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									      Grading Difficulties of Tasks by Analyzing the State of

                            Speakers' Performance
                                                                                Naoki Takei
                                                             Tokyo Institute of Technology
                                2-12-1, O-okayama, Meguro-ku, Tokyo, 152-8550, Japan

1. The purpose of this study:
    The purpose of this study is to show an objective way of grading tasks according to
their difficulties by analyzing the speakers' states of performance in executing tasks
through principal components analysis (PCA), and to demonstrate the validity of this way
of grading by comparing the results of the grading with other subjective grading systems,
such as ACTFL's oral proficiency interview (OPI).

2. Grading tasks:
    Various studies on the task complexity and difficulty pointed out many factors that
affected them (Ellis, 2003; Nunan, 1989; Skehan, 1998,). However, these studies did not
provide clear and objective standards to grade task complexity or difficulty.
    Ellis (2003) stated, "grading tasks cannot follow a precise algorithmic process but
rather must proceed more intuitively in accordance with a general assessment of task
complexity” (p. 227).
    This is not to say that qualitative or intuitive grading by experienced teachers is
unreliable, but points out the necessity to study objective ways to measure complexity or
difficulty of a task.
    Robinson (2002) distinguished task difficulty and complexity. However, speakers feel
a task to be difficult irregardless of the cause. In this study difficulty and complexity are
not distinguished. If the speaker feels the task is difficult, some phenomena, such as
hesitations, pauses, the change of speech rate, and the change of plan of speech,
communication strategies etc. in the surface of speech performance. In this study, it is not
analyzed the properties of task itself, like other qualitative or subjective analysis on task
difficulty. Instead the phenomena appear in the surface of speech, that is the state of
performance is analyzed to rate difficulty of the task in this study.

3. The state of performance and difficulty of tasks
    The quality of speaker’s performance is affected by the difficulty of the task,
speaker’s proficiency etc.. The quality of performance, namely the state of performance
has various properties, such as complexity of utterances, speech rate, variation of
expressions. It would be possible to know the degree of difficulty of the task by analyzing
the state of performance in executing the task.
    If Difficulty becomes higher, generally speaking, forms to be used in utterances
become more complex and a wider range of vocabulary are needed. If the speaker has
sufficient linguistic resources and ability to process them, he or she can afford to use more
complex forms and various words in a certain level of fluency and accuracy.
    If the difficulty of a task becomes higher, allover performance rises, as long as the
speaker is proficient enough. If it is possible to summarize the state of various properties
of speaker’s performance into a single dimension, the relations between the sate of
performance and difficulties of tasks can be drawn in the green line in Graph 1.

       Graph 1: State of performance
                       level of proficiency

         state of performance

                                              task difficulty

    The vertical axis is the height of the state of performance, and the horizontal axis is
the task difficulty. The higher the task difficulty is, the higher the state of performance as
long as the state of performance is not higher than the level performance that the
speaker’s proficiency can afford.
    However, L2 learners often face a lack of L2 knowledge and ability to process
complex utterances. Hence, they need to use various strategies to cope with these
communication problems. A Communication Strategy (hereafter CS) is a strategy to
compensate for insufficient linguistic knowledge of a second language.
    And L2 speakers often simplify the contents of messages or linguistic forms, because
they do not have enough self-confidence or cannot afford to process complex forms
and/or information. This is the strategy of simplification.
    When simplifications and CSs are executed the forms the speaker uses are controlled
or forced to be limited to the simpler ones.
    Then variation of linguistic forms does not increase even if the speech becomes
longer, and often erroneous utterances appear; because sometimes speakers contrive new
expressions by using strategies like word coinage, direct translation from words and
expressions in their first language etc. (Faerch & Kasper, 1983). In addition, speakers
naturally need time to process these strategies. These make the overall state of
performance lower,
   Graph 2: The crucial point
             states of performance

                                           level of proficiency


                                                                  task difficulty

    Up to a certain level of Difficulty of tasks, speakers do not feel difficulty in executing
tasks because their proficiency is high enough to cope with these tasks, even if they use
some CSs and simplifications.
     However, at a given point, Difficulty becomes higher than or equal to the speaker’s
proficiency. From here on, the state of performance will not become higher than before.
After this point, the state of performance will decline or at least remain unchanged, even
though Difficulty rises, because the speaker needs to execute various time-consuming
strategies and face serious communication problems. Let us name this point the crucial

     Graph 3: state of performance

      State of Performance

                                           Crucial Point

                                             Task Difficulty
    Therefore, it is possible to assume (1) (2) (3) as follows,
    (1) The states of performance rise along with Difficulty as long as the level of
Difficulty is lower than the crucial point.
    (2) If Difficulty becomes higher than the crucial point, the states of performance do
not rise but decline or at least remain unchanged
    (3) Values of the states of performance and Difficulty at the crucial point of speakers
of high proficiency are higher than those of low proficiency
    Hypotheses (1) to (2) are visualized like this graph (Graph 3).

           Graph 4: the crucial points and proficiency

        states of performance               more proficient speaker

                                                       Crucial points

                                                            of tasks

    The values of the crucial point are decided by the proficiency. When speaker’s
proficiency is higher, the crucial point is located upper right like in Graph 4.

4. Way of grading task difficulty

   Graph 5: Difference of performance

   Let us draw the graphs of three groups of speakers at the
    different levels of proficiency. High is the graph of the state of performance and
difficulty of tasks, of the speakers at highest proficiency, and Low is that of the speaker at
lowest proficiency, and Mid is between High and Low.
    When we compare the difference of states of performance of 3 groups of speaker at
the point d1, the differences are not large, and at d2, after the crucial point of Low, the
differences spread, and at d3 after the crucial point of mid, the differences become largest.
    HYPOTHESIS (A) If Difficulty is low, the differences between subjects of different
proficiency tend to be smaller; and if Difficulty is high, the differences tend to be larger.
    If (A) is right, the differences of means of the states of performance among the groups
of subjects of different proficiency can be a measure to grade Difficulty of tasks.
    This is not to insist, the state of performance behave exactly in the way shown in the
graphs, but the graph is a visualization of Hypothesis (A).
    What the hypothesis means is proficient speakers have higher tolerance against
Difficulty of the task, and the low proficient speakers are not. Their state of performance
decline in lower Difficulty of tasks and decline rapidly.
    It is measured the state of performance by (1) selecting the parameters to represent the
state of performance, which is multi dimensional data, and (2) summarizing the data by
principal component analysis (PCA) into single dimension. The principal component
scores represent the sates of performance (Takei & Akahori 2005a).

5. Experiment
1. Tasks are set by having the interviewer ask questions. Interviews are recorded and
   parameters to represent the state of oral performance are measured
2. The data are analyzed by PCA, and the result is compared with the ratings of the
   proficiency of learners according to the standard of ACTFL’s oral proficiency
Subjects are classified into three groups
i) Native speakers of Japanese Language, the number is 17, shown as (N).
ii) Learners of Japanese Language at advanced level according to ACTFL’s standard, the
   number is 19, shown as (H)
iii) Learners of Japanese Language at intermediate level according to ACTFL’s standard,
   the number is 18, shown as (L)
BL: Description of daily life, such as the schedule of weekdays and the route to go to
   school or work place etc. This task is thought to be a task at the intermediate level
   according to the ACTFL standard (Buck, 1989).
     NR: Narrating a story, such as explaining the contents of a novel or a film the subject
knows. This task is thought to be at the advanced according to the ACTFL standard.
     OP: Giving opinion on social, political and cultural issues or problems. This task is
thought to be at the advanced or superior level according to the ACTFL standard.
1. Complexity of Utterances (rGM): this parameter represents the degree of complexity of
  the forms used in execution of tasks.
2. Semantic Variation (rUL): when the value of semantic variation is high, speakers
  transition smoothly from one topic to another in their speech (Ito, 2002).
3. Grammatical Variation (rUG): this parameter represents the richness of grammatical
  forms in utterances.
4. Modal Frequency (rPM): modality is a very important element in Japanese language;
  this parameter shows the frequency of modalities.
5. Speech Rate (sSR): this parameter shows how fast or slow the speech is. If speakers
  pause to think many times, this parameter becomes low.
Ways to calculate the parameters;
1) Complexity of Utterances (rGM): tokens of functional words and modalities of truth
  and value judgment (Masuoka 1991) in terms of every 100 semantic words. Namely:
the number of functional words (token) nFN
the number of modalities of truth and value judgment (token) nJM
the number of semantic words (token) nSW
∴ rGM= 100*(nFN+nJM)/nSW
2) Semantic Variation (rUL): the number of lexis of semantic words (vSW) in terms of
  every 100 semantic words
∴ rUL= 100*vSW/nSW
3) Grammatical Variation (rUG): the number of lexis of functional words (vFN) and the
  modalities of truth and value judgment (vJM) in terms of every 100 semantic words.
∴ rUG= 100*(vFN+vJM)/nSW
4) Modal Frequency (rPM): frequency of modalities except truth and value judgment; the
  numbers of tokens of these modalities (nPM) in terms of every 100 semantic words.
∴ rPM= 100*nPM/nSW
5) Speech Rate (sSR): the average number of moras uttered in a second; the number of
  mora (nMR) is divided by the total time of the speaker’s turn, taken to complete the task
∴ sSR= nMR/tMT
 The parameters measured are analyzed by principal component analysis in each task. The
  principal component that is thought to reflect the differences between the states of
  performance of subjects is identified from the pattern of values of eigenvectors. Then
  principal component score of each subject in each task are calculated by the appropriate
  eigenvector, and means of principal component score are compared between each group
  of subjects at the different proficiency level.

6. Result and discussions
    Table 1 shows the eigenvector of PCA.

   Table 1: Eigenvector of PCA

    BL                  NR                 OP
    1st    2nd   3rd    1st   2nd   3rd    1st   2nd    3rd
rGM 0.589 -0.136 -0.483 0.421 0.603 -0.371 0.500 -0.461 -0.242
rUL  0.136 0.659 0.480 0.453 -0.497 -0.172 0.378 0.281 0.855
rUG     0.516 0.455 -0.336         0.501 -0.328 -0.420       0.497 0.267 -0.274
rPM     0.496 -0.084 0.570         0.411 -0.202 0.749        0.373 0.616 -0.343
sSR     0.351 -0.578 0.313         0.444 0.492 0.309         0.470 -0.507 0.133
    The parameters used in this study represent high states of performance when their
values are high. According to this Table, all values of eigenvectors of the first principal
component are positive and comparatively larger than other. As for other eigenvectors,
the values of some parameters are negative, and one or two specific parameters are too
small or too large comparing to other values of the same eigenvectors. Therefore, only
eigenvectors of the first principal component can represent the states of performance of

   Table 2: Means of principal component scores
             BL            NR        OP
    N          0.613         0.735     0.917
    H          0.085         0.158     0.108
    L         -0.669        -0.861    -0.980
    N-H        0.527         0.577     0.809
    N-L        1.281         1.596     1.897
    H-L        0.754         1.019     1.089

   Graph 6: Means of principal component scores



                  BL            NR          OP


    Principal component score of each speaker in each task is calculated based on the data
of eigenvector of the first principal component.
    N is the native speakers of Japanese, H is the learners at advanced level, and L is the
learners at intermediate level. N-H shows the differences between native speakers and the
learners at the advanced level and so on.
    Means of principal component scores of the first principal component of each group
of subjects (N, H, L) and the differences of means of principal component scores between
every two groups of subjects in three tasks are shown in the table.
    The means of principal component scores of each group of subjects in three tasks are
plotted in the graph.
    According to these results, native speakers' mean of principal component scores is
lowest in BL, and higher in NR, and highest in OP. That is in order of BL, NR, and OP.
However, intermediate learners’ means of principal component scores are reverse. It
declines in the order of BL, NR; OP. Advanced learners’ means of principal component
scores are almost unchanged.
     According to this graph, differences among three groups of speakers spread in order
BL, NR and OP. Therefore, according to the hypothesis, OP is the most difficult task, and
NR is the next, BL is the easiest.
    According to ACTFL’s OPI standard, OP is higher than or equal to NR, and BL is the
easiest. Broadly speaking, the grading in this study has the same result as ACTFL’s OPI.
This is the confirmation for the validity of the objective grading using PCA.
    In Principal Component Analysis, the values of eigenvectors reflect the variability of
parameters. For examples, In BL, the value of Semantic Variation (rUL) is obviously
smaller than other parameters. If speakers fail to explain what they would like to say, they
tend to try to repeat the same explanation in different ways. In this case, many of the same
words would be used again. Therefore, the variety of semantic words does not increase.
     Then if speakers have difficulties transmitting what they have in mind, Semantic
Variation (rUL) becomes lower. Because BL is not a difficult task, most subjects do not
seem to have difficulties in executing the task. Therefore, the variability of Semantic
Variation (rUL) in BL is small. In this way, it is possible to know the characteristics of a
task in an objective way.

7. Future study
    More precise study is possible according to the result of the statistical analysis.
Though the values of eigenvector can suggest the difference of the characters of tasks, the
precise analysis should be undertaken by other statistical method, such as multiple
comparisons etc.

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