Case Study – Primary – Merkez Ortaokulu – Denizli, Turkey

In Denizli, Turkey, 27 11-year-old students worked in groups to investigate whether there is any relationship between students’ psychology and several different variables that each group was interested in, such as weather conditions, family relationships, health conditions, traumatic events, achievement, economic situation, bullying and technology.

Key skills aimed to be developed included formulating statistical questions, measuring and collecting data, using CODAP (https://codap.concord.org/) to organize and visualize data using dot plots, describing data distributions and their characteristics, such as arithmetic mean, mode and range, interpreting data and drawing conclusions from data. The project took up approximately 27 class periods (each 40 minutes) over ten weeks.

The weather-related data were gathered from the national meteorology office website and the other data were collected by the students using questionnaires that they developed. Based on the national mathematics curriculum students have had prior experience with formulating investigation questions, collecting, visualizing and interpreting categorical data as well as calculating the average. Nevertheless, the first two pilot projects indicated the need for considering (1) the notion of distribution as an aggregate group of data values, (2) dot plot representation to visualize distribution shape and two categorical variables (in the curriculum they learn only bar graphs or pie charts), (3) different types of statistical questions, such as summary, comparative and relationship questions, and (4) a trial activity for exploring how to use CODAP to organize and analyze data before the actual project.

The students were confident to use ICT tools but they have not used any data analysis software, such as CODAP, to explore data before. Thus, there was a CODAP trial activity early in the sequence of tasks involved in the project to introduce how to use CODAP tools to organize and analyze data after three lessons on features and types of statistical questions. During this activity students explored students’ reaction times by collecting data in the class. It was during this activity that students were introduced to dot plots, which is not used in the national curriculum, and encouraged to think about distributions and their characteristics, such as shape, center and spread/variability, rather than only to focus on calculating statistics without really understanding what they mean when interpreting results. This activity also demonstrated how to use the DA cycle in a statistical investigation.

For the project, students were given a scenario stating that the school’s Counselling Services Department would like to know whether students’ low motivation, bad marks, absenteeism and disputes among students are associated with the weather conditions.  Then they were asked to investigate if the weather and students’ psychology are related and whether students’ psychology are related with the variables other than the weather.

Groups of 3-4 students developed their own research questions within this context and conducted a sample survey in their school to collect data over 5 days in December to answer these questions. The students used CODAP to visualize their data (about 200-300 cases and 8 variables). These data visualizations helped students to interpret their data and to make informal inferences. They also evaluated the results and make suggestions for what actions need to be taken. In the last 3 lessons, groups presented their findings to the class using the smart board and discuss them as a whole class.

Some of the conclusions that they have reached were as follows:

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  • According to the survey and graph we did, in cloudy days 82% of students were happy and 5% were sad; in sunny days 69% of students were happy and 6.2% were sad; in partly cloudy days 69% of students were happy and 19% were sad; in heavy rain days 79% of students were happy and 7.1% were sad. So emotional state is mixedly distributed and accordingly there is no relationship between weather and emotion. (group 4)

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  • In the graph of bullying and emotion, there is no difference in the state of emotion between who are bullied and who are not bullied. So this shows that there is no relationship between the two. (group 3)

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  • There might be other factors other than the weather conditions affecting students’ psychology. For example, students who have higher grade point average are happier than those with lower grade point average. (group 9)

When the students were asked what they would do to be more certain about the inferences they made, they generally suggested that by increasing the number of students they surveyed and by including also upper grade level students in their survey they could increase the representativeness of their sample for the whole school and thus the results would be more reliable.

The students increased their scores on both individual and group knowledge post-tests after the project. The most noticeable improvement was seen in comparing two distributions on the individual knowledge test and making inferences about the relationship between two categorical variables on the group knowledge test.

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