Standards in mathematics are designed with a clear purpose: to build on prior knowledge and gradually introduce more complex skills. This progression of skills ensures that students develop a deep understanding of mathematical concepts, enabling them to make connections and apply their knowledge effectively in new situations. Whether designing lessons or creating practice tasks, recognizing and utilizing learning progressions is crucial to fostering a strong foundation in mathematics for young learners.
Mathematical skills build on each other, which is why it’s essential to design lessons and practice tasks that reflect this gradual progression. Take, for example, the concept of addition across the K-5 years. In early grades, students start with simple single-digit addition, acting out scenarios or using objects or drawings, then progressing to mental math strategies as they advance. As they move into multi-digit addition, they recognize and apply their place value understandings to model (hands-on, drawings…) and explore the addition process, then build algorithms to show their addition. In later grades, they apply their addition skills to more complex concepts, like adding fractions or decimals or using multiple operations to solve problems. Students who are exposed to the progression of skills, have confidence when encountering each more-advanced task, because they have the foundational understanding needed to tackle these challenges.
Even within a single school year, math skills follow a progression. Instead of offering a single practice task for a skill (e.g., a worksheet filled with two-digit addition problems), students benefit greatly from tiered practice tasks that build upon each other to strengthen students’ skills with two-digit addition. Tiered tasks might begin with concrete experiences, such as using manipulatives like base-ten blocks to physically show the addition and find the sum. This hands-on exploration allows students to develop a solid understanding of what the numbers and operations mean, rather than just memorizing procedures. After these concrete explorations, students might explore addition using drawings or number lines and discussing the insights gleaned from the models. Finally, they move toward performing the two-digit calculations with abstract number representations and student-created algorithms.
One of the most effective ways to facilitate learning through progressions is by utilizing math centers in the classroom. Math centers provide students with opportunities to explore and investigate concepts with their peers in a hands-on, interactive environment. Working with manipulatives and real-world materials encourages exploration, creativity, and deeper learning. As students work together, they can discuss strategies, share insights, and learn from each other. These collaborative, hands-on experiences are particularly beneficial in helping students see mathematical connections and build deep understanding, particularly when the centers are built on learning progressions.
Through carefully-crafted tiered math centers, teachers create an environment where students not only learn math skills but also understand the underlying concepts. As a result, students develop a solid mathematical foundation that allows them to confidently tackle more advanced topics next week, next month, or in the years to come. Ultimately, paying attention to progressions, and offering opportunities for meaningful practice, ensures that all students are prepared for the challenges that lie ahead in their mathematical journey.
To explore some centers that are built on learning progressions, check out Navigating Numeracy Learning Progression Centers for grades K-5. To find out more about how these centers can lead to deep understanding of your priority number standards, visit http://www.hand2mind.com/navigating-numeracy
