Relearning elementary math - eye opening!

For the last two years I’ve been working with a couple of elementary students.  Unfortunately I only see them every other week, which really isn’t much tutoring time.  But it is what their mom can afford and will allow.

I’ve learned a lot by working with these children.  The math curriculum in our elementary schools is excellent.  The curriculum emphasizes finding solutions using multiple methods.  Typical algorithms are introduced after exploring a variety of other strategies designed to help students internalize place value and the meaning of each operation.

That’s been a bit eye opening for me.  I grew up with “old school” mathematics although I did attend school during the “new math” period following the Sputnik launch.  I was introduced to a few interesting things during that period – the one I remember was doing math in different bases.  But I didn’t really learn anything about decomposing or composing numbers per se – especially not that language.  Nor do I remember multiple strategies for addition or partial products, partial quotients. I have enjoyed learning new vocabulary and processes. 

I retired just as number talks were beginning to blossom at the secondary level.  I see number talks as a bridge between elementary and secondary math - a way for students to express how they compose, decompose numbers to facilitate arithmetic thinking.  I'm wondering if secondary teachers have the vocabulary to help students identify the strategies they are using ... making tens, compensating, doubling and combining nice numbers then fixing the differences.  I wonder if using the vocabulary to identify the thinking is significant.

Number sense is huge!  Marilyn Burns, in her 2007 book, About Teaching Mathematics, describes students with a strong number sense: “[They] can think and reason flexibly with numbers, use numbers to solve problems, spot unreasonable answers, understand how numbers can be taken apart and put together in different ways, see connections among operations, figure mentally, and make reasonable estimates.” This is a huge task for elementary math teachers! And describes well our hopes for every student!

Tutoring elementary students has made me wonder about teacher training.  I believe secondary math teachers would do well to spend some time learning how math is taught at the elementary level.  I know this idea is not new; SaraVanDerWerf mentioned it in a blog post some time ago.  In her post she encouraged us all to spend some time with Graham Fletchy’s progression videos ...  we might find them quite helpful in understanding elementary math!   If you missed that post and are curious about the bigger picture, the connections between elementary and secondary math, check out the resources she mentions!

My elementary students struggle with math facts and have some difficulty with problem solving.  Last year I felt like a lot of our time was worksheet focused, or test prep focused with some games thrown in.  This year I want to expand our work.

I’m thinking about using three-act type problems, hoping to inspire, excite, as well as provide opportunities for multiple representations, problem solving and productive thinking.

I’m aware of the collection of 3-act tasks for elementarymath that Graham Fletchy has created.  Can you point me to other “good” problems for elementary students?

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