Tuesday, October 20, 2015

Common Core Haters, You Really Should do Your Homework!

***DISCLAIMER*** This blogger in no way endorses, supports, or advocates for Common Core State Standards, or any other federal or state legislation that robs educators of their autonomy in the classroom!

This news report just came across the virtual desks of a group of fellow teachers. We hashed it out, and came to the realization that this news reporter doesn't know 1) a thing about these standards, and 2) what is involved in the "old way" of doing simple math problems, and 3) how this strategy works.

How many times have you seen a video like this over the past 6 years?

I see two faulty lines of reasoning in this example which leads me to believe these opinion pieces are not meant to inform the public nor are they produced with the kids in mind. They are just simply haters who are gonna hate, no matter what the cause. And to be honest, I think it makes everyone who jumps on their bandwagon look like a bunch of numbskulls!

First, this guy (news reporter, NOT teacher) doesn't use an example that makes sense. Those of us teaching second graders this strategy are NOT using examples that DON'T require regrouping or higher order thinking. It is a strategy to apply in those exact situations. Second, just like all of the other CCSS haters out there, he oversimplifies the old school way.

Note to haters and hater lovers: It's only as simple as you make it because your K-2 teachers labored for hours to help you "get it" the way you got it! And chances are, your parents were complaining to anyone who would listen that this "new way" of doing math was ridiculous and should be thrown out of the schools.

Here's the real background to all that "simple subtraction" when using a subtrahend that requires regrouping:

Step 1 involves at least 3 other steps. Sure when you are using numbers like 23-3 you can eliminate those extra steps, but problem is, most of the problems our students will come up against later in life won't be that simple! What's more, when we tell them over and over again for 3-5 years that you can't take 5 from 3, it confuses them when they start working with negative numbers. Not only does this way bog down the processing power of our students, it also creates false mathematical reasoning that comes back to bite them in a few short years.

Instead, we start by teaching math partners, grouping in 5s and 10s. Students learn to quickly recognize partners of 5 and 10, this starts the same time they are learning to count to these numbers, so it's natural. Then we teach them to add, and that subtraction and addition are intrinsically connected (ok, maybe not that term). But they learn number bonds rather than addition/subtraction facts, helping them automate the fact families 2+3=5, 3+2=5, 5-3=2, 5-2=3. Then we teach them about place value, that 10 ones can be grouped to make 1 ten, and so-on. All of this groundwork is laid BEFORE problems like this are introduced.

Compare that "old way" to the real thought process of the "new" and "overly complicated way": 

Now our student sees this problem in all of its component parts. They are quick to find partners of 5 and ten, and they've developed mental math strategies that help them build up (the natural counting order) rather than count back (and get stumbled over 13, 12, 13). Just as in the case of the old way, most of this thought process isn't written out, it takes place in the competent mind of a young learner.

The question here isn't whether one way is more difficult, or even developmentally appropriate. It's which method lays a better framework for future maths. What is the purpose of K-2? Isn't it to help students develop the fundamental skills of reading and computing so they can tackle the more challenging content that will be thrown at them for the next 10 years? Decomposing numbers, using ten partners, and looking at subtraction problems as missing addend problems may be new ways of teaching fundamentals to second graders, but it's not "new math." The numbers still all follow the same rules as work together the same as they always have, no legislation has the authority to change that!

Here's a look at that first problem the news reported attempted to explain. First, there is no need to break this problem down once you've separated the tens and ones. This "new math" looks like this:
Looks pretty simple, doesn't it? 

No, this doesn't do this justice, let me see the examples that require regrouping to solve, side-by-side. And while we're looking at these, think about 2 things. 1) which one will cause less frustration in the middle grades when kids are going crazy with hormonal changes and life is just starting to get real? 2) which one requires the student to memorize less steps, thus freeing up valuable processing space for solving real life problems? AKA which skill transfers better into the real world of buying groceries and paying taxes?

And I just have to clarify, if the news reporter would have done his homework to learn how to use this strategy, and still chose the same problem, it would have looked like this: 

Final thoughts: News reporters, parents, and even concerned citizens, if you are going to complain, berate, and deride a way of teaching something, please, PLEASE do your homework! Stop making yourselves look like fools. When you jump on an emotionally charged bandwagon and retweet and hashtag everything you see that is against the same issue, without scrutinizing it, you are just giving the case into the hands of those you oppose! 

Dear teachers, tutors, and other educators, help me get the word out, pin, share, like, tweet, and repost (with a link back please) to help inform these poor uninformed haters! ;)

Monday, October 19, 2015

Teaching Math as a Second Language

I've had a dry spell here on the blog, so I want to start with, "Hey! How ya doin'? It's been a while!"

Today was a great day, I had 0 regularly scheduled students, and 3 reschedules. These days are great because there's really no rhyme or reason, and I get to learn a lot about myself. I started with an Algebra student, then went to work with 2 second graders (1 math and reading and the other just math).

I was reminded today about an old project that has been sitting in the dusty back edges of my "some day I will get to this" files. Ages ago, when I was in my 3rd year of college, I took a Teaching English Language Learners course. It was really a "for fun" course for me. There isn't a real need in my area, and I'm not fluent in any other language. I was just curious. I LOVED the course. There were so many valuable tidbits that I could see myself applying to so many areas of teaching English speaking students.

Of course, you well know that math is my thing. And I've heard time and time again, people crying, "I just don't understand!" It was the same cry I was hearing ELLs bemoaning! It hit me that Math is truly a completely unique language. Sure there are words that sound like everyday language, but they usually have a different meaning or application. I found, through some blind studies with my children, that understanding the vocabulary was a determining factor to understanding content.

Ok, now I have to shamelessly admit something here. I thought that this was a brilliant construct of my own, that no one else on Earth had thought of this, made this connection. Unfortunately, I cannot take the credit. While, yes, in my mind, it's all mine. I did some research that landed me on the page of a teacher, Herb Gross. I haven't done a ton of research into his philosophy and methods, but from what I've read, we'd have a lot of fun teaching math together. Herb, if you are out there reading this and ever find yourself in Michigan, look me up!

The basic idea is that as teachers we take a step back from the math curriculum, whether it's 9th grade Algebra or 2nd grade skip counting, and we look at it through the eyes of someone who doesn't speak the language. Rather than teach them "how" to solve a problem, we help our students understand "why" the solution works. Instead of using algorithms and formulas as our backbone of instruction, we use vocabulary and language development.

How does this look? 

The first rule is to front load vocabulary and key terms. I'll use the Algebra student I was working with today as an example. We've been working together for a few months, and I noticed right away that he didn't speak Mathenese ( I promise I didn't make that word up! See this search for proof:). I started each lesson with a moment to collect our thoughts and think about what we already knew about the key words. Sometimes it was nothing, sometimes it was a related word in science. For example, when we discussed dependent and independent variables he quickly remembered that a dependent variable was something that would be caused by something else, and that something else was an independent. Activating this prior knowledge, and connecting his science notes with his math lesson helped him to make sense of the entire lesson. 

The second rule is to infuse your lessons with visual aids.
A strategy borrowed from Teaching English Language Learners, providing visual aids helps our students process the information in a spatial way. They can connect colors and shapes to verbal cues. These visual aids can be 3-dimensional manipulatives, anchor charts, posters, charts, diagrams, or simple little drawings. I find that it is most beneficial to get  the students involved in creating these visual aids. After I've provided a cue I give them an opportunity to develop their own, and then we analyze their developments. This entire process not only helps each student develop understanding of the concepts, but also cements a learning strategy they can take with them on their life long learning journey!

The third rule is to use your student's native language as often as possible. I know this sounds a little strange when we are talking about teaching math to a student who speaks the same language as us. However, if my student is particularly interested in science, or quickly refers to science terms, I use that, and try to make those connections as soon as possible and as often as possible. A few years ago I was working with a 10th grade Geometry student who saw absolutely no need for math. This particular student had plans to be an artist, and was convinced math couldn't help her. When we started discussing perspectives in drawings and angles of lighting, I was able to see a light bulb glow for her. Immediately, everything we had discussed about adjacent angles of a triangle, and angles of elevation became crystal clear to her. Learners will naturally make connections to contexts they have a high interest in, so use it!

Ok, I think I've kept you long enough. I'll save some more of this for another post later. Here's to helping our students develop their Mathenese!

By the way, I'm developing an interactive notebook type of vocabulary journal for my 9th grade Algebra students, If that's something you'd be interested in, head over to my store and pre-order your copy. I promise to have at least a unit complete by the end of the month, and I'll keep adding to it throughout the year. As with all of my growing units, the sooner you you grab it the less it will cost ;) Here's just a little snippet of the first few pages.

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