Geoff Osterland EDSP 579 Spring 2011
Invented Strategies for Mathematics
What is it?
Invented Strategies can refer to any strategy other than the traditional algorithm. Invented Strategies do not employ the use of physical materials or counting by ones to produce a product. It may be easier to think of them as personal and flexible strategies (as described by Van de Walle). These strategies are built on students’ own ideas and understandings, and often rely heavily on story problems and children’s literature.
Benefits of Invented Strategies
- Enhancement of base-ten concepts: research has found a relationship between the development of base-ten concepts and the process of inventing computational strategies.
- Built on student understanding: students will not often use a strategy they do not understand, and frequently cannot explain why traditional algorithms work.
- Students make fewer errors: systematic errors are much less typical of invented strategies as opposed to traditional algorithms.
- Serve students at least as well on standard tests: students using this method achieve similar results to students using traditional algorithms. Students using Invented Strategies also tend to fair better on word problems.
How does it work?
Explain to students that the standard algorithms are not always the best methods to use. Break students into “teams” and challenge them to try to come up with a faster way to solve a problem. Make sure they can explain how they got to the answer. Try embedding the computational tasks within a simple context, such as a story problem. By using this method, you can tailor your story problems to your advantage, to try to coax a particular strategy out of your students. The use of children’s literature may also be helpful here. Van de Walle (2006) suggests a book called Cookies about the history of the Famous Amos cookie business. This may help get students engaged in the subject matter. The most important aspect of Invented Strategies, however, is that students are able to explain their solution methods. This is where whole-class sharing is essential. Students must be able to share and explain their methods, to ask and answer questions of their classmates and to learn and build on others’ strategies. Van de Walle suggests making a firm rule that no one may use a strategy that he or she does not understand.
Examples of Invented Strategies
Four strategies for 46 + 38:
1. Add tens, add ones, then combine (40 + 30 = 70, 6 + 8 = 14, 70 + 14 = 84)
2. Add on tens, then add ones (46 + 30 = 76, 76 + 8 = 84)
3. Move some to make tens (44 + 40 = 84)
4. Use a nice number and compensate (46 + 40 = 86, 40 – 2 = 38, so 86 – 2 = 84)
Information gathered from Teaching Student-Centered Mathematics, by John A. Van de Walle and LouAnn Lovin (2006).