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# Why a Spiral Curriculum Works

## Overcoming the Forgetting Curve in Math

By Sarah Burns, UChicago STEM Education Curriculum Developer

How many of you have had a teaching experience similar to this?…

You know that fractions are a particularly tricky topic for your fourth graders, so you spent extra time planning your fractions unit this year. You worked slowly through the content and spent extra time on the unit, and that work paid off! Your students had amazing scores on the end-of-unit test! You felt really great about fractions…until the end-of-year math assessment. It was like most your students had never seen fractions before in their lives. Their scores on the fraction content on that test were the same as other years — not that great. You really thought they understood fractions. What happened?

## Understanding the forgetting curve

In order to better understand what and how people learn (including how your fourth graders do or don’t learn those pesky fractions), it’s important to understand what and how people forget. Some of the early pioneering work on memory was done in the late 1800s by a German psychologist named Hermann Ebbinghaus, who performed a series of experiments on himself that involved testing his learning and retention of nonsense words. In 1885, he published a book, translated into English in 1913, that reported on the results of his experiments. In this book, he proposed a “forgetting curve,” which depicted the exponential rate at which new knowledge is forgotten after it is learned (Brown, Roediger, & McDaniel, 2014). Ebbinghaus’s work, and decades of subsequent research, shows that 70% of what we read and hear is quickly forgotten. The remaining 30% is forgotten more slowly (Brown, Roediger, & McDaniel, 2014).

## How can a spiral curriculum help overcome the forgetting curve?

70%?!! That’s a huge amount of learning literally in one ear and out the other. Why bother to teach your class fractions — or math, or spelling, or grammar — at all if they are going to forget over half of what you teach?

Fortunately, Ebbinghaus and other cognitive psychologists have found ways to disrupt the forgetting curve and ensure more successful learning. One approach that is especially well-supported by research is a “spiral” or “spaced” approach to learning. You may have also heard this referred to as a “distributed” approach. What does this mean? In a spiral approach, learning is spread out over a longer period of time, rather than concentrated in a short amount of time. You can contrast a spiral approach to what might be called a “massed” approach. The fraction example above (and many commonly-used textbooks in the United States) employ a massed approach: one topic is taught in each unit to “mastery” and not addressed again instructionally the rest of the school year. In contrast, a spiral approach might spread the instruction and practice on a particular topic over the course of several months, or even the entire school year, allowing students to interact with the content repeatedly over time.

Distributing instruction and practice over time in a spiral is very effective in helping learners retain knowledge over a longer period of time. Research has shown it to be effective in a variety of contexts (in the lab, in the classroom, across numerous content areas) and with a variety of students (elementary-school, high school, and college students) (Roediger III & Karpicke, 2006; Roediger III, Putnam, & Smith, 2011). The U.S. Department of Education’s Institute of Educational Sciences recommends “Space learning over time” as the first overarching principle that teachers should attend to as they plan instruction (Pashler et al., 2007).

## What are the pros and cons of a spiral curriculum?

So, what’s the catch? If spiraling works so well, why isn’t everyone doing it? The short answer is that it is counterintuitive and hard. Researchers have found that people who study content in a massed format overestimate their knowledge of that content, while those who study content in a spaced format underestimate their knowledge, even though the spaced studiers outperform the massed studiers on subsequent tests (Bjork, 1999; Kornell and Bjork, 2008) . This outcome reflects the fact that a spiraled approach to learning is hard. It is what psychologist Robert Bjork (1999) refers to as a “desirable difficulty” — it requires learners to work harder to recall information. This work, although difficult, leads to better long-term learning.

## How to spiral in your classroom

We know that a spiral approach is difficult, but it pays off with better results in long-term learning. So how can you implement a spiral approach in your classroom? Here are some suggestions to get you started:

• Use a spiraling curriculum. There are commercially-available curricula that spiral learning and practice. If you are in a position to make decisions about the curricula used in your classroom, consider finding one that spirals.
• Use center time. If you have regular learning time at centers, dedicate one of your centers to review of previously-taught content.
• Leverage morning bell work. As students enter your classroom and settle in for the day, have them complete an activity that reviews content they haven’t seen in a while.
• Use choice boards. If students have extra time during the day, or if you have time built-in for some small group work, present students with a menu of activities that revisit learning from previous weeks or months.

A spiral approach can be incorporated into your classroom in many ways both big and small. It will be more difficult for your students, but the research shows it is worth the effort.

## References

Bjork, R.A. (1999). Assessing our own competence: Heuristics and illusions. In D. Gopher & A. Koriat (Eds.), Attention and performance XVII: Cognitive regulation of performance: Interaction of theory and application (pp. 435–459). Cambridge, MA: MIT Press.

Brown, P. C., Roediger III, H. L., & McDaniel, M. A. (2014). Make it stick. Harvard University Press.

Kornell, N., & Bjork, R. A. (2008). Learning, concepts, and categories: Is spacing the “enemy of induction?” Psychological Science 19, 585–592.

Pashler, H., Bain, P., Bottge, B., Graesser, A., Koedinger, K., McDaniel, M., & Metcalfe, J. (2007). Organizing instruction and study to improve student learning (NCER 2007–2004). Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education.

Roediger III, H. L., & Karpicke, J. D. (2006). The power of testing memory: Basic research and implications for educational practice. Perspectives on Psychological Science, 1(3), 181–210.

Roediger III, H. L., Putnam, A. L., & Smith, M. A. (2011). Ten benefits of testing and their applications to educational practice. In Psychology of learning and motivation (Vol. 55, pp. 1–36). Academic Press.

Sarah Burns works at UChicago STEM Education, a center devoted to research and development that aims to support high quality STEM instruction and learning for all students. Sarah can be reached at burnss@uchicago.edu.

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