Writing the World through Statistical Investigations: One Variable at a Time!

2025 NCCTM

Caitlin Ireland and Travis Weiland

Agenda

01

02

03

04

05

Why Statistics and Data Science are Important?

Data Investigation Process

Standards and Data Investigation Flow

Connecting Standards to Investigation Questions

Example Statistical Investigation Brief

2

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

Why are Statistics and Data Science Important?

4

Statistics & Data Reasoning

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.

Source: https://www.nctm.org/Standards-and-Positions/Position-Statements/Data-Science/

Data science is an investigative process.

Data science understandings and experiences are for everyone.

Data science educators must develop and practice ethical uses of data.

Declarations

1

2

3

Data science is contextual and interdisciplinary.

4

Source: https://www.nctm.org/Standards-and-Positions/Position-Statements/Data-Science/

NCTM Position

Teaching Data Science in High School: Enhancing Opportunities and Success

Ensuring that all students have the mathematical experiences necessary to increase their opportunities for personal and professional success is essential. Data science is a rigorous, engaging, and practical field of study and can be a significant part of a high school student’s mathematical experience. Knowledge of data science is important, and a data science course should be accepted as a high school mathematics course that can be used for credit towards graduation, provided the course includes or builds on previous, substantive student work with essential concepts, knowledge, skills, and habits of mind in mathematics and statistics, as described in Catalyzing Change (NCTM, 2018).

Source: https://www.nctm.org/Standards-and-Positions/Position-Statements/Teaching-Data-Science-in-High-School_-Enhancing-Opportunities-and-Success/#:~:text=NCTM%20Position,high%20school%20student's%20mathematical%20experience.

1)

2)

3)

Declarations

All students should have the opportunity to take four years of high school mathematics, and data science content should be available to all students in order to complete their high school mathematics graduation requirement.

​

A high school data science course merits mathematics credit if it includes substantive student work with essential concepts, including those from Functions, Quantitative Literacy, Visualizing and Summarizing Data, Statistical Inference, and Probability (NCTM, 2018).

​

A high school data science course merits mathematics credit if it includes substantive student work with skills students develop from their understanding of the essential concepts.

​

Source: https://www.nctm.org/Standards-and-Positions/Position-Statements/Teaching-Data-Science-in-High-School_-Enhancing-Opportunities-and-Success/#:~:text=NCTM%20Position,high%20school%20student's%20mathematical%20experience.

4)

5)

6)

Declarations

A high school data science course merits mathematics credit if it includes substantive student work with habits of mind in mathematics and statistics.

​

Students should have access to mathematical action technology within and out of school to support their mathematical and statistical work in any high school mathematics course they choose to take.

​

A high school data science course involves significant content knowledge and skills. A data science course is a valuable resource for students in learning how to appreciate and understand the world around them.

​

Source: https://www.nctm.org/Standards-and-Positions/Position-Statements/Teaching-Data-Science-in-High-School_-Enhancing-Opportunities-and-Success/#:~:text=NCTM%20Position,high%20school%20student's%20mathematical%20experience.

Step 1

Describe how the team will mitigate this challenge. Use specific and actionable steps.

​

Step 3

Describe how the team will mitigate this challenge. Use specific and actionable steps.

​

​

Step 2

Describe how the team will mitigate this challenge. Use specific and actionable steps.

​

​

Describe a challenge that might come up during the project.

​

How we’ll address or avoid this challenge

Skills

Step 1

Describe how the team will mitigate this challenge. Use specific and actionable steps.

​

Step 3

Describe how the team will mitigate this challenge. Use specific and actionable steps.

​

​

Step 2

Describe how the team will mitigate this challenge. Use specific and actionable steps.

​

​

Describe a challenge that might come up during the project.

​

How we’ll address or avoid this challenge

Habits of Mind

Data Science 4 Everyone

Source: https://www.datascience4everyone.org/

Status of Data Science in K-12

Source: https://www.datascience4everyone.org/

Status of Data Science in K-12

Source: https://www.datascience4everyone.org/_files/ugd/0a9d2b_f183f7139980484a9816319a99393bc9.pdf

Data Science Learning Progressions

This work is in a draft stage but should be done this coming year.

​

It is meant to be cross disciplinary

​

We are doing things in this framework already

Source: https://docs.google.com/spreadsheets/d/1ONsOA4reprZf9imfXD76uTKAbx-iuSfV3-3lrZXdPek/edit?gid=0#gid=0

Guidance Documents

• Data Sciences Learning Progressions
• Guidelines for Assessment and Instruction in Statistics Education
• Statistical Education of Teachers
• Dana Center Launch Years Initiative Course Frameworks
• International Data Science in Schools Project Curriculum Frameworks

Data Education

Data Education

NC Math Standards Revisions

In March 2024, the Office of Teaching and Learning announced the kickoff of the review phase for the K-12 Mathematics Standards. This process is guided by State Board policy as outlined in the Internal Standards Manual. The review phase involved research, data collection, and analysis. During the summer and fall of 2024, the K-12 Math team prepared and distributed various surveys, conducted focus groups and interviews, gathered research from other states, as well as national and international standards, and reviewed current legislation and policies.

NC Math Standards Revisions

The K-12 Math team is excited to announce that during the meeting, the Board voted to begin the revision process for the NC K-12 Math Standards. One of the first steps is establishing a Standards Writing Team (SWT), tasked with revising the current K-12 Math standards based on research and recommendations from the Data Review Committee (DRC), which were compiled from feedback collected during the review phase.

The first step is establishing the Standards Writing Team (SWT). Working in grade-level/content area groups, the SWT considers possible revisions to K-12 Math when and where applicable. This may involve slight modifications, major modifications, deletions, additions, or no changes to current standards.

Data Investigation Process

Confidential

21

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

Frame the Problem

Data Investigative Process

​

We are not leaving the argumentation process we are just shifting to focus predominantly on the investigative process.

In particular, by focusing on what we have spent a lot of time on in the past which is considering the data we have, exploring and visualizing it in CODAP, and modeling it to create evidence for our argument and to develop claims

Methods

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.

Walkthrough of an Investigation

Confidential

28

Frame the Problem: What question will we answer?

​

How well can a person’s age be predicted based on their total annual income for people who lived in the U.S. in 2020?

Turn-and-Talk: What standards in your course could be tied to this question?

29

Tour of CODAP

​

Access the CODAP workspace here.

​

http://bit.ly/4p55sRd

Confidential

30

Frame the Problem: What question will we answer?

​

How well can a person’s age be predicted based on their total annual income for people who lived in the U.S. in 2020?

Consider and Gather Data: What variables will we use?

• What types of quantitative data do we have?
• What are the possible outcomes for the quantitative data? Can you talk about the range of the data?
• Is this a sample or a population?
• What attributes in the dataset are quantitative?
• How were the quantitative attributes measured? What are the units of measurement?
• What variables would it make sense to look at relationships between?

​

Access the CODAP workspace here.

31

Two Quantitative Variables:

​

Ties to Math 1, Math 4, and AP Stats standards

• NC.M1.S-ID.1 Use technology to represent data with plots on the real number line (histograms, and box plots).
• NC.M1.S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Interpret differences in shape, center, and spread in the context of the data sets.
• NC.M1.S-ID.3 Examine the effects of extreme data points (outliers) on shape, center, and/or spread.
• NC.M1.S-ID.6a Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a least squares regression line to linear data using technology.
• NC.M1.S-ID.6b Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. b. Assess the fit of a linear function by analyzing residuals.
• NC.M1.S-ID.7 Interpret in context the rate of change and the intercept of a linear model. Use the linear model to interpolate and extrapolate predicted values. Assess the validity of a predicted value.
• NC.M1.S-ID.8 Analyze patterns and describe relationships between two variables in context. Using technology, determine the correlation coefficient of bivariate data and interpret it as a measure of the strength and direction of a linear relationship. Use a scatter plot, correlation coefficient, and a residual plot to determine the appropriateness of using a linear function to model a relationship between two variables.

32

Process the Data - Data Moves to consider:

• Filtering: involves examining a specific subset of the data you collected
• Grouping: entails classifying data into distinct groups, varying from a minimum of two to several groups, based on the question guiding your investigation
• Joining: involves incorporating additional data into your dataset. This process can be straightforward, such as integrating more data that closely resembles your existing dataset
• Summarizing: help make sense of lots of data by simplifying it. These summaries can be means, interquartile ranges, or other measures that represent the data.
• Calculating: the information needs to be transformed somehow and placed in a new column that you can use to do what you want. This often means that you will need a formula to compute the contents of that new column.
• Recoding: a categorical attribute may contain numerous categories that need to be consolidated

33

Process the Data - Data Moves to consider:

• Filtering
• Grouping
• Joining
• Summarizing
• Calculating
• Recoding

​

​

Turn-and-Talk: What needs to happen to the data in order for us to use it to answer our question?

34

What needs to happen to the data in order for us to use it to answer our question?

​

• One data move we need to carry out is to filter out the individuals that have the value 9999999 for their income.
• We can filter out these individuals because if we look in the metadata file that comes with this dataset we can see that that value is not an income, but it is used to signify missing data, which we do not want to include in our statistics.
• This could be done by hiding selected cases using a graph. This allows us to remove outliers to see the spread of the rest of the distribution better.

​

Other options:

• We might also want to filter out people on the younger end of the age range as they are not old enough to work legally in the workforce.
• Another filtering or grouping data move that could be used is to create quartiles or quintiles for the income data which is typically heavily skewed right and then look for relationships within quartiles or quintiles instead of overall.

35

Explore and Visualize the Univariate Data

• Find descriptive statistics for both variables
• Visualize the data for both variables

36

Explore and Visualize the Bivariate Data

• Now that you have examined some variables and decided which ones to use to answer your question, consider:
• Which variable should be independent?
• Which one should be dependent?
• What would you predict about the relationship?

37

Consider Models

• What ways do you know of that would model the relationship between two quantitative variables?
• What are important indicators of a good model?
• Can you model this in CODAP?

​

38

39

40

41

42

43

44

Communicate and Propose Action

• Can you interpret the results?
• What do they mean to someone who may not understand statistics?
• What actions can you propose based on your results?

45

Useful sentence starters for interpretation

• Correlation coefficient: Since the correlation coefficient is [fill in r], there is a strong/weak, negative/positive, linear/nonlinear relationship between [variable 1] and [variable 2].
• Coefficient of determination: [fill in r² as a percent] of the variation in [dependent variable] is explained by [independent variable].
• Slope: For every one [independent variable unit] increase in [independent variable], [dependent variable] is expected to increase/decrease by [fill in slope value] [dependent variable unit].
• Intercept: If the [independent variable] is 0 [independent variable unit], the expected [dependent variable] is [fill in intercept value] [dependent variable unit]. This does/does not make sense in our context, because [fill in explanation].
• Residuals: Since the residual plot is/is not random or scattered, and does/does not show some pattern, the model is/is not a good fit for this data.

46

NC Standards Flowchart & Making Connections between Standards and Questions

Confidential

47

Putting the Pieces Together

To help guide your process of constructing an investigation for your students consider our flowchart with linked investigation briefs.

Let’s take some time to explore this resource linked here.

You may also want to consider how the standards questions and type of data connect

Here is another tool to help

Explore & Visualize Data

Explore & Visualize Data

Consider Models

Consider Models

Links to Investigation Briefs

• One quantitative variable
• One categorical variable
• One quantitative grouped by one categorical variable
• Two quantitative variables
• Two categorical variables

53

Reflection

​

​

How would you use this in the classroom?

How would you adapt this activity to better suit the needs of your students?

54

Thank you!

Contact our team

csmit499@charlotte.edu

55