Guiding Principles

The focus of Mathworks curriculum project is to engage all students in doing mathematics at a high level, and to ensure that the needs of all students are addressed. The Mathworks curriculum project has been established on a foundation of research-based guiding principles that are critical for successful implementation. The bibliography provides connections to the underlying research. Research has shown that student success depends on an integrated approach that supports student learning in each of these domains.

  1. Doing mathematics is about making sense of and thinking deeply about fundamental concepts. Students should learn to “think deeply of simple things,” (Arnold Ross). Students need to:
    1. Build on prior knowledge by making connections that follow the flow of ideas from what they previously understood to new ideas being studied
    2. Promote a deep understanding for why things work using visual models
    3. Focus on the math problems, not the answers
    4. Reflect on what they have learned to make sense of the mathematics
  1. Persistence is critical to success in problem solving and doing mathematics. Students need to:
    1. Develop a “growth mindset,” understand and believe that ability can be developed with hard work
    2. Be willing to take risks and understand that mistakes present opportunities for learning
    3. Take ownership of their own learning
    4. Develop confidence to tackle new situations without giving up easily
  1. Teachers need to establish a classroom culture that develops students’ curiosity and imagination. The keys to establishing this culture are to:
    1. Make math interesting, fun and relevant with challenging, well-sequenced problems
    2. Support student’s productive struggle by responding to student questions with appropriate guidance
    3. Allow sufficient time for learning ideas deeply
    4. Use techniques to engage all students
    5. Balance individual and group work; both can be appropriate depending on the task
  1. Communication between students and teachers is critical for learning. To facilitate this, teachers should:
    1. Ask probing questions to develop student understanding, and encourage students to question why things work
    2. Expect students to present their work and defend their reasoning using precise mathematical language
    3. Take student attempts seriously, and examine both right and wrong approaches
    4. Expect students to articulate and explain the key math concepts