An Effective Mathematics Program…
An effective mathematics program includes conceptual understanding, procedural fluency, problem solving, and its human dimensions. Students need to learn math in a logical, sequential manner1, and commensurate with their maturity and personal experiences. Continual connections should always be made between past mathematical understanding and new concepts; connections between concrete experiences, pictorial representations, symbols, and algorithms. Teacher clarity and content knowledge are essential. Immersing students in relevant mathematics language and vocabulary, dialogue, experiential learning, collaborative construction of meaning, independent practice and reflection are all components of a balanced math approach. Click on titles below for more detailed descriptions of important instructional approaches in mathematics:
Mathematician’s Workshop or Framework2
- This instructional framework guides teachers to provide opportunities for whole class, small group, partner, and individual learning. Students are more engaged, grow in their mathematical understanding and see themselves as mathematicians when they collaborate in their learning.
An effective mathematics program balances many pedagogical tools in response to student needs and relies on the professional judgment of the teacher. In a mathematics classroom, there is a balance between explicit instruction and discovery. While universal principles of high quality instruction apply to mathematical contexts, there are some principles that are unique to mathematics that are necessary to understand.
Differentiation through Responsive Pedagogy
In the Saskatchewan context, differentiation is addressed through the Adaptive Dimension which enables all teachers to respond to student diversity, including their strengths and needs, interests, backgrounds, life experiences and motivations. The Adaptive Dimension refers to the concept of making adjustments to any or all of the following variables: learning environment, instruction, assessment and resources. Adjustments to these variables are intended to make learning meaningful and appropriate and to support student achievement. Tomlinson (1999) states, “Differentiation is an organized yet flexible way of proactively adjusting teaching and learning to meet kids where they are and help them to achieve maximum growth as learners” (p.14).
“The first line of instruction is always the classroom. No series of interventions – even highly effective ones – can take the place of good classroom instruction that builds a rich base and creates a community of learners” (Fountas & Pinnell, 2009, p. 497)
- Intervention is a team approach that involves targeted data-driven actions to support learners who are not responding to the high quality, responsive instruction of the teacher. Differentiated instruction and intervention assume that not all students learn at the same pace and in the same way. Some students respond to a specific pedagogy more quickly and some students need a different approach to reach understanding.
1This is referring to the notion that additive thinking comes before multiplicative thinking, which precedes exponential thinking. This progression of thinking is reflected in the SK k-9 Math Curriculum.
2Adapted from Saskatoon Public Mathematician’s Workshop Framework, 2017
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