Key 1: Ambitious Instruction
Ambitious instruction deliberately creates an environment in which all students, regardless of ethnicity, race, socio-economic status, and gender, develop a deep and profound understanding of the content and are confident problem-posers and problem-solvers.
Our vision is informed by the work of Abraham Maslow and his hierarchy of needs. Using his hierarchy as a model, we have created a mathematics hierarchy that guides our work in Merced County and acts as a roadmap for achieving our vision of creating empowered and confident problem-posing and problem-solving students. The ambitious, high-quality mathematics system necessary for achieving our vision occurs when students experience each of the layers in the hierarchy (Newman, Smith, Allensworth, and Bryk, 2001). Instructional improvement at scale is only possible in practice when district leaders deliberately coordinate each layer of the math hierarchy so that they constitute a system in the true sense of the term (Cobb & Jackson, 2011).
In the same way that Maslow’s Hierarchy of Needs is a roadmap for how a person might experience the joy of experiencing self-actualization, with needs lower down in the hierarchy being satisfied before individuals can attend to needs higher up, the Math Hierarchy of Needs is a roadmap for how teachers and leaders might guide students towards becoming mathematically literate humans.
Each layer consists of a plethora of things a district can choose to focus on with respect to their goals, personnel, resources, and strengths. Lower layers are not intended to be prerequisites before beginning work higher up the pyramid, but the layers in their entirety do tell a coherent story of an ambitious mathematics system.
Ambitious, high-quality instruction is achieved when students experience each of the layers in the hierarchy.
Every student has a teacher with appropriate mathematics content knowledge and the knowledge for teaching mathematics. Math lessons are rooted in a solid understanding of grade-level standards through rigorous, high-quality curriculum and meaningful tools.
Mindset and Culture:
Every student is immersed in a mindset and culture that intentionally communicates all students can learn math at high levels while being responsive culturally and personally in a learning environment that considers each and every student’s unique background, experiences, cultural perspectives, traditions, and knowledge. Mistakes in mathematics are normalized. Students regularly experience high-quality, grade-appropriate lessons and assignments.
Every student regularly experiences instruction that is student-centered and is designed to maximize students’ use of language. Lessons create space for students to participate in discourse to promote conceptual understanding, which then leads to procedural fluency, problem-solving, and application.
Every student is regularly and humanely assessed in order to have understanding of their own growth and to receive productive feedback for next steps in learning. Students use the feedback to know where they are in their learning, assess any misconceptions that need to be addressed, and then use the results to drive the next level of learning.
Every student becomes a confident problem poser and problem solver.
Let’s take a look at the mathematics hierarchy of needs and some practical examples for each layer of the pyramid. When trying to create an ambitious mathematics program for a school site or an entire district, each of the four layers must be fully addressed for students to become confident problem-posers and problem-solvers. In other words, students who are mathematically literate. It is recommended that a site/district choose one item from one or two layers to focus upon each year.
Here is a slide deck we used at a conference that explains our hierarchy and how we use it...