How Students Use Statistical Computing in Problem Solving

Figures & data

Table 1 Framework for identifying statistical computing actions in student’s work.

Statistical computing action	Affordance for the student: The student is able to do the following:
Automation of computational procedures	Use the technology to efficiently create graphs or summaries to make sense of the data, without overloading cognitive processes. Use the technology to perform statistical calculations and use the results to make appropriate statistical decisions without overloading cognitive processes.
Computational thinking	Create a solution strategy and communicate that strategy to the computer software. Demonstrate critical or abstract thinking about a concept that the technology presents. Revise code that has been provided to them, to perform a new task.
Utilizing new methods	Build one of many possible solutions to a problem to answer a statistical question (does not follow a prescribed set of procedures). Provide their own reasonable methods for analysis while utilizing the technology. Identify and understand information gathered that will be useful in solving the current problem.
Pattern recognition and decision making	Recognize patterns in the output of a statistical analysis and use that information to determine the next step of the process. Recognize patterns in the way things are coded and use that pattern to help solve the problem.

Table 2 Problem solving phases.

Phase	Definition of the phase
Analysis	Students attempt to understand the problem, its constraints and consider useful perspectives for the problem.
Planning	Students work toward devising a sequence of actions or formulate a strategy to pursue a solution.
Implementation	Students carry out a preplanned strategy, which may or may not be explicitly stated.
Assessment	Students take explicit actions to monitor their progress toward a solution.
Verification	Students believe they have a solution and either evaluate whether or not it is correct, or engage in activities to explain or justify their solution.
Organization	Students take actions to arrange their environment (either with paper or in the technology tool) in a way that they perceive will be beneficial in working toward a solution.
Research	Students use external resources available to them to aid in forming a strategy to pursue a solution.

Table 3 Participant background information.

Pseudonym	Relevant courses in addition to introductory statistics	Extracurricular	Statistical ranking	Computational ranking
Allison	Statistical computing with R Probability Linear algebra	Intro Stats Tutor DataFest Participant	1st	1st
Cora	Statistical computing with R	Intro Stats Grader	2nd	3rd
Genevieve	Psychology statistics with SPSS		3rd	4th
Moira	Intro programming with Java Databases with SQL		5th	2nd
Samantha		Independent Study with R	4th	5th

Fig. 1 Interview task.

Fig. 2 Script of the data provided to students.

Fig. 3 Sequence of problem solving phases in the task-based interviews.

Fig. 4 Proportion of time each student spent in problem solving phases with statistical computing actions overlaid.

Table 4 Completion of anticipated steps by student.

Steps of analysis	Allison	Cora	Genevieve	Moira	Samantha
Identify as ANOVA	✓	✓	■	■	✓
Graph data	✓	∼	✗	✓	✗
Check conditions	∼	✗	✗	∼	✗
Format the data	■	■	■	■	■
Conduct ANOVA	✓	✓	■	✓	■
Interpret results	✓	∼	✓	∼	∼

Fig. 5 Website with misleading information utilized by Samantha (http://www.endmemo.com/r/lm.php).