Moreover, by “counting all” to get to 63, they’re essentially solving 63 groups of one (63 x 1) instead of nine groups of seven. One-step word problems like this shouldn’t feel like a race, but for most students, answering it correctly holds little value if they need to ruminate for several minutes.
Performing standard addition, subtraction, multiplication and division algorithms are also not useful if they can’t be done efficiently. Boaler is correct in stating that easy to use machines can solve these calculations for us. However, she fails to mention the longitudinal implications of not mastering standard algorithms through paper and pencil practice.
Addition with renaming helps children understand subtraction with renaming and multi-digit multiplication, both of which lead to comprehending long division. Mastering the long division algorithm is essential to understanding repeating decimals and later learning long division of polynomials. These concepts lead to partial fraction understanding, a prerequisite of learning how to quickly solve differential equations. Anybody pursuing a strong STEM degree (physics, chemistry, math, engineering, computer science, etc.) needs a well-developed understanding of long division and the other standard algorithms to learn many calculus topics. Therefore, denigrating or minimizing the value of teaching and independently solving algorithms in elementary grades can lower the ceiling on a student’s long-term mathematical trajectory.
Succeeding in mathematics requires deliberate concentration and prolonged focus, but there are regions of the subject in which efficiency is essential for success. Quick retrieval of math facts allows students better access to the discipline and many concepts they learn hold little value if they can’t be performed efficiently. Many Boaler disciples correctly understand that rapid computation does not make one an excellent mathematician. Too often, however, they interpret her teachings to mean that automaticity is not useful and practicing basic skills has no place in elementary math class.
They’re wrong.
Because every child possesses academic talents and deficiencies, teachers must make their students aware of both. The wisest teachers determine which students need encouragement, which need humbling, and the best words and timing to convey both. Regardless of a child’s academic confidence, every student needs to regularly receive positive recognition for their efforts. Praising students, therefore, is an integral part of being an elementary school teacher.
The best math instructors balance their lessons with fluency, problem solving, instruction, and practice. To build fluency, they teach strategies and carefully sequence problems that lead students to quicker retrieval of number facts. From time to time, they might celebrate children who have improved their basic skills, especially those who have been struggling. During other lesson sections, they recognize student cooperation, creativity, and most of all perseverance. Celebrating efficiency as well as slow, deliberate thinking – they understand – are coordinated, not mutually exclusive goals.
