# Preparing Undergraduates Conceptually & Procedurally

# Preparing Undergraduates Conceptually & Procedurally

## What We Do

Thinking With Algebra (TWA) is a curriculum development project funded by the National Science Foundation (DUE: 2021414) to prepare undergraduate students conceptually and procedurally for introductory or intermediate algebra. Specifically, TWA consists of 30 lessons centered on the major topics of a first course in algebra which are theoretically and pragmatically grounded. The lessons consist of problem sets and whole-class, game-like activities.

## What Makes Us Unique?

The Thinking With Algebra (TWA) curricular materials is unique primarily because of its focus on algebraic structure and how it is presented to instructors! The curriculum materials provide a lengthy discussion on the theoretical aspects of structure. A key point is that algebraic structure is often implicit, as experienced algebraist we often do not see the underlying structure which students do not see. Our goal is to make algebraic structure explicit to instructors and they in turn make it explicit to students. Each activity has notes where structure is frequently highlighted. These notes help instructors provide opportunities to learn algebra topics with consideration of algebraic structure. By making algebraic structure explicit, students have an opportunity to learn about algebra from a different perspective, particularly helping students who have struggled with algebra.

#### Explicit Algebraic Structure

Our goal is to make algebraic structure explicit to instructors and students. Each activity has notes where structure is frequently highlighted. These notes help instructors provide opportunities to learn algebra topics with consideration of algebraic structure.

#### Equity

In addition, the project takes the learner into consideration by focusing on how people learn algebra. The instructional materials are designed to be used for introductory algebra at universities and especially at community colleges.

#### Distributed Practice Approach

Distributed practice provides opportunities for enhanced learning as students reflect on algebra topics learned previously and make connections with their experience and other mathematical principles before new topics are introduced.

#### Advocates Whole-class Discussions

Small-group work and whole-class discussions provide opportunities for students to share different solution methods, learning from mistakes or misunderstandings, and consider the reasoning of other students.