Math Learning is a Three-Step Process

So Little L is starting to really love math, and numbers, and skip-counting (2's, 5's and 10's for now, but she does ask about the other numbers as well). I'm admittedly a bit relieved, because for a while, she was only interested in reading, and I was a bit concerned that she would shy away from the STEAM subjects altogether. I'm a big fan of the humanities too, but in this world, you kind of need Math and Science to get anywhere.

Anyway, we just recently (as in this past week) started using our Math-U-See curriculum, which I love. We are still just covering place value, but the whole "Decimal Street" stuff was very intuitive for my kiddo, who was surprisingly engaged in placing the units in the units house, and the ten-rods in the tens' house. She has also taken to making tens out of the other various manipulative pieces (5+5, 7+3, etc). and since these particular materials are stackable like LEGO, you can squish them together to see just how different combinations can equal 10. It's totally K-1 curriculum appropriate, and I am loving it.

They say that to really comprehend math, you can't start with abstract representations. Numerals are abstract. They're like the last step of the math learning ladder. Before that, you have to learn about numerals as representative of a value, and before even the representation phase, you have to understand concretely what you're trying to solve.

CONCRETE -> REPRESENTATIONAL -> ABSTRACT

Math-U-See starts at the concrete level. I totally let her go wild playing with the pieces and matching them on the Decimal Street poster for the first day, and then we started counting with them. Once she started to understand place value (ones vs. tens positioning), I had her do some of the worksheets where she had to build the value they asked for, or colour in to show the value on the page. Since the worksheets aren't onerous (there are literally only 4-6 questions per double-sided page), she didn't balk when I made her do both sides. We counted out loud and used foam numbers to show what amounts the blue and green pieces represented, and then we introduced the abstract idea of showing the same value using numerals. 

Honestly, we did all of this in one lesson, but of course as with all things, your mileage may vary depending on your kid. Yours might not even need the concrete tools for these number concepts, or your kiddo may need tons and tons of practice with the concrete materials before you even think about having them draw pictures or colour to show "how much." 

Anyway, my blogging presence has gotten quite infrequent of late, due in part to Christmas, and also because of work and Christmas and a million other things. 

I wanted to share this, though, because many who choose to homeschool face the daunting tasks of having to interpret curriculum, and try to select from a vast and varied plethora of options for their kids' math learning. I'm a bit of a traditionalist due to the whole "teacher background" thing, so I love that Math-U-See comes with a teaching guide and the student workbook plus instructional DVDs (although we haven't used any of the DVDs since we no longer have a DVD player, because: Netflix and Apple TV). 

The best part, I think, is that the integer manipulatives we are using now for basic math concepts will also come in handy when we do start to look at the operations. There is also a fractions/decimals kit that we will eventually need to pick up, although that's still a few years away.

Anyway, what curriculum do you use with your littles? I've heard of Life of Fred and a few others, but this one has really been a great fit for us.