I'm not an expert on standards by any means, but I know that the standards in British Columbia (where I was trained to teach) were coherent and made sense. You could follow the threads through the years and understand why they had been designed that way. I know that the Common Core content standards in Math have the same level of coherence.
I don't know if they are always appropriate, or how one even defines appropriate given the strong relationship between what set of standards students learn under, and what they are therefore capable of learning in later years. I know that recent research suggests that young kids are capable of learning higher level math than what is currently expected, with many or even most kindergarten classrooms practicing skills with students almost all of whom have those skills. I believe in play based early years teaching, but this doesn't preclude teachers from focusing on problem solving and pattern finding and continuing to develop students' number sense.
What I do know is that the Common Core Standards for Mathematical Practice (SMP) are not pedagogy-neutral.
These non-content standards require students to be able to make sense of problems and persevere in solving them. This requires teachers to offer opportunities for students to problem solve (this is how some people define "doing mathematics").
Students have to be able to construct viable arguments and critique the reasoning of others. While this could be done entirely through paper and pencil means, it is far easier to teach students to do this by regularly engaging them in dialogue and giving them opportunities to discuss mathematics together.
Students have to be able to model with mathematics, which again means that they have to be given opportunities to do mathematical modelling. The type of mathematical modelling described in the standards requires students to be able to make sense of problems resulting from everyday life, which means that teachers should be using examples of problems that result from the cultural contexts students live in (it's not everyday life if it's someone else's life).
These are just three of the eight SMP, and the other five SMP also have pedogical signficance attached to them as well. The SMP require that some teachers teach differently than they do, and that therefore hopefully more students will get opportunities to grapple with mathematical ideas.
What I think we need to be careful to recognize is;
David is a Formative Assessment Specialist for Mathematics at New Visions for Public Schools in NYC. He has been teaching since 2002, and has worked in Brooklyn, London, Bangkok, and Vancouver before moving back to the United States. He has his Masters degree in Educational Technology from UBC, and is the co-author of a mathematics textbook. He has been published in ISTE's Leading and Learning, Educational Technology Solutions, The Software Developers Journal, The Bangkok Post and Edutopia. He blogs with the Cooperative Catalyst, and is the Assessment group facilitator for Edutopia. He has also helped organize the first Edcamp in Canada, and TEDxKIDS@BC.
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Common Core Practice
I read some of the SMP stuff, and it is so much more readable than the CCSS documents. Well done them!
And do we expect a grade 1 teacher to understand the higher mathematical jargon which appears, for example "associative law of addition"?
However, the stuff on fractions is still designed to create confusion. Is a fraction a number or isn't it? It cannot be both. Not even at different times.
I asked one of the mothers in our ballet studio "Are fractions numbers?" and the answer was a very definite "No!".
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