Keys to Effective Teaching of Algebra

             In this article in Mathematics Teacher, Jill Newton (Purdue University) says that when she returned to a classroom during a sabbatical, she encountered many of the same challenges she’d experienced in her years as a high-school math teacher – plus some new ones: enforcing the school’s cellphone policy, a high rate of student absenteeism, and the pressure of standardized testing.

            As she re-immersed herself in teaching algebra, Newton compiled a list of what she wished she’d known as a new teacher. “I loved my students,” she says, “supported them, and did what I was taught to do, but as they say, When you know better, you can do better.” Here are her suggestions to her younger self – and other teachers of algebra: 

• Help students see the bigger picture of algebra – conceptual understanding and connections across algebraic procedures and topics. This is more helpful, says Newton, than breaking down algebraic procedures to the smallest steps.
• Discuss the uses of variables with students – for example, unknown, constant, argument, parameter, label, and varying quantity. Discussing conceptions of variables, Newton has found, really enhances students’ understanding of algebra.
• Give students opportunities to investigate strategies and make decisions about selecting methods for solving. “Learning when and why to use an algebraic procedure is just as important as learning how to use it,” she says.
• Facilitate students’ thinking about taking algebraic objects apart, putting them back together, and transforming them. Thinking about “doing” and “undoing” in algebra helps develop students’ procedural fluency and conceptual understanding.
• Begin with the idea of function families, and work with students to summarize their properties and compare and contrast different function families. This helps students make sense of algebra.
• Introduce the many ways to represent algebraic ideas, make connections among them, and make decisions about their uses. Focusing on multiple representations and building representational fluency builds students’ understanding of algebra.
• Engage students in exploring the power of algebra to investigate real-world issues and develop possible solutions.
• Model correct algebraic language, connecting ideas through words, and avoid imprecise terms. This helps students participate in mathematical discourse.
• Discuss the history of algebraic ideas, stories about important mathematicians, and the contributions of female and non-European practitioners. This sparks students’ interest in and understanding of algebra.
• Be frank about algebra’s historical role stratifying students in schools and its gatekeeper role for post-secondary opportunities. “I wish I had viewed algebra teaching and learning through a more-critical lens,” says Newton, “and asked more questions about who benefited and who was disadvantaged by school policies related to algebra.” 

“10 Things I Wish I Had Known About Teaching Algebra” by Jill Newton in Mathematics Teacher, September 2026 (Vol. 119, #9, pp. 742-747); Newton is at janewton@purdue.edu.

Please Note: This summary is reprinted with permission from issue #1155 of The Marshall Memo, an excellent resource for educators.