions to guide the reading data visualization discussion.
Step 5: Choose how you will teach the data visualization activity
Slow Reveal Graph
https://www.roymorgan.com/findings/wealth-inequality-in-australia-is-getting-worse
Reflection
Turn and talk with a neighbor
Morning Tea
10:30 - 11:00
Data Visualization as a Launch into Data Investigations
Data Investigation Process Activity
https://www.abc.net.au/news/2022-06-27/wgea-report/101186358?utm_source=abc_news_web&utm_medium=content_shared&utm_campaign=abc_news_web&utm_content=link
Authentic Practice: Data Investigation Process
Argumentation Process
Data argumentation is part of the data investigative process, but is a part of the process that has not been commonly focused on in teaching and is the part of the process that other people generally interact with and learn from making it especially important.
To highlight the argumentation process we have chosen to depict it as an embedded process that merits individual attention.
Argumentation
Process
Argumentation Process
The argumentation process is a part of the entire investigative process.
However there are two components of the data investigation process where the argumentation process is particularly important and often under emphasized in teaching. Those are during framing the problem and communicate and proposed action.
Frame the Problem
Data investigations are driven by the desire to explore an issue/problem. Therefore a first step is often to try and frame the problem you want to investigate. This starts informally as just trying to put into words an issue you have noticed.
Conjecture Examples
It appears that when students use flashcards for vocabulary, their test scores tend to be higher.
My observation suggests that students who actively participate in school clubs are less likely to experience academic stress.
Based on the patterns I've seen in our class, I'd conjecture that the average time spent on homework per night is around 1.5 to 2 hours for most students freshman year and increases each year and as classes get more difficult.
It seems plausible that if we start school later in the morning, then students would be happier and better able to pay attention.
I'm inclined to believe that students who teach a concept to someone else retain that information better themselves.
Frame the Problem
Example: Putting it all together
Conjecture
Research Question
Investigative Question
Hypothesis
It seems plausible that if we start school later in the morning, then students would be happier and better able to pay attention.
I hypothesize that mean self-reported attentiveness and mood of high school students will increase significantly from a normal start time to starting school one hour later.
How would student mood and attentiveness change if school started later?
How does mean self-reported attentiveness and mood of high school students change from a normal start time to starting school one hour later?
Problem/Issue: Many high school students struggle with sleep deprivation, which is believed to negatively impact their attentiveness and mood during early morning classes. However, the direct impact of later school start times on these specific student outcomes in a high school setting has not been sufficiently quantified to inform policy decisions.
Frame the Problem
An opinion or conviction formed on the basis of anecdotes, guesswork, or intuition
Conjecture
A problem or issue relevant to you to investigate
Problem/Issue
A question focused on a problem/issue that is framed for open-ended inquiry that guides a research study
Research Question
A possible explanation or educated guess about a phenomenon that can be tested through investigation
Hypothesis
A specific and answerable question that serves to guide a well-bounded data investigation that can be conducted with available resources in a finite period of time
Investigative Question
Consider/Collect & Process Data
Consider Data
Reflect Back
Research Question
Conjecture
On Your Own
On Your Own
A research question is focused on a problem/issue that is framed for open-ended inquiry that guides a research study. In other words, it's a question that the research aims to answer, providing the starting point and guiding the entire research process. This is generally a large and broad question that would require multiple analyzes to begin to answer. It serves as a starting point to then refine to specific investigative questions
A conjecture is an opinion or conviction formed on the basis of anecdotes, guesswork, or intuition. In other words it is a speculation, or an educated guess that is believed to be true based on lived experience, but lacks formal proof or substantial evidence. Creating conjectures helps to write out what you think you will find based on your own lived experiences.
Write a conjecture(s) you have related to the problem/issue you identified?
Write a research question you have related to the problem/issue you identified?
Idea comparison
Framing the Problem-OYO
Example
We are going to go through a lesson I have created a detailed plan for that you can find here.
Consider and Collect Data
Get Data for Your Country
Getting Started in CODAP
Selecting Data
With this plugins you can choose what locations you want to draw samples from in terms of location (i.e. States in the U.S.) and time point (i.e. year) as well as the attributes to include, and the size of the sample
Selecting Attributes
There are many attributes to choose from nested in 6 main groups including:
You can view the attributes in each group by clicking on the down arrow next to each group
Selecting Attributes
I will walk through how to select attributes selecting a small subset but feel free to add in any you like.
If it is easier for some I also created a workspace with all the attributes selected already that we can use together if you want to work with the same dataset.
Meta-Data
Structure of Data
Visualize
Consider, Explore, and Visualize
Let’s take a look at the data. The questions below will help focus your attention to important aspects of the data to consider for your investigation.
What do we do about this?
Consider Metadata
Filter
Filter
Filter
Tools to Help Guide the Process
Worksheet for Consider, Process, Explore, Visualize and Model Data
Data Investigation Briefs
Data Moves
We have developed resources and tools to support teachers in learning about data investigations and the argumentation process as well as to help them do it with their students. We designed many of these tools to be used with teacher or student audiences.
Writing an Investigative Question
Research questions are a great starting point but they are often larger than we can easily answer in a short period of time and would require multiple analyses to answer. To help break the work up we are next going to narrow down to an investigative question.
An investigative question is specific and answerable and serves to guide a well-bounded data investigation that can be conducted with available resources in class today and tomorrow.
Criterion for Investigative Questions
Writing Questions
In your group, use what you learned from considering the census data to now write a good investigative question
Framing the Problem-OYO
Share
Now that you have questions, the best way to see if they make sense is to have someone else review them and provide constructive feedback.
Pair up with someone and review their investigative question.
Does it match the criterion?
Provide constructive feedback.
Reflect and Refine
Now go back to your own question and review the feedback.
Do you have any question on the feedback to ask?
Refine your Question based on the feedback.
MINS
15
Hypotheses
A hypothesis is a possible explanation or educated guess about a phenomenon that can be tested through investigation. In other words it is your prediction about what might happen, based on your understanding.
Key characteristics of hypotheses
Tentative: It's a proposed explanation that hasn't been proven yet.
Testable: It can be put to the test through experiments, observations, or other research methods.
Specific: It clearly states what the researcher expects to find or observe. This should include some detail on the measures that will be used and statistics that will be relied on in the analysis.
Based on existing knowledge: It should be informed by previous research and observations, not just a random guess.
Addresses a research question: It provides a clear answer or prediction to the question being investigated.
Create Your Own
Now go back and write a hypothesis for your investigative question.
MINS
10
Framing the Problem-OYO
Visualize Data
Explore Data
In a Group
In a Group
A picture says a thousand words. Start with a picture of your data. Play around with different types of data visualizations and see what new aspects of the data you are able to observe. Consider processing the data in different ways in conjunction with visualizing it. Try overlaying different types of visuals. Consider what visualizations of the data create the best evidence for your question.
Exploring the data can take many forms. In general it is important to collect summary statistics for the variables you are considering for your investigative question. This may also involving going back and forth between exploring the dating and processing the data in conjunction with visualizing the data.
FInd the descriptive statistics relative to the variables you are investigating and the question you have posed
Play with different visualizations of the variables you are exploring for your investigative question
Idea comparison
Visualize
Visualize
Visualize
Visualize
Descriptive Statistics
Model
Models
Share for Feedback
Share your model with one other group
Does the model fit the question?
Does the model fit the data?
Does the model help explain the data?
MINS
5
Models and Hypotheses
How does your model compare to your hypothesis?
If your model confirms your hypothesis look over it again and consider if there may be other models that might also be appropriate and perhap beter
If your model refutes your hypothesis consider why and what that means in the context.
Communicate and Propose Action
After carrying out a data investigation it is important to communicate what you have learned from this process and relate it back to your original framing of the problem you are investigating. Some call this a data story as data does not speak for itself; people create stories with data. Others refer to this as a principled argument.
We choose to focus on principled arguments as the “principled” part of that name implies an argument that follows certain agreed upon norms or chains of reasoning.
A chain of reasoning is a multi-step explanation where each step logically leads to the next, such that someone else can follow them to the same final conclusion.
Lunch
12:30 - 1:15
Making a Claim
After exploring, visualizing, and modeling with data, our next step is often to make a claim(s) related to the investigative question you have been investigating. A claim should be a concise and specific statement that is debatable and can be supported with data.
Concise: It should be 1-2 sentence at most
Specific: It should narrow down to a specific point, rather than being overly broad.
Debatable: Your claim should not merely be a statement of fact or summary – you need to take a position based on your analysis
Evidence
Claims cannot stand on their own in a principled argument, they must come with evidence and reasoning. In statistics there are many types of evidence to provide including:
To help make sense of how to use evidence we have created a rubric in this document
Reasoning
You cannot simply provide evidence though. To create an argument you must also provide reasons for why that evidence justifies the claim that you have made. The reasoning is like the glue that holds it all together. In the end you combine claims and evidence through a chain a reasoning such that someone else can follow your think to come to the same conclusions you have.
We have also created a rubric for considering the reasoning in an argument in this document.
Communicate and Propose Action
Claim
Evidence
Evidence
Evidence
Reasoning
Propose Action
Connecting the Pieces
Let’s start with some initial argument development to try identify and connect the basic pieces of the argument. For evidence in your final argument you will want to provide select data visualizations and statistics but for now you can just take notes as to what those things will be and focus on connecting the piece of evidence to the claim with reasoning.
This document may serve as a helpful reference for this activity.
This organizer can also help you arrange your argument.
Connecting the Pieces
Share
Now that you have a rough outline of a chain of reasoning the best way to see if it make sense is to have someone else review it and provide constructive feedback.
You all have access to each others documents.
Pair up with another group and review their argument organizer
Does it match the criterion?
Provide constructive feedback.
Reflect and Refine
Now go back to your own argument organizer and review the feedback.
Do you have any question on the feedback to ask?
Refine your argument based on the feedback.
MINS
15
Elements of a Principled Argument
Propose Action
Generally an argument does not end with merely supporting a claim it usually goes into what we often call the “So What.” So what do we do know based on what we have learned? How does this help us make decisions? What actions are recommended based on these results? This is different for every question and issue and will draw upon your know of the issue you are investigating not just the results of your investigation.
Argument Presentation
Now that you have learned about the various components of the Data Investigation Process and Data Argumentation, let’s spend time creating your own data argument. You will present your arguments to the workshop. Find these in our shared folder.
Present
Now we will share our arguments with the community.
Feedback with Rubrics
Reflection
How has this helped you be critical of data arguments?
Has this changed or shaped your perception of using data argumentation in the classroom?
What do you find beneficial?
Website
We have a website live now with all the refined resources you have helped us to develop.
Questions?
Caitlin Ireland: csmit499@charlotte.edu
Travis Weiland: tweilan1@charlotte.edu
How might you use this in your class?
How does this framing make you think differently?
What was helpful?