Library of Mathematics

This article is the follow-up to The Beauty of the Library.

To create a library of mathematics, we will need a few things in no particular order:

• a library of mathematics with engaging titles and covers
• a place everyone can access this library
• series of problems/activities for the person who likes a certain style and doesn’t want to have to make choices over and over again
• non-series problems/activities for people who like to make choices
• an adult or older child who can help them or give them hints when they need a tiny bit of help and ask for it (just like when a reader needs help with a word)

This last one seems like a big challenge for 2023 America, where many adults are unsure how to give a hint or a little bit of help. Perhaps each math problem/activity in the library could have a hint hidden inside of it (or a video hint?). Hopefully we will have less math phobia in a decade or two, but that is a topic for a different article.

As for the other bullet points, I will address each in this order:

• a library with engaging titles and covers
• which everyone can access
• series
• non-series

A Library with Engaging Titles and Covers

Currently there are several math resource libraries, listed alphabetically here: ALEKS, IXL, Khan Academy, Mathigon, and NRICH.

Of the first three, only Khan Academy has cover images (once you click on a title). You may be able to picture them: black backgrounds like chalkboards with handwritten pastel math work. The titles are usually much like those in textbooks: “Equations with Variables on Both Sides,” for example. While these may be useful to teachers, I wouldn’t call them interesting— or hooks. The cover images definitely help students determine if the math looks like the right level of difficulty to them, but calling the covers engaging would be a stretch.

Mathigon has engaging covers — colorful pictures. Its Activities section has interesting titles to hook students, whereas its Lessons section has more textbook-style titles like Khan Academy. I presume the Lessons section was designed with a teacher audience, and the Activities section with a student audience.

The University of Cambridge hosts a free website called NRICH with engaging titles and cover images. In fact, while writing this, my own child saw NRICH on my computer screen and asked for a particular problem by its title. No joke.

Which Everyone Can Access

Many people have heard of IXL and Khan Academy. While Khan is free, IXL has a limited amount available before a paid account is required. Khan and IXL accounts can be set up by either guardians or teachers (or students 13 and up). The same goes for ALEKS, which is an exclusively paid service. All three of these are much like textbooks, offering repeated math problems and word problems grouped by type.

Meanwhile, Mathigon, a free website with accounts optional, is not well-known by parents or even necessarily by teachers. Everyone can afford to access it, but may not know it exists.

NRICH features free engaging puzzles and problems. While some teachers are familiar with NRICH, guardians have probably not heard of it.

Series

Khan Academy and IXL offer a series for the student. Khan suggests an exact next thing much like a train proceeds from station to station without deviation. IXL is more like a train station in Europe. You just rode a train, and now you find yourself looking at a marquee with many train options. IXL looks like a list with 200–400 titles in about 10 different category headings — for each grade. And no images.

ALEKS, which I am less familiar with, offers courses and adjusts its series based on students’ existing knowledge, continually feeding students more problem sets.

Mathigon has four main sections: Polypad (visual tiles), Courses (three areas of mathematics, both middle school and high school for each), Activities, and Lessons. The Courses section provides a series for students to follow. They make two choices. The first is between Geometry, Numbers and Algebra, and Probability and Applications. From there, the student goes to either Middle School or High School. The second choice is between 3–4 options, each with one image. After these two decisions, the student is given a series of roughly 6 problem sets.

NRICH gives one problem/puzzler at a time to the student. Some problems recommend another NRICH problem as follow-up, which sometimes with a link. Overall NRICH is not series-oriented.

Non-Series

NRICH and Mathigon, the two with engaging cover images and titles, can be chosen “off the shelf” like books in any order and based solely on cover appeal or recommendation.

In addition to the cover image and the title, NRICH always displays an age range (ex. 7–11, 14–16, 7–14) and a challenge leel (1 star, 2 stars or 3). The keyword search engine can filter by ages, challenge level, or both.

In Mathigon, the Activities and Lessons sections are non-series choices. As mentioned above, they all have cover images. The Activities have engaging titles, whereas the Lessons have textbook-style titles.

IXL and Khan can be used for individual skill practice and found via internet search, but they lack the hook of engaging title and cover image for students.

In Conclusion

NRICH is a math library for K-12 with engaging titles and covers, but it is not widely known (in the US at least). Mathigon is also an enticing math library, aimed at middle and high school students. For people who prefer series, Mathigon has roughly ten series per age level whereas NRICH does not have obvious series to follow. Both have vibrant non-series math that feels like play.

Resource Links:

ALEKS (3–12)

IXL (K-12)

Khan Academy (K-12)

Mathigon (6–12)

NRICH (K-12)