# Early Years Math Education at Corlears

## Laying the Foundation to Think Like a Mathematician** **

We focus on the way young children learn to think like mathematicians. From the nursery years to upper elementary grades, our program lays the foundation for fluency in mathematics, including:

Strong number sense

Deep understanding of the relationships between numbers

Knowing how to compose and decompose numbers

Recognizing multiple strategies and entry points

Developing flexibility with mathematical algebraic thinking and computation

We strongly believe that to be successful, our students must be able to apply their understanding beyond the classroom, and develop problem-solving skills that can be utilized throughout life.

### what makes our math program different

The Corlears math program follows the constructivist approach and incorporates fact fluency rather than rote memorization of facts. Attaining fact fluency allows children to use facts that they know to recall facts they are still developing. The emphasis on developing mathematical thinking and deeper understanding of the math concepts inside the numbers allows children to become more flexible problem solvers, paving the way to higher level, algebraic thinking.

## Faculty Expertise in Math Education

#### EARLY YEARS MATH RESOURCES FOR PARENTS:

*What’s Math Got to Do With It?*

by Jo Boaler

*This is Why it’s So Hard to Help with Your Kid’s Math Homework.*

by Jessica Lahey, Washington Post

*Mixing in Math*

Resources from TERC to help mix math into every day life

Our focus on faculty expertise in math education began in 2014, and has continued to grow with the support of our full time Math Coach and partnership with outside training resources like Metamorphosis Learning and TERC.

All classroom teachers at Corlears participate and learn from a significant amount of training in both math content and math teaching techniques, which allows them to unlock the same level of creativity and differentiation in math that is applied in other areas of the classroom.

This level of consistency and depth of training in math education reflects our ongoing commitment to math as a vital piece of the integrated learning that all students deserve.

## Corlears Math Program Overview

### Nursery + Preschool

The Corlears math program begins at the youngest ages, where we create active learning environments that are rooted in our understanding of age-appropriate experiences and knowledge in child development.

We do this by providing experiences that are:

Rich in mathematical language

Encourage mathematical thinking through daily experience

Promote problem solving and critical thinking through exploration

Allow time to construct and reflect on their thinking around math concepts

**Nursery Years**

As the 2s move through the nursery years, children experience exploration, play, and activities like sorting, labeling, and categorizing, which help them to organize their thinking and their world – and begin the process of problem solving.

Open-ended activities and materials help young learners to solidify what they already know about numbers, colors, and shapes, foster an innate interest in solving problems, and encourage risk-taking.

**3/4s – Preschool Years**

As they advance to Pre-K, students engage in routines that are reinforcing math language and concepts, such as the daily attendance, days of school, snack menu, and graphing surveys. By integrating math in their everyday surroundings, preschoolers are able to explore new ways to gain information, make predictions, and understand relationships.

### Kindergarten + Lower elementary

**Kindergarten**

Kindergartners explore tools like the Rekenrek, 10 Frame, and bead strings to focus on visualizing how numbers are constructed through part-whole relationships.

Efficiency in counting is practiced through:

Taking inventory and organizing data

Offering realistic experiences in which keeping track, determining quantity, and recording are important.

In this work, students are counting and unitizing as they use numbers to count not only objects but also groups. They are also challenged to keep track, and begin to understand the value of grouping objects, especially into groups of 5 or 10. Throughout the process and as they complete their work, communication is key, as kindergartners are challenged to record and communicate their mathematical thinking accurately using symbols, numerals, and labels.

**6/7s – First and Second Grade**

In our 6/7s classrooms, children move through their two-year math sequence with a focus on developing an approach to problem solving.

In the 6s, children begin to learn a variety of ways to problem solve such as counting all, counting on, and counting back. In the 7s, they continue to build on these strategies while working with larger numbers. They also learn the standard algorithm for addition and subtraction.

By the end of the 7s, the children have developed a flexible approach of choosing strategies that match the numbers and operations they are working on. All of these strategies become part of their toolbox for problem solving moving forward.

Through this approach, students are growing as problem solvers while simultaneously continuing to develop fluency with their math facts and understanding how those facts become tools for conceptual math thinking. This fluency helps children reason the relationships between numbers, ultimately promoting students’ accuracy and flexibility.

### Upper Elementary

**8/9s – Third and Fourth Grade**

Here, we use math models to demonstrate the multiple ways to conceptualize mathematical thinking and the many flexible entry points there are for problem solving.

Key mathematical ideas taught in these grade levels include:

Developing multiplicative thinking

Equal groups

Addition and subtraction of larger numbers

Multiplication facts

Models for multiplication

Models for multiplication and division

Division (4th grade)

Standard algorithm for multiplication and division (4th grade)

Fractions (end of 4th/5th grade)

Multiple operations

During the 8s, children are working on concepts relating to multiplicative thinking, such as equal groups. Through the use of a variety of models, they unpack the relationship between factors and multiples. As this understanding is developing, they also continue to build on multiplication math facts. They continue to work on operations such as addition and subtraction with 3- and 4-digit numbers.

In the 9s, multiplicative thinking is again re-enforced with double-digit multiplication and division. Their work focuses on using efficient strategies for solving these types of problems and building conjectures and generalizations related to these operations.

**10s – Fifth Grade**

Our 10s students’ problem solving incorporates larger numbers and multi-step problem solving, with a focus on mathematical proofs. Being able to prove your thinking and computation instead of answering, “I just know,” lays the foundation for higher level mathematics and moves students into algebraic thinking.

The 10s work on moving away from solving specific math problems in isolation and learn to generalize their thinking, noticing patterns and attributes of numbers, and go beyond rote guessing and reliance on an algorithm. Through this work they learn to explain the “rule” and what is happening inside the math. Once they begin to readily interpret the underlying math concept and they establish mathematical thinking, this allows them to problem solve more efficiently, and prove their work by demonstrating and articulating each step they took to arrive at the answer.

Some other mathematical concepts focused on include:

Fluency with standard algorithm for multiplication and division

Automaticity with multiplication and division facts

Problem solving with multiple operations

Developing mathematical proofs

Operations with fractions, decimals, percentages