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Warm-Up

What makes a good data argument?

Take a minute to think about the following question. Share with the group or write your response in the chat.

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June

2026

Applying Claims-Evidence-Reasoning to Statistical Argumentation

ECOTS

Caitlin Ireland

Travis Weiland

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Agenda

01. Warm-Up

02. Why is data argumentation important?

03. Data Investigative Process

04. Data Argumentation Infographic

05. Argumentation Process

06. Make a Claim

07. Evidence and Reasoning

08. Communicate and Propose Action

09. Putting It All Together

10. Share

11. Reflect

12. Thank You!

Check out our website: CriticalStatisticalLiteracy.org

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This material is based upon work supported by the National Science Foundation under DRK-12 Grant #2143816 and #2517085. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the view of the National Science Foundation.

Acknowledgement

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Why is data argumentation important?

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Abelson (1995) provides more specific details for statistical arguments by providing a set of laws and criteria for well-principled arguments.

  • Magnitude
  • Articulation
  • Generality
  • Interestingness
  • Credibility

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NCTM Joint Position Statement on Data Science

Data science bridges disciplines and thus should be introduced and taught across the curriculum in K-12 schools to help develop informed users of data. Data science captures the complexity of data and data methods that have arisen with advances in technology, including breakthroughs in artificial intelligence. It is a collaborative science that uses complex data and methods to explain trends and patterns with a critical piece being its interdisciplinary nature. K-12 education plays the critical role of scaffolding students' experiences in addressing complex data sets. All subjects in school should recognize the contribution of data to their discipline and take curricular approaches that integrate data with disciplinary lessons where appropriate.

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Mathematics often focuses on Proof, which is very deductive or follow Toulmin’s Argumentation Process

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What is the Data Investigation Process?

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Lee, H., Mojica, G., Thrasher, E., & Baumgartner, P. (2022). Investigating data like a data scientist: Key practices and processes. Statistics Education Research Journal, 21(2), 3. https://doi.org/10.52041/serj.v21i2.41

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Argumentation Process

Data argumentation is part of the data investigative process, but it has not been commonly focused on in teaching. It 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

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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

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Communicate and Propose Action

It is important to communicate what you have learned from carrying out the Data Investigative 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.

Chain of Reasoning

a multi-step explanation where each step logically leads to the next, such that someone else can follow them to the same final conclusion.

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Making a Claim

02.

03.

Concise

Specific

Debatable

After exploring, visualizing, and modeling with data, the 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.

It should be 1-2 sentence at most

Your claim should not merely be a statement of fact or summary – you need to take a position based on your analysis

01.

It should narrow down to a specific point, rather than being overly broad.

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Evidence

Reasoning

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:

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.

  • descriptive statistics
  • data visualizations
  • measurement considerations
  • descriptions of sample and sampling
  • a point of comparison
  • inferential statistics.

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.

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Communicate and Propose Action

Claim

Evidence

Evidence

Evidence

Reasoning

Propose Action

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Communicate and 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.

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Putting It All Together

  1. Come up with a claim and write it on the next slide
  2. The evidence will be based on this graph
  3. Write a quick reasoning sentence using your evidence to justify the claim and write it on the “Reasoning” slide
  4. Be prepared to share with the session.

TIME: 10 minutes

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Claim

Share - Post your statistical arguments here

Some example claims from the group

TIME: 10 minutes

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Evidence

Share - Post your statistical arguments here

Use this data visualization as evidence to support your claim

What parts of the data visualization supports your claim?

TIME: 10 minutes

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Reasoning

Share - Post your statistical arguments here

Example reasoning statements from the group

TIME: 10 minutes

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Rubric for evaluating the strength of the evidence in a statistical argument

Increasing Complexity —--------------------------------------------------------------------------------------------------------------------->

Increasing Complexity

Evidence

Missing

Partial

Developing

Strong

Descriptive Statistics

No descriptive statistics are provided or the few that are provided are completely inappropriate

One or more measures of center are provided but with few or no measures of spread are provided. For example, the mean is reported with range rather than standard deviation in a symmetric distribution.

A measure of center and a measure of spread are provided but may not be the most appropriate given the situation or a conversation of shape and outliers are missing. For example, using mean and standard deviation in a heavily skewed distribution

Multiple measures of center (mean and median) and spread (min, max, quartiles, and standard deviation) are presented in conjunction with the shape of the distribution and outliers.

Data Visualizations

No Data visualizations are provided

A data visualization is provided but is missing key aspects (labels, units of measure, etc.) or is not appropriate for the type of data visualized. For example, using a histogram to display categorical data.

An appropriate data visualization is presented but it only shows part of the data and may miss key features or patterns. For example, displaying a histogram of a continuous quantitative variable but with too few bins to see underlying patterns.

One or more data visualizations are provided that show all important aspects of the data distributions being considered.

Measurement

No discussion of what measurements were taken or how they were taken is provided

The units of measure are included but with no description of the measurement process. For example, units of inches are included with descriptive statistics like mean or on axis labels in data visualization but no description of how length was measured is provided.

The units of measure are included with some description of the measurement process. For example, units of inches are included with descriptive statistics like mean and the tool used to measure such as a ruler is mentioned but not the process of using the ruler to measure length.

The units of measure and a detailed description of the measurement process is included, including:

  • Measurement tools
  • Process for measuring
  • Process for recording measures
  • Type of measurements are analyzed (categorical, quantitative)

Sample and Sampling Description

No description of the sample of data is provided

The observational units (things being measured) and sample size are provided but little information about the process of gathering the sample or who/what was included in the sample.

The observational units (things being measured), sample size and some information about the process of gathering the sample or who/what was included in the sample is provided.

A complete description of the observational units (things being measured), sample size, process of gathering the sample, and who/what was included in the sample is provided.

Comparisons

No point of comparison is provided for the descriptive statistics that are being used to support a claim. For example, a sample mean is discussed, but with no reference to an expected mean from prior research or hypothesis.

A point of comparison is provided for the descriptive statistics that are being used to directly support a claim, but it is not the same type of statistic and is not appropriate. For example, providing a mean to compare to a median.

A point of comparison is provided for the descriptive statistics that are being used to directly support a claim, but it is not appropriate or has limitations. For example, providing a mean for a related population but not one that the sample is representative of.

A point of comparison is provided for the descriptive statistics that are being used to directly support a claim that is correct and appropriate with as few limitations as possible.

Inferential Statistics

(Optional given question and grade level)

No inferential statistics are provided

Incomplete inferential statistics are provided missing key details or incorrect inferential statistics are provided. For example a confidence interval is stated but without a confidence level.

Inferential statistics are provided and statistical significance reported but without considering practical significance or effect size.

Inferential statistics are provided and practical and statistical significance reported.

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Rubric for evaluating the strength of the reasoning in a statistical argument

Increasing Strength of Reasoning Connecting Evidence and Claim —--------------------------------------------------------------------->

Increasing Complexity

Evidence

Missing Reasoning

Partial Reasoning

Strong Reasoning

Descriptive Statistics

No connections are made between the descriptive statistics and claim reported

Some but not all key descriptive statistics are explicitly connected to the claim or all key descriptive statistics are connected to the claim but with weak or fault chains of reasoning. For example, the mean and median of a distribution are reported and used to support the claim but without discussing which is a better measure of center in a heavily skewed distribution.

All key descriptive statistics are explicitly connected to the claim with strong chains of reasoning.

Data Visualizations

No connections are made between the data visualization(s) and reported claim

Data visualizations are used to justify the claim but justifications do not include all key points or not all data visualizations presented are used to justify the claim

All data visualizations are used to justify the claim using clear chains of reasoning

Measurement

No connections are made between the measurements/ process and reported claim

Measurement units are used in the explanation of how evidence supports the claim but without considering the measurement process or vice versa

Measurement units and the process of measuring are used in the explanation of how evidence supports the claim

Sample and Sampling Description

No connections are made between the sample/sampling and reported claim

The sample is used in the explanation of how the evidence supports the claim but without considering the sampling process or the claim is over generalized given the sample. For example, causal claims when the measurement process followed an observational study approach

The sample and the sampling process are used in the explanation of how evidence supports the claim and the sample matches the scope of the claim. For example, causal claims are only made if the measurement process followed experimental design

Comparisons

No connections are made between the comparison points and reported claim

A weak connection between a comparison point and the key statistic used in a claim is made but the chain of reasoning is unclear

A strong connection between a comparison point and the key statistic used in a claim is made. Explanations are provided about the possible reasons for the sample and comparison point to be significantly different or similar.

Inferential Statistics

(Optional l)

No connections are made between the inferential statistics and reported claim

A weak chain of reasoning is used to justify the claim with inferential statistics or the claim is over generalized given the inferential statistics

A strong chain of reasoning is used to justify the claim using inferential statistics that are appropriate for the given claim

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Lessons Learned

Teachers were able to use CODAP to analyze and visualize data to help find evidence for their claims.

Teachers learned how to relate conjectures and hypotheses to Claims.

They learned how to provide Reasoning for their arguments based using sentence starters.

However, teachers were not as inclined to include data argumentation in their lesson plans or classroom videos - This is why we want to support math teachers in the creation of data investigations similar to math investigations they are familiar with!

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How to use in the classroom:

  • Instead of assigning traditional problems like "Calculate the standard deviation of this dataset," frame assignments around a flawed or incomplete argument and ask students to critique it.
  • Use simulation: When students see their observed sample result sits way out in the tail of the simulated distribution, they have a visual, logical warrant to argue against the null hypothesis, completely independent of memorizing a p-value formula.
  • Use sentence starters: When students begin writing arguments, they often use unscientific or definitive language, so provide them with sentence frames that reinforce statistical standards
  • Incorporate data analysis projects: where students ask their own question, find a messy real-world dataset, choose the appropriate analytical design, and write a data-driven brief. Rather than grading solely on whether they clicked the right buttons in a software program to output a graph, allocate a significant portion of the rubric to the coherence and ethical boundaries of their final written or oral argument.

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Website

We have a website live now with all the refined resources you have helped us to develop.

www.criticalstatisticalliteracy.org

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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 about data argumentation?

What was helpful?

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THANK YOU!