The Title I coordinator for the district has been tasked with developing a plan to test two new intensive remediation programs for students with dyscalculia (like dyslexia, only numbers are the problem, rather than words!). The students are 60 8th graders at a magnet school for kids with their particular learning disability. Order the plans below, #1 being the best choice, and #3 being the worst.

a) She randomly assigns the children to three groups by drawing names from a hat; the first name goes in group A, the second in group B, the third in group C, and so on. Group A receives no new services, but continues with their current curriculum. For six weeks, Group B continues with their current curriculum and is pulled out of class during reading for the alternative 30 minute intervention. For 6 weeks, Group C follows the same procedure--they are pulled out during reading for a 30 minute intervention. Then, Group B and C switch programs for the next 6 weeks, to counterbalance. At the beginning and end of the intervention phase, all of the children are given a diagnostic exam and mathematics concept test by the school psychologist.

b) She randomly assigns the children to three groups by drawing names from a hat; the first name goes in group A, the second in group B, the third in group C, and so on. Group A receives no new services, but continues with their current curriculum. For 12 weeks, Group B continues with their current curriculum and is pulled out of class during reading for the alternative 30 minute intervention. Group C follows the same procedure--they are pulled out during reading for a 30 minute intervention. At the beginning and end of the 12-week intervention phase, all of the children are given a diagnostic exam and mathematics concept test by the school psychologist.

c) She randomly assigns the children to two groups by drawing names from a hat; the first name goes in group A, the second in group B, and so on. For 12 weeks, Group A continues with their current curriculum and is pulled out of class during reading for a 30 minute intervention. Group B follows the same procedure--they are pulled out duriAg reading for the alternative 30 minute intervention. At the beginning and end of the 12 weeks, all the children are given a diagnostic exam and mathematics concept test by the school psychologist.

To determine the best plan for testing the new intensive remediation programs for students with dyscalculia, let's evaluate each option:

a) In this plan, the students are randomly assigned to three groups, and each group receives a different intervention. Group A receives no new services, Group B receives one intervention, and Group C receives the other intervention. After six weeks, Group B and Group C switch interventions. At the beginning and end of the intervention phase, all students are given diagnostic exams and mathematics concept tests.

b) This plan is similar to option (a), but the duration of the intervention phase is extended to 12 weeks for Group B and Group C. Like before, Group A receives no new services and serves as the control group. Diagnostic exams and mathematics concept tests are administered at the beginning and end of the 12-week intervention phase.

c) In this plan, the students are randomly assigned to two groups, and each group receives a different intervention. Group A receives one intervention, and Group B receives the other intervention. Both groups undergo the intervention for 12 weeks, with diagnostic exams and mathematics concept tests administered at the beginning and end of this period.

Now, let's rank the options from best (#1) to worst (#3):

1) Option (b) is the best choice because it allows for a longer intervention phase of 12 weeks, providing more time for the programs to potentially show their effectiveness. Using a random assignment of students to groups, and assessing them with diagnostic exams and concept tests at the beginning and end of this phase, ensures a fair evaluation.

2) Option (c) is the second-best choice because it also includes a 12-week intervention phase. However, it only involves two groups, so there might be potential confounding factors impacting the results. The random assignment of students helps mitigate this issue to some extent.

3) Option (a) is the least favorable choice. While it includes a six-week intervention phase, its design of switching interventions midway can create a confounding variable. Moreover, the lack of a 12-week duration for any intervention phase might limit the effectiveness of the programs. Random assignment and assessment with diagnostic exams and concept tests are positive aspects, though.

In conclusion, based on the information provided, the best plan for testing the new intensive remediation programs for students with dyscalculia is option (b), followed by option (c), and then option (a).