Recommend review of the work of Jo Boaler (Inspiring Students to Math Success and a Growth Mindset) and, to a lesser extent, Keith Devlin (profkeithdevlin).
Project-based math encourages students to discuss ideas about math and numbers. (The discussion part is very important, as it encourages students to think about different approaches to problems, and to explore how ideas can work or not). By focusing on projects, it allows students to get away from the idea that math is a set of rules and formulas to be learned.
The key takeaway is that math is something to be discussed and explored, rather than a fixed set of ideas to be transmitted from teacher to student.
Here is an article from Jo Boaler’s website:
How Students Should be Taught Mathematics:
Reflections from Research and Practice
Jo Boaler, Professor of Mathematics Education, Stanford University
Mathematics classrooms should be places where students:
Develop an inquiry relationship with mathematics, approaching math with curiosity, courage, confidence & intuition.
Talk to each other and the teachers about ideas – Why did I choose this method? Does it work with other cases? How is the method similar or different to methods other people used?
Work on mathematics tasks that can be solved in different ways and/or with different solutions.
Work on mathematics tasks with a low entry point but a very high ceiling – so that students are constantly challenged and working at the highest and most appropriate level for them.
Work on mathematics tasks that are complex, involve more than one method or area of mathematics, and that often, but not always, represent real world problems and applications.
Are given growth mindset messages at all times, through the ways they are grouped together, the tasks they work on, the messages they hear, and the assessment and grading.
Are assessed formatively – to inform learning – not summatively to give a rank with their peers. Students should regularly receive diagnostic feedback on their work, instead of grades or scores. Summative assessments are best used at the end of courses.
Mathematics classrooms should be places where students believe:
Everyone can do well in math.
Mathematics problems can be solved with many different insights and methods.
Mistakes are valuable, they encourage brain growth and learning.
Mathematics will help them in their lives, not because they will see the same types of problems in the real world but because they are learning to think quantitatively and abstractly and developing in inquiry relationship with math.