This integrated statistics and quantitative reasoning (ISQR) course framework describes a course that integrates quantitative, algebraic, statistical, geometric, and data literacy concepts and strategies to empower students to live skillfully and productively in our data-driven society. Integrating these disciplines gives students a more realistic picture of how these concepts and strategies are used to approach problems. This approach pulls together all of the available tools and resources to tackle different parts of the task to reach a more comprehensive solution.
An integrated statistics and quantitative reasoning course allows for approaching problems from multiple perspectives rather than from only a mathematical or only a statistical approach.
•Authentic and relevant applications, including financial, media, health, and civic literacy should be integrated throughout the course. Examples of other potential applications:
°student-researched examples that illustrate their personal interests (e.g., sports, music, gaming)
°local community issues that can be investigated using data analysis
°historical data that can be analyzed to understand trends
Expanding previous quantitative skills to develop dexterity in comparing messy and very large and very small numbers allows for analysis of authentic situations.
Ordering small numbers (numbers less than 1) supports the interpretation of probabilities, P-values, and comparing P-values to significance levels.
Distributional thinking is an important component of statistical thinking, preparing all students for future work.
•Interpret and make decisions related to authentic and relevant uses of quantities, including very large and very small quantities. For example:
°incidence of medication side effects
°student/local/state/federal budgets
°interest rates related to investments, loans, and credit cards, including compound interest
°environment, land management, and agriculture
°weighted averages, indices, coding, and ranking and voting methods
°growth and decline represented as fractions rather than percentages
other applications related to media, financial, health, and social literacy from the perspective of analyzing, communicating, understanding, and revealing inaccuracies/deceptions
•Summarize large numerical data sets to learn about a population or the behavior of a random variable. For example:
°polls and surveys
°social media use
°distribution of food and technology deserts
°access to clean water
An integrated approach has the potential to better develop the ability to analyze and detect inaccuracies in media infographics, which often include both numerical and statistical information. It also develops the ability to present both numerical and statistical information to others (e.g., peers, employers) in a variety of forms.
•Examples from simple to complex multiple variables that address:
°media, financial, health, civic, and social literacy
°comparing groups to identify systemic inequalities
°student-researched examples that illustrate their personal interests (e.g., sports, music, gaming)
°analyzing graphs
The treatment of deterministic relationships modeled by functions supports the conceptual development of statistical relationships that take variability into account and leads to deeper understanding of functional relationships.
•Simpson’s Paradox and other examples illustrating the importance of multivariable thinking can be drawn from the following areas:
°media, financial, health, civic, and social literacy
°racial and gender disparities in health care
°student-researched examples that illustrate their personal interests (e.g., sports, music, gaming)
An integrated course provides exposure to both mathematical modeling and statistical modeling, rather than to just one of these approaches. Mathematical modeling involves using algebraic functions and graphical techniques to describe authentic situations.
Many of the financial applications in quantitative reasoning are not seen in a typical high school statistics course. Mathematical modeling extends into advanced algebra/precalculus models, keeping the bridge open back to STEM.
Statistical modeling extends mathematical models by allowing for and describing chance variation, and by accessing the accuracy of predictions—both of which are often missing in quantitative reasoning courses.
•Model applications such as population growth/decline, business production/income/profit, credit card debt, installment savings, amortization schedules, and mortgages.
•Model disease spread, scheduling, and routing situations.
•Apply geometric concepts to model situations and solve problems such as those arising in art, architecture, and other fields.
•Use data to model applications such as student debt, social media use, and access
to technology.
An integrated course allows for deeper understanding of proportional reasoning through expanded consideration of conditional probabilities. While the typical quantitative reasoning course often includes interpretation of conditional probabilities, understanding of conditional probabilities would be deepened by connecting conditional probability to the assessment of error probabilities when drawing data-based conclusions.
The integration of quantitative reasoning probability topics and the probability topics usually included in a statistics course allows for a better understanding of different approaches to probability (classical probability [equally likely outcomes] versus relative frequency approach to probability).
•Assess potential for error when drawing conclusions from data.
•Analyze the likelihood of false positive and false negative test results, and the consequences of making decisions based on such results.
•Compare relative risk and absolute risk.
•Analyze demographic disparities in areas such as health care and access to advanced courses.
Quantitative reasoning courses typically only have a surface treatment of data collection and would benefit from the treatment that is typical in statistics and data science.
•Exploring ethical and privacy issues related to:
°data collection, including privacy and informed consent, such as data collected by Facebook and in the Tuskegee experiments
°students’ own data on their health, financial, and personal identification information
An integrated course supports development of both statistical and mathematical thinking. Rather than a focus on decontextualized skills practice, the focus is on practical applications of these types of thinking to draw conclusions and make decisions.
•Analyze data and numerical summaries from examples that address:
°media, financial, health, civic, and social literacy
°environment, land management, and agriculture
°student-researched examples that illustrate their personal interests (e.g., sports, music, gaming)
Quantitative reasoning looks at drawing conclusions from data, and statistics takes this a step further by also assessing risks associated with using sample data to draw conclusions. That is, statistics considers sampling variability in a more explicit way.
Statistical significance and the difference between statistical significance and practical significance are important concepts for civic and media literacy that are not typically addressed in a quantitative reasoning course. An integrated course provides exposure to these concepts.
•Analyze and provide feedback on numerical/quantitative and statistical arguments made:
°in the media
°in workplace examples
°by classroom peers in projects and presentations
(*Taken from the ISQR framework developed by the Dana Center)
School Country
United States
School state
Arizona
School city
Phoenix
High school
Alhambra High School
Betty Fairfax
Bioscience High School
Bostrom Alternatve Ctr Ed/Bace
Camelback
Carl Hayden High School
Central
Cesar Chavez
Desiderata
Franklin Police & Fire High School
Linda Abril
Maryvale
Metro Tech
North
PXU City
Phoenix Coding Academy
The Academies at South Mountain
Trevor G Browne High School
Wilson College Prep