Levels 1 to 5

This set of exemplars is one of two that describe possible progressions in statistics. It shows the development in students' ability to display data. (The other set shows the development in students' understanding of probability.)

The ability to present statistical data in an appropriate form, so that others can interpret it, is fundamental to statistical investigations. The ability to read and understand data presented by others is equally important. As students progress through the data display progression, they become familiar with a wide range of data displays of increasing complexity and learn to select the appropriate format for different types of data.

Sort objects or whole-number data and group these appropriately

At this stage in the data display progression, students are able to sort objects or whole-number data into groups and talk about the results.

Present category and whole-number data appropriately

At this stage in the data display progression, students are able to group and organise category and whole-number data and present it in an appropriate format, such as a tally chart or bar graph, complying with standard conventions.

Present discrete data appropriately

At this stage in the data display progression, students are able to choose and use an appropriate format for displaying discrete data. This may include bar graphs and stem-and-leaf graphs.

Present a wide range of statistical data appropriately

At this stage in the data display progression, students are able to present statistical data in a variety of ways. They are able to present simple comparative data in back-to-back stem-and-leaf graphs.

Present comparative data in a variety of ways

At this stage in the data display progression, students are able to present comparative data in appropriate statistical displays, such as back-to-back stem-and-leaf graphs and box-and-whisker plots.

Background to the task

The task chosen as a context for this set of exemplars gives the teacher enough scope to observe the development in the students' ability to display data through levels 1 to 5.

• To help the students consider how to sort items into groups, the teacher gives them a set of pictures of objects and asks, "Which type of object do we have the most of?" This task is suitable for all students although it may be too simply worded for older or more advanced students.
• The teacher provides the students with numerical data for the time (to the nearest second) it takes each student in a class to run 100 metres. The teacher asks the students to make a display showing how fast the students in this class can run. This task is suitable for all students except those who are operating early in level 1, and may have difficulty seeing numbers as "objects" that can be grouped.
• The teacher provides the students with numerical data for the heart rate of each student in a class before and after exercise. The teacher asks the students to make a display comparing the students' heart rates before and after exercise. This task is suitable for students who are operating at levels 3 to 5.

The task

The teachers asked the students whose work is shown in these exemplars to complete one (or more) of the following three tasks, according to their level of development.

• Level 1: The teacher gave the students a set of pictures of toys and asked, "Which type of toy do we have the most of?"
• Level 2: The teachers provided the students with numerical data for the times (to the nearest second) it takes each student in a class to run 100 metres. They set the task of making a display showing how fast the students in this class can run.
• Levels 3, 4, and 5: The teachers provided the students with numerical data for the heart rates of each student in a class before and after exercise. They set the task of making a display comparing the students' heart rates before and after exercise.

Parallel tasks

The data display progression could be explored using any set of statistical data. Students will be able to relate to data better if they have some input into its collection. Sets of data such as those above would be better if generated by the class rather than provided by the teacher (for example, use the students' own times for the 100 metres).

Some other sets of data you could easily gather with your class include:

• month of birth
• eye colour
• favourites (for example, colour, flavour of ice cream, animal, or sport).

Some comparative data sets could include comparisons between older and younger classes (for example, heights, hand spans, shoe sizes, or distances in the long jump).

References

Department of Education (1985-1989). Beginning School Mathematics: Cycles 1-8. Wellington: School Publications.

Ministry of Education (1992). Beginning School Mathematics: Cycles 9-11. Wellington: Learning Media, Ministry of Education.

Ministry of Education (2001). Figure It Out, Levels 3-4. Wellington: Learning Media.

Ministry of Education (1992). Mathematics in the New Zealand Curriculum. Wellington: Learning Media.

Ministry of Education (1996). Te Whāriki: He Whāriki Mātauranga mō ngā Mokopuna o Aotearoa/Early Childhood Curriculum. Wellington: Learning Media.