Developing Critical Numeracy Across the Curriculum

Student Reasoning about Inference

Formal statistical inference is beyond students at the middle school level but many opportunities exist for students to begin to draw conclusions based on data, statistics, graphs, and chance statements. This includes beginning inference about differences in two or more samples, about relationships between two variables in graphical form, or the asking of further questions based on observations. The most likely progression of understanding includes some of the following.

1. Beginning inference as prediction based on data (e.g., how will a child get to school tomorrow based on a class graph?)

  • Idiosyncratic reasoning: “car, because I come by car”

  • “Anything can happen” reasoning:
    “I can’t tell because I don’t know the child.”

  • Using missing categories of data:
    “By train because no one is there yet.”

  • Frequency: “Bus, most come by bus.”

  • Frequency tempered by uncertainty:
    “Maybe bus, because it is most popular.”

2. Beginning inference as hypothesising:

  • Looking at a data set and suggesting what future data collection might support

3. Beginning inference as comparing two groups:

  • Small equal-sized samples with no overlapping values

  • Small equal-sized samples with some overlapping values

  • Equal-sized samples with the same mean

  • Unusual-sized samples requiring proportional reasoning

4. Beginning inference in associations

  • “Linear” scatter graphs

  • “non-linear” graphs

  • Two-way tables

Being able to question inferences made without adequate justification by others is one of the goals of the school chance and data curriculum. By the end of middle school, students should be able to do this in straightforward contexts.