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Celebrating Graland’s Math Program

Graland is dedicated to providing a strong academic program for students, and our mathematics program is no exception. Graland’s instructional leaders have a consistent pulse on classroom instruction and learning, adjusting and supplementing resources and classroom experiences when appropriate. Here are several reasons to celebrate what’s happening in our math classrooms: 
Children are conversing about mathematics. Explaining thinking behind problem solving is one key way students make meaning of the math behind the algorithm. Enter a classroom and hear students talking to one another about how they solved the same problem in multiple ways. Mathematical Mindsets author and Stanford professor, Jo Boaler notes, “Many parents have asked: What is the point of my child explaining their work if they can get the answer right? My answer is always the same: Explaining your work is what, in mathematics, we call reasoning, and reasoning is central to the discipline of mathematics.” 

Reasoning through “Number Talks” also happens in classrooms thanks to Lower School instructional coach, Nikki Spiers. She coaches teachers on how to ask “just the right question” to get students thinking deeper. Number Talks build students’ ability to solve problems mentally and help reinforce multiple strategies.

In 2017, Nikki Spiers was named Lower School Math Instructional Coach. With a wealth of mathematical knowledge and classroom expertise, Ms. Spiers moves the bar with regard to instruction. While keeping the integrity of Math in Focus at the center, she coaches teachers on anything from inquiry-based lessons to differentiating assessments. She offers instructional cycles to teachers which include co-planning, observing, coaching and feedback. In December she completed a MSed in Math Education from the University of Colorado, Denver. 

Inquiry-based instruction is on the rise.
Teachers use questions and scenarios to engage students with concepts, allowing students to creatively apply prior knowledge. With inquiry-based instruction, we see students having ah-ha moments of understanding while productively struggling with hands-on or visual problems. This method also allows students to enter a concept at their individual level of understanding making it an effective differentiation strategy.

Middle School implements skills-based rubrics.
To help students and parents understand specific skills that students are working towards mastering and to help outline learning targets, math department chair Nanette Newman guided teachers through a year-long process of defining mathematical skills for Grades 5-8.  At student-led conferences, students were able to better express their understanding and identify goals.

With problem solving at its core, Math in Focus provides strong scaffolding for students.
Based on the Singapore Math model, Math in Focus moves students through concrete and pictorial stages of understanding, ultimately arriving at abstract problem solving and reasoning. Middle School teachers also believe that the best way to learn mathematics is to ask students to solve challenging problems. When students discover something on their own, they will understand concepts much better than if a teacher simply tells them how to solve it. 

Former high school math teacher and TED Talk presenter Dan Meyers notes, “Math reasoning is the application of math processes to the world around us. This is hard to teach. This is what we would love to have students retain even if they don’t go into mathematical fields.” 

Faculty embrace professional development opportunities.
Ms. Spiers recently led faculty in “Supporting Productive Struggle” during a Lower School division meeting. Additionally, some faculty visited lab classrooms around Denver to observe inquiry-based practices in action. Others are taking the Empowered Problem Solving online workshop. Middle School teachers also actively work with Shelly DuBose, an independent consultant and Math in Focus expert. 

On standardized tests, Graland students consistently outperform independent schools. Graland students take the Educational Record Bureau’s Comprehensive Testing assessment each spring, a rigorous test of student achievement. Year after year, our graduates show higher than expected gains in quantitative reasoning and math achievement. Graland’s scale scores reflect impressive growth at all grade levels. 

“Nikki and I worked on organizing math lessons that allowed for productive struggle through exploration. The lessons were fun and engaging, and students established a deeper level of content understanding. Productive struggle gives students opportunities to develop perseverance and grit, and encourages flexible math thinking.”  
- Julie O’Connor, Grade 3 Teacher


Graland Country Day School

Graland Country Day School is a private school in Denver, Colorado, serving students in preschool, kindergarten, elementary, and middle school. Founded in Denver in 1924, Graland incorporates a rich, experiential learning approach in a traditional classroom setting, emphasizing the development of globally and socially conscious leaders who excel academically.