Cooking Up Arrays

Do multiplication arrays need to be introduced as a ready-made convention, or can they be “constructed” by children using concrete objects while engaged in an open-ended task?

(An action research collaborative effort by second grade lead teachers, Tasha Hernandez, Bill Miller, and Lower School Math Coordinator, Debra Rawlins)

We began this project as a way to build math relevance into the annual second grade canned food drive. The students visit Saint John’s Food Pantry and spend a morning learning about the needs of the community. Then they pitch in and help out the staff for a few hours. When they return to school, they create signs advertising the canned food drive, and place collection boxes at various locations around the school.

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LREI Math Philosophy

A Summary of LREI’s Math Philosophy Written by Teachers from Lower, Middle, and High School: 

Children at every developmental level deeply engage in the discovery of mathematics through the inquiry and investigation of interesting problems. LREI students collaborate on solving worthwhile problems that have rich mathematical underpinnings. Problems can be solved on a variety of levels, have multiple entry points, and therefore provide both accessibility and challenge to the abilities of all students in a class.

A good problem is also defined as not having a predetermined solution pathway that is known in advance. A worthwhile task, or problem, will often open the door to other interesting conjectures and theories that students have, and support an emerging mathematical habit of mind.

Throughout each unit of study, students develop and maintain computational fluency. Students are instilled with an enthusiasm for mathematical challenges and the open-endedness of mathematical inquiry. Our students develop perseverance and a sense of ownership of mathematics. Students achieve genuine understanding when they actively construct knowledge rather than passively absorb; when they use it to solve problems rather than memorize facts and formulae.

Students throughout the divisions learn through inquiry and collaboration. Emphasis is placed on the presentation and communication of mathematics in written, oral, graphic and symbolic forms. Students are encouraged to clearly describe, explain and support their findings with valid evidence.

In the Lower School, students display their work using a document camera and engage their peers in the discussion of a problem. In the Middle School, students can share their thinking by reflecting work done on an iPad or graphing calculator to a Smartboard. Working in small groups is a commonly used practice across the grades. In High School, students put their mathematical ideas on small whiteboards and then each group presents to the rest of the class, and the classmates ask questions.

Consistent with LREI’s philosophy, the mathematics department values creativity and critical thinking, as well as risk-taking when problem solving as a means to confront life’s challenges and variables. Our students understand that mathematics has the power to model the world around us on multiple levels. Projects and problems, offered in math classes, have relevance to students and their lives.

How Many Sides Does A Circle Have?

Teachers posed this question to first graders during their study of geometry.

First graders went beyond naming basic two-dimensional shapes to exploring specific characteristics, or attributes, that define them. Their conversations evolved from seeing a shape as a “whole” such as a triangle, to analyzing and deciding the specific features that prove that it is a triangle. Students decided that a shape can only be called a triangle if it has three straight lines that make up the sides, three corners, or vertices, and does not have any openings (it needs to be closed).  Through this specific definition, they discovered that there are many types of triangles. They used this critical thinking foundation to explore a variety of two-dimensional shapes.

“Does a Circle Have Sides?”

 This was an interesting question to ponder. First grade teachers, Sarah and Ariane, posed it to their students to see if they could apply the skills they had learned about defining geometric attributes to this question. It turns out that it wasn’t an easy question to answer! Continue reading