Curriculum Insights • Developing Fluency in Math

In 2018, PBS completed a rigorous math review, which included sending a faculty research team to perform in-depth interviews and review best practices at seven middle schools. We amplified this qualitative research with quantitative information from these schools, standardized test scores, and aggregate data on PBS student learning outcomes. Over the past three years, we have prioritized steps to enhance our math program, focused on differentiation, and added resources for parents in a new Family Math Portal.

One top focus area is math fluency, an important skill for our young mathematicians. Sometimes called procedural fluency, it is the ability to compute math problems with accuracy, efficiency, and flexibility. It also includes mastery of math facts yet goes deeper by requiring PBS mathematicians to assess which problem-solving strategies to apply to particular problems. There are no fluency short-cuts such as rote memorization or drilling. Instead, we want students to produce an accurate and efficient solution by engaging in meaningful practices and applying the strategies they’ve learned.

PBS families are great partners supporting our math curriculum. We also acknowledge that there have been persistent questions about how to best achieve fluency for your children. This is understandable. Many of us recall our own elementary math classes with timed quizzes, drilling math facts, and rote memorization. With that in mind, we want to increase everyone’s understanding of current best practices for building strong fluency in our students. We’re using some FAQs below to support community-wide understanding.

How is fluency achieved?

• Three phases

1. Counting: Either counting physical objects or mentally
2. Deriving: Reasoning and flexibly applying different strategies
3. Mastery: Highly efficient production through quick strategy application or recall

• Ample opportunity to practice and develop math reasoning strategies
• Problem solving from a place of understanding
• Strategies that are intentional, deepen in complexity over time, and reinforced throughout the curriculum
• Mastery of foundational and derived facts: Production of an accurate solution within three seconds

Where does fluency development show up in the PBS math curriculum?

• Morning Meeting: Daily routines and community-building games that emphasize fluency, particularly in the early grades
• Number Corner: Daily routine that introduces, reinforces, and extends fluency strategies
• Workplaces: Games and collaborative activities that require strategic thinking and application of concepts introduced during direct instruction
• Problem Strings: Series of connected and purposefully sequenced problems that nudge students toward more efficient strategies
• Math Forums: Teacher facilitated discussions where students present work samples and discuss problem solving
• Assessment: All of the curricular elements above provide opportunities for teachers to formally and informally monitor and assess student progress

What are the research-based fluency objectives at each grade level?

• Kindergarten: Add and subtract within 5 (“Within” means that students can fluently compose and decompose numbers up to and equal to 5.)
• 1st Grade: Add and subtract within 20; by end of year, know from memory addition and subtraction facts to 10
• 2nd Grade: Add and subtract within 100 (using pencil and paper); by end of year, know from memory all sums of two one‐digit numbers
• 3rd Grade: Multiply and divide within 100; add and subtract within 1000; by end of year, know from memory all products of two one‐digit numbers
• 4th Grade: Add and subtract multi-digit whole numbers using the standard algorithm and other efficient strategies
• 5th Grade: Multi‐digit multiplication using the standard algorithm and other efficient strategies

How can families support fluency development at home?

• Use the fluency page of the PBS Family Math Portal, particularly:

1. Fact strategy posters for all four operations
2. Fluency game library organized by targeted strategies
3. List of questions to elicit flexible thinking and strategy application

• Play a math game since many commercial games elicit mathematical thinking
• Offer your children opportunities to think flexibly and apply efficient strategies for math problem-solving
• Promote a positive mindset by celebrating evidence of reasoning and progress toward mastery
• Reinforce best practices that result in mastery rather than speed and slow down to ensure understanding

To learn more about math at PBS, please watch for upcoming parent education opportunities:

• October 5: Article on assessment
• October 5: Parent education at 8:00 p.m. Topics: Unpacking the revised math progress report and standards for mathematical practice

Thank you for supporting our math program objectives!

Scott Erickson, Jon Fulk, and Michelle Donahoe
Head of School, Head of Academic Programs, and Math Enrichment Coordinator