Focus key competencies: Using language, symbols, and texts, participating and contributing
Learning area context: Mathematics and statistics
Contents:
In this story the teacher was keen for her year 10 students to experience a statistical inquiry that would really engage them in passionate discussions. She wanted their statistical inquiry to contribute to wider social outcomes in addition to the more immediate new mathematical knowledge being built. But achieving meaningful social outcomes through statistical inquiry can be easier said than done because there are not many rich databases easily accessible to students on topics likely to really interest and challenge them. (The New Zealand Census at Schools database is a useful resource for statistical inquiry but the teacher was looking for something different as she has used this a number of times already.)
Working in a boys’ school, this teacher was aware of her students’ strong interest in cars and driving. She had been challenged to develop a resource that would contribute to a road safety package for secondary schools being developed by the New Zealand Transport Agency and she saw the chance to develop and trial a database for this purpose. She built the database herself: it took her most of a Saturday to do this task but once made, she had a rich statistical resource for her students to use. The database has 120 sets of five variables (road conditions, speed, reaction distance, braking distance, and total stopping distance). (This database is now freely available at NZ Transport Agency: Mathematics.)
The students began the unit by choosing the combination of categorical and numerical variable that interested them, for example braking distance and road conditions. They posed an investigative question to start their investigation. For each of the continuous variables they calculated summary statistics: mean, median, and quartile values. They then created two side-by-side graphs which allowed them to compare the numerical data for the two categories (for example, wet and dry road conditions). A box and whisker plot presents a very broad picture of the data while a dot plot graph shows the underlying distribution and clustering of the specific data points. The teacher noted that students needed to see both graphs side by side or overlaid to get a feel for what each can and cannot show and how they complement each other. With guidance on what to look for in their graphs, each student then wrote a few short statements about what they could see in their data.
Since the database provided opportunities for several different investigations, the students then pooled their separate analyses to discuss the collective meaning of what they had found. The teacher guided the conversation to ensure that students backed up their conclusions with evidence, and there was explicit discussion of the difference between evidence and inference. She noted that the next step of the statistical inquiry cycle is where the potential for powerful social outcomes resides and the sense that students make of the investigation is what really matters. The students were challenged to check their findings against the overall context of safe driving:
This discussion required students to draw on their own knowledge and experiences of cars and road safety and provided the platform from which they each shaped a follow-up inquiry of their own. The teacher noted that students went in different directions at this point, with some of them shaping questions in areas she had not anticipated. Potential inquiry topics included the ways in which driving speed is controlled in different parts of the city; deeper investigations of reaction times and what influences them; and the contribution made by features of the car itself (for example, the suspension). The teacher was pleased with the deep and insightful discussions that resulted at this “next questions” stage. She felt these discussions would be more effective than “messages” about road safety in ensuring that students would make good decisions when driving themselves. The inquiry even impacted on her personally: she said she is much more careful about her own following distances now and this awareness has not abated as time has gone on!
The teacher designed this unit to meet the requirements of the level 1 NCEA standard for statistical inquiry. She felt it was important for her students to experience a carefully supported rich inquiry before they got to year 11 when assessment is more high stakes.
NZC clearly states that statistical inquiry involves “interpreting statistical information, evaluating data-based arguments, and dealing with uncertainty and variation” (p. 26). At level 5 students build their statistical literacy by evaluating “statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings”. This type of statistical inquiry and critique cannot be context free because questions of meaning and validity reside in the interplay between the context, questions, methods etc (Neill, 2012 provides a discussion of this point in the context of statistical inquiry at the primary school level). In this way, mathematics and statistics opens up opportunities to explore important issues that have the potential to impact strongly on students’ beliefs and actions, now and in the future.
In this example, year 10 students participate and contribute to an extended statistical inquiry into safe driving practices. The wider social outcomes for the unit include their future participation as responsible road-users who will actively contribute to their own and other’s safety when driving.
Students learn about specific mathematical tools and approaches used for statistical thinking. Their competencies in using language, symbols, and texts are expanded as they construct, compare, and discuss the meanings that can be drawn from, and the limitations of, different visual representations of the same data set. These are important dimensions of statistical literacy.
This unit made rich connections between student interests (especially the powerful motivation to become a driver) and research-based safety concerns about the manner in which inexperienced drivers can suddenly find themselves in unsafe situations (for example, following too closely, going too fast for the conditions). The choice of this authentic context was critical to the success of the unit as a whole.
The problem finding aspects added to the challenge in the unit. Students had to clarify their own question for investigation, and later they needed to think about how what they had found connected to road safety rules and procedures in the wider community.
In contrast to the more open problem-finding aspects, the teacher chose to explicitly lead the creation of different visual representations of the same data set. Juxtaposing these allowed her to demonstrate their different meaning-making features, which students might not have noticed without this explicit support.
Discussion starters: Meaning-making with students’ futures in mind
This teacher had a very explicit future focus in mind when she designed a mathematics unit that was also mindful of important citizenship outcomes for students (that is, being more responsible drivers). In what subject-specific ways did this teacher support students to develop meaning-making aspects of the key competency using language, symbols, and texts? Why might these specific aspects be important to her overarching focus on longer-term citizenship outcomes?
How might participating and contributing in the present be similar to, and different from, future participation and contribution as a responsible citizen? What types of learning challenges are highlighted by the differences between immediate and much longer-term goals for development of this key competency (and competencies more generally)?
How does the treatment of statistical inquiry in this unit compare and contrast with what the teacher did in the story “Investigating like a scientist?” How many rich inquiry experiences do you think it would take for students to really start developing a “feel” for statistics (that is, statistical literacy) that might stand them in good stead in their adult lives?
Neill, A. (2012) Developing statistical numeracy in primary schools. set: Research Information for Teachers, 1, 9–16.
Published on: 15 Apr 2014
