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 intensive remediation programs, we need to analyze the strengths and weaknesses of each option. Let's break it down:

Plan a:
- Random assignment of students to three groups (A, B, and C) provides equal opportunity for each student to be in any group, minimizing bias.
- The intervention is implemented for a period of 6 weeks, which allows for an adequate duration to assess the effectiveness of the program.
- The counterbalancing of Group B and C switching programs helps control for any potential confounding variables or individual differences.
- Diagnostic exams and mathematics concept tests are conducted by the school psychologist at the beginning and end of the intervention phase, providing pre- and post-intervention data for comparison.

Plan b:
- This plan is similar to Plan a but extends the intervention phase to 12 weeks, providing more time for potential effects to be observed.
- The additional duration may lead to more conclusive results for the effectiveness of the programs.

Plan c:
- Random assignment of students to two groups (A and B) still provides equal opportunity for each student to be in any group.
- The intervention is implemented for a period of 12 weeks, allowing for a sufficient intervention duration.
- However, the absence of a control group (Group A) not receiving the new services makes it challenging to isolate the effects of the intervention.

Considering all these factors, the best choice would be Plan a (#1) since it includes random assignment, a control group, a counterbalancing design, and pre- and post-intervention assessments. Plan b (#2) could also be a viable option due to the extended intervention period, but it lacks the counterbalancing aspect of Plan a. Plan c (#3) is the least favorable choice since it lacks a control group, making it difficult to evaluate the true impact of the intervention.

Disclaimer: The choice of the best plan ultimately depends on various factors, including available resources, time constraints, and any other specific considerations relevant to the district's situation.