One of a math coach’s primary responsibilities is to help build teachers’ mathematics content knowledge. To be truly effective as a facilitator of students’ mathematics learning, a teacher must first see herself as a competent and confident mathematician. But what if she doesn’t?
Many teachers possess fragile understanding of mathematics as a result of weak math instruction they received in elementary and secondary school. At the university level, pre-service teachers working towards elementary teacher certification in a traditional teacher preparation program typically complete just one mathematics methods course, a mere 45 clock hours to learning all about the elementary mathematics curriculum and math-specific pedagogy. Alternatively-certified teachers, approximately 25% of the current teaching force (Research News@Vanderbilt, 2016), lack even this minimal preparation for teaching mathematics.
Compounding a weak math background and inadequate preparation for teaching the subject is the fact that mathematics curriculum standards have changed in significant ways in recent years. Driven by concerns about international comparisons of student achievement, increasingly rigorous standards with a strong emphasis on problem solving and the mathematical practices have been handed to teachers whose own learning experiences revolved around an entirely different definition of mathematics.
Example: Computational Fluency
Most practicing teachers learned to add, subtract, multiply, and divide by mechanically applying standard algorithms. Research has provided us with important insights into how students learn to compute. As a result, our curriculum now requires students to develop computational strategies which are flexible and efficient, and based on place value understandings, properties of operations, and the relationship between operations. According to the National Research Council Report Adding It Up: Helping Children Learn Mathematics,
More than just a means to produce answers, computation is increasingly seen as a window on the deep structure of the number system. Fortunately, research is demonstrating that both skilled performance and conceptual understanding are generated by the same kinds of activities. (2001, p. 182)
Because of their own experiences, teachers may not understand how computational strategies are different from algorithms. Furthermore, unless they have taken the time to learn a repertoire of computational strategies, when faced with a situation requiring computation they likely default to using the traditional algorithm. Without understanding of and proficiency in using computational strategies, teachers are ill-equipped to help students develop such strategies.
Coaches can strengthen teachers’ mathematics content knowledge by providing teachers with opportunities to develop their own computational strategies based in understanding of number and operations. They can help teachers consider the benefits of strategy-focused computation for students.
| Differences Between Strategies and Algorithms: 1. Strategies are number oriented rather than digit oriented. 2. Strategies are left-handed rather than right-handed. 3. Strategies are a range of flexible options rather than “one right way.” Benefits of Strategies: · Students make fewer errors. · Less reteaching is required. · Students develop number sense. · Invented strategies are the basis for mental computation and estimation. · Flexible methods are often faster than standard algorithms. · Algorithm invention is itself a significantly important process of “doing mathematics.” · Strategies serve students well on standardized tests. (Van De Walle, Karp, & Bay-Williams, 2016, p. 256) |
Questions for Reflection and Discussion:
- What types of experiences might you provide for teachers to build their understanding of computational strategies?
- What are some ways you can help teachers see the value of strategy development prior to learning traditional algorithms?
- What professional learning structures do you already have in place which allow your teachers to be math learners? What other opportunities might there be to strengthen your teachers mathematical content knowledge?
References:
National Research Council. (2001). Adding it up: Helping children learn mathematics. J.Kilpatrick, J. Swafford, and B.Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
Van De Walle, J, Karp, K. S., & Bay-Williams, J. M. (2016). Elementary and middle school mathematics: Teaching developmentally. Boston, MA: Pearson.
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