I'm looking for studies on how and to what degree a teacher's conception of what mathematics is influences their way of teaching and, in the case of students, how this conception influences their learning.
here are some free thoughts:
A mathematics teacher's conception of what mathematics is can profoundly influence their teaching approach, strategies, and interactions with students. Here's how:
Perception of Mathematics as a Set of Rules vs. A Conceptual Framework:
If a teacher sees mathematics primarily as a set of rules and procedures to be memorized, they might focus more on rote memorization and practice of algorithms. This could lead to a more procedural-based teaching approach. In contrast, if they see mathematics as a conceptual framework, they might emphasize understanding underlying concepts, problem-solving, and making connections between different areas of mathematics. Fixed vs. Growth Mindset:
A teacher who believes that mathematical ability is innate might not invest as much time in students who they perceive as "not math people." They might also not encourage a culture of making mistakes and learning from them. Conversely, a teacher with a growth mindset might believe that every student can develop mathematical skills with the right support. Such teachers would emphasize the importance of effort, resilience, and learning from mistakes. Mathematics as Static vs. Dynamic:
Viewing mathematics as a fixed, unchanging subject might lead to teaching from the same textbook year after year without adapting to new educational research or integrating real-world applications. Seeing mathematics as a dynamic and evolving field would encourage a teacher to integrate current events, technology, and interdisciplinary connections, making the subject more relevant and engaging for students. Relevance of Mathematics:
If a teacher believes that mathematics is only important for passing exams, they might not draw connections to real-world applications or other disciplines. On the other hand, if they believe that mathematics is a tool for understanding and interacting with the world, they might consistently integrate real-world problems, interdisciplinary projects, and discussions about the broader importance of mathematical ideas. Student Engagement:
A teacher who sees mathematics as a series of abstract, disconnected topics might struggle to engage students or might rely heavily on extrinsic motivators like grades. Conversely, a teacher who views mathematics as an interconnected web of ideas, relevant to everyday life, might utilize project-based learning, discussions, and exploratory tasks to foster intrinsic motivation and curiosity. Role of Technology:
A teacher's view on the place of technology in mathematics can influence whether they integrate tools like graphing calculators, computer algebra systems, or dynamic geometry software into lessons. Attitudes Toward Collaboration:
If a teacher believes that mathematics is a solitary endeavor, they might prioritize individual work and discourage group projects or discussions. A more collaborative conception of mathematics would lead to more group work, peer teaching, and cooperative problem-solving.
but instead of wishful thinking I am looking for more serious studies and references AND SOLID STATEMENTS