We conduct two randomized controlled trials (RCTs). Common features of the two are the didactics of mathematics promoted in the teacher trainings, and the time allocated for the remediation classes. Specifications of the target group, class size, the topics covered, and the level of additional financial resources differ. We review the common features and then the specifics of each RCT.
The teacher trainings aim to change teaching practice through promotion of a set of best practice didactic principles and strategies. The principles are in most cases not new to the teachers but by showing how they can be applied and focusing efforts, the practice is expected to change. Succinctly, teachers should:
- motivate the students for each lesson,
- structure communication to foster comprehension,
- explain the links between concepts, and
- set high but realistic expectations.
And apply the following strategies:
- Engage students with 'Low Threshold High Ceiling' tasks that allow the students to begin at their level while providing challenge for all students in the group;
- Use the 'Think, pair, share' method to stimulate both individual thinking and group learning;
- Use visualization tools such as 'thinking blocks'; and
- Use journals as a tool to reflect on what was learned.
The classes replace 20 hours of the regular mathematics classes in the first semester and 15 hours in the second semester; total instruction time is unchanged.
For treatment and control group schools alike at both levels, other initiatives to improve performance continue independently of the RCTs described here. Such other initiatives should be uncorrelated with the treatment assignment.
RCT 1: Grade 8, lower secondary school:
The lower secondary schools are randomized into one of three groups:
1. Wave 1 treatment group
2. Wave 2 treatment group
3. Control group
The target group is defined as students scoring at the two lowest levels on the Norwegian standardized test in numeracy. Students sit the test around a month before the remediation classes begin.
The topics covered in the remediation are numeracy, mental calculation, the four operations (addition, subtraction, division and multiplication) and fractions.
Wave 1 Treatment Group
Students receive one of two treatments depending on the number of target group students in the school. The threshold number for year 1 is 24, and for years 2 and 3, 18, such as:
- If the school has 24 (18) or fewer students in the target group, only treatment A is implemented.
- If more than 24 (18) students, treatment B is also introduced. In this case, the 16 (12) lowest-performing students receive treatment A, while additional students receive treatment B.
Treatment A is remediation in a group size of 4-8 students in year 1 (4-6 students in years 2 and 3); lessons should be structured according to plans designed to facilitate the change in teaching practice.
Treatment B is remediation in groups of 15-20 students. Teachers are not provided lessons plans.
The schools receive financial resources to cover the additional cost of providing remediation in smaller groups. For schools with Treatment A only, the schools receive sufficient funding to establish the relevant number of small groups. For example, a school with 1-8 (1-6) students receives funding to establish one small group, while a school with 17-24 (13-18) receives funding for three groups.
For schools implementing Treatment A and B, the schools receive funding for establishing the two groups for the lowest-performing 16 (12) students, and only very limited extra funding for Treatment B sized groups as these are only slightly smaller than the regular classes.
Wave 2 Treatment Group
The first year, these schools receive financial resources to implement remediation for up to 24 students in the target group, as if they were in wave 1. Remediation is provided in groups of 4-8 students, for the same period as the intervention in Wave 1 Schools. The teachers teaching these classes are not given additional training, schools are provided only financial resources sufficient to reduce the class size (similar to the schools in wave 1). Refer to this as Treatment C. This treatment arm allows us to separate the impact of financial resources from the didactic recommendations.
Years 2 and 3
The second and third year, these schools receive interventions according to the scheme for the Wave 1 Treatment Group in Years 2 and 3. Thus Treatment C is implemented only the one year.
The schools in the control group continue with the regular treatment, business-as-usual, the three years of the project.
RCT 2: Grade 11, upper secondary schools
The target group is Grade 11 students who
1. selects the academic track of the Norwegian upper secondary schools system;
2. selects the easiest of two math courses; and
3. scores at the lowest two levels on a standardized numeracy test administered around a month before the intervention starts.
There is one treatment: Teachers with training as described above teach the topics where weaker students usually have gaps and misconceptions. The remedial classes are taught in classes similar to the regular class size. The schools are free to organize the remediation as they please i.e. they choose whether to separate target and non-target group students or not. Financial resources are provided to cover the cost of sending teachers for training only.
The topics covered in the remediation are numeracy, strategies for performing mental calculations, the four operations (addition, subtraction, division and multiplication), fractions, percentages, decimal numbers and measurement.
The schools in the control group continue as usual the three years of the project.