Review of Journal Article : Oops, Scratch That! Monitoring One’s Own Errors During Mental Calculatons
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REVIEW OF JOURNAL PAPER
JOURNAL: COGNITION
ARTICLE: OOPS, SCRATCH THAT! MONITORING ONE’S OWN ERRORS DURING MENTAL CALCULATONS
ABSTRACT:
The Feeling of Error (F.O.E) is an experience differing from person to person stating that something has gone wrong during a reasoning or calculation task. The primary goal of the article was to assess the accuracy of F.O.E in the context of mental mathematical calculation. Number bisection task (N.B.T) was used to evoke this metacognitive feeling and it was assessed by asking participants if they felt that they committed a mistake.
In this task the participant were asked whether the number in the middle of a triplet corresponds to the arithmetic mean of the outer two numbers (e.g 07_16_25) with a yes or no answer. The result from the study showed that the F.O.Es were strongly correlated with arithmetic errors and properties of the triplets. This finding indicates that even very fast metacognitive feelings are reliable when it comes to evaluating one’s own mental performance.
The occurrence of F.O.E is determined also by the fluency with each triplet was solved and the post decision process after answering. In addition the participants were asked to report their confidence in their answer when there was no report of an F.O.E. This was to test whether there was a feeling of error on a sub-conscious level even when it wasn’t consciously reported.
AIM OF THE EXPERIMENT:
1. To prove metacognitive feeling of error is a reliable error signal during calculation. 2. The fluency and post decision evaluation processes jointly determine feelings of error 3. Implicit detection of error can occur even when no feeling of error is reported
METHODS ADOPTED FOR THE EXPERIMENT IN THE JOURNAL:
Thirty volunteers participated in the study. The volunteers did not include participants who were mathematically inclined like engineers, mathematicians or physicists for whom the NBT data would be too easy. To test for the FOE numbers were used from Nuerk and colleagues,cp. Nuerk et al., 2002.
200 triplets from the data set were chosen. The study also included the study of participants reaction time and the complexity of the triplets increased or decreased as a function of the participants’ reaction time.
The triplets used in the data set were of different level of difficulty. The triplets which were unbisectable i.e the arithmetic mean of the outer two numbers in the triplet is not an integer. Such triplets were considered to be more fluent while the ones having the middle number as the arithmetic mean of the outer numbers were considered not so fluent. By fluency the authors meant to state the difficulty of the triplet.
Moreover triplets were graded more difficult if the middle number was very close to the actual mean and easier if the middle number was away from the arithmetic mean. Experiment was conducted and the results were deduced.
METHODS USED BY ME TO CONDUCTED IN THE EXPERIMENT
Since the volunteers I used for the experiments were NYU graduates I decided to take a relatively tougher triplet set.Below is the procedure of my experiment 1. A set of 60 triplets were generated the range being from 0 to 100 2. 30 were correct, 30 incorrect 3. Out of the 60 triplets 30 were bisectible, 30 unbisectable 4. To simulate the range of level of difficulty as in the original experiment, the triplets where the center number was not the arithmetic mean, 10 of the 30 numbers had the middle number were at a distance of 1 from the mean, 10 were at a distance of 3-5 from the mean and the rest were at a distance 5-8 from the mean. 5. 3 volunteers were were given the excel sheet given below. A phone was used to time the participants response time. The phone beeped at regular intervals of 3 seconds, the first beep indicated the participant to solve the triplet and the following beep to report his F.O.E No A | No B | Show | Answer | F.O.E | Confidence | 13 | 61 | 42 | 1 | 1 | | 76 | 88 | 82 | 1 | 0 | 5 | 95 | 40 | 66 | 0 | 1 | 7 | 43 | 69 | 57 | 1 | 1 | | 95 | 10 | 51 | 0 | 1 | | 75 | 30 | 48 | 0 | 0 | 8 | 13 | 90 | 42 | 0 | 1 | | 44 | 2 | 23 | 1 | 0 | 10 | 5 | 28 | 16 | 0 | 0 | 9 | 28 | 40 | 28 | 0 | 0 | 7 | 27 | 36 | 31 | 0 | 0 | 8 | 92 | 30 | 61 | 0 | 0 | 5 | 39 | 92 | 57 | 0 | 1 | | 1 | 82 | 33 | 0 | 0 | 10 | 33 | 64 | 45 | 0 | 0 | 9 | 95 | 77 | 83 | 1 | 1 | | 23 | 35 | 19 | 1 | 0 | 6 | 7 | 63 | 35 | 1 | 0 | 10 | 86 | 90 | 81 | 0 | 0 | 10 | 47 | 70 | 57 | 1 | 0 | 6 | 16 | 48 | 32 | 1 | 0 | 8 | 19 | 54 | 35 | 0 | 1 | | 35 | 26 | 29 | 0 | 0 | 8 | 86 | 14 | 50 | 1 | 0 | 10 | 25 | 5 | 11 | 0 | 0 | 9 | 5 | 48 | 26 | 1 | 1 | | 43 | 44 | 35 | 0 | 0 | 10 | 74 | 20 | 41 | 0 | 0 | 8 | 30 | 64 | 37 | 1 | 1 | | 79 | 63 | 65 | 0 | 0 | 8 | 55 | 31 | 45 | 0 | 0 | 6 | 16 | 62 | 30 | 0 | 0 | 10 | 59 | 60 | 56 | 0 | 0 | 10 | 63 | 10 | 35 | 0 | 0 | 8 | 75 | 33 | 50 | 0 | 0 | 7 | 15 | 55 | 25 | 1 | 1 | | 95 | 54 | 70 | 0 | 0 | 6 | 29 | 12 | 12 | 0 | 0 | 10 | 93 | 62 | 77 | 1 | 0 | 6 | 29 | 6 | 9 | 0 | 0 | 8 | 45 | 64 | 54 | 1 | 0 | 5 | 85 | 36 | 57 | 0 | 0 | 9 | 25 | 47 | 32 | 0 | 1 | | 92 | 18 | 56 | 0 | 1 | | 50 | 56 | 45 | 0 | 0 | 8 | 27 | 66 | 46 | 0 | 0 | 8 | 18 | 54 | 36 | 0 | 1 | | 87 | 10 | 48 | 0 | 0 | 7 | 10 | 26 | 18 | 1 | 0 | 7 | 90 | 38 | 64 | 1 | 0 | 7 | 31 | 52 | 41 | 0 | 1 | 7 | 57 | 32 | 43 | 0 | 1 | 7 | 43 | 56 | 41 | 0 | 0 | 10 | 27 | 94 | 57 | 0 | 0 | 10 | 67 | 98 | 82 | 0 | 1 | 7 | 7 | 96 | 48 | 0 | 0 | 9 | 33 | 71 | 52 | 0 | 0 | 5 | 74 | 32 | 55 | 1 | 0 | 8 | 71 | 3 | 29 | 0 | 0 | 8 | 24 | 58 | 42 | 1 | 0 | 6 |
Table 1: Response table of one of the participants
The participants responded to the two given numbers. If they felt the Mean shown was the actual mean they responded with 1 otherwise with a 0. After their calculation they were asked to report F.O.E and confidence. If they felt they committed an error they were asked to mark 1 in the F.O.E column else state their level of confidence in the Confidence column.
6. The results were evaluated using excel, the correct response was either 0 or 1 for the trials. Following is the table of evaluation of one of the participant’s response.
7. Fluency here is the deviation of the shown number from the actual mean. If the deviation was 1 then the degree of difficulty or fluency was Difficult, if the deviation was in the range 2-5 , the degree of difficulty medium and lastly the degree of difficulty was Easy if the deviation was in the range 5-8
RESULTS:
The results obtained from the experiment were comparable to the results in the Journal. 1. The following line very generally shows the correlation between F.O.E and Error.
Fig: FOE and cumulative errors vs Number of trials
We see from the curves that as the number of F.O.Es increased, so did the number of errors. Though the graph isn’t conclusive about the correlation between errors and F.O.E s, we see that there is a similarity in trend. 2. On further analysis to the F.O.E response following deductions were made:
Fig: Chart showing correctness of F.O.Es
In case of bisectable triplets whose level of difficulty is higher as compared to the unbisectable triplets, Number of F.O.Es reported were more in case of bisectable triplets as compared to the unbisectable triplets. Moreover the correctness of F.O.E was found to be 86%, hence strengthening our hypothesis that F.O.Es correctly indicate error.
3. The figure below gives the detailed segmentation of the F.O.E analysis. Here we see that F.O.E omission occupies quite a considerable space in the analysis set.
Fig: Detail analysis of the F.O.Es reported
On further analysis of the instances where F.O.Es were not reported even when an error was made. The following results were found.
Fig: Confidence of Participants when F.O.E was omitted
From the above figure it is clear that the confidence level of participants on omission of an F.O.E is significantly lower as compared to when they answered the NBT correctly. Hence, although the participants did not explicitly report an F.O.E there is an intrinsic feeling of error
COMPARISON BETWEEN EXPERIMENTAL AND JOURNAL VALUES
Fig: Comparison between experimental and journal values.
The results obtained from the experiment are comparable to the journal values, hence we can conclude that the hypotheses of the journal article are true.
CONCLUSION:
1. From the experiments it is clear that F.O.E is a reliable measure of error. 2. In case of bisectable triplets number of F.O.Es reported were more from which we can deduce that fluency determines the feelings of error. 3. The post calculation analysis time elicited F.O.Es in participants proving decision evaluation determines the F.O.E 4. It is also evident from the Confidence curves that implicit detection of error can occur even when no feeling of error is reported.
