As both a teacher and administrator, I often heard from parents whose children were exceptionally good at math. “My daughter already knows how to multiply four-digit numbers, so third grade math is too easy for her. She needs to be accelerated.”
There’s lots of research to support acceleration as a strategy for gifted learners. The Acceleration Institute, part of the Belin-Blank Center at the University of Iowa, recently produced a report entitled “A Nation Empowered” which details the enormous benefits to accelerating a student when he or she is performing well above grade level.
Researcher Jonathan Wei of Duke University says, “All students deserve to learn something new each day.” In math, the obvious way to learn something new is to accelerate the instruction, letting the student go on to the next topic or grade level. But “learn something new” is not the same as “learn the next thing on the district’s scope and sequence.”
There are three dangerous and faulty assumptions behind our rush to accelerate everyone who’s a little advanced in math:
- Elementary math is a race to algebra, and the first one there wins.
- Learning math means accumulating basic facts, algorithms, and content knowledge.
- The only things worth learning in math are in the curriculum.
Instead of immediately leaping on the “faster is better” bandwagon, let’s consider why slower may, in fact, be better.
3 reasons slow math is best
1 – Elementary math should provide a solid foundation for algebra and higher math.
Just as you would never dream of building a house without a foundation, we shouldn’t rush to algebra without solid and deep understanding of our number system and its properties.
Algebra is critically important for being able to do higher level math such as geometry and calculus. Many of the skills and concepts needed to do algebra well, however, are things that young brains are not ready to grasp.
Instead of flying ahead into content that is beyond the neurological capability of many children, why not allow them to dig deep into more sophisticated applications and understanding of the core concepts of the elementary curriculum? Just because a student can successfully multiply four digit numbers doesn’t mean she understands how the standard algorithm works or why it’s an efficient way of doing that computation.
Exploring those ideas will give the student a much better grasp of concepts which will make algebra much easier to learn and comprehend when the time comes.
2 – Learning math means applying facts and skills to solve important problems.
Taking the last idea a step further, we not only want students to be able to accurately compute the product of two four-digit numbers, we want them to know what kinds of problems can be solved with that computation, and when to choose that approach. Instead of just playing scales, let kids play real music.
It’s one thing for someone to know how to operate each control on an automobile. It’s an entirely different thing to be able to use them all effectively to navigate on a road. And it’s yet another thing to know what to do when someone unexpectedly pulls out in front of you on the highway to maintain control of the vehicle.
3 – Math is much wider and deeper than the school curriculum.
We treat math as if it were a river. The school curriculum tells us where on the river we should be at a given point in time. This thinking limits our options when a student already knows the content wherever we are in the river: row faster and go farther downstream.
When we realize that math is a vast ocean, though, we have many more opportunities. The curriculum may be the Gulf Stream, flowing steadily and reliably towards Europe (i.e. Algebra), but there are plenty of other places we could travel on our journey across the sea.
For one thing we could dive deeper: take a concept and explore it from different angles, discover interesting or complex applications and connections, write about it, or simply pursue an idea more thoroughly than is possible in a regular classroom lesson.
We can also explore the regions of the ocean beyond the Gulf Stream. In other words, instead of going faster or deeper, we can go sideways. There are many areas of mathematics that are not part of the K-12 content standards but which can enhance and support overarching problem solving skills.
Combinatorics, set theory, game theory, cryptography, and historical number systems are just a few of the topics we don’t touch in schools but which are both engaging for students and important parts of mathematics in the real world.
Keep your options open. If you have a student who’s really good at math, celebrate! Then, instead of hitting the accelerator, try taking the scenic route.
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Gerald Aungst has more than 20 years experience as a professional educator, specializing in digital technology, mathematics, and gifted education. In his various roles as a classroom teacher, gifted support specialist, administrator, curriculum designer, and professional developer, he has worked to create a rich and vibrant learning culture. He is also passionate about improving learning opportunities for all students. Gerald is a founder of AllAboutExplorers.com and ConnectedTeachers.org.