AOPS Introduction to Algebra: a review

This review is intended to share our experiences of working through the AOPS Introduction to Algebra textbook. It covers questions such as how we used the course, areas of particular challenge, using Alcumus, and length of time spent.

AOPS is a challenging maths curriculum, which expects quick absorption of new concepts and a high degree of tolerance for hard problem-solving. It is a good fit for some of my children and not for others. I haven’t gone into detail in this review about the AOPS approach to maths, but it is important to consider whether that is a good fit for your child before starting out with AOPS Introduction to Algebra.

• What maths were we doing before AOPS Introduction to Algebra?
• How we used AOPS Introduction to Algebra
• Alcumus and AOPS videos
• How did we find AOPS Introduction to Algebra?
• How long did AOPS Introduction to Algebra take?
• Where to purchase AOPS Introduction to Algebra

What maths were we doing before AOPS Introduction to Algebra?

Previously my child had completed AOPS Pre-Algebra. They had also worked on the first half of AOPS Introduction to Number Theory, but I don’t consider this to be in any way a pre-requisite for moving on to the Algebra textbook.

I was glad that my student had the opportunity to adjust to AOPS textbooks and methodology on the pre-Algebra course, which was mostly familiar material, before moving on to the Algebra course which is more challenging. We had also covered the general skillset of using a textbook, and laying out your workings methodically.

How we used AOPS Introduction to Algebra

My child worked on maths independently for 45 minutes each day. I didn’t have a set amount of work for them to complete each day, just whatever they could get done in the available time. The order of working was usually like this:

• Complete the Problems for a Section
• Read answers to Problems (in textbook) and mark own work
• Complete Exercises for a Section (parent marks these later)
• Complete Alcumus online for that Section
• When all Sections of a Chapter are complete, do the Review and Challenge problems.

After each day’s maths lesson, I would then mark their work, discuss anything they hadn’t understood, and write up corrections for the next day. Sometimes these corrections were quite extensive. I would use the answer guide to help me write a hint for each incorrect question.

I did allow my child to occasionally leave a ‘question mark’ for questions they were really stuck on, especially in the challenge sections, and we would look at those together. I didn’t want them to get really frustrated and stuck. This seemed to work well for us.

My child worked through the whole textbook, in order. When we worked on Pre-Algebra, I had my child complete every single problem in the textbook. For Introduction to Algebra, I asked them to attempt all the problems, but I usually found that we would end up working on about half of the Challenge problems together after they had had a go. I did often skip 1-3 of the final challenge problems in a chapter. Some of the questions went so far beyond what my child needed to know at this point, and I did not want them to become frustrated.

I would also observe that some of the Challenge problems ask the student to ‘show’ or ‘prove’ something. Reflecting back at the end of the course, this is an area where we probably need to do some additional work on how to set out a proof, and what things need to be included. Writing a proof is not the sort of skill that all students absorb by osmosis.

Alcumus and AOPS videos

We also used Alcumus alongside the textbook. After completing the Exercise problems at the end of a section, my child would then complete the associated Alcumus section online until it has a blue progress bar. My child really likes Alcumus, and would sometimes work on it for fun outside of lessons. The mild ‘gamification’ of the Alcumus progress bars and challenges is highly motivating.

There are free online videos from Richard Rusczyk accompanying the Introduction to Algebra course. We did not generally use the videos, but we did look at them for some topics that were proving particularly difficult, and on several occasions they did bring extra clarity of understanding for my student.

How did we find AOPS Introduction to Algebra?

Generally my child had a good experience working through this text, though they did need to put in concerted effort most of the time. When others ask me about this text, I usually comment that it goes well above and beyond what I think a typical student needs to know. The challenge problems in particular can be really….well, challenging! There were points when I questioned whether doing maths this intensively was a good use of our time. That said, my child made excellent progress in their understanding of algebra, and tenacity for problem solving. If I had one small criticism, it would be that some further material on graphing would have been helpful to us. I believe the topic will be revisited in Intermediate Algebra.

How long did AOPS Introduction to Algebra take?

It took us just over one full school year to complete AOPS Introduction to Algebra, so roughly 39-40 weeks. My child worked for 45 minutes, 5 days per week, and occasionally did some Alcumus in their free time. Having read a few other people’s experiences, my understanding is that this is a fairly usual amount of time to take on the curriculum, and it would also be quite normal to spread the book over a year and a half or even two years.

Where to purchase AOPS Introduction to Algebra

This post contains affiliate links. As an Amazon Associate, I earn from qualifying purchases.

For us in the UK it can sometimes be quite challenging to purchase AOPS products. Postage directly from AOPS can be prohibitively expensive. I have used shipping agents in the past, but recently I have found Amazon the most cost-effective solution. It is worth checking out both the UK Amazon website and the US Amazon website, as the latter will often ship to the UK, and it can work out cheaper. I generally find the delivery times to be about the same, as the books are usually coming from the US anyway. You will need both the textbook and the solutions manual. If purchasing new it is generally cheaper to purchase them together, but if you are purchasing used, it may work out better to purchase them separately.

You may also be interested in my review of AOPS Pre-Algebra.