Collecting Student Data

As part of your role as a teacher, you will need to collect and analyse data. These data can include student ages, number of times they do their homework each week, test results, incremental changes in learning, and attendance. However, you can also measure student responses to your lessons or units of work with entry and exit cards.

1. Frequency tables and dot plots

A useful way to visualise data is through using frequency tables and dot plots. Watch the following video

1.1 Frequency tables

Tables help us to organise and analyse a set of data. A frequency table is a visual representation of a data set in an ascending order of size (scale) with their matching frequencies. It is a simple way to provide a count of how often a data value occurs. In this sense, the word ‘frequency’ means ‘how often’.

Example: Frequency of Student Marks (May) Data Set 1

The marks out of 10 were awarded to a year 9 class of 25 students for mid-term test were as follows:

Raw:

4     3     5     9     5     6     7     7     4     5     6     2     5
5     8     3     4     4     3     6     2     3     7     6     2

ds1 <- c(4, 3, 5, 9, 5, 6, 7, 7, 4, 5, 6, 2, 5, 5, 8, 3, 4, 4, 3, 6, 2, 3, 7, 6, 2)

Ordered:

sort(ds1)

 [1] 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 5 6 6 6 6 7 7 7 8 9

Putting the mark (score) into a table with the corresponding frequency (i.e. number of times it occurred), we get a frequency table like this:

1.2 Analysing the frequency table (Data set 1)

By looking at the table, we can do a quick analysis of the test scores in Data Set 1:

1. Frequent: the most frequent score is 5
2. Lowest: the lowest score is 2
3. Highest: the highest score is 9
4. Range: the range, the difference between the lowest score and the highest score is 9 – 2 = 7
5. Median: the score that falls in the middle is 5
6. Mean: the mean or average is the sum of all of the scores divided by the number of scores. The mean is 121 ÷ 25 = 4.84

Of course, you can let R do the number crunching (note that capitalisation matters!):

min(ds1)
max(ds1)
range(ds1)
median(ds1)
mean(ds1)

Question: Why don’t we use ds1_categorical here?

And when you feel lazy, use summary:

summary(ds1)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   2.00    3.00    5.00    4.84    6.00    9.00 

To learn more about how the Median is computed, check out this video:

Question: What does it mean when the Median and the Mean have quite different values? How can this come about?

1.3 Bar chart

Bar charts are a simple way to help us to visualise or see data. We do this so that we can see if there are any patterns or trends in the data that can help us to make sense of the scores. So if we put the scores from the frequency table (data set 1) into a bar chart, we would end up with a graph like this:

library(ggplot2)

package ‘ggplot2’ was built under R version 3.3.2

qplot(factor(ds1))

1.4 Conclusions for data set 1

So as a teacher, what can be said about these mid-semester test results? Well, there are 25 people in the class and half of the class scored equal to or less than 5/10 or 50%. As a teacher, we might surmise that the test was too hard or that the students had not yet grasped the content. This type of analysis can help us as teachers to effectively monitor student progress. What would happen if you revised the content and then re-tested the students at the end of semester? This may help to see if the student knowledge of the content has improved. This gives us a valid measure of student learning gains as a class and as individuals.