Our mathematics instruction proceeds from the belief that all children are curious about mathematics, all children can take pleasure in solving mathematical problems, all children can learn to think and communicate mathematically, and all children can develop the skills and confidence to be successful users of mathematics for a lifetime. We take seriously the important foundation of early childhood and elementary school to develop these important skills, habits and attitudes. A detailed sequence of math skills and concepts is presented in our Mathematical Milestones, a document available from school.
In our mathematics curriculum we focus on five core areas of learning:
- Number Sense and Operations
- Geometry and Spatial Thinking
- Data and Probability
- Mathematical Habits and Practices
Children of all ages need concrete materials, real-world problems and emergent questions to work with before they can internalize symbols and abstraction. As children encounter concepts like number, time, measurement and shape in their early years, they begin to form mental constructs of how these work. Later, when they encounter facts others have discovered and organized they must integrate these new ideas into their previous constructions. The child’s ongoing process of making these necessary adjustments is called constructivism. The teacher’s role in this process is to ask provocative questions, design lessons to challenge assumptions and always be aware that risk-taking and wrong answers are essential steps on the way to concept formation. Although learning with breadth and depth might take longer than rote memorization, it creates genuine ownership of concepts which is the essential foundation for future learning.
At this level the main focus is the foundation of number sense: counting, one-to-one correspondence and the understanding of numerals to represent quantity. Children gain the ability to sort and count quantities of objects, to group numbers and objects into sets, and to understand and represent relationships in number, size, shape and quantity. Recognizing patterns and sorting by attributes are intrinsically satisfying ways for young children to see numbers as relationships among objects not isolated facts. The foundations of understanding addition, subtraction, equality, zero and bigger numbers are established as children work with concrete objects and problems in the real world. Teachers plan and facilitate rich experiences with many materials along with the social construction of mathematical knowledge – talking about and using numbers in play, blocks, puzzles, games, manipulatives, nature, and real-world situations, songs and finger plays. As children explore and play in the classroom and outdoor settings they gain experience with comparison, measurement, geometry, collecting and representing data. Math activities at circle time, picture books, and a daily calendar routine allow teachers to model and develop mathematical communication. The TERC Investigations curriculum, beginning in Kindergarten, serves as a foundational resource to build consistency of method, language and experience.
At this level children are busy constructing their understanding of the base-10 number system and operations (addition, subtraction, multiplication and division) through instructional times that are rich in games and hands-on experiences. Children have daily opportunities to reason outloud, experiment and develop accurate mathematical strategies. They become capable of using numerals and other symbolic representations such as graphs, equations and diagrams. The strong grasp of place value concepts with base-10 allow students to develop increasingly efficient strategies for adding, subtracting, multiplying and dividing. The construction of these conceptual mathematical ideas is embedded in physical activities within a social context, and students are encouraged to think outloud about their strategies and discoveries. Children benefit from ongoing opportunities to build with puzzles and blocks, sort, classify, measure, count and divide up materials for real-world problems. They also benefit from many opportunities to practice skills and master a fluent repertoire of math facts. Daily routines and daily exercises like skip-counting around the room and a calendar routine also build fluency and rote skills. The TERC Investigations curriculum is used as a foundational resource to build consistency of method, language and experience. Math-talks are guided discussions that build deeper understanding about computational strategies and facilitate the exploration of mathematical ideas and questions. During a math-talk, teachers model mathematical curiosity, communication and vocabulary. They also help students understand the value of mistakes or errors in promoting deeper understanding. These concrete activities along with rich immersion in mathematical language and materials lay a foundation and a bridge to the more systematic and abstract study of mathematics at the next level.
At this level whole number operations are mastered with an emphasis on their application to real-world problems and scenarios. Students learn and practice efficient and accurate strategies for multi-digit addition, subtraction, multiplication and division. The learning of fractions, decimals and percentages is integrated with data analysis and probability, and also developed through games, models and number lines. Students learn to apply formal terminology and standard units as they work on skills and concepts in two- and three-dimensional geometry and measurement. For the most part, the foundations of algebra are constructed through real-world problems where students generate formulas, work with variables and solve for unknowns. Students also develop a strong grasp of important properties of operations, such as the distributive, commutative and associative properties, as well as the order of operations. The use of mathematical tools, games and technology allow students to refine and extend their learning. Mathematical understanding is strengthened in the social context of learning, where students are challenged to communicate and participate as mathematicians. They must explain their thinking, use a variety of materials and models, express different ways to solve a problem, formulate conjectures and rules, describe patterns, agree and disagree with good reasoning, and evaluate their own mistakes and misconceptions. The TERC Investigations curriculum is used as a foundational resource to build consistency of method, language and experience. Emergent themes and projects sparked by student curiosity add to the emphasis on mathematics as a compelling form of inquiry and connection to the real world. Students are poised to be engaged, articulate and skilled mathematical thinkers when they make the transition to middle school.