In my experience, there are two main types of curriculum designs:

mastery – each concept is taught only once, but thoroughly; students are not taught the concept again. Ex: Math-U-See, many penmanship programs

spiral – concepts are reviewed throughout the year, more depth of knowledge is added at each visit. Ex: Saxon Math, many foreign language programs

The merits of each type are debated, but given that cognitive science supports interleaved, interval spaced retrieval practice, a spiral design benefits most students. I choose spiral curriculum whenever possible.

“a spiraling series of exercises that cycle back to key skillsets in a seemingly random sequence that adds layers of context and meaning at each turn”

Many US curricula combine the worst parts of mastery and spiral curricula. For example, most math textbooks have a chapter on fractions. Students learn one type of fraction per lesson, take a chapter test, and don’t learn about fractions again until the next year. While technically this is a spiral, this is not a useful spiral—instead, as Willingham writes, “students don’t stick with any topic long enough to develop a deep conceptual understanding.” I call these exposure curricula.

In poor curricula:

practice is not spaced—students have one or two days to learn

practice isn’t interleaved—homework has 10 problems of type 1, 10 of type 2, and 10 of type 3, in that order.

practice is not varied—homework is only on that day’s concepts or procedures.

Teachers and students tend to dislike intensive spiral curricula because:

spacing out practice means that students have to put forth more effort to remember

interleaved practice feels more difficult than massed practice; it seems hard, chaotic, or boring

varied practice loses the sense of mastery students get from successfully completing ten problems in a row

Choose a curriculum with built-in interleaved, interval spaced retrieval practice whenever possible.