In Part 1 of this series, I explored the importance of social-emotional learning in mathematics and how developing a positive mathematical identity can help students build confidence and perseverance. Once students begin to see themselves as capable mathematicians, we can further support their success by strengthening their foundational numeracy skills.
One of the most important aspects of foundational numeracy is helping students see numbers as flexible quantities that can be composed and decomposed in multiple ways. Developing this understanding allows students to think more efficiently, make connections between concepts, and approach problems with confidence.
From Kindergarten to approximately grade 3, we spend a lot of time focusing on the foundations of math. Creating opportunities for number talks/math talks and teaching a variety of strategies to help students solve problems quickly and build their number sense. Skills such as composing and decomposing numbers, calculating efficiently, and understanding place value are essential building blocks for future learning.
As students move into the Junior grades, the focus naturally shifts from developing foundational skills to applying mathematical thinking in more complex ways. Students arrive with a wide range of experiences and levels of understanding, and when foundational concepts are not yet secure, new learning can feel overwhelming or stressful. This presents an opportunity for educators to reflect on instructional design, consider how time is allocated for revisiting key concepts, and identify the strategies and supports that will help students develop confidence, fluency, and long-term success in mathematics.
In the primary grades, this often involves providing rich experiences with concrete manipulatives such as ten-frames, rekenreks, connecting cubes, and counters. These tools help students visualize quantities, recognize patterns, and develop a deeper understanding of how numbers are constructed and related to one another.
As students move into the junior grades, these foundational understandings continue to support increasingly sophisticated mathematical thinking. Regular opportunities to explore numbers in different ways help students develop flexibility and efficiency. For example, students can recognize that 12 can be represented as 10 + 2, 6 + 6, 8 + 4, or 5 + 5 + 2. This ability to break apart and recombine numbers strengthens mental math strategies and supports success with increasingly complex operations.
Place value remains one of the most important concepts in elementary mathematics. A strong understanding of place value provides students with a powerful tool for reasoning, estimating, calculating, and communicating mathematical thinking. It supports not only whole-number operations but also future learning involving decimals, fractions, and proportional reasoning.
One effective approach is encouraging students to represent numbers in expanded form when solving problems. Rather than relying solely on procedures, students can use place value reasoning to make their thinking visible.
For example, when solving 57 + 36, students might think of the problem as:
(50 + 30) + (7 + 6)
which can then be recomposed as:
80 + 13 = 93
Approaches such as these help students understand the value of each digit and the relationships between numbers. They encourage conceptual understanding while simultaneously supporting procedural fluency.
Foundational numeracy can be strengthened through a variety of instructional approaches. Number talks, math games, small-group instruction, problem-solving tasks, and targeted mini-lessons all provide opportunities for students to deepen their understanding of number relationships and develop efficient strategies. These experiences are most effective when they occur regularly and are embedded within daily mathematics instruction.
Professional judgment also plays an important role. There will be times when students benefit from additional opportunities to consolidate foundational concepts before moving forward to new learning. Providing this time ensures that students have the necessary understanding to access increasingly complex mathematical ideas with confidence.
When we prioritize foundational numeracy, we are setting students up for long-term success. Strong number sense helps students approach math with confidence, flexibility, and independence. When combined with a positive mathematical identity, these skills create a strong foundation for deeper learning and help students see themselves as capable mathematicians.
