This unit involves students in formulating questions about data sets, displaying and analysing data, and reporting conclusions. Information about the pregnancies of 56 woman and their newborn babies is used as a context.
A five phase approach has been used throughout this unit to help students identify the key processes involved in the comparison of two sets of data.
The qualitative data is number coded as is often the case in survey results. The terminology of data types, statistical calculations, and data displays (statistical graphs) are explored in this unit. Statistical measures of both the centre and the spread of the data are used to justified comparative statements and answer questions posed by the students about the data set provided.
Qualitative data is information about non-numerical qualities, e.g. Colour of school bags, modes of transport to school. You cannot find the mean or median for qualitative data only the mode (most common result).
Quantitative data is represented in number form and can be discrete or continuous, e.g. Number of CD’s you own (discrete) or weight of your school bag (continuous).
Discrete data can be obtained from counting and has no results between the values obtained in the data, and can be grouped or ungrouped, e.g. Birth date (grouped) or number of children in your family (ungrouped).
Continuous data is obtained by measuring. For any two possible values other results can be found in-between them. E.g. Weight of new born babies (you could get continuous data by sticking a pin in a number line).
Bi-variate data is used where a comparison is made between two variables with reference to the one group. You are looking for a possible connection between bi-variate data. E.g. Comparing birth weight and length for new born baby boys. The birth weight and the length are the two different variables.
Uni-variate data is used where a comparison is made between a common variable for two different groups or categories. E.g. Birth weight of baby girls compared with baby boys. The only variable is the birth weight.
Averages or measurements of the centre of a distribution of data.
The learning opportunities in this unit can be differentiated by providing or removing support to students, and by varying the task requirements. Ways to differentiate include:
This unit is focussed on the real world context of pregnant mothers. If you feel this context is not appropriate for your learners, the tasks can lend themselves well to another dataset. CODAP offers a range of datasets to be explored. Alternatively, you might use a dataset from CensusAtSchool New Zealand - TataurangaKiTeKura Aotearoa, or collect data as a school community.
Te reo Māori kupu such as raraunga kounga (qualitative data), raraunga tatau (quantitative data), hora raraunga (spread of data), ine whānui (range), tau waenga (median), toharite (average, mean), tau tānui (mode), raraunga motukore (continuous data), raraunga motumotu (discrete data), raraunga matatahi (univariate data), raraunga matarua (bivariate data), kauwhata rautō (stem and leaf graph), kauwhata kauamo (box and whisker graph), kauwhata pou hiato (composite bar graph), and kauwhata marara (scatter graph/plot) could be introduced in this unit and used throughout other mathematical learning.
This session introduces the data set being used and explores some of the ways in which statistical data can be analysed and presented. Here are the model answers for the questions.
Gravida: number of pregnancies
Para : number of births
Term: number of weeks the pregnancy lasted
Sex: male or female
Medic: type of medical personnel who delivered the baby
Deliv: nature of the delivery (caesarian, forceps or normal birth)
Sex: Boys 13, Girls 6
Medic: GP 7, Midwife 8, Obstetrician 15
Deliv: Caesar 3, Forceps 6, Normal 14
Consider Row 11 what does it tell us about this particular mother and her baby?
Which of her babies is represented in this data?
Why are some data items in the Gravida and the Para columns different? (Consider rows 26 and 42)
Ensure they justify their answers using appropriate descriptive terms like numeric data.
If necessary, review individual graphs with the class. Have different groups of students focus on one of the following graphs: bar, pie, histogram or stem-and-leaf. Students should select an appropriate data set and represent this with their chosen graph type. Have students present these graphs to the class, explaining the key features of their chosen graph type and their reasoning for choosing a specific data set. Alternatively this could be used as a homework task following this first lesson.
Have each group of students find the total number of women at a selection of specific ages (e.g. one group will find the number of women at each of the specific ages 16, 17, 18, 19, 20, another 21, 22, 23, 24, 25 etc). Have a student record the results on the board. Leave this open to see how they will record the information from the groups. The difficulty in recording every age should arise.
The need to collate the summarised results in an organised way could lead to grouping the age data in a table. Highlight the difficulty in finding a specific mode if the data is presented in grouped form without knowing the individual data items.
Encourage the students to be selective and critical about the best representation of the central tendency of the data rather than just calculating all three.
Have students, in groups of 2-4, make up questions that interest them and that would allow them to compare different aspects of the data. Ensure students do write questions rather than comparative statements. Allow and encourage both bi-variate and uni-variate comparisons. You may need to share a good example from one group or model making one up to support students' thinking.
For example:
Use scaffolding questions to support students' understanding of how their questions will enable comparison of different aspects of the data.
E.g. 1 Do mothers of boys tend to be older than the mothers of girls? This is a uni-variate data comparison, where the age of the mothers is the only variable and it is being compared for two different groups, boys and girls.
E.g. 2. Do the heavier babies come from longer term pregnancies? This is a bi-variate data comparison, where the two variables are the baby mass and the term.
E.g. Do older woman have more difficult births? (I.e. forceps and caesareans)
You could grade the Nature of the Delivery on an Easy to Difficult scale, where normal is easiest, then forceps, then caesarian the most difficult delivery. This would allow you to do a form of scatter graph analysis to explore the relationship between age and difficulty of birth.
Have the students, working in pairs, either explore one question in each lesson, or work on both questions during the next two lessons.
Get the students to consider what statistics they can calculate that will help them to make comparisons and build up some supporting evidence that will enable them to answer their questions.
Tally charts, frequency tables or stem-and-leaf plots may be helpful. Encourage the students to calculate appropriate measures of central tendency (mean, median) as well as measures of spread (range, upper, lower quartiles and inter-quartile range) relevant to uni-variate data comparisons.
Percentages may be useful. E.g. Percentages of various medics involved in each type of delivery may be an appropriate statistic related to the question “Are General Practitioners present during more normal births than other medical professionals?”
The students may wish to use statistical graphs from the start to help them calculate these statistics. A stem-and-leaf plot is useful for finding the median, quartiles, range and inter-quartile range.
Encourage the students to:
Initially encourage the students to write brief statements (three to five) comparing the groups or variables using their calculations and graphs. Just quick key points at first that compare the different statistics they have calculated and the interpretations they put on the graphs they have drawn.
Then get the students to write a clear statement that answers their question based on the statement they have written.
Next ensure they justify their conclusion with full statements (three to five) that support the answer to their questions. They need to identify the differences in the statistics and those highlighted by the graphs for the two groups or variables, as well as explain what this means in relation to the context and the question they are considering. Include interesting aspects of the data shown by the graphs that make the conclusion reached a confident one or not.
E.g. 1. It is not sufficient to say “the mean age of the boys’ mothers is 25 and the girls’ mothers is 23.” But rather “the mean age of the boys’ mothers at 25 years is 2 years greater than the girls’ mothers, at 23 years. This supports the trend that the boy babies have older mothers than the girl babies, although the difference is not very great”.
E.g. 2. Yes, heavier babies do tend to come from longer pregnancies. The trend line on my scatter graph goes up steeply showing that the bigger babies usually come from the longer pregnancies, but there are a few exceptions to this.
Share students’ statements for each of the three developmental stages of statement writing above and highlight good in-context statements that clearly relate to and justify the answer to the question.
NB. The answer may be that no relationship exists between two variables and this conclusion still needs to be justified from the scatter graph.
Use the following questions to support students in reflecting on their work:
Provide time for students to summarise their findings in poster or report form. This may be done as a pair task depending on you class arrangement. Consider what presentation methods can be used to encourage students to express their mathematical understanding and ideas in a variety of ways (e.g. they may present an oral report to the class on their key findings supported by their poster or hand in a more formal written report).
Students should include the following key pieces of information in their Presentation or Report:
Two sample reports are included as attached resources.
Dear families and whānau,
Recently, we have been investigating a dataset about the pregnancies of 56 woman and their newborn babies. We have formulated questions, displayed and analysed data, and reported conclusions about this dataset. Ask your child to share their learning with you.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/stork-delivery at 8:46pm on the 26th February 2024