In a recent blog post I discussed 3 websites which can (should ?) be used by parents to engage their children in mathematical activities. I suggested that classroom teachers urge parents of their students to use these websites to build their own confidence and reduce their reluctance to help their own children. Parents, without formal training, can present a growth mindset for their children and participate in a positive manner that supplements the instruction going on in the classroom.

I’ve identified two additional websites below. I suggest these websites are not only for teachers of young children but for math teachers in general. I teach graduate math content and methods courses, and I always find interesting, informative, and important content at these two sites. Why? Because there are obvious connections between the math activities of very young children through elementary, middle grade, and secondary students, to the graduate students I teach. For example, I taught a graduate History of Math for Teachers course this summer, and I’m using a pre-school counting activity to enhance my instruction of early number systems (e.g. Egyptian, Babylonian).

So, don’t dismiss these websites as ‘beneath’ the grade level you’re teaching; I expect you’ll be pleasantly surprised by the research and resources you’ll find.

DREME Network (https://dreme.stanford.edu/)

The Development and Research in Early Math Education network at Stanford University was founded in 2014 to advance research in early childhood mathematics and improve opportunities to develop math skills,

The site contains a sub-site devoted to teacher education including resources for some of the ‘big’ ideas such as counting, operations, etc. Each of these contains learning modules and handouts. There are other sub-sites focused on Family Math, Executive Function (sustained attention), and coherence between Early Childhood and Elementary School math. For example, this link will take you to the learning module ‘Patterns and Algebra’ which contain pages of print, video, and vignettes resources for teachers. (http://prek-math-te.stanford.edu/patterns-algebra)

Early Math Collaborative (https://earlymath.erikson.edu/)

In 2007 the Erikson Institute launched the Early Math Collaborative to improve early math education through professional development, conducting research, and providing a source of information about foundational math knowledge in mathematics.

My favorite part of this website is the library of articles, videos, modules, and discussions. For example, the following link will take you to a short video showing a 2nd grader extending a repeating shape pattern to the ordinal numbers. (https://earlymath.erikson.edu/pattern-with-child-14-basic-geometry-in-elementary-school/)

Another example from the Early Math Collaborative is a professional learning module focusing on Measurement. The following link will take you to a portion of that module that my graduate students use frequently; the Children’s Literature link with dozens of recommendations for children’s books that don’t ‘teach’ math; they’re rich in possibilities for math activities. (https://earlymath.erikson.edu/modules/measurement/?fwp_formats=video&fwp_found=measurement)

I follow both of these organizations in my Twitter feed, and I’m regularly ‘stunned’ by the things I learn, the resources I use, and the suggestions I’m able to distribute to my math methods students.

“Because there are obvious connections between the math activities of very young children through elementary, middle grade, and secondary students, to the graduate students I teach.” I’d love to see a follow up post that elaborates on further examples here.

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The first concept that comes to mind is decomposition. We ‘expose’ children to decomposition in very early arithmetic (8 + 7 = 8 + 2 + 5 = 10 + 5). Decomposition is a powerful idea that develops fluency while employing problem solving and other high order thinking processes. There is no single procedure that can be applied to decompose ‘all’ situations. In general, students must think deeply about the problem and choose the decomposition most ‘suited’ to a particular problem.

We visit decomposition again and again throughout mathematics from factoring polynomials, to simplifying complex area problems into simpler collections of rectangles, to partial fraction decomposition for integration in calculus, etc.

Perhaps other followers of this blog can provide other examples.

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