Exploring Data & Probability

Have you ever thought about how often you make estimations or determine the probability of an event in your everyday life? Whether it's estimating how long it usually takes to drive to work in the morning or determining the likelihood of our favourite sports team beating their rival in an upcoming game, we are constantly involved with measurements and estimations of central tendencies and probability. Given the fact that data and probability are so relevant to our everyday lives, it is critical that we as educators create a learning environment where our students have the opportunity to explore and develop a more meaningful understanding of these topics.

Making the Measures of Central Tendency Meaningful

In her discussion of the measures of central tendency in Chapter 21 of Making Math Meaningful, Marian Small not only describes what mean, median, and more are but also when each of these measures are useful. When teaching my own students, I would definitely take Small's approach of teaching not only the meaning of the three measures of central tendency but also their usefulness with regards to different scenarios and different sets of data. 

In order to understand what the mean or average of a data set is, my students and I could talk about what it would mean to make everything fair or to level the bars. In class, we were given word problems where students received an unequal number of items. We were challenged to use Cube-A-Links to show how we could split these items evenly among the group of students who sharing them. 

Olij, B. © 2016

Olij, B. © 2016

Marian Small discusses how the mean is useful when the numbers in the data set are fairly close together but that the mean may not be the best indicator of the "average" group size when there are one or two extremely high or extremely low values. In order to demonstrate this concept to students, I could ask them to level bars where there was a considerable difference in the number of Cube-A-Links each bar contained. As students leveled the bars, they would be able to visually see and physically experience how the size of the leveled bars (the average) did not accurately represent the initial sizes of the various bars in the data set. 

I could then have my students explore the concept of a median in order to understand how the median is a valuable measurement when the data contains one or two extremely high or low values. Students could interact with several different data sets and compare the median and mean for each of these sets in order to see how the median can sometimes provide a more accurate reflection of the data. 

When discussing when the mode is a useful measure of central tendency, we could use the example of a glove factory. In order to know what size glove the factory should focus on manufacturing, the glove designers could look at which size glove is most frequently bought in order to determine the most common glove size. In order for our students to understand the measures of central tendency and when it is appropriate to use them, it is important to explore and discuss examples of these measures in real-life, engaging scenarios. 

Exploring Probability Using TinkerPlots

During class, we also had the opportunity to explore TinkerPlots which is a data analysis software where students can manipulate a set of data in order to create graphs and other representations which compare different properties of the data. In Chapter 22 of Making Math Meaningful, Marian Small discusses the importance of using a large set of data in order to more accurately determine the trends or the probability of an outcome or event. TinkerPlots is a particularly valuable resource for the classroom as it offers data cards which contain large sets of data for students to interact with. TinkerPlots is also very beneficial for visual and tactile learners as it is very easy for students to sort and manipulate the colour-coded data by clicking and dragging different points on the plot to explore different connections between various properties and to create colourful graphs. At the start of the activity, students could develop a number of "I wonder if..." statements related to the data set. Students could then explore whether their hypotheses were true by sorting and analyzing the data in order to determine what the trends and connections are among the various properties of the data set. TinkerPlots is a fantastic resource for encouraging students to develop a more meaningful understanding of data and probability as they make sense of real data and recognize trends in an interactive, visual, and tactile way. 

Learn Troop. 2014, December 27. "TinkerPlot Basics."
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