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    Graphical representations can help to simplify complex arguments.

    Using strong frameworks is the most important part of clearly structuring communication. Strong frameworks involve straightforward reasoning, clear premises and conclusions, clear distinctions between premises and conclusions, and judicious use of clarifiers.

    However, even with strong frameworks, constructing reasoned arguments can be complicated. For example, arguments may involve many premises. Alternatively, we may wish to present several related arguments (with several premises and conclusions) in the same overall discussion. Therefore, communicating arguments can involve substantial organizational challenges.

    Structure is one key to clarity despite complexity.

    Graphical representations (diagrams, tables, etc.) can help strengthen the structure and clarity of arguments. The old adage "a picture is worth a thousand words" is true even for scientific communication. Graphical representation can be simple. For example, expressing the measurable predictions of general hypotheses in a table format can clarify the criteria for rejecting or supporting hypotheses. 

    Consider a specific (somewhat complicated) example. Imagine that we are interested in how best to organize a series of 1-hour long study sessions before a math test. Imagine that the test covers three types of problems: algebra, geometry, and word problems. Imagine also that we are interested in comparing three types of study strategies: 

    1) "Blocked" study, where a person studies a single topic before moving on to another topic. For example, in Blocked study, each person would spend an hour studying algebra, then an hour studying geometry, and then an hour studying word problems.

    2) "Serial" study, where a person studies all three topics together in a determined order. For example, in serial study, each person could spend 10 minutes studying algebra, then 10 minutes studying geometry, then ten minutes studying word problems. The person would then repeat the process for one hour of studying.

    3) "Random" study, where a person studies topics in 10-minute blocks, but the order of presentation is random. Therefore, the sequence could be: geometry, algebra, word problems algebra, word problems, geometry... etc.

    We can illustrate the three types of study strategies using a table (Table 1; Lee and McGill, 1983): 

    Study Schedules

    Table 1. A "graphical framework" for illustrating different ways to schedule study.

    Which type of study strategy (blocked, serial, or random) do you think will be most effective? Why?

    An additional important question is: what does "effective" even mean? "Effective" is a fairly general term and could mean different things. Among the possible ways to measure effectiveness are:

    1) Effectiveness during practice. We could potentially determine how effective each study strategy is by measuring how much people improve during the study session itself. For example, we could compare test performance at the beginning and end of each hour-long study session.

    2) Effectiveness for retention. We could potentially determine how effective each study strategy was by testing for how well people retain the math skills that they studied after a period of time. For example, we could give people tests on the math problems one day, or 10 days after finishing their study sessions and measure how much of information/skill the people retained.

    3) Effectiveness for transfer.  Another way to measure the effectiveness of different study strategies would be to determine if people are able to transfer skills learned during practice to different types of problems. We could test people's performance on a different type of math problem such as applied engineering problems that were NOT included in the types of problems that the people studied. If studying using a particular strategy helps people solve new types of math problems, then we could consider the study strategy effective.

    Is the example getting complicated? We have three types of math problems, three types of study strategies, and three ways to assess "effectiveness." For most people, 9 values in three different categories is a lot to think about at one time. 

    Imagine for simplicity that (as most people do), we hypothesized that a "blocked" practice schedule was the most effective practice schedule in all three respects: during studying, for retention, and for transfer. We could create measurable hypotheses for all 14 specific predictions that result from our hypothesis. For example:

    1) We hypothesize that blocked study will result in significantly higher scores on algebra tests than serial study during practice.

    2) We hypothesize that blocked study will result in significantly higher scores on algebra tests than serial study during the retention test.

    3) We hypothesize that blocked study will result in significantly higher scores on algebra tests than serial study during the transfer test.

    4) We hypothesize that blocked study will result in significantly higher scores on algebra tests than random study during practice.


    14) We hypothesize that blocked study will result in significantly higher scores on word problem tests than random study during the transfer test.

    Clearly, listing 14 measurable hypotheses would be repetitive and tedious. However, using a graphical framework such as a table could help to illustrate our predictions

    Structure is one key to clarity despite complexity.


    A graphical representation could help to organize our thinking and consolidate our presentation. For example, we could summarize our predictions in a table (Table 2):

    Study Schedule Predictions

    Table 2. Study predictions. The symbol ">" denotes "significantly greater than."

    The graphical representation represents a concise representation of our experimental predictions. 

    You might wonder: what are the likely results of the study? Is blocked study better than other study schedules?

    Researchers in linguistics, motor control, and education (among other fields) have experimentally addressed similar questions (Battig, 1979; Shea and Morgan, 1979; Rohrer, 2012). Based on many similar experiments, the likely results of of the study would be (Table 3):

    Study Schedule Results

    Table 3. Study results. The symbol ">" denotes "significantly greater than."

    Although blocked practice results in greater test performance during practice, both serial and random practice commonly lead to more retention and transfer! Retention and transfer reflect how well people remember and are able to apply material that they study to different problems. Therefore, retention and transfer indicate how well people learned the material that they studied.

    Although serial and random schedules may not seem as effective during study sessions (because test performance during study sessions is significantly lower than for blocked practice), serial and random schedules actually result in greater learning. Practice like serial and random practice can be called "Desirable Difficulties" (Bjork, 1994). Non-repetitive, alternating practice of multiple skills makes practice more difficult than blocked presentation and decreases performance during practice. However, the difficulties are desirable because non-repetitive practice results in more learning than blocked practice.

    The graphical framework concisely represents a large set of measurable predictions that support the general hypothesis that "Desirable Difficulties" actually increase learning.

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    Using graphical frameworks can help to simplify and clarify complex arguments. Consider using graphical frameworks to help structure every section of a scientific paper.