In this unit students will identify how to plan and carry out a statistical investigation about a topic of interest.
It is vital, when planning statistical investigations, that students understand the importance of the way in which they collect, record and present their information (data). Inconsistencies in the carrying out any of these steps can lead to altered findings, and therefore an invalid investigation. Students will first look at choosing a topic to investigate, making sure that the topic lends itself to being investigated statistically. They will then look at a variety of ways of collecting their data and choose the best way to record it. Once they have collected and recorded their data they will investigate the best way to present their findings, taking into consideration the needs of their intended audience. To evaluate the investigations there can be a combination of methods used, depending on the students, the topics and the intended audience. It could be useful for the students to send their completed investigations and findings to interested parties for more realistic feedback.
Investigative questions
At Level 3, students should generate broad ideas to investigate, before refining their ideas into an investigative question that can be answered with data. The teacher supports the development of students' investigative questions through questioning, modelling, and checking appropriateness of variables. Investigative summary, simple comparison and time series questions are posed, where the entire data set can be collected or provided. The variables are categorical or whole numbers.
An important distinction to make is that of the difference between investigative questions, meaning the questions we ask of the data, and data collection or survey questions, meaning the questions we ask to get the data. The data collected through survey of data collection questions allows us to to answer the investigative question. For example, if our investigative question was “What ice cream flavours do the students in our class like?” a corresponding survey question might be “What is your favourite ice cream flavour?” As with the investigative question, survey question development is done by the students with teacher support to improve them so that suitable survey questions are developed.
Analysis questions
Analysis questions are questions we ask of displays of data as we start to describe it. The teacher will often model this through asking students about what they see in their displays. A series of analysis questions can be developed in conjunction with the students. Analysis questions include questions about the features of the display. Questions such as: what is the most common? the least common? how many of a certain category? what is the highest value (for numerical data)? lowest value (for numerical data)? are analysis questions.
Dot plots
Dot plots are used to display the distribution of a numerical variable in which each dot represents a value of the variable. If a value occurs more than once, the dots are placed one above the other so that the height of the column of dots represents the frequency for that value. Sometimes the dot plot is drawn using crosses instead of dots. Dot plots can also be used for categorical data.
Bar graphs
In a bar graph equal-width rectangles (bars) represent each category or value for the variable. The height of these bars tells how many of that object there are. The bars can be vertical, as shown in the example, or horizontal.
The example above shows the types of shoes worn in the class on a particular day. There are three types of shoes: jandals, sneakers, and boots. The height of the corresponding bars shows that there are six lots of jandals, 15 lots of sneakers and three lots of boots. It should be noted that the numbers label the points on the vertical axis, not the spaces between them. Notice too, in a convention used for discrete data (category and whole number data), there are gaps between the bars.
Strip graphs
A strip graph represents frequencies as a proportion of a rectangular strip. For example, the strip graph below shows that the students saw five light blue cars, seven yellow cars, 11 maroon cars and two grey ones. The strip graph can be readily developed from a bar graph. Instead of arranging the bars beside one another join them end to end. (Alternatively, you can easily get a bar graph from a strip graph by reversing the process.)
Tally charts
A tally chart provides a quick method of recording data as events happen. If the students are counting different coloured cars as they pass the school, a tally chart would be an appropriate means of recording the data. Note that it is usual to put down vertical strokes until there are four. Then the fifth stroke is drawn across the previous four. This process is continued until all the required data has been collected. The advantage of this method of tallying is that it enables the number of objects to be counted quickly and easily at the end.
In the example above, in the time that we were recording cars, there were 11 red cars, four yellow cars, 18 white cars and five black ones and 22 cars of other colours.
Using software for statistical displays
Microsoft Excel or Google Sheets are readily available tools that allow summarised data to be entered onto a spreadsheet and then graphed.
Other online statistical tools that are good for graphing data, for example CODAP – Common Online Data Analysis Platform, work with raw data and allow a more flexible approach to data analysis. Support videos for students and teachers in New Zealand on using CODAP can be found here.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
The context for this unit can be adapted to suit the interests and experiences of your students. For example:
Te reo Māori kupu such as tūhuratanga tauanga (statistical investigation) and taurangi (variable) could be introduced in this unit and used throughout other mathematical learning
This unit is set out to cover the topic of statistical investigations in depth will likely take 1-2 weeks. Some of the sessions may take more than one classroom session to complete. There is an introduction session followed by five sessions that follow the statistical enquiry cycle (PPDAC cycle) as described in the New Zealand Curriculum. Data detective posters showing the PPDAC (problem, plan, data, analysis, conclusion) cycle are available to download from Census At School in English and te reo Māori.
While this unit plan uses the five phases of the PPDAC cycle as a step by step process, in reality when using the PPDAC cycle one often moves between the different phases. For example, students might need to revisit the investigative question (problem) as a result of the planning phase.
This session provides an introduction and purpose to statistical investigations. The teacher will need to provide the students with plenty of magazines, newspapers and websites that have some good examples of how data can be presented effectively and perhaps some examples of poorly displayed data. This could be collated into a chart or slideshow. Prior to the session, ask the students to spend some time at home looking through magazines and newspapers to find examples of statistics to bring in for the session.
This session is ultimately about choosing an appropriate topic to investigate. You will need to discuss what data is actually measurable within your context and realistic topics that can be investigated in the given time frame. It would be a good idea to provide the students with a list of topics (perhaps relating to a current school issue, relevant curriculum area, or your students' cultural backgrounds and interests). Encourage students to come up with something original where possible.
Data collection is a vital part of the investigation process. The teacher will need to stress to the students, once again, the importance of being consistent in the collection of their data. There will also need to be sufficient discussion around efficient methods for data collection and recording.
Managing surveys: depending on the target groups and how you plan to manage the survey process there are a few options here to choose from.
Option 1: an online questionnaire is developed for each group that will be surveyed. This following should be considered:
Option 2: a paper questionnaire is developed for each group that will be surveyed. Similar considerations to the online questionnaire are needed, except that a paper copy will need to be printed for each person to fill out. These should be collected up and brought back to the class if the people who have filled them out are not in the class
Other data collection methods
Depending on the topics, students might be collecting data about litter, cars, pedestrian traffic. These are not things that we would use a questionnaire for so the students will need to think about a plan to collect the data. They may decide to use a pre-prepared table or grid to do this. The table should be set up so that the information for each of their data collection questions for a single object can be recorded in a single row. For example:
Collecting information about vehicle make and colour – students might also think to collect the vehicle type too.
Set up a table with four columns:
Number plate | Vehicle type | Vehicle make | Vehicle colour |
AAA123 | Car | Audi | Blue |
BBB456 | Ute | Ford | Gold |
CCC789 | Car | Holden | Red |
DDD111 | Truck | Isuzu | White |
123AA | Motorcycle | Suzuki | Red |
Students need to check with the teacher before commencing data collection to ensure that their method of collection is the most appropriate and will result in data that is useful for analysis.
Note for teachers:
Students will use their .csv file to make their displays in the next session. If it is not possible for them to save as a .csv then the teacher may need to do this and share with them or set up the CODAP document with their data and share a link to this. See the video or written instructions on how to do this. Note the video and the instructions include getting started with CODAP too.
In this session the students will be introduced to using an online tool for data analysis. One suggested free online tool is CODAP. Feel free to use other tools you are familiar with. This session is written with CODAP as the online tool and assumes students have not used CODAP before.
If you do not want to use an online tool, then continue to Making Displays, and construct paper versions of bar graphs and dot plots.
Learning how to use CODAP
Making displays for the data they have collected to answer their investigative question
This last session will focus on the final presentation of the data each group has found out. Encourage the students to be constantly evaluating what they are doing. Explain that it is fine to discover that a particular way of presentation is not working, and that it is a good idea to adjust.
Dear parents and whānau,
During the next two weeks we will be working on statistical investigations. Over this time, your child will be gathering data and presenting it using tables and graphs. Your child now needs to be thinking about choosing a topic to investigate. It would be helpful for your child if you could support him/her with selecting a topic, gathering data and perhaps watching for relevant newspaper or television items that will help him/her with analysing the information and forming a conclusion.
Thank you for helping with your child's statistical investigation.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/planning-statistical-investigation-level-3 at 8:46pm on the 26th February 2024