An expert problem solver must be endowed with two incompatible quantities: a restless imagination and a patient pertinacity.
— Howard W. Even
The Garden problem   

The math program at Running River School strives to help students create meaning of processes and operations through the use of manipulatives and real-world problem solving. Our method is heavily based in the constructivist approach, which suggests that children are at all times broadening their construct of the logical and symbolic world through the assimilation of new experiences, which conflict and align with previous knowledge and understanding: thus, creating new meaning.

One strength of our program lies in the way math arises out of our project based learning. For example, when the Kindergarteners want to know how big dinosaurs were, we study measurement. They study length, height, and weight of dinosaur footprints, tails, and heads. They also compare and contrast with animals in their world, a pre-skill of ratio. By engaging kids emotional center, we quickly activate excitement in the brain as well.

Another strength of our program is that we give kids every opportunity we can to use math as a tool in life. We teach in a way that gets all kids excited to apply their developing skills to real life practical projects such as carpentry, gardening, cooking, and orienteering in the outdoors. Research shows that although students may be able to perform well at arithmetic computation, often they are not able to use those skills to solve problems. Attached is an example of a Garden Problem. This problem demonstrates a standards-based approach to a real thematic problem: “How can you design the garden we are building?”

A third strength of our program is our multi-age grouping. We intentionally create multi-age classrooms because peers are great teachers. When students present their findings and ideas, they are solidifying new information and teaching one another what they have learned. We are constantly challenging kids to teach one another. When kids struggle and reach out for help, we often direct them to other students. Our teachers evaluate students’ knowledge by observing the ways in which individuals and groups of students work and rework the problems together.

Finally, knowing where students are in their mathematical understanding is crucial. We use one-on-one assessments to gauge how students are progressing through the curriculum. We also rely heavily on the work that students are doing in their daily math work and journals. We use journals to give kids an opportunity to demonstrate their thought processes through writing and pictures, thus activating both sides of the brain. These math journals become roadmaps for the students to review the paths we’ve taken throughout the year. At Running River School students drive the instruction. Because we have such a small student : teacher ratio, we are able to tailor instruction to each individual’s needs.

Below is one example of our Garden problem done with 2nd and 3rd graders, which integrates fractions, addition, money, spatial design and a variety of language arts. It is great to work with kids who are so engaged in what they are learning.


Middle School Math

The Running River School Middle School Math Curriculum follows our philosophy of experiential and real life learning while also recognizing the importance of a solid background in number sense and continued practice for retention and support of mathematical operations. In the past few years, with the adaption of Common Core Standards there has been more focus of the depth of learning rather than the breadth. This has always been our focus, thus aligning ourselves with the Common Core Standards, while working within our philosophy connects well with our curriculum. It also means that students are well prepared to tackle high school math programs. Unlike some interpretations of the Common Core Standards, we do not continue to move students forward without ensuring that they have a solid understanding in the number sense behind the operations and concepts. We work with students where they are, addressing their strengths and challenges.

The middle school math program is a mixture of students working independently with the Khan academy and one on one or small group conferencing and work with a teacher, and small group or whole class projects, real life applications and problem solving. The Khan Academy is an online individualized math program that allows children to work and learn at their own pace. Teachers and parents have access to what the students are learning and doing, as well as their struggles and challenges. Students can work on predetermined lessons from the teacher, or explore on their own. To assist in understanding, students can watch videos to learn or relearn concepts and then practice on the computer with instant feedback. Since our middle school is a three year program, this allows children to work and be challenged where they are at while also allowing for class time for projects and using math as a tool for life. As a whole class, or in smaller groups, they will also work on larger problems and projects that support and extend their individualized learning.


focus on

(Colorado Common Core Standards)

  • Number sense, properties and operations
  • Patterns, functions and algebraic structures
  • Data analysis, statistics and probability
  • Shape, dimension and geometric relationships

middle school expectations

(Colorado State standards)

  • Ratios and proportional relationships, the number system, expressions and equations, functions, geometry, and statistics and probability
  • Robust learning in geometry, algebra, and probability and statistics in middle school
  • Preparation for high school mathematics
  • Personal finances and fiscal responsibility