MATHEMATICS
Collection of educational textbooks from the 1800s to mid-1950s
with additional valuable teaching and learning resources
INTRODUCTION
The subject of mathematics has caused and continues to cause much upset in the general education of many students worldwide. Whilst there may be many reasons for this, I believe the crux of the problem lies in the following:
(1) that time-honoured methods to learn and develop mathematical skills and knowledge have not only been erased from Western school curriculums, but where traces of them have remained, they have been significantly altered or modified to the point where students from primary school onwards quickly come to the conclusion that maths is "too hard" and "that they are not good at it" or that it is such a complex subject, only a few can understand it. This is of course a fallacy created quite intentionally to erode intelligence in the population;
(2) that good quality, well-designed mathematics textbooks like those so popular and readily available prior to World War 2, have disappeared out of circulation and no modern mathematics textbook of the same standards has replaced them, at least in the English-speaking nations such as UK, USA, Canada etc. The UK now provides no mathematics textbooks to pupils in primary and secondary schools. No standard, high-quality school textbooks exist or are made available; and
(3) a lack of fundamental clarification of key terms in mathematics, including the difference between the meaning of the words "arithmetic" and "mathematics", something which is so often misunderstood. Not understanding the key words related to mathematics and specific topics being learned in mathematics will prevent students from mastering the subject. Arithmetic is the PRIMARY field of mathematics which a student must fully master if he is to succeed with mathematics.
It is my goal here to provide as many mathematics resources as possible from the 1800s to mid-1950s, with additional more recent material which I have come across and successfully used for my own children when I home-schooled them in the early 2000s - material created by independent individuals of goodwill who have also attempted to help students learn maths while filling the gap of non-existent national mathematics resources.
MATHEMATICS KEY WORDS LISTS
Key words lists are essential tools in learning. A full discussion of this subject can be found here.
Basic Maths Key Word List 1: I wrote A Useful Guide to Understanding Science, Technology, Engineering and Mathematics (STEM) as a first guide to students, teachers and parents to clarify key words related to these subjects. The Mathematics section of the guide will set you up on with key definitions. Illustrations help to convey the ideas. Download.
Secondary School Maths Key Word List 2: This key words list is more suited to secondary school students and contains many definitions which the student and teacher should review to ensure full comprehension. More words and definitions can be added to the list. Download.
PRIMARY SCHOOL ARITHMETIC AND FURTHER MATHEMATICS
The best solution I can recommend to take your child from no knowledge of arithmetic to complete mastery of the subject is the 1800s Ray's Arithmetic Series by Dr Joseph Ray.
Dr. Joseph Ray (1807–1855) was a 19th-century American mathematician and educator. He is best known for writing Ray's Mathematical Series, a famous set of arithmetic and algebra textbooks. His books were taught in schools across the United States and sold over 120 million copies. His books were used well into the 20th century and mysteriously removed from state school curriculum in the United States.
The following website is fully dedicated to Ray's Mathematics Series offering much information on the best way to teach maths and to use the books. You can download in pdf the complete series on the website. As a back-up, I have also added the pdf downloads here:
Primary Arithmetic: Teaches numbers 1 to 100 and basic adding or subtracting. Kids use fingers, blocks, or beans to physically count before writing numbers.
Ray’s New Primary Arithmetic (1-2)
Intellectual Arithmetic: Focuses entirely on mental maths and oral word problems. Students learn to solve problems in their heads without using pencil and paper.
Ray’s New Intellectual Arithmetic (3-4)
Ray’s New Intellectual Arithmetic (3-4) Answer Key
Practical Arithmetic: Covers fractions, decimals, and measurements. It applies maths to real jobs like farming, carpentry, and running a business.
Ray’s New Practical Arithmetic (5-6)
Ray’s New Practical Arithmetic (5-6) Answer Key
Higher Arithmetic: The most advanced book. It covers ratios, percentages, and advanced logic.
Ray’s New Higher Arithmetic (7-8)
Ray’s New Higher Arithmetic (7-8) Answer Key
Ray’s New Geometry and Trigonometry (9-10)
SECONDARY / HIGH SCHOOL MATHEMATICS
Mathematics Textbooks from 1800s to mid-1950s
The Elements of Modern Mathematics - by Pearce & Atkinson, early 1900s, McDougall's Education Co Ltd, London - Edinburgh
An early 1900s mathematics textbooks for students 12 years onwards as described in the introduction. It covers arithmetic, algebra, geometry and mensuration. Clear explanations, background history of arithmetic and mathematics, as well as extensive practical exercises for every day living. Download
Many more scanned pre-WW2 maths textbooks to follow throughout 2026. Added as and when they are scanned.
