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”Make It Stick, by Brown, Roediger III, & McDaniel, 2014
Spiral Curriculum Challenges:
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.