Students need to master key skills before we move them on to new topics in math.
When I taught world history to middle school students in San Mateo, California, I gave them a decent run through history. We touched on the Greek and Roman Empires, the Battle of Hastings, the French Revolution, and so on. I took my job pretty seriously, believing that if students understood why things happened, learned about different perspectives of events, and were able to construct an argument, these skills would serve them well in the future.
One thing I did not have to worry about was how the material built over the course of the year. If one of my students didn’t grasp the Battle of Hastings, there was still a good chance that, if they focused, they could understand the French Revolution.
Math teachers have a totally different challenge. In math, one skill builds on another. From the day a student starts learning math -- adding and subtracting blocks, for example -- they are building a foundation. This foundation will determine the strength of their math 'house.' So if a student doesn’t learn how to add fractions, it will be difficult for them to learn to multiply fractions or determine ratios.
This leads to an important question: Why aren’t we ensuring that students have mastery of key skills before we move them on to new topics? Nowhere in the K-12 curriculum is mastery more important than in mathematics. If we allow a factory model where students are pushed through topics before they're ready to learn a new one, we are dooming them to failure. Yet many math classrooms still use this push-through model.
Since learning new math skills is so dependent on prior learning, students would be better served learning fewer topics and developing mastery than learning more topics without mastery. I would be willing to bet that the mastery approach would also result in higher test scores.
Sometimes teachers can be apprehensive about letting students progress at their own pace in MATHia. Yet moving students through content before they've mastered the necessary skills results in even bigger skill gaps and huge amounts of frustration. Likewise, keeping students back when they're able to go faster limits what they can learn. Neither is a good scenario.
MATHia is designed to give students exactly what they need to help them master those skills in their own time, because math learning isn't like history at all. Mastery is the key to success. In LONG + LIVE + MATH classrooms, kids are allowed to be masters of their own learning, which is something they'll need to do throughout their lives!
Peter is an educator with over 20 years of strategy, education and product development experience. He led the redesign of a university, built new educational programs, designed content and taught middle school. At Carnegie Learning, Peter shapes our organizational and product strategy and ensures that we continue to develop leading-edge products and services that help all students learn.Explore more related to this author
In math, one skill builds on another. So why aren’t we ensuring that students have mastery of key skills before we move them on to new topics?
Peter LaCasse, COO, Carnegie Learning