InsightMath - Connecting the Standards for Mathematical Practice

The Standards for Mathematical Practice (SMPs) outline key mindsets for engaging with mathematics, as well as the types of learning opportunities that students need to encounter to internalize these practices. InsightMath has been intentionally designed to not only incorporate the SMPs into daily lessons, but to create meaningful connections within and across grade levels, ensuring students develop as confident, capable mathematicians throughout their elementary journey. 

We believe that students learn best by diving directly into problem solving and explaining their thinking, so that students utilize the mathematical practices from day 1. We believe that all students at all ages can fully enact all of the mathematical practices in meaningful ways, though students’ abilities to be metacognitive about the SMPs becomes more sophisticated as they grow older. 

Student Strengths: Developing Mathematical Practices Across the Grades

InsightMath translates the Standards for Mathematical Practice into student-friendly language through a coherent pathway of Student Strengths that build in complexity across the grades. The Student Strengths represent an overlapping set of practices that students explicitly focus on developing and improving at each grade level, while still using the full range of SMPs in their ongoing learning. 

Kindergarten students use five Student Strengths that establish the foundation of ongoing mathematical habits:

• I learn from my mistakes.
• I take time to think.
• I try my best.
• I talk about my ideas.
• I listen to other people's ideas.

By grade 2, students use a set of 10 Student Strengths that deepen conceptual understanding and reasoning: 

• “I try my best” evolves into "I keep trying, even when a problem is hard"
• “I talk about my ideas” becomes "I explain my thinking" and focuses on mathematical reasoning
• "I listen to other people's ideas" broadens to include responding to others’ ideas, developing skills for mathematical discourse
• Problem solving becomes a focus as students make a plan and identify tools, strategies, and models that are most useful for finding solutions and communicating their thinking

By grade 6 the complete set of 13 Student Strengths reach full sophistication:

• "I value mistakes" represents a mature understanding of learning.
• "I ask my classmates to clarify their reasoning" demonstrates advanced discourse skills.
• "I use math to represent real-life situations, and I create contexts to match the given math" shows bidirectional thinking.

This progression demonstrates how students' explicit focus on specific mathematical practices deepens and becomes more sophisticated across grade levels. While kindergarten students engage with all of the SMPs in their mathematical work, they explicitly focus on developing these five foundational strengths. In later grades, students can explicitly focus on and articulate a larger set of more sophisticated practices, while continuing to use all of the Standards for Mathematical Practice throughout their learning.

Weaving Practice Standards Together

The Student Strengths also create powerful connections between the SMPs themselves. Rather than treating each mathematical practice as isolated, the Student Strengths naturally integrate multiple standards within single practices. Even at the grade K level, "I talk about my ideas" focuses on SMP 3, construct viable arguments and critique the reasoning of others, and also includes SMP 6, attend to precision, for its focus on precise language and meanings. The second-grade strength “I make a plan to solve a problem and change my plan if I need to” connects SMP 1, make sense of problems and persevere in solving them, SMP 2, reason abstractly and quantitatively, and SMP 4, model with mathematics. In the upper grades, "I use math to represent real-life situations, and I create contexts to match the given math" features SMP 2, reason abstractly and quantitatively, and supports SMP 4, model with mathematics, and SMP 5, use appropriate tools strategically. This interconnected approach helps students understand that mathematical practices work together, creating a more cohesive and authentic mathematical experience while also making the practices accessible to students. 

Embedded Professional Learning

Each lesson in InsightMath embeds the Standards for Mathematical Practice by engaging students in authentic problem solving, modeling, and communicating thinking, with multiple opportunities to utilize tools and identify patterns. By providing students with rich mathematical tasks and the opportunity to take ownership of their learning, students engage with the SMPs just by bringing their interest to the lessons. 

To support teachers in recognizing how the SMPs are enacted through the lessons, each lesson and unit highlight how the SMPs are used as embedded professional learning. 

Lesson-Level Integration: Each lesson includes specific descriptions of how student work exemplifies each SMP, serving as professional learning for teachers and concrete examples of standards in action.

Unit-Level Synthesis: Every unit contains comprehensive descriptions of how each SMP appears throughout the unit's progression. Since students at every grade level use all SMPs in their mathematical work, these descriptions provide teachers support in recognizing these standards across different contexts.

The Goal Pages: Supporting Metacognition

The Goal Pages support students in actively thinking about and internalizing the Student Strengths. At the beginning of each unit, students select from among a few Student Strengths and choose one to focus on throughout that unit. In grades K-1, students choose a goal as a class, then midway through grade 2 they transition to choosing individual goals. At the beginning of the unit, students make a plan for achieving their goal, then check in on their progress at the middle and end of the unit, developing metacognitive skills for noticing their own thinking alongside their growth with the SMPs themselves.  

The Goal pages create multiple connection points:

• Within units: Students repeatedly engage with their chosen Student Strength across lessons, with three focused times to talk or write about their progress.
• Across units: The same Student Strengths appear multiple times throughout the year.
• Across grades: Student Strengths evolve in sophistication, building on previous understandings.
• Student ownership: Students choose their focus, as a class (grades K-2) or individually (grades 2+), creating personal investment while ensuring that they self-reflect on each of the goals over time. 

Celebrating Student Strengths

To keep the SMPs alive in the classroom and find opportunities to recognize students enacting them, the Celebrating Student Strengths tool supports teachers in noticing and rewarding these powerful habits of mind. 

Across InsightMath, the Standards for Mathematical Practice come to life through rich tasks and classroom discourse, Student Strengths and Goal Pages, and embedded professional learning about the practices. Together, the embedded mathematical practices develop students as creative, flexible, and thoughtful mathematicians and problem solvers.

Appendix: The Full Set of Student Strengths