A classical, liberal arts education includes integrated instruction in many diverse disciplines and curricular programs which, taken together, constitute a comprehensive and holistic view of human knowledge and experience. Below you will find information on some of our core curricular programs.

Singapore Math

At the Lower School, we utilize a Math program called Singapore Mathematics after the country where it was first used. Singapore Math doesn’t limit itself to the “what” and “how” of Math, although those are important, but focuses also on the “why.” While getting the right answer is important, Singapore Math helps students “think mathematically” by ensuring they understand the underlying Math concepts and principles at work in a problem.

Concrete-Pictorial-Abstract Framework

Ordinarily, Singapore Math lessons progress through a similar sequence. Each new topic begins with concrete exploration—usually using some kind of Math manipulative such as counters, place value discs, or snap cubes. After students have discovered the principles at work using manipulatives, Singapore Math moves to the pictorial stage, offering students a visual representation of the principle at play which often takes the form of a number bond or bar model. Only once students have mastered the Math concept at the concrete and pictorial stages does Singapore Math move on to introduce a purely abstract algorithm such as stacked addition or subtraction, long division, or cross multiplication.

How Parents Can Help

Though it may be different from what parents encountered when they were young, we ask all our parents to support the depth and intentionality of our Math instruction by helping their children using the strategies and vocabulary taught at school.

One of the best ways you can help your child achieve mastery in Math is to seize upon opportunities to build Math into your everyday life. Ask your child to help with the measuring when cooking family meals. Pose a “challenge” Math question while traveling in the car such as, “If Grandma’s house is 20 miles away and we’ve already traveled 7, how many miles do we have left to travel?” or “If we went into the store and apples cost 50 cents each, how much would we have to pay altogether if we bought 12 apples?” Thinking and talking through real life problems like these together helps students see that Math isn’t just a class in school but is a way of understanding the world. It can also make traveling in the car a time to spend in thoughtful conversation with one another as a family.

Math Facts

In Singapore Mathematics no less than in any other Math program, automaticity with basic Math facts (2+2=4, 2+3=5, etc.) is crucial. While we devote as much time as we can during the school day to practice with Math facts, we strongly encourage all families to reinforce our scholars’ mastery of basic facts through regular practice at home. Purchasing flash cards such as these may be helpful.

When it comes time for multiplication, “skip counting” by different denominations is an extraordinarily helpful way to practice Math facts. For example, you might ask your child to skip count by 2s starting at 14 (14, 16, 18, 20, 22), or you might ask her to skip count by 5s until you get to 40 (5, 10, 15, 20, 25, 30, 35, 40). When your child is ready, try more difficult numbers like 3s, 4s, 7s, or 9s. Try skip counting by 11s! It’s not as hard as it sounds (at least through 99).

For more about Singapore Mathematics principles and pedagogical methodologies, visit singaporemath.com.


Spalding Phonics

Great Hearts Lower Schools teach students to read, write, and spell using a program called Spalding. Spalding is a phonics program that uses a meticulously-detailed and multisensory approach to help students decode unfamiliar words and understand how the English language works. For more on Spalding, visit spalding.org.


Parents of Lower School scholars can support their children’s mastery of the phonograms necessary for English reading, spelling, and writing by purchasing a set of these Spalding Phonogram Cards to practice at home.

Phonogram Cards

There is also a Spalding Phonograms App available for iPhone and Android available for purchase to facilitate phonogram practice at home.

Phonograms App for Android

Phonograms App for iPhone

Spalding Phonogram Videos

Click on the letter to play the video for each sound:

1(a)   2(c)   3(d)   4(f)   5(g)   6(o)   7(s)   8(qu)   9(b)   10(e)   11(h)   12(i)   13(j)   14(k)   15(l)   16(m)   17(n)   18(p)   19(r)   20(t)   21(u)   22(v)   23(v)   24(x)   25(y)   26(z)   27(sh)   28(ee)   29(th)   30(ow)   31(ou)   32(oo)   33(ch)   34(ar)   35(ay)   36(ai)   37(oy)   38(oi)   39(er)   40(ir)   41(ur)   42(or)   43(ear)   44(ng)   45(ea)   46(aw)   47(au)   48(or)  49(ck)   50(wh)   51(ed)   52(ew)   53(ui)   54(oa)   55(gu)   56(ph)   57(ough)   58(oe)   59(ey)   60(igh)   61(kn)   62(gn)   63(wr)   64(ie)   65(dge)   66(ei)   67(eigh)   68(ti)   69(si)   69(ci)

Core Knowledge

The starting place for Great Hearts’ Lower School History, Science, Music, and Visual Art curricula is the K-8th Core Knowledge Sequence. Based on the work of E.D. Hirsch, the Core Knowledge Foundation (which is not the same thing as Common Core) seeks to ensure all students graduate as culturally-literate citizens, having encountered all the topics a well-educated person needs to know something about. To ensure our instruction is as rich, rigorous, and classical as possible, Great Hearts supplements the Core Knowledge Sequence with selections from other texts such as The Story of the World, the Famous Men series, and more.


Grammar and Sentence Diagramming

Grammar is one of three arts or disciplines that in ancient times were grouped together as part of the trivium, which are the three arts having to do with language. The term trivium didn’t appear until the Middle Ages, but Western Civilization’s knowledge of the fundamental importance of the three arts of grammar, logic, and rhetoric goes back all the way to Ancient Greece.

But why teach grammar? Isn’t it a bit old-fashioned? At Great Hearts Irving, we believe that, just as there are objective standards of beauty, there are objective standards for using language—humankind’s most powerful tool. Some ways of using language are better than others. Grammar is nothing less than the art of using language well; that is, in accordance with the Good. What is more, there is increasing scientific evidence in support of a proposition that the ancients knew long ago, namely, that language and thought are intimately connected with one another. By bringing order to their use of language, grammar teaches children how to order their mind.

We love grammar, and we love teaching grammar by means of diagramming sentences. Sentence diagramming is to grammar what number bonds and bar models are to math; they allow us to picture with our eyes the order inherent in the sentence, showing us a visual representation of the words, phrases, and clauses in the sentence, the functions they are performing, and their relationships with one another.

If you’d like to learn more about sentence diagramming to help your child with his/her Grammar homework (or maybe your family just loves sentence diagramming as much as we do and you’re looking for some extra practice), here are some resources we recommend: