FREE DOWNLOAD: First-Lessons in Arithmetic, Jones Bros., 1878. This math book will provide home school parents and public school teachers a incomparable tool from the past to help their students master the fundamentals of arithmetic. This book was handed down to me by my family. My ancestors used it. It is my privilege to make this precious family heirloom available to the public. My main purpose in publishing this book on the web is not just antiquarian, I fully expect that parents and teachers will download this book and use it to produce a generation of children who are experts at basic math calculation. Personally, I think it is better than Ray's Arithmetic, and vastly superior to the confusing modern consumable workbook that plagues today's classrooms.  The final pages were scanned and published here on 10/3/04 (Revised 3/25/05) NOTE: It is a very large file (209.66.23 MB). Because the file is so large, I have divided it into 10 smaller files for easier downloading. 

1. First-Lessons in Arithmetic: Pages 1-31, Lessons 1-18. Counting & Addition.

2. First-Lessons in Arithmetic: Pages 32-50, Lessons 19-30. Addition & Subtraction.

3. First-Lessons in Arithmetic: Pages 51-71, Lessons 31-42. Multiplication

4. First-Lessons in Arithmetic: Pages 72-92, Lessons 43-54. Division.

5. First-Lessons in Arithmetic: Pages 93-104, Lessons 55-63. Fractions.

6. First-Lessons in Arithmetic: Pages 105-112, Lessons 64-67. Fractions continued, Notation & Numeration. 

7. First-Lessons in Arithmetic: Pages 113-121, Lessons 68-71. Addition & Subtraction. 

8. First-Lessons in Arithmetic: Pages 122-127, Lessons 72-73. Long Multiplication. 

9. First-Lessons in Arithmetic: Pages 128-133, Lessons 74-76. Long Division. 

10. First-Lessons in Arithmetic: Pages 134-144, Lessons 77-85. Money, etc. 

Here is First-Lessons in Arithmetic. Here I have combined all the pages above for teachers and parents who would like to download the entire document onto their computers.   

Samuel L. Blumenfeld’s Arithmetic Program. Here is some of the best information on teaching arithmetic you will find anywhere. I consider Mr. Blumenfeld’s arithmetic program as revolutionary as his Alpha-Phonics reading program. 

Math with Kathy Gonzalez: Working with the Number Six. Step 1: Counting to five. 

Arithmetic Can Be Fun by Munro Leaf. 

Learn Math Fast: I am currently using this program with my tutoring students. Here the author’s LMF Website. Here are LMF Progress Charts that I have made for keeping track of students' progress. 

Ferrell’s Elementary Arithmetic (1903) A superb method that would be excellent for anyone wanting to improve their basic arithmetic skills. Ferrell’s Advanced Arithmetic (1903) Methods in Arithmetic: A Monogram (1904) by James A. Ferrell. 

Elementary Arithmetic (1905) by J. W. McClymonds and D. R. Jones. Contains clear explanations and ample practice. 

The Normal Elementary Arithmetic Embracing a Course of Easy and Progressive Exercises in Elementary Written Arithmetic (1893) by Edward Brooks, A.M., Ph.D. A very commendable book. delivers information and online calculators for a wide variety of applications - math & statistics, science, business & finance, technology, home & garden, sports, health & fitness, games, and much more. The author sent me the link on 2/14/22.

I appreciate a homeschool mom in Australia who sent me the following link to First Lessons in Numbers, (1888) This book is a real gem and quite similar to First-Lessons in Arithmetic.

First Book in Arithmetic is a wonderful supplement to First Lessons in Arithmetic.

Ray's New Intellectual Arithmetic was quite successful. This edition was published in 1877. Here is the Ron Paul Math Curriculum which is baed on Ray’s Arithmetic. 

David Tower's 1850 Gradual Lessons in Oral and Written Arithmetic 

Davies’ Primary Arithmetic (1863) A solid arithmetic book for young or remedial students. Strong on basic operations. 

S. W. Baird 1897 Graded Work in Arithmetic: Numbers 1 to 20. Perhaps the best beginning book on arithmetic that I have seen. On January 21, 2010 a lady sent me an e-mail that she has been teaching it to her kindergarten daughter. She is amazed at how well the girl is able to solve complex problems. I hope to republish Baird's work in hardback for wider distribution. Here is Graded Work in Arithmetic Second Year, Numbers to 100. And Graded Work in Arithmetic: Numbers to 1,000,000.

George Albert Wentworth (1893) An Elementary Arithmetic. Somewhat similar to Baird's work. A very excellent beginning approach to arithmetic. I hope modern curriculum designers will take note and follow Wentworth's lead. Put a book like this in every classroom in America and you will see our country surge ahead of the rest of the world in this field. 

First Book in Arithmetic (1899) by Frederick Wiemer. Similar to Baird. 

First Steps Among Figures: A Drill Book in Fundamental Rules of Arithmetic (1878) by Levi N. Beebe. A very valuable and unique approach to teaching arithmetic facts to automaticity. More information on the Grube method is available in Grube's Method of Teaching Arithmetic (1891) by Levi Seeley. Students of the history of the teaching of arithmetic will enjoy reading, The Falsity of the Grube Method of Teaching Primary Arithmetic (1895) by Saul Baldness. 

The Franklin Primary Arithmetic Book (1879) by Edwin P. Seaver & George A. Walton. A worthy book to consider. Franklin Second Book of Arithmetic

How to Teach Arithmetic: A Manual for Teachers and a Textbook for Normal School (1914). This is a major reference book.  

Caution:  Be sure to show students the side of the math flashcards with the answers on them because if you show them the side without the answer they might memorize the side without the answer. Think about that. It is more important that you might think. We want students to associate two numbers in an addition problem with the correct answer not with a blank space.    

I heartily recommend Sam Blumenfeld's How to Tutor as an excellent source for a basic understanding of how to teach arithmetic. His method may seem a little strange to teachers used to modern textbooks, but a close reading will yield profound insights into best procedures for helping students master the fundamental arithmetical operations. Arithmetic operations should be memorized and over-learned to the point that they become automated procedural processes, fully automated and perfectly accurate. Unit counting should be avoided at all costs. Students who have the mechanics of calculation automated (able to run with out conscious attention) will inevitably be able to allocate more attention to problem solving and higher level math. Here is a 1998 lecture on Arithmetic vs. Math

Here is a link to a most unusual arithmetic book, but one which may hold great promise as a tool for teaching basic calculating skills.The arithmetical primer. Underhill's new table-book; or, Tables of arithmetic made easier. By D. C. Underhill ...Underhill, D. C. (Daniel C.), New ed., rev., enl., and improved.:  36 p. illus. 15 cm. New York, R. Marsh [c1854]  calculating skills: Arithmetical primer. 

Hall's Arithmetic Primer (1901). A marvelous method that every teacher and home school parent should have. You can download it from this URL at Google Book. Hall also wrote an Arithmetic Reader. which something of a combined reader and arithmetic book. 

Here is Adam's New Arithmetic (1848). Here is the Teacher's Key to Adam's New Arithmetic

Practical Arithmetic (1847) by James Thompson. 

The Stone-Millis Arithmetics: Primary (1914). Important for practical and theoretical purposes.

Here is a new site I recently found: Systematic Math. It will open your eyes.

Mental Arithmetic  (1854) by Benjamin Greenleaf

Mental Arithmetic  (1896) by George Hull. 

The First Steps in Numbers (1892) by Wenthwort and Reed. Of fundamental importance. Also Elementary Arithmetic (1901) by the same authors. Here is Wentworth's Primary Arithmetic (1890). 

 The Alexander-Dewey Arithmetic: Elementary (1921)

 Figures Made Easy: A First Arithmetic Book  Answer Key. Notable for its math tables. Learn these tables and will quickly become a master at arithmetic. 

The Psychology of Arithmetic by Edward L. Thorndike (1922) A valuable work.

The Teaching of Arithmetic: A Manual for Teachers (1916) by Paul Klapper. A thoughtful and helpful study of the psychology and methodology of teaching arithmetic. 

Automaticity of Basic Math Facts: The Key to Math Success (2011) by Camel E. DeMaioribus. This is a through provoking Master’s Thesis about a subject that merits further research. 

A Brief History of American K-12 Mathematics Education in the 20th Century (2003) by David Klein. A very important study concerning why student math ability is on the decline in the USA. 

Primary Arithmetic (1900) Colaw and Ellwood. Published by B. F. Johnson Publishing. This is a superb arithmetics book covering all the basic elementary arithmetic facts. Here is a School Arithmetic: Practical Book by the same authors and publisher. 

How you can be good at math, TedxStanford presentation. 

Easy Unit Converter. This is a handy converter for every unit you can imagine. 

Why Your Child Can't Understand Math

My search of good math material has been most frustrating. I have never felt that the typical math adoptions were effective, but  was at a lost as to how to improve things. Recently I have come upon a very perceptive article by Jerry Schnell which sheds much light upon this universal problem. Jerry Schnell's website is no longer on the Internet. I was fortunate to keep a copy of the his article, Why Your Child Can't Understand Math. I will publishing more of his materials on math on this page in the near future. Jerry stopped by my school for a short several years ago. His daughter contacted me last year to tell me that he had passed away. 

 Multiplication Matrix

My good friend, Charlie Richardson, recently sent me a Multiplication Matrix that he and his wife developed to help students learn their multiplication table. He has given me permission to publish it here. The Matrix should prove very valuable in math classes around the world. Mr. Richardson passed away a few years ago. How time flies! 

Multiplication Made Easy. An excellent YouTube Videos. 

IXL Online Math Practice. This has many excellent interactive math problems for every grade level. 

AAA Math - Interactive Math Skills Site

Recently I came across a very useful, interactive math site: AAA Math. I highly recommend that parent and teachers direct their students to this site to help improve their calculation skills.

Teaching Tables

Recently I happened upon a very helpful interactive math site for learning the times tables. The program is available  for purchase, but there is a fully functional version on-line:

Saxon Math Warrior: The story of John Saxon. 

Free Math Help. This is one of the best sites for algebra and up. 

Math-U-See: has a lot of good information. 

Here is Art Reed's book on Using John Saxon's Math Books

Stern Math by Catherine Stern. This is an approach worth investigating. 

Rocket Math  A great way to learn the math facts. 

"Addition and Subtraction with Whole Numbers” by Mamrilyn D. Suydam and Fred J. Weaver. This is a research document. 

Practical Exercises in Mental Arithmetic. Practical exercise in basic operations. 

Abacus: 10 x 10 Abacas

Here is a very important article by Joan Cotter, “Using Language and Visualization to Teach Place Value.” This explains the use of the AL Abacus. Here is Joan’s article, “Activities for the AL Abacus.” Here is a good YouTube video explaining the AL Abacus

How to Memorize the Times Tables The Great Courses Video. I did not find it all that helpful, but maybe you will. 

It Takes Ganas: James Escalante’s Secret to Inspired Learning by Bill Dempski and Alex Thomas.  This is the inspiring story of James Escalante. You can read the whole book Online. Here is an ERIC article on "The Jamie Escalante Math Program.” On Creating Ganas: A conversation with Jaime Escalanate (1989). Jaime Escalante Math Program (A lot of information about the man and his program).

Math Education: A University View (2007) by David Preston

A Close Look at the Mathematician’s Brain by Prof. Stanislas Dehaene. (September 11, 2017)

Here are Songs for Memorizing the Multiplication Tables

Calculator Soup for solving any problem. 

Cognitive Science and Learning Mathematics

Children Discover Arithmetic (1971) Catherine Stern. 

It’s the Story that Counts (1995) by David J. Whitin and Sandra Wilde. I mention this book because I have always felt that math would be best taught from stories. Internet Archive Math Story Resources.

RightStart Math 

Nimble Numeracy (2002) by Phyllis Fischer. 

Algebra - All the help you need - FOR FREE!

A high school student recently told me that he had improved his Algebra grades by studying the information on the Purplemath website. A brief visit to the sight makes it obvious that this is a true national educational treasure. Here is almost everything you need to know about Algebra. Click here: purplemaths.

The unusual title of this valuable essay says a lot: "In Defense of "Mindless Rote." Ethan Akin make a strong defense of the importance of learning the basics to automaticity. Here are some other excellent articles on the need for "overlearning" of basic skills: "Practice Makes Perfect: But Only If You Practice It Beyond the Point of Perfection” by Daniel Willingham. 

How does the brain do math (YouTube video on neurology of math)

Here is a mind boggling video on How Not to Teach Math

I have heard that Singapore Math is very good. Here is an explanatory video.  Introduction to Singapore Math. 

Calculus Made Easy: Being a Very-Simplest Introduction to Those Beautiful Method of  Reckoning which are Generally Called by the Terrifying Names of: Differential Calculus and the Integral Calculus (1914) by Silvanus Phillips Thompson.   

The Changing Faces of the Math Student: Images in U.S. Early Elementary Math Textbooks, 1909-1999 (2019). This has little to do with teaching math, but explains how the textbooks can reflect and influence culture. 

The Importance of  Automaticity Development in Mathematics (2018) by Austin T. Baker & Josh Cuevas. 

Targeting Difficult Multiplication Problems: Increasing Multiplication Fact Fluency Through a Learning Trials Intervention (2017) by Kelly McCullough Thomason. 

A Comparison of Two Approaches to Promote Multiplication Fact Fluency in Fifth Grade: A Quantitative Research Methods Proposal (2023) Jordyn Berger.

Improving multiplication fact recall; Interventions that lead to proficiency with mathematical facts (2013) by Brandon J. Bauer.

The Oughtred Society Slide Rule Reference Manual. Very interesting history. I still have my slide rule!