Instructional design is a part of curriculum development. When designing tasks for students that are tightly aligned to the Vision of the Graduate, NPS Competencies, and curriculum, instructional strategies are embedded. Some strategies:

Questioning: The three components of a math lesson also encourages teachers and students to engage in inquiry by developing and asking questions. Questioning strategies should encourage exploration and deeper thinking about mathematics and its connections to the world. Teachers can facilitate learning through carefully crafted questions that lead students to new learning and new understandings.

Facilitation: Teachers guide the learning by providing students with a framework for discourse. Naugatuck Public Schools embraces a model of mathematical discourse that promotes questioning, challenging one another’s thinking, attempting multiple strategies to solve a problem, developing action plans, and accountable talk. Through discourse, students can probe one another’s thinking, justify their own ideas and approaches to problem-solving, and model potential solutions.

Purposeful Design: Curriculum and its accompanying resources are tools for teachers to be purposeful in how they design and execute a lesson. Competencies are the “for what?” to learning. For example, when designing instruction around place value, it is not only understanding that each digit holds a particular value that is dependent on the place it occupies in the number (for example, in 261, the 6 is a representation of 60 because it occupies the tens place, and 261 is actually 200+60+1), but also that place value understanding is a tool to accurately and efficiently solve more complex problems.

Intentionality: Being intentional happens on many different planes: planning for the learning, planning for your role in the learning, and planning for differentiation.

• Planning for the learning: When planning what students will learn, it is also important to connect with how they will learn it and how will you know they learned it? By setting a goal for the learning through exploration of how standards referenced in enVisions 2.0 connect to Competencies and Performance Indicators, you will not only create a vision for what students need to master, but where it is situated in the overall math learning (i.e., place value is housed in Process Tools for Precision, therefore place value is a tool students use to make sense of numbers) and where it is situated in the Vision of the Graduate (i.e., when students use a tool like place value they are Informed Thinkers). When planning for the learning, ask not only what students will do, but what students will learn and understand as a result of doing.
• Planning for your role in the learning: A guiding question when planning for learning is, “What will I be doing?” Be intentional about your role in student learning and place students at the center of that learning. How will you guide the learning? How will you facilitate the learning? How will you empower students to take ownership of their learning? What structures and processes (i.e. discourse protocols, success criteria) will you create and/or implement to ensure that students are thinking deeply and making sense of mathematical concepts for themselves?
• Planning for Differentiation: Differentiating learning is more than just a few leveled activities. When you differentiate the learning, you offer students a variety of ways to experience the learning. Students benefit from multiple pathways to a single goal. How will you monitor the learning and perform checks for understanding? What tools can you use to ensure all students are meeting high expectations and learning at deep levels? Differentiation goes beyond what students will do; it captures how different experiences can deepen the learning in different ways for all students. According to Carol Tomlinson, differentiating instruction means accommodating the different ways in which students learn. It requires active planning for student differences so that all students achieve the same deep levels of learning.