Setting Small Goals to Achieve High-Impact Math Gains

 A well-designed Multi-Tiered System of Support (MTSS) for elementary math supports teachers in effectively meeting students’ diverse needs by prioritizing high-quality, universal instruction that is inclusive and engaging for all students. 

In an MTSS, students have access to intervention focused on high-impact math concepts that support grade-level learning. In order to accelerate learning, we need to prioritize math concepts that have the most impact across a grade level. As elementary educators, we are often unsure which concepts to prioritize. When designing instruction for intervention, teachers should start by asking the following questions: What is the current high-priority grade-level math content? What is the most critical content that students need in this grade level in order to access next year’s grade-level learning? These questions can guide the design of high-impact instruction.

designing high-quality math intervention

High-leverage concepts are the key understandings identified at each grade level that help focus math instruction by identifying the big ideas at each grade level that will support success in the next grade. We know that this growth is not necessarily linear. However, this resource allows teachers to understand the key prerequisite understandings along the way toward mastery. When designing for Tier 2 and Tier 3 layers of support in an MTSS, it is critical to prioritize the most impactful math content if the goal is to accelerate learning.

Once teachers have identified the highest-impact math concepts at their grade level, they need to consider the small goals related to that math concept that will indicate progress toward understanding. Teachers should ask themselves these questions: What evidence will I see to indicate understanding? What models do I expect students to use? What strategies do I expect students will apply? 

These learning progressions are a resource to break down these larger concepts into small goals along the way. The idea is to identify and monitor the developing stages along the continuum of critical math concepts, including models and strategies that students should explore. When designing for intervention, teachers intentionally plan lessons based on what a student already knows and understands to help move them forward in their understanding. This process highlights an asset-based approach for instruction. It may be necessary to start on the concepts from one or two grade levels prior that largely impact the current grade-level math content.

Finally, teachers must consider the learning opportunity that includes both teaching and assessing students’ understanding. They need to consider the high-cognitive-demand tasks that students can engage with during intervention that will allow them to show their understanding of these critical concepts. Beyond straight calculation, we need to know the models and strategies that students are using and whether or not those strategies are increasing in complexity. When we look for small gains in strategy use, we are able to increase our impact on student learning while feeling a sense of efficacy in the implementation of our instructional design. 

High-quality Instruction in Practice 

I recently worked with a group of special educators in Illinois to hone their skill set in designing intervention that promotes the acceleration of math learning. Here are the steps we followed.

1. Identify the high-priority grade-level math content to prioritize. The small group of students we planned for were in second grade. The high-priority grade-level math content in second grade is addition and subtraction

The Common Core State Standard (CCSS) states the following: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.

This group of students was still working on understanding number values and sequences to 20. The concept is critical for addition and subtraction, as students must be able to identify both the name and the total value of a given number in order to add and subtract whole numbers within 100. As a group, we lined up the kindergarten and grades one and two high-leverage progressions documents to identify where instruction should start based on this goal. We identified counting, comparing, and composing/decomposing within 10 on the kindergarten document.

2. Identify the critical strategies and small goals to achieve as an outcome of this intervention. Using the kindergarten and first-grade high-leverage concepts, we discussed our expectation for students to be able to count within 20 both forward and backward and compare quantities within 10. We identified the critical strategy of composing and decomposing quantities using models, specifically a tens frame. We also expected to see evidence of counting by ones, subitizing, organizing, and tracking. 

3. Identify the strategy for teaching and assessing student understanding. Students are much more relaxed and able to show their thinking when playing. We decided to play a simple dice game involving counters or bingo chips, blank printed tens frames, and six-sided dice. In this game, each student rolls a die and answers these questions: How many dots are there? Who has more dots? How do you know? How many chips will you need? How close are you to 10? Students then place that many chips on the tens frame. When all chips are placed, we discuss answers to these questions: How many chips do we have altogether? How do you know? How are your strategies for counting the same, how are they different? 

As we play this game, we are looking for the following:

• Evidence of subitizing
• One-to-one correspondence
• Strategies for counting and cardinality
• Sums to 10 using the tens as a thinking tool and strategies beyond 10 if the situation arises

Following this process, we were able to focus on high-impact math content at the current grade level. We were able to deconstruct the small goals along the way that help us understand student growth toward this concept. Finally, we could design a learning opportunity that was focused on a specific, small learning goal. 

With a small learning goal, we are able to monitor progress toward understanding because we are crystal-clear about what we are looking for. The goal here is for us to set small goals so we know exactly when students know and understand a concept and are ready for the next instructional step on the progression. 

Every small goal we move toward is focused on math concepts that are critical for understanding current grade-level concepts, so that we begin to see impact on grade-level learning at a much faster rate. Through high-quality Tier 1 instruction and high-impact Tier 2 and Tier 3 layers of instruction, we are more readily able to accelerate student learning of key mathematical concepts.