For Part One of our Singapore series, click here.
In the 1960s, educational theorist and cognitive psychologist Jerome Bruner articulated the concept of the spiral curriculum: an approach to teaching that reinforces student comprehension through revisiting concepts at particular intervals across a period of time.
Thanks to Bruner, the spiral of reinforcement is a standard approach to conceptual mastery across a variety of disciplines. It may even be true that most curricula spirals, but not always in the same way. Some math curricula, for example, may have students working with clocks on Monday, addition and subtraction on Wednesday, and money on Friday, and then begin the cycle again the following week. Moving rapidly between concepts may maintain student interest, but it won’t necessarily allow the opportunity to work slowly enough to develop genuine comprehension. Some educational researchers refer to this as a horizontal spiral, much like a landline telephone cord.
Contrary to the pacing of other math curricula, Singapore Math moves on a less hurried, ascendant vertical spiral. Students spend more time working with particular concepts in each level of math, but as they do, they are revisiting principles they have previously learned to deepen comprehension. This is a vertical spiral, similar to a spiral staircase.
Some researchers also refer to the ascendant spiral as a strand curriculum, as it integrates various concepts like strands throughout the spiral. This approach emphasizes mastery of foundational math concepts over exposure. It allows students more time to practice various operations, increasing their accuracy and speed.
At Clapham, teachers are constantly discussing math concepts with their classes, allowing them to orient themselves on the spiral. “What do we know? What do we need to know to find the solution? What do you notice about the last three problems on the board? How are they alike or different? Can you think of another way to find the solution? What is being asked of the statement 1/2 of 3/4? Can you demonstrate this question?”
Discussions like this encourage students to retrieve past methods of problem solving and to apply them in new ways to new problems. Of course, they also provide valuable information to the teacher, who is constantly gauging student comprehension and making individual adjustments based on how well each student understands a concept. This is one of the advantages of a our small class sizes at Clapham; teachers have more time to devote to each student individually and to customize their discussions or pace to different levels of understanding.
Spiral in Action:
- first we add 1 one and 6 ones which is 7 ones (7)
- then we add 3 tens and 2 tens which is 5 tens (50)
- finally we add 5 hundreds + 4 hundreds which is9 hundreds (900)
- Our answer is 957
It is a common misconception that Singapore is a mastery curriculum rather than a spiral curriculum. As Clapham faculty member Andree Escobar explains, “It’s both.” It is true that Singapore does not spiral as quickly or briefly as other math curricula might. However, Singapore’s longer, more in-depth upward spiral ultimately serves to deepen student comprehension and allow for more time with each math concept. This type of spiral is more conducive to mastering foundational concepts and strengthening student accuracy, understanding, confidence, and problem-solving ability.