For students in pre-K-5 there are four key elements to math education — content, competencies, ways of thinking, and motivators, according to a new report by the nonprofit PowerMyLearning cited in an article by The 74. The findings build on hundreds of earlier studies and will help kids enter middle school with a strong math foundation, PowerMyLearning CEO Arun Ramanathan says.
According to its Foundations of Numeracy report, content centers on the core mathematical ideas that are the basis of all future learning while competencies are the skills students need to use math meaningfully.
Ways of thinking encompasses the cognitive processes that support reasoning and problem-solving while motivators are the beliefs and mindsets that foster engagement and persistence.
“If you asked teachers what they think numeracy is, you will get a lot of different answers,” says Gloria Lee, lead author of the report. “There is not a clear framework or scaffolding for people to communicate all of these parts.”
The ongoing math debates pit explicit instruction, procedural fluency, guided practice and repetition against inquiry-based learning and conceptual understanding and result in unnecessary distraction, says the organization.
PowerMyLearning hopes its paper becomes a guide for educators and policymakers and says each of these foundations has four different categories:
- The four areas of content are integers, fractions, shapes and data;
- The four competencies are conceptual understanding, fact fluency, procedural fluency and application;
- The four ways of thinking are symbolic understanding, pattern recognition, explaining and sense-making;
- The motivators include math identity and persistence.
“Teachers, administrators and families must make intentional efforts to communicate that math is for everyone and everyone belongs in math,” the paper notes. “This requires explicitly promoting inclusive messages and countering negative ones, creating inclusive classroom environments, and establishing policies for support and acceleration rather than exclusivity.”
“Hopefully (the report) helps to bridge the divides in mathematics education,” says Jo Boaler, a mathematics education professor at Stanford University who co-authored California’s new math framework.
Despite ongoing disputes about how math should be taught, there is an enormous amount of agreement on what students need to succeed, says CEO Ramanathan.
“When you look at the areas folks are disagreeing about — conceptual understanding, fact fluency and procedural fluency — we put them all in one area, as competencies,” he says.
Students can’t spend all their time repeating certain skills, he says.
“They also have to be able to dig deeply into the reasons why certain elements of mathematics result in a correct answer,” he says. “For folks to be focusing on one element of that versus all of them together, when you see them all in one place, you don’t see them as (being) in conflict but in alignment.”
There is no need to favor one element of learning over another, the report notes.
“The evidence is clear that fluency with facts and procedures helps students with conceptual understanding and vice versa. Numeracy requires fluency with facts and procedures as well as conceptual understanding and the ability to apply these mathematical capabilities to situations in the real world.”
The 74
