Data Analysis and Statistics are all around us. From understanding the median home price to the average rainfall in a year, "statistical literacy is needed by all students to interpret our world" (Van de Walle et al., 2013, p.435). When practicing data analysis, "data is gathered and organized in order to answer questions about the populations from which the data come" (Van de Walle et al., 2013, p.434). Data is collected from only a sample of the population, which in turn represents and is proportional to the larger population and allows us to make inferences about the population as a whole. This is what doing statistics is all about, and it differs from doing mathematics.
When teaching students about statistics and data analysis, we do it through the combination of Mathematics and the Scientific Method. This 4-step process involves: formulating questions, collecting data, analyzing the data, and finally interpreting the results. This is what educators should focus on as they are teaching Data Analysis and Statistics. Following this simple outline will lead educators to developing curriculum geared toward the CCSS.
Overview
The 4 Step Process
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Formulate Questions
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- Have students formulate the questions. "When students formulate the questions, the data they gather become more meaningful. How they organize the data and the techniques for analyzing them have a purpose." (Van de Walle et al., 2013, p.436)
- Primary grades begin with formulating questions about themselves which can be answered by class members, while older grades will start to focus on expanding the questions to include a larger population sample (other classes, community, etc.) -
Collect Data
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- There are 2 main types of data. Categorical data can be grouped by labels, like color of cars in the parking lot, favorite TV shows, etc. They are not in any particular order. Numerical data counts things on a continuous scale, like age of students, measurement of length of objects, etc.
- Data can be collected through polls, observation, or existing data sources (like newspapers, magazines, wikipedia, etc.). -
Represent & Analyze Data
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In this third step of the Data Analysis process, students take the data they collected and analyze it using graphs and statistics. We decide what graph or statistic to use based on our original question, and "students should be involved in deciding how they want to represent their data" (Van de Walle et al., 2013, p. 440). It is essential that students think about what graph or statistic will best convey the information about their data. We want to "help students see that graphs and charts tell about information and that different types of representations tell different things about the same data" (Van de Walle et al., 2013, p. 440). -
Interpret Results
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This is the essential 'after' stage of any data analysis unit. Students should discuss what the graph shows, or what the statistics tell, about the data, focusing on:
- What would someone that was not involved in collecting and analyzing the data think if they looked at this graph or these numbers? What would they understand about the data?
- What factual information is clear from the graph? What can we infer?
- What is the "shape of the data"? Students should think about the data not just as a collection of numbers, but should focus on the "big picture" (Van de Walle et al., 2013, p. 434).
- Can we see the answer to our original question?
- Why does the data look like this? What are some possible reasons? (Van de Walle et al., 2013)
"To engage students meaningfully in learning and doing statistics, they should be involved in the full process, from asking and defining questions to interpreting results." (Van de Walle et al., 2013, p.436)
Connections to the CCSS
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We see data analysis in the Measurement and Data and Statistics and Probability domains of the CCSS Mathematical Content standards. The data analysis standards of the Measurement and Data domain, which are for K-5, set the foundation for students to begin learning Statistics in grade 6.
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CCSS MEASUREMENT AND DATA DOMAIN
The CCSS Measurement and Data domain includes standards that require students to classify and categorize and make graphs and line plots. In kindergarten, students must classify objects according the their attributes. In Grade 1, we have CCSS.MATH.CONTENT.1.MD.C.4: "Represent and Interpret Data: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another" (Common Core Standards Initiative, 2014). -
This same "Represent and Interpret Data" standard is repeated in grades 2, 3, 4, and 5, but every year students are required to learn to make and analyze a new and more advanced type of graph.
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CCSS STATISTICS AND PROBABILITY DOMAIN
The CCSS Statistics and Probability domain begins in 6th grade and is a continuation of the Measurement and Data domain that was the focus in early and middle elementary. Now, students must apply their understanding of data analysis, developed by working with graphs, to statistics: they begin studying statistical variability and statistical distributions (e.g. mean, median, mode) (Common Core Standards Initiative, 2014).
Group Members
"The price of success is hard work, dedication to the job at hand, and the determination that whether we win or lose, we have applied the best of ourselves to the task at hand." (Vince Lombardi)
"Finnmeister"
Lesson Planner Extraordinaire
"Da Mechanic"
Design Guru &
Evil Mastermind
"The intent is to get the students involved in accurately communicating a message about their data" (Van de Walle et al., 2013, p441)
"My Heartbeat" Mini-Unit
Unit
Overview
Lesson 1:
Vocabulary & Pre-Assessment
Lesson 2:
Formulate Questions & Collect Data
Lesson 3:
Analyze Data
Lesson 4:
Interpret
Data
Lesson 5:
Review & Post-Assessment
References
Van de Walle, J.A., Karp, K.S. & Bay-Williams, J.M. (2013). Developing Concepts of Data Analysis. Elementary and middle school mathematics: Teaching developmentally (8th Ed) (pp. 434-453). Boston: Pearson Education.
Common Core State Standards Initiative (2014). Measurement and Data. Common Core State Standards Initiative [Website]. Retrieved from http://www.corestandards.org/Math/Content/MD/.