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I taught IT in an engineering school during three years in problem based learning (PBL) only. Now I teach maths to pupils between 10 and 15 years old who have a lot of educational difficulties.

I'm thinking to use PBL to increase their motivation and, by the way, increase their learning.

But, I have a question: is PBL adapted to pupils who have already know a lot of failures (in school and elsewhere)?

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PBL, especially if you have a lot of students that struggle with mathematics, is definitely something that you will have to design carefully; ordinary project based approaches can sometimes exacerbate already existing difficulties. At the same time, it is important not to lower the rigor or expectations for those who struggle, and so the standard recommendation that folks might offer of differentiated instruction, where you give instruction at different levels and with different emphases to different students, is probably ill-advised, particularly if you are hoping to have all students work together on projects.

Having reviewed the literature in this area, I think there is one study that really stands out as an example of what you would ideally be striving for. Bottge et. al (2007) demonstrated the effectiveness of a method called anchored instruction with students with learning disabilities. In anchored instruction, students are presented with a video case (or "anchor") that serves as a source of data for a project-based lesson. More basic mathematical skills are presented to the students in the context of the problem, on an as-needed basis, rather than being taught prior to engaging in the project.

You do mention that you worry about your students being on different levels and trying to keep them together working on the same material. You might consider using an instructional system known as Complex Instruction (Cohen and Lotan, 2014). In Complex Instruction, teachers carefully design both intellectually rigorous and accessible tasks for students to work on in groups and then carefully observe (and sometimes intervene) to make sure that all students are actively participating.

Bottge, B. A., Rueda, E., LaRoque, P. T., Serlin, R. C., & Kwon, J. (2007). Integrating Reform-Oriented Math Instruction in Special Education Settings. Learning Disabilities Research & Practice, 22(2), 96–109. https://doi.org/10.1111/j.1540-5826.2007.00234.x

Cohen, E. G., & Lotan, R. A. (2014). Designing Groupwork: Strategies for the Heterogeneous Classroom Third Edition. Teachers College Press.

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I cannot provide any research results supporting my claim, but intuitively, I'd assume that it can work out if the level of the exercises is low enough to provide success experience.

For example, I had a pupil aged about 15 who had really big problems in maths (and also other subjects because she attended a Montessori school), failed entry exams for a regular school and had to go to a private school in the end. I gave her exercises which were intended for primary school kids, that is, required no prior knowledge but at the same time required some thinking and trying around. I had the impression that they fitted her level quite well and increased her motivation. Also, they motivated the introduction of some mathematical tools (say, systems of linear equations) quite nicely.

But of course, if you are dealing with a group of pupils rather than a single one, it is nearly impossible to fit everybody's level so you might bore some and overwhelm others.

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