Ingresos provenientes del resto del mundo (sub matrices C6, F1, F2 y F3)

Once again, it was our intention to achieve ecological validity, namely, to simulate conditions that are feasible in actual implementation in a classroom given the time constraints of teachers and students. As in the first part of the study in the previous section, we performed the same

Table 3.19. Rubric scoring for self-diagnosis study for quiz 7.

The student featured in figures 3.9 and 3.10 is graded to serve as an example for quiz 7. Please see table 3.3 for an explanation on notation. General Task Specific Criteria RDS SDS RSD PHYSICS PRINCIPLES (Ph.) Invoking physical principles

Ideal knowledge incorrect ideas

1. Conservation of mechanical energy (student correct)

calculation of energy/energies without energy

conservation + x n/a

2. Momentum

conservation calculation of momentum without momentum conservation - x -

Incorrect ideas

3. inappropriate principle: “-” marked if inappropriate principle is

used in student’s solution or diagnosis n/a x n/a

Ideal knowledge incorrect ideas

defining appropriately and consistently the system

defining inappropriately and inconsistently the

system + x n/a

Applying physical principles

1. conservation of

mechanical energy The initial speed is incorrect, or not completing calculation - - + 2. Momentum

conservation The speed of skate board before collision is not zero n/a n/a n/a

(etc.)

ALGEBRA (Alg.)

Algebra Algebraic manipulation - - +

PRESENTATION (Pre.) Description (Des.): 1. Invokes a visual representation

masses & velocities before and after collision, velocities and heights or potential and kinetic energies before and after climbing

+, +/- +,+ +,+/- 2. Clear/appropriate knowns (here: all knowns are listed) + + +

Plan/Solutio n Constructio n (Plan): representing the problem as a set of sub- problems

1. Appropriate target quantity chosen (here the student does not finish

work, not fixed in diagnosis) - x -

2. did not write down surplus equations or intermediate variables n/a n/a n/a 3. appropriate intermediate variables explicitly stated (here student

does not find v) - x -

4. explicitly stating in words or a generic form the principles used to

solve for this intermediate variables ( not done by student) _{- - +}

Evaluation (Che.)

1. writing down the units (student sometimes did so) +/- x +/-

2. checking the answer - - +

Table 3.20. Sample scoring of the student analyzed in Table 3.19.

Category Grading

RDS Ph: 0.40; Pre: 0.36

SDS Ph: 0.80; Pre: 0.72

procedures in actual classrooms and accepted the modifications introduced by the instructor who participated in the experiment.

As before, the study involved the same introductory algebra based course for students interested in health professions (N~200), the same instructor and the same two teaching assistants teaching their respective groups (one TA taught groups A and B, and the other taught groups C and D). Including both TAs, the recitations were distributed into control groups and three self-diagnosis treatments groups each of which carried out the self-diagnosis task with different scaffolds. In all treatment group recitations, students first solved a quiz problem, and in the next recitation session they were asked to circle mistakes in their photocopied solutions and explain what they did wrong (see table 3.21 and compare to table 3.1). Group B is split into two subgroups, B and B’, that are defined by recitation sections and which received an instructor outline and diagnosis rubric. We report numbers for these groups separately.

The treatments for each group were the same as in the first study. Groups A and A’, which are two separate recitations that combined are group A from the companion study, again form the control group and received no intervention. In addition to group B in the first study, another group (group B’) received an outline of the problem and the diagnosis rubric demonstrated in figure 3.3. Group C, as in the first study, received a complete written expert solution, and group D was asked to self-diagnose with their text and notebooks.

Table 3.21. Distribution of groups in quiz 7 by self-diagnosis tasks.

Control Self-diagnosis tasks

Groups A and A’ Groups B and B’ Group C Group D

control Instructor outline,

diagnosis rubric Worked out example Minimal guidance: notes + text books ~100 students 3 sections 2 groups: (B)- 31 students, (B')-29 students 1 group (C),

Table 3.22. Physics quiz scores for self-diagnosis groups on quiz 7.

Quiz 7 _Control Intervention B+B' _{Outline + Rubric Sample solution} Intervention C _{Minimal guidance}Intervention D

Group A A' B B' C D

Solution - physics _{Std. Dev.} Mean 0.47 0.53 0.45 0.50 _{0.18 0.25 0.15 0.21} 0.40 _0.22 0.50 _0.18 Solution -

presentation

Mean 0.40 0.40 0.49 0.43 0.36 0.38

Std. Dev 0.12 0.1 0.12 0.13 0.07 0.13

Table 3.22 shows students’ scores on the quiz for both physics and presentation. Interestingly, despite the hypothesis that this problem would be a relatively easy quiz problem, students still struggled on the quiz problem, which involves two fundamental physics principles. One common tendency was to fail to invoke the momentum conservation principle altogether and implement mechanical energy conservation assuming that the friend’s running velocity was the same as the velocity of the friend on the skateboard. The relatively poor performance on the quiz across all groups was not only true for the “physics” part but also for the “presentation” part where students were given scores on their problem-solving strategy. The difficulty with this quiz problem suggests that even substituting a difficult concept such as Newton’s 2nd Law in a non-equilibrium application involving centripetal acceleration with a one-dimensional conservation of linear momentum does not make the quiz problem significantly easier for the students, since students tend to focus only on one part in a two part problem.