Set Goals That Shape Lessons, Spark Thinking, and Build Understanding
- Shannon Olson
- 3 days ago
- 9 min read
If you think establishing mathematics learning goals just means writing an objective on the board, think again. Real math goals go way beyond a sentence at the top of the whiteboard. They help us get clear on what we really want students to understand and how today’s lesson connects to the bigger story of their learning. Strong math goals aren’t about what students will do—they’re about what students will understand.
Establishing Mathematics Goals to Focus Learning
In Principles to Actions (NCTM, 2014), the very first effective teaching practice is Establish Mathematics Goals to Focus Learning—and there’s a good reason for that. Clear goals give direction to everything else that happens in math class. When we’re guided by goals, students start to see how ideas connect, we can choose or tweak tasks to fit what we want kids to learn, our questions and discussions stay focused, and it’s easier to see what students really understand (NCTM, 2014; Taking Action, 2017). When both teachers and students keep a clear learning goal in mind, math stops feeling like a collection of random activities and starts to become a meaningful story of deep mathematical learning.
The Power of Goals
What do we mean when we say a good goal can turn a set of math tasks into a meaningful story of learning? Well, when goals are written clearly, they can actually create a pathway of understanding from task to task, and from unit to unit, and from year to year instead of just being a stand-alone, disconnected idea. When learning goals are thought through and written well (see more on how to write a strong learning goal below!), they give EVERY lesson a sense of purpose and direction. Think of it as each goal becomes a stepping stone toward the bigger concept we want students to deeply understand.
Here’s an example of what we mean using a second-grade unit on double-digit subtraction. Without clear goals, it can easily turn into a jumble of fun but disconnected lessons and tasks we’ve gathered from Pinterest and our curriculum. We know we want students to learn how to subtract, so we try a little bit of everything—maybe a shopping task with money that involves regrouping, a sports-themed subtraction task from our curriculum, and a “monster subtraction” game to wrap it up. Each activity might be engaging on its own, and there is a goal of helping students subtract two-digit numbers, but without the kind of clear, intentional learning goals we’re talking about, it’s hard for students (and us!) to see how the pieces fit together. When we start with intentional goals, though, the learning begins to build purposefully from one idea to the next. Here’s how it looks.
You might begin with helping students understand subtraction as “taking away” by implementing a task in which students use tens and ones manipulatives. The goal could be, “Students will understand that subtraction means taking away and can represent this idea by subtracting ones from a two-digit number using physical and visual base-ten models.”
Next, the focus could shift to subtracting tens from a two-digit number: “Students will understand how to subtract tens by decomposing numbers into tens and ones and subtracting tens from tens.” Students begin to see how place value helps simplify subtraction and make sense of bigger numbers.
Once they’re comfortable subtracting tens and ones separately, the next lesson might tackle subtraction across a ten—introducing the need to regroup. The goal might be, “Students will understand that when there are not enough ones to subtract, they can decompose a ten into ones to solve the problem, connecting concrete models to symbolic notation.”
Each goal along the way gives both teachers and students a sense of purpose. You know exactly what understanding you’re building toward, and students can see how each new lesson connects to the last. Over time, that clarity helps them move from just doing math to truly understanding math. When goals guide the learning, students develop stronger connections, deeper understanding, and greater confidence as mathematicians. If you have a highly-rated curriculum, the sequence of lessons will likely establish goals in this way.
Writing Strong Learning Goals
So, how do we write strong learning goals? First, let’s remember: learning goals aren’t just statements about what students do—they describe what students will understand about mathematics as a result of our teaching. A strong goal gives meaning and purpose to every lesson.
Effective learning goals usually include these key parts:
What students will learn and understand
This is the big math idea you want them to grasp.
Where the goal fits in a learning progression
Today’s lesson should build on prior understanding and connect to what comes next. They should be designed with an awareness of where students are coming from and where they’re headed. This might include yesterday and tomorrow, last week and the next unit, or last year and the future grade level.
Specific to the lesson
Goals should be clearly focused on what students will come to understand in this particular moment of learning.
Aligned to grade-level content
Goals should directly connect to the mathematical ideas and expectations for your grade, rather than being too broad or generic.
Strong learning goals should also be:
Guides for your teaching – it should help you choose the right tasks, ask meaningful questions, and decide which representations will support understanding.
Addressed throughout the lesson – revisited and reinforced through the tasks, discussions, and representations you use—not just written on the board.
The difference between a weak goal and a strong goal can completely change how students experience a lesson. For example, a weak goal for a lesson on the area of a triangle might be:
“Students will find the area of triangles.”
This goal focuses only on what students do, not what they understand. It doesn’t connect to prior learning or future lessons, and it’s not specific enough to the lesson to give much guidance for selecting tasks, asking questions, or choosing representations for the day.
A stronger goal would be:
“Students will understand that the area of a triangle depends on its base and height and be able to show this relationship using a visual model.”
This version is a stronger goal because it:
Clarifies student understanding.
It's not just ‘doing’: Students are focused on understanding the relationship between base, height, and area.
Situates the lesson in a learning progression.
It builds on prior work with rectangles and parallelograms (where students have already practiced and understood that area for these shapes can be found by multiplying the length x width, or base x height) and lays the foundation for applying the triangle area formula later.
Guides instructional choices.
It points you toward tasks that involve drawing or manipulating shapes, possibly by cutting out triangles and laying them within rectangles, asking questions that prompt reasoning towards understanding the base x height relationship, and highlighting multiple ways to represent the concept.
Is specific to the lesson.
It can be addressed throughout the lesson, and relates to grade-level content: This goal is designed for a grade level where students are learning to find the area of a triangle. It can be naturally revisited throughout the lesson as students use visual models, explain their reasoning, and make connections between the base and height of different triangles. It’s a goal that’s specific to one lesson—the key understanding can be introduced, explored, and assessed within that single class period.
Even though the goal is narrow, it gives every part of the lesson a clear purpose. Tasks, questions, and representations are all intentionally chosen to support understanding. Throughout the lesson, the goal remains visible and central—teachers and students return to it often, checking how each task and discussion moves their thinking forward. It is based on grade-level content. Over time, lessons like this help students build a strong conceptual foundation and move toward more complex ideas and applications— in this case - developing a base/height understanding as they work to fluently find the area of triangles using the area formula - without overwhelming them or rushing through the depth of concept involved in the standard.
Getting Started: Making Goals Doable and Visible
Here are a few simple ways to bring learning goals to life in your classroom—or in your coaching work—without adding extra stress.
1. Start with the big idea, not the task.
Before selecting an activity, ask: “What mathematical idea do I want students to understand this year, in this unit, and specifically today?”. Make sure it can be understood in a lesson and that it is a part of your core standards. See the examples below and how learning-focused goals can be much more powerful than performance-focused goals.
Elementary Example
Performance-focused: “Students will understand the meaning of multiplication and solve multiplication equations.”
Learning-focused: “Students will understand the structure of multiplication as comprising equal groups within visual or physical representations (e.g., collections or arrays), understand the numbers in multiplication equations (i.e., number of equal groups, size of each group, total amount), and connect representations to multiplication equations.”
Middle School Example
Performance-focused: Students will be able to use cross multiplication to find the missing value in problems in which the quantities being compared are in a proportional relationship.
Learning-focused: Students will recognize that a proportion consists of two ratios that are equivalent to each other (e.g., a/b = ax/bx) and that missing values in the proportion can be found by determining the scale factor x that relates the two ratios or by determining the unit rate—the relationship (multiplicative) between a and b and recognizing that ax and bx must have the same relationship as a and b.
High School Example
Performance-focused: Students will identify a function of the form y=bx as an exponential function where x is the exponent and b is the base. Students will be able to substitute values for x and b to evaluate exponential functions.
Learning-focused: Students will understand that exponential functions grow by equal factors over equal intervals and that, in the general equation y=bx the exponent (x) tells you how many times to use the base (b) as a factor.
See the difference? Each example moves from describing what students do to what they understand—a subtle shift that makes a powerful impact.
2. Situate the goal within a learning progression. Ask yourself: “What understanding does this goal build on, and where is it leading?”
Before understanding slope as rate of change (grade 8), students need a foundation in ratio and proportional reasoning (grades 6–7).
Before tackling systems of equations, students should understand what a solution to an equation represents.
Framing goals this way helps lessons connect over time and shows students that math is a coherent story, not a set of isolated topics.
3. Use goals to focus discussion and reflection. During class discussions, link back to the learning goal:
“Why is it important to tag only one object while saying one number when counting?”
“How does your strategy help us understand what happens when we multiply by a power of ten?”
“Which representation best shows how changing a in y = ax² affects the graph?”
At the end of the lesson, revisit the goal together:
“What did we learn about our goal today?”
“What evidence do we have that our understanding is deepening?”
This keeps the goal alive—not just a sentence on the board.
Coaching Tip
When reflecting with teachers, start with the goal. Instead of asking,
“How did the lesson go?” try:
“What was the mathematical goal today, and how did student thinking connect to it?”
This simple question shifts conversations from general impressions to evidence-based reflection, helping build clarity and coherence across classrooms.
Small Shifts That Make a Big Difference
Here are a few practical tweaks you can try tomorrow:
Shift from performance-first to learning-first planning. Write your learning goal before selecting the task.
Align representations. Ask, “Which representations will help students make sense of this goal?”
Connect during closure. Always end the lesson by returning explicitly to the goal.
Collaborate around goals. In grade-level teams or PLCs, examine how goals progress across grades to build coherence.
Final Thought
Establishing mathematics goals isn’t an extra step—it’s the foundation for everything that comes next. Clear goals help teachers make intentional decisions and help students make sense of the math they’re learning.
When we start with the why, every task, question, and conversation gains purpose. Learning becomes something students can see, talk about, and own.
Looking Ahead
Focusing on goals isn’t about adding more work—it’s about shaping every part of a lesson around the understanding that matters most. When teachers are clear on what students should understand, every question, task, and representation becomes intentional.
In our next post, we’ll explore how implementing tasks that promote reasoning and problem solving builds naturally from these clear goals—and how the right tasks turn goals into meaningful learning experiences.
Single Page Reference Guide
Sources:
National Council of Teachers of Mathematics. (2014). Principles to Actions: Ensuring mathematical success for all. National Council of Teachers of Mathematics
Adapted from: Boston, M., Dillon, F., Smith, M., & Miller, S. (Eds.). (2017). Taking action: Implementing effective mathematics teaching practices in Grades 9–12. Reston, VA: National Council of Teachers of Mathematics. P. 16
Adapted from: Huinker, D., & Bill, V. (Eds.). (2017). Taking action: Implementing effective mathematics teaching practices in Grades 6–8. Reston, VA: National Council of Teachers of Mathematics. P. 16
Adapted from: Huinker, D., & Bill, V. (2017). Taking action: Implementing effective mathematics teaching practices in K-grade 5. National Council of Teachers of Mathematics. P. 19
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