As part of some of the other discussions I've had about it, here's a blog post that was posted from someone in my area:
Is it Common Core or is it Good Number Sense?
A recent Facebook comment stream criticized Common Core standards as well as second grade homework. Some misconceptions were evident. I hope that the information found in this blog entry will make the goals of math learning in Leicester (and in Massachusetts and the rest of the country!) more clear.
Second graders have been practicing addition through grouping. This idea comes more naturally to some than to others, but is, in fact, something good number thinkers do at all ages. Here’s what I mean….
If you were adding ½ cup sugar to ¾ cup sugar, you’d know you’d have a cup and a quarter, not because you found the least common denominator, converted both numbers to equivalent fractions with that least common denominator, then converted to a mixed number and fraction, like this:
1 + 3 = 2 + 3 = 5 = 1 ¼
2 4 4 4 4
Instead, you would know because you would “deconstruct” (in your head) ¾ as being ½ + ¼ then you would recognize (grouping!) that ½ + ½ = 1, so the end result would be 1 and ¼. Of course we do want to teach our students the standard algorithm of finding the least common denominator, but we DON’T want them to only know that way!
Second graders are not working with fractions but, instead, are working with whole numbers and grouping 10’s. For 9 + 4 …. We know that 9 + 1 = 10 and 4 is just made up of 3 + 1 so we’d have one ten and another 3 so the answer would be 13: 9 + 4 = 9 + 1 + 3 = 10 + 3. I know parents know this but if you are doing it automatically, realize that your child isn’t, so we’re working on teaching them that.
Here’s another real life example: When adding and subtracting money, we group by dollars (100 cents). If I added 85 cents to 30 cents, I know in my head that another 15 cents would make the 85 cents a dollar and I also know that 30 cents is 15 cents plus 15 cents, so I’d group the 85 cents with one of the 15 cents to make a dollar, leaving 15 cents. So, the answer would be a dollar and 15 cents.
The way this second grade standard is written is:
Fluently add and subtract within 20 using mental strategies (counting on, making ten (e.g. 8+6=8+2+4=10+4=14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 =9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6+7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Now, you might say, “who in their right mind would subtract 4 from 13 using 3 steps like the example just provided?????” Of course, one wouldn’t do this in practice, but as we teach these young students the strategy we want them to do it out the long way. Once they learn it, it can be done in their head. Through this work, we are making great mathematicians.
While I did provide the current standard, please don’t think this is anything new. My son is 27. He was in 2nd grade in 1994 – well before the “Common Core.” He learned math this way 20 years ago and I am proud to say that he can do mental math (and any other kind of math as well) with ease. Some requirements of Common Core are, in fact, a bit different, but mostly in the depth of understanding of these mathematics concepts we are asking our students to show.
Why do some blame the Common Core for these approaches? Unfortunately, the Common Core has become a political football. Those who are against central control or government in general don’t want to see national standards or anything that looks like national standards. So, while we argue whether or not to have national standards and whether or not the ones we have are any good, a significant portion of the world’s nations that have national standards are running circles around us. We need to move forward in a positive way and to do that we need everyone here in Leicester – students, teachers, parents, and politicians alike – to help ensure a positive learning environment both within and outside our school walls. When homework or assessments aren’t clear, ask a teacher; we have wonderful teachers that are ready to help parents as well as students.
