"An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically."
~ Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014)
Each new school year brings excitement and anticipation for students and teachers. As family members and friends prepare for a new school year I find myself doing a fair amount of writing and thinking about Math Recovery® research set within the greater body of mathematics education research. In particular, I have been investigating the variety of ways Add+VantageMR® can come to life within the classroom and can impact the math experience for children. This work continually draws me into the core theory and principles of Math Recovery®. The Math Recovery® Guiding Principles for Classroom Teaching help identify Add+VantageMR® happening in the classroom. The Guiding Principles offer a road map for teachers on how connect classroom instruction and student learning.
The quote above comes from Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014). The authors describe conditions, structures, and policies that must exist for all students to learn mathematics. The first of six essential elements is teaching and learning. Math Recovery® is all about teaching and learning mathematics!
The National Research Council (2001) defines learning of mathematics to include the following five interrelated strands 1) Conceptual Understanding 2) Procedural Fluency 3) Strategic Competence 4) Adaptive Reasoning 5) Productive Disposition.
A focus on the Guiding Principles creates an environment for this learning to happen. Understanding of children's thinking provides teachers with the knowledge necessary to be intentional in the mathematics classroom. An environment focused on conceptual understanding begins with comprehensive initial assessment and then uses that data for intentional instructional design. Teachers draw upon a bank of teaching procedures. Exemplary Math Recovery® settings and tasks provide the vehicle for engendering more sophisticated strategies building upon children's intuitive, verbally based strategies as well as linking to formal symbolic mathematics and leading to procedural fluency. Students are given sufficient time to persevere and solve problems. Ongoing assessment on behalf of the teacher places the momentum in motion to continue this teaching and learning cycle throughout the school year. Math Recovery® Guiding Principles become the culture of the classroom. As a result, children gain strategic competence, adaptive reasoning and a productive disposition for mathematics.
May the fresh start of a new school year bring about opportunities to share and reflect with colleagues the many ways Math Recovery® Guiding Principles are happening in your instructional setting.
Math Recovery® Guiding Principles
Guiding Principle 1
The teaching approach is inquiry based, that is problem based. Children routinely are engaged in thinking hard to solve numerical problems which for them, are quite challenging.
Guiding Principle 2
Teaching is informed by an initial, comprehensive assessment and ongoing assessment through teaching. The latter refers to the teacher's informed understanding of children's current knowledge and problem-solving strategies, and continual revision of this understanding.
Guiding Principle 3
Teaching is focused just beyond the 'cutting-edge' of the child's current knowledge.
Guiding Principle 4
Teachers exercise their professional judgment in selecting from a bank of teaching procedures each of which involves particular instructional settings and tasks, and varying this selection on the basis on ongoing observations.
Guiding Principle 5
The teacher understands children's numerical strategies and deliberately engenders the development of more sophisticated strategies.
Guiding Principle 6
Teaching involves intensive, ongoing observation by the teacher and continual micro-adjusting or fine-tuning of teaching on the basis of her or his observation.
Guiding Principle 7
Teaching supports and builds on the child's intuitive, verbally based strategies and these are used as a basis for the development of written forms of arithmetic which accord with the child's verbally based strategies.
Guiding Principle 8
The teacher provides the child with sufficient time to solve a given problem. Consequently this child is frequently engaged in episodes, which involve sustained thinking, reflection on her or his thinking and reflecting on the results of her or his thinking.
Guiding Principle 9
Children gain intrinsic satisfaction from their problem-solving, from their realization that they are making progress, and from the verification methods they develop.