Review: Discovering Mathematics (Singapore Math, Secondary Level)

Note: Since beginning Discovering Mathematics, Singapore Math has released a new edition, Discovering Mathematics Common Core. The order of lessons vary a bit, and new topics have been included. At this writing, only a few levels are available. We tried the new ones, and they are fine, but as they’ve been slow to release, we’re still working through the earlier series. The differences are slight, with changes in order and a few additions being the bulk of what varies from the old to the new. 

Providing a challenging mathematics education was one of the key reasons we started homeschooling. Deeply disappointed by the depth of the math provided by two schools, my older son, then seven, assumed he was the problem.

“I don’t think I’ve very smart, Mom,” he told me.

“Why not?” I inquired.

“Because they don’t give me anything hard to do,” came his sad reply.

Math (and science) were his loves at age 4 and 5 in Montessori and while at home. He was appropriately challenged in the first at school and free to explore the second at home. First grade ended all that, where math became repetition of previously mastered lessons. Second grade, at our local gifted and talented public school, it was nonexistent  which was because, we were informed, he knew all the material for that year already.

So once home, math took a starring role. Singapore Math quickly became our preferred curriculum (reviewed here) for the elementary sequence. Even doing the Challenging Word Problem books, we burned through it quickly. Almost 10, my older insisted on Algebra, so we started the standard sequence, happily making our way through a fine text, Jacobs’ Algebra. (reviewed here).

When my younger finished 6B, I wondered if there was another way. We vamped for much of last year, working through a variety of books while choosing our next course of action. After much consideration, we decided to stay with Singapore, specifically, their Discovering Mathematics series. This four-year series is designed to cover some prealgebra, algebra (I and II), geometry, and a smattering of other topics, like probability and counting. Unlike most American programs, these topics are interwoven throughout the years, with chapters on algebra followed by chapters on geometry with a side trip to data handling. It’s challenging, with plenty of problems, tests with answers, and teacher’s support books if needed.

But I hesitated. Accustomed to the four-year math sequence I’d known as a child and that my older son had followed, I was hesitant to commit to a different path. What if we didn’t like it after a year? What then? (Answer: Start a traditional Algebra program and compact or test out of what has already been covered. Ditto the next year with Geometry.) I presented my younger son, then 10, with the options. Singapore, Jacobs, or Art of Problem Solving? He looked at samples of all online and liked the familiarity of the Singapore. Thus, we reached a decision.

We’ve not been disappointed. We started Discovering Mathematics 1A soon after it arrived and found that while it certainly felt like the Singapore Math we’d enjoyed the previous years, it was a step up in challenge and pace. He’s enjoying it, but we don’t whip through the pages as we did at the elementary level. Concepts aren’t broken down in such small parts, and even the sample problems (Try This!) are fairly challenging. Fortunately, this increase in challenge has resulted in an increase of effort. As a result, he’s feeling rather accomplished while learning large amounts.

At the minimum, the user will need to purchase two textbooks for the year. These paperbacks are affordable and reusable, in keeping with Singapore Math’s reputation for affordability.   Each of the four levels requires two textbooks, each generally over 200 pages long. The year is broken up into 11 to 17 chapters, roughly evenly divided between the two books. (The fourth level is shorter, with a significant proportion of 4B dedicated to review tests, similar to the elementary level 6B.)

The chapters are broken up into shorter sections, some amenable to a single lesson or day of work, others requiring multiple days, given the depth of the lessons. Each section ends with problems in four categories: Basic Practice (the easiest problems), Further Practice (definitely a bit more work), Maths@Work (word problems just as challenging as the aptly named Challenging Word Problems of the elementary series), and Brainworks (sometimes too hard for Mom but worth trying if no one is crying). The so-called Revision Exercise (test) at the end of each chapter is at the level of the Further Practice and Maths@Work level. Aside from the Brainworks problems, all the answers for the problems are in the back of the book. If you desire worked solutions (and so far, I’m good without), there are Teacher’s Guides available, which include other teaching assistance, activities, and a breakdown of lessons and timing.

An additional workbook is available for each level, providing some extra practice as well as more problems at the more challenging level. Unlike the traditional workbook, these don’t provide a place to do the problems, making them more of a reusable problem bank. I assign some of these at the end of each chapter, before the revision (test). The number I assign depends on how well he’s handling the material — some sections just require more practice than others. Generally, these workbook problems are more challenging than the textbook ones. They are broken down into sections called Basic Practice, Further Practice (both a bit more involved than the same-named section in the text, it seems), Challenging Practice (and it generally lives up to its name), and Enrichment (excellent problems that we don’t get to most of the time). As with the text, answers are in the back, but solutions require the Teacher’s Edition of the workbook. I’d strongly suggest the workbook to supplement all learners, with the Teacher’s Edition on the shelf if a parent is a bit math wary and wants guidance on the trickier problems.

The strengths of the elementary level of Singapore Math continue at the secondary level. The pace is swift, which is excellent for the mathematically talented child but could be overwhelming for others. The problems in the text at the secondary level are far more challenging that what is in the workbooks for the elementary level, but on par with the Challenging Word Problems books. (I’ve not used the Intensive Practice books at the elementary level, which are designed to increase the challenge at their respective levels.) The depth we’ve encountered thus far is also impressive. Math is not taught via algorithm but by deep understanding, which, in my opinion, is by far the superior method. It is applied, not simply in one-step word problems, but across the sciences and into the work world. Math lives in these books, with all its complexity and beauty there for the learning.

The downside to the Discovering Mathematics series? If one isn’t math-comfortable, these could be a challenge to teach. That said, for the math-uncomfortable, these are an excellent way to build a new relationship with math. I know that throughout teaching even the elementary level of Singapore Math to my boys, this math-comfortable mom moved from number capable to number savvy. I’ve said before that I believe that math is best taught rather than learned solo. Discussion is part of the process, and many times, I’ve had a child teach me and correct me, thus delighting the child and enlightening me. (For more on thoughts about strong mathematics programs, read my post, Math Matters.)

We’re early in our exploration of this four-level series, and I’ll post again as we move through the program. I’m hoping we continue to enjoy Discovering Mathematics over the next several years, allowing us continuity with a strong mathematics educational program.

As always, I only review what we’ve used, and I never accept compensation of materials or money for my reviews. 


15 thoughts on “Review: Discovering Mathematics (Singapore Math, Secondary Level)

  1. Thank you, as ever. I’m curious, as one just starting out on Discovery Mathematics myself, did you use Sketchpad at all for those geometry problems that required it?

  2. I, too, have used Singapore Primary Mathematics from the get-go (now finishing up 6A/6B). I found your review to be very helpful in confirming what I already knew–that the Discovering Mathematics would probably hold true to the analytical/critical thinking type math that makes you think and not just plug in numbers. I, too, have noticed that my mental math in particular and understanding of concepts has really sharpened doing this math with my girls. I, too, have had the more than one occasion of my daughter teaching me a problem. My husband always says, who is home schooling whom? It does make for a great confidence builder for your child! Do post later if you end up using Sketchpad–I just read about that today as I was reviewing the Discovery Mathematics series. Thanks for the information!

  3. Thanks for this review. We have used Singapore all the way through, and I do think we will stick with Discovering Mathematics after Singapore 6. My husband is a high school math teacher and speaks highly of what the kids have learned so far.

  4. I started out with Singapore NEM, but thinking of switching to DM. So, I may be able to only use the textbook and workbook alone without having to buy the teaching notes and solution book and the workbook solutions book?

  5. finding your wonderfully helpful post today (2014) as I am desperately searching for any remaining copies of Discovery Math level 2 workbooks to purchase. My children are all still in the elementary series, but I see that the DM series has been discontinued and is being replaced by a common core version (UGH!!). I have gone ahead and scooped up the rest of the series, but can’t find the level 2 workbook anywhere. Someone suggested that we could use the New Math series for the level 2 year, but I worry about the two series not being interchangeable.
    any suggestions?

    • The Common Core sequence, as far as I can tell, simply added some subjects and rearranged. We own BOTH for level 1/7 because the the CC level was coming out as the other was fading. I realized that CC level 8 wasn’t going to appear in full by the time we needed it, so I bought both to make sure he had all he needed to move to level 2 of the old Discovering Mathematics. (Clear as mud, huh?) Anyway, you’re sacrificing nothing by moving to the new series, as far as I can tell.

      • There is nothing wrong with the Common Core version; the Singapore Math methods and strength of teaching remain unchanged. The fact is, Singapore’s DM series still exceeds the CC; it did not dumb itself down or fundamentally change a single thing other than rearranging a few sections, and those rearrangements were not pushing any material off to later years in the net result. Respectfully, rather than reacting to the label, look at the content before rejecting it or trying to influence others to do so as well.

      • Jen,
        I don’t see where I reacted at all to the label of Common Core or influence others to reject it. We didn’t continue with the series, as I noted in my intro paragraph, because they weren’t released quickly enough. We did use them for the first year, but the second wasn’t out in time. I’ve bought ahead for the old series simply for continuity’s sake, as the order has shifted somewhat. Please read carefully before you make accusations.


  6. Hi there! I could have sworn I’ve been to this blog before but after
    going through a few of the articles I realized it’s new to me.
    Anyways, I’m definitely delighted I found it and I’ll be book-marking it
    and checking back often!

  7. I’ve just purchased NEM 1-4a (looking for 4b), and now have come across Discovering Mathematics series. I’m a bit confused by the numbering though. Does it run from 1-7, and how does this correspond with topics/US grade levels? Thanks.

    • It looks like Discovering Mathematics is now called Dimensions Mathematics, and the series starts with 7A, as it picks up where the elementary series ends. The numbers are supposed to align with grade levels.

  8. March 2017: Your blog is such a valuable resource for me! We’ve just begun DM Common Core 7A and I felt a little disoriented. Thank you again!

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