Explanation of Educational Statistics

Educational statistics is the practice of teaching and learning of statistics, along with the associated scholarly research.

Statistics is both a formal science and a practical theory of scientific inquiry, and both aspects are considered in statistics education. Education in statistics has similar concerns as does education in other mathematical sciences, like logic, mathematics, and computer science. At the same time, statistics is concerned with evidence-based reasoning, particularly with the analysis of data.

Therefore, education in statistics has strong similarities to education in empirical disciplines like psychology and chemistry, in which education is closely tied to “hands-on” experimentation.

Note: Statisticians and Mathematicians often work in a department of mathematical sciences. Statistics courses have sometimes been taught by non-statisticians, against the recommendations of professional organizations.

Cognitive Goals

In the 2008 joint conference of the International Commission on Mathematical Instruction, editors Carmen Batanero, Gail Burrill, and Chris Reading noted worldwide trends in curricula reflecting data-oriented goals. Educators seek to have students:

  • Design investigations
  • Formulate research questions
  • Collect data using observations, surveys, and experiments
  • Describe and compare data sets
  • Propose and justify conclusions and predictions based on data

Key Definitions

There is a focus on three distinct outcomes:

  1. Educational Statistical Literacy: Being able to read and use basic statistical language and graphical representations to understand statistical information in the media.
  2. Educational Statistical Reasoning: Being able to reason about and connect different statistical concepts (e.g., how outliers affect the mean).
  3. Educational Statistical Thinking: The type of thinking used by statisticians involving the nature/quality of data, choosing appropriate models, and interpreting results in context.

Non-Cognitive Goals

Non-cognitive outcomes include affective constructs such as attitudes, beliefs, emotions, dispositions, and motivation.

Beliefs vs. Attitudes

  • Beliefs: Individually held ideas about statistics and oneself as a learner. They provide the context for a student’s approach to the classroom.
  • Attitudes: Relatively stable and intense feelings that develop over time through experience.

Many students enter a statistics course with apprehension. Therefore, it is important for instructors to use assessment instruments to diagnose student beliefs early.

Dispositions

Disposition refers to how students question data and approach problems. Within the Wild and Pfannkuch’ framework, it contains:

  • Curiosity and Awareness: Generating questions and ideas to explore data.
  • Engagement: Being observant in areas of interest.
  • Imagination: Viewing problems from different perspectives.
  • Scepticism: Evaluating the appropriateness of study designs and analysis.
  • Being Logical: Detecting when one idea follows from another.
  • Seeking Deeper Meaning: Not taking everything at face value.

Importance of Educational Statistics

  1. A Tool for Modern Development: It is not merely a device for collecting data but a means of developing sound techniques for representation and analysis. As Robert W. Burgess stated: “The fundamental gospel of statistics is to put back the domain of ignorance… principles are formulated on the basis of analyzed quantitative facts.”
  2. Definite Conclusions: Statistics turns contentions into figures. For example, saying “Italy is richer than India” is vague, but saying “The per capita income of Italy is 20 times greater than India” provides a definite, convincing conclusion.
  3. Simplification: Complex data involving millions of people is simplified through techniques like tabulation, diagrams, averages, and percentages.

Data Example (R Code)

To demonstrate the “hands-on” nature of educational statistics, here is a simple visualization of sample test scores:

# Sample data for student scores
scores <- c(85, 90, 78, 92, 88, 76, 95, 89, 84, 91)

# Create a histogram
hist(scores, 
     col = "skyblue", 
     main = "Distribution of Student Scores", 
     xlab = "Test Scores")

```

How to use this:

  1. Open RStudio.
  2. Click File -> New File -> R Markdown…
  3. Delete all the default text in the new file.
  4. Paste the code above.
  5. Click the Knit button (the ball of yarn icon) to generate your HTML.
  6. Once the HTML is generated, you can click Publish to upload it to the web.

Note: If you still get the error from your previous message, make sure to run install.packages("rsconnect") in your console first.