# Meet the Challenge for Struggling Math Students This Summer

For many years, my professional focus has been on finding ways to more effectively teach arithmetic, the cornerstone of elementary mathematics. In every class I’ve taught, there are always students who present a challenge. Many are already at least a year behind and lack the foundation of mathematical understanding on which to build new learning. They typically have multiple misconceptions that hamper their progress, have experienced failure, and lack confidence. And they often find themselves being asked to catch up on foundational skills in summer school.

Such students not only demand more time and attention; they also benefit from instruction that is designed specifically for their success. Ariana, Paul, Belinda, and Trent are examples of the students my team of master teachers and I wanted to reach as we developed our math program for struggling learners. Here are some strategies to help teachers reach students in four foundational skill areas.

##### Ariana’s class was learning about subtraction.

Ariana’s explanation for why she couldn’t figure out 100 – 98 revealed her lack of knowledge of the inverse relationship between addition and subtraction.

Support students with this content by:

• Using models such as ten-frames and counters before transitioning to abstract computation
• Breaking the numbers into place-value parts, which maintains the meaning of each digit when adding and subtracting
• Introducing strategies for mental computation and developing proficiency through practice and game play
• Focusing on making estimates and considering the known and unknown quantities in problems that can be solved with addition and subtraction

##### Paul’s class was studying multiplication.

When I probed Paul’s thinking, I learned that he saw each multiplication fact as a separate piece of information to memorize. Because of his weak foundation of understanding, he was falling behind.

Support students with this content by:

• Introducing multiplication through the combination of equal groups
• Representing combining equal groups with related addition and multiplication equations
• Analyzing products to investigate patterns and relationships
• Offering games and partner activities to develop, cement, and extend student understanding
• Providing opportunities to practice multiplication using strategies that focus on the value of each digit

##### Belinda’s class was studying division.

Talking to Belinda made me realize that she thought of division as something new to learn, without the benefit of its relationship to multiplication.

Support students with this content by:

• Focusing on 10 as the basis of our number system
• Highlighting the connection between multiplication and division
• Promoting sense-making when dividing greater numbers by focusing on taking out partial quotients—to make the division more meaningful and manageable for struggling students
• Providing problems that develop an understanding of two types of division problems: grouping and sharing

##### Trent's class was studying fractions.

I realized that Trent had learned rules, like multiplying numerators and denominators by the same number, but didn’t fully understand when to use them or why they made sense.

Support students with this content by:

• Using concrete materials like fraction strips to help students develop an understanding of fraction relationships, recognize the need for common denominators, and learn how to generate equivalent fractions
• Providing students with multiple strategies for comparing and ordering fractions
• Developing the computational tools and strategies to add and subtract fractions—including improper fractions and mixed numbers with like and unlike denominators

You may recognize these students in your classrooms. My work with them highlighted the importance of making mathematical connections, identifying relationships, building on prior learning, and understanding how they reason. I wanted them to grow to be interested in math, curious about new ideas, and willing to take risks by exploring new problems.

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Looking for a summer school solution that helps you quickly identify where students are struggling and offers clear strategies to help them catch up and keep up? Explore Do The Math Summer School and contact us to request a free sample pack.

This blog post was updated in February 2019.