As a part of my work for
Cognito Mentoring, I compiled a list of recommendations for gifted elementary and middle school school students who are learning math. Some of these recommendations have come up on the Davidson forum before, but some of them may be new to you. Some of the middle school recommendations may be suitable for elementary school students who are above grade level.
In addition to our recommendations, you might be interested by the
Poland McKinley Elementary School PTO Math Enrichment Family Resource Book, which contains a fairly comprehensive list of the resources available.
Elementary schoolMiddle school- Prealgebra by Richard Rusczyk, David Patrick, Ravi Boppana and Introduction to Algebra by Richard Rusczyk. These books are part of the Art of Problem Solving series. The books in the series teach elements of mathematical thinking and problem solving, as opposed to rote drill. The series has been reviewed very favorably, for example, on Quora. The prealgebra book is accompanied by a series of free videos, which cover all of the topics in the textbook. Both books are synchronized with the free adaptive online learning system Alcumus.
- Algebra by Israel Gelfand and Alexander Shen. This is a very highly reviewed algebra textbook coauthored by a great mathematician.
- Vision in Elementary Mathematics by W.W. Sawyer teaches readers how to visualize elements of algebra.
- Mathematical Circle Diaries, Year 1: Complete Curriculum for Grades 5 to 7 by Anna Burago contains many problems that teach mathematical reasoning.