Mathematics

21st Century Curriculum Design in ACPS Content and Program Areas: Mathematics

Students in classroom We live in a time of extraordinary and accelerating change. New knowledge, tools, and ways of doing and communicating mathematics continue to emerge and evolve. The need to understand and be able to use mathematics in everyday life and in the workplace has never been greater and will continue to increase. In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures. Mathematical competence opens doors to productive futures.

21st century mathematics calls for a shift to focus on sense making, reasoning, and connections to real-world situations. Students will need knowledge and skills that prepare them to apply mathematics in a variety of contexts, including their future lives as responsible citizens. A transformation is required that results in a greater emphasis on the many ways that math helps us understand the world, and less on math for its own sake. There needs to be a focus on understanding and concepts, not just computation or procedures.

Looking ahead to the 21st century, developing and applying real-world situation will require new technology tools and new approaches to teaching and learning. It will also require new assessment methods and a commitment to teacher professional development that is collaborative with time allotted for vertical discussions and alignment across grade levels and high school courses.

Key Curriculum Design and Learning Principles for the ACPS Mathematics Curriculum:

  • To achieve the vision of reasoning and sense making as the focus of students' mathematical experiences, all components of the educational system — curriculum, instruction, and assessment — must work together and be designed to support students' achieving these concepts and skills.
  • Teachers will need long-term professional development and support, including opportunities for reflection on their practice and guidance in improving it.
  • Students will need the resources to prepare them for our rapidly changing world.
  • They will also need to recognize that studying mathematics in high school is important for their future careers.
  • A coherent and cohesive mathematics program requires a strong alignment of curriculum, instruction and assessment.
  • Another key goal is to refocus classroom practice so that algebraic thinking becomes a part of all students' daily experiences. Moving towards functional thinking involves attending to how things change and grow, looking for patterns, and how quantities vary in relation to one another.
  • A major commitment of the ACPS mathematics curriculum is toward a holistic and integrated approach to curriculum design, development, and implementation, combining the following essential design elements: (1) Pedagogy: ensuring that curriculum reflects and models research-based instructional design principles and practices; (2) Content: emphasizing recurrent big ideas and essential questions that unify students' experience of mathematics, stressing a balanced and performance-based approach to common assessments of student progress, and reinforcing clear vertical and spiraling articulation of core standards; and (3) Relationships: promoting positive student-teacher, student-student, and student-content relationships, including responsiveness to the unique strengths and needs of individual learners — including students' need to see the authenticity and purpose of what they are learning.

Exemplary ACPS Mathematics Programs Reflecting These Principles:

PEDAGOGY:

  • K-8 Professional Development: Developing Mathematical Ideas: Offer Developing Mathematical Ideas professional development. This four-course sequence consists of 1) Building a System of Tens, 2) Making Meaning of Operations, 3) Reasoning Algebraically About Operations, and 4) Patterns, Functions, and Change.
  • Students in classroom Math Specialists: Move towards having math specialists, teachers with strong math content knowledge, teach upper elementary mathematics. This departmental model will be supported by on-going professional development for these teachers.
  • K-8 Math Coaches: Improve teacher practice and student learning through the math coach program. As change agents, the school based math coaches help teachers improve math instruction through a job embedded staff development model which focuses on in-depth learning experiences which are on-going, reflective, and close to classroom practice.
  • ELL and Special Education Best Practices: Offer training on how to incorporate English Language Learners and Special Education best practices (e.g. developing schema, teaching key vocabulary) with mathematics content and pedagogy. These will also be integrated into all math professional development sessions.
  • Accessible Mathematics at the Middle School Level: Offer embedded professional development on how to make mathematics accessible to all. The sessions will engage teachers in reflecting on their instructional practices and making key shifts in instructional strategies to help students have a deeper understanding of the mathematics.

CONTENT:

  • Vertical Articulation with a Focus on Algebra: ACPS is currently developing a continuum of algebra curriculum offerings from K to Algebra I by the Math Curriculum Committee. The goal is to refocus classroom practice so that algebraic thinking becomes a part of the student's daily experiences. Moving towards functional thinking involves attending to how things change and grow, looking for patterns, and how quantities vary in relation to one another. The tools of algebra — tables, graphs, function machines, input/output charts — will be integrated throughout the curriculum.
  • A Focus upon Unit Design: Units will emphasize the "big ideas" of mathematics across grade levels. These will be used as the basis for developing unit designs for K through Algebra I.
  • Focus on Misconceptions: Curriculum and related professional development will engage teachers in conversations about the key misconceptions at different grade levels. The Ramp-Up to Pre-Algebra program is a model for this process.
  • Essentials Concepts and Skills: All curriculum will identify the essential concepts and skills that students need to know and be able to do when entering a grade level or course. The Math Curriculum Committee is currently developing this resource.
  • Shared Assessments: Moving beyond standardized testing as an exclusive focus, this shared and balanced approach to assessment will include developing common summative assessments (based upon performance tasks); creating resources for daily formative assessments to provide students with on-the-spot feedback; common rubrics and related scoring guides; and professional development in key aspects of effective assessment design and implementation.
  • Individual Assessment Plans in Mathematics: These plans are designed to identify student strengths and areas of need in mathematics with clearly articulated interventions to ensure student success.

RELATIONSHIPS:

  • Grade Level Meetings for K-5: Grade level meetings throughout the school year will offer opportunities for staff collaboration, discussion of math concepts and sharing of effective instructional strategies.
  • Transition Meetings between 5th and 6th Grade Teachers: The district will coordinate teams of 5th and 6th grade teachers who will focus on vertical articulation. They will participate in Singapore Math Bar Method for Problem Solving professional development. The teachers will visit each others' classrooms and collaborate on developing strategies to support student learning. Follow up sessions will focus on: (1) How can 5th grade teachers prepare students for the transition to 6th? (2) How can 6th grade teachers support the mathematical strategies developed in 5th?
  • Develop Coaching Cultures in Schools: ACPS is committed to developing a coaching culture in schools. Through the facilitation of Lucy West, author of Content Focused Coaching, coaches and principals continue to build leadership capacity in their schools. This culture is a learning culture. Teachers and leaders are constantly learning more about teaching practice, expanding their capacity, getting better at what they do.
  • Data Teams: Teams of teachers will investigate data through a collaborative inquiry process that influences the culture of the school to be one in which data are used continuously, collaboratively, and effectively to improve teaching and learning.