Math Goals as Anchors: Efficiency and Organization

In your classroom, you may already be familiar with Adrienne Gear's writing goals and literacy anchors for reading and writing. Did you know that you can harness the power of math goals to anchor your mathematical conversations, investigations, and sharing? 

I was inspired to create these math goals to serve as valuable guides and focal points for both educators and children, fostering a common, kid friendly language to navigate the mathematical landscape. Relating to Adrienne Gear’s targeted and effective writing and reading goals, the math goals; efficient and organized, anchor math learning. These math goals have been thoughtfully crafted based on the influential work of Cathy Fosnot's Landscape of Learning and Pam Harris' use of models and strategies.

The Art of Introducing Math Goals:

Before formally introducing the overarching math goals; efficiency and organization, it's beneficial to weave them organically into your daily conversations. For example: “{NAME} I love how efficiently you put away your materials.” “That is a very interesting way to organize our loose parts.” Celebrate and highlight these words (efficiency and organization) frequently as the children engage in investigations. Praise their organizational skills and commend their efficiency, as mathematicians, as they share strategies and ideas. This initial exposure sets the stage for a deeper understanding and integration of these math goals into your classroom culture.

For the official launch, consider co-creating a math wall with the children, structured as a T-chart with the header, "Mathematicians are..." This visual representation helps solidify the concept of math goals and reinforces the shared language among the community of learners. The co-created T-Chart becomes your anchor throughout the year, as you co-create and add to it over time, alongside the children. As you seamlessly integrate the language of organized and efficient into your classroom, children are likely to tell you that mathematicians are…organized and efficient!

Navigating Non-Linearity:

It's crucial to emphasize that math goals are not intended to map out a linear trajectory of how children learn math. After all, math learning is not a linear journey! Instead, they provide children with anchor points within their vocabulary to describe, utilize, and generate ideas for problem-solving.

Efficiency:

Efficiency, in alignment with Cathy Fosnot and Pam Harris' strategies, plays a central role in establishing math goals. When exploring the Landscapes of Learning, children encounter various efficient strategies depending on the mathematical topic. For instance, when delving into multiplication, they may employ repeated addition, skip counting, partial products, doubling, or halving to solve problems. All of these strategies are valid and essential for their development. However, it's crucial to recognize that children will develop these strategies at different rates, times, and sequences.

By framing it as "Mathematicians are efficient," we empower children to tap into their unique, efficient methods for problem-solving, tailored to their individual understanding and development. It's essential to clarify that efficiency does not equate to speed. Instead, it signifies the flexibility to employ the most effective strategy for a problem, considering each child's place in their mathematical journey. Some may be transitioning from repeated addition to partial products, while others are solidifying their grasp of partial products. Math goals create a space where everyone can progress at their pace, identifying their specific next steps in learning.

Organization:

Organization, in line with Cathy Fosnot and Pam Harris' models, is another cornerstone of the math goals. Pam Harris delves into various model types in her podcast, enriching our understanding and language surrounding models and organization. Children's ability to comprehend and orally communicate mathematical concepts often surpasses their capacity to represent them visually. This discrepancy is entirely normal and not a cause for concern. Examples of models that might be used are number lines, arrays, etc.

As new models of thinking are introduced during problem strings, children are encouraged to employ them during problem-solving as tools for organizing their thoughts effectively. Additionally, it's valuable to convey to children that mathematicians organize their work not only for themselves but also for their peers. This ensures that others can understand their thought processes. Concepts such as color-coding, labeling, and using arrows are all excellent methods of organization and should be acknowledged. However, these practices do not directly align with the mathematical models discussed by Fosnot and Harris.

Recognizing this, our aim is to offer children both approaches to organization. Over time, in our classrooms we shift our focus from the latter organization methods (colour coding, arrows etc.) to the utilization of mathematical models. This transition supports children's ongoing mathematical development and deepens their understanding of mathematical concepts.

How might you use math goals, as anchors in your classroom? As we navigate the mathematical journey together, let's embrace the power of math goals as guides, fostering efficiency and organization, and empowering our young mathematicians to excel in their explorations.