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processes such as rounding a whole number and solving      internalizing, and generalizing process knowledge, the
problems with proportions; Foundations of Algebra:         fact is that not only are methodologies rarely presented in
Active Learning Workbook (Ellis & Apple, 2012) included    student curricula without accompanying modeling of the
22 methodologies; and Quantitative Reasoning and           use of the methodology; students are also challenged to
Problem Solving (Ellis, Apple, Watts, Hintze, Teeguarden,  step through the methodology themselves, in a problem
Cappetta, & Burke, 2014) contained 30 methodologies. For   that is similar to the modeled use. See Figure 2 for an
example, Figure 1 shows the Data Analysis Methodology.     example from Foundations of Algebra: Active Learning
While methodologies are extremely effective in learning,    Textbook (Ellis, Teeguarden, Apple & Hintze, 2013).

Figure 1 Data Analysis Methodology

Step                                Explanation

1. Clarify the data                 What does each variable and row represent? Are there issues of quality such
                                    as errors or missing data? What are the values being measured? What are the
                                    relevant units? Are there any outliers that were removed? Is bias a problem?

2. Clarify the context              Who is asking for the analysis, what is the agenda, and what are the types
                                    of results that they want or expect to see? Identify the objectives (3 to 5) and
                                    always consider possible reasons for bias in the reporting of this data.

3. Develop inquiry questions        Identify three to five key questions central to the inquiry to clarify what results
                                    you want to produce. What are the fundamental questions that you hope to
                                    answer? What characteristics of the data set are you looking to identify?

4. Produce relevant graphs          Choose to construct a collection of histograms, box plots, pie charts, or bar
                                    graphs to help answer the original research question.

5. Identify data analysis tool      Select spreadsheet, stat package, modeling language, database, or special-
                                    ized software.

6. Transform the data               Make structural changes in your table to facilitate better view, perspective,
                                    and understanding of what the data is representing.

7. Produce a preliminary analysis Perform the basic descriptive statistics to go along with the graphs produced.

8. Identify data shortcomings       What are the concerns associated with using this data, are there agendas for
                                    people producing the data, concerns about the data collected, and data that
                                    has not been included?

9. Report findings and generate      Summarize the top 3 to 4 findings that you can make with confidence. Also
     new questions                  add 3 to 5 new issues or questions that need to be addressed based upon
                                    the findings.

10. Find additional data            Go back to the original source for the data and see if they have additional
                                    data that can supplement to answer some of the advanced questions.

11. Identify findings                Identify the top 3 to 5 findings that are most significant related to the initial
                                    objectives and determine the outline you will use to present your findings.

12. Perform an additional analysis What are the key questions in the presentation that are currently unanswered
                                                    and what are the statistical tools used to answer these questions?

13. Generalize the implications     What can we say about implications outside our current context of analysis?
                                    Determine whether it is fair to generalize the results to a wider population.

14. Produce an analytical report    Report the findings of the data analysis, documenting and justifying your
                                    process, techniques, and conclusions, including any issues or concerns, or
                                    ideas for future investigation.

15. Lessons learned                 In the process of analyzing your data, assess your performance, identifying
                                    what you did well and why, what can you improve upon, and what you learned.

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