Learning Outside The [Lattice] Box

This is a picture of a method of multiplication called "lattice box".

I learned it in elementary school (I think 4th grade); a friend taught it to me (not the teacher). I learned it at a time when I was struggling with multiplying numbers by hand, and this idea was just what I needed to get me through! I have been doing it ever since. It made sense to me when other methods of multiplication really did not. I think it is awesome and I still use it on tests and homework today. I will draw the little boxes out in the margins of my paper (see right).

I have had a few (3) interesting encounters with people when they discovered I use this technique. I'll just list those right now.

1.) my first math teacher this year (no longer working here), called me out in front of the class when I asked him to work out a multiplication problem on the board, by saying to me
"You use a different method. I can work this problem out with you later."
2.) my current math teacher, when in private, just me and her, acknowledged that I use this method and said "I don't like this method. My daughter started using it and I'm so glad her teacher doesn't letter. I just prefer the other way. I'll still let you use it, but it doesn't make sense logically or mathematically. I don't like it".
3.) fellow classmates (Amber & Kaela) when en route to the Pumpkin Patch, saw me doing it on some math homework, and they both were really curious. Both of them wanted me to teach them later, they were so intrigued. I taught Amber the basic premise right there because she was beside me but seeing as how Kaela was driving at the time...we agreed later would be better. :)

What I gather from these three instances, is that there is a way to go about external criticism correctly and successfully and then there is another way to make a student feel terrible and like their hopes and dreams were stomped on. It's a good thing I use almost all my negative teacher observations for the edification of my own future career and philosophy because otherwise...wooo-wee, I know I would be absorbing a lot of these to-me hurtful comments. I feel like a teacher never needs to voice to a student (regardless of how old they are), that they don't like a certain method they are using. Nor do they need to bring the entire class's attention to the fact that they are using it. If it's working, if that student is getting correct answers and learning something and not cheating or using a calculator, WHAT'S THE PROBLEM?! I hate the mindset of public education, that enforces there is ONE way to solve a problem. Not everyone learns in the same way! Not everyone uses the exact same techniques. That's a beautiful thing. That's what makes us unique!

(This is just random math).

I want to as a teacher, really strive to use the "Amber/Kaela approach". I want to be genuinely interested in the ways my students use to approach a problem. Especially if it is in a subject area I know is not their favorite, or not their strongest, I want to be first of all appreciative that they are trying. Instead of being critical of their difference, and desiring that they conform to the "textbook method", I am going to try to celebrate their own way, and encourage them to keep using it if it works for them. If they are trying to use a method that is not effective, I will tell them when alone, not in front of the whole class, and I will work very patiently at trying to teach them until they do learn it, or maybe we can try to put our heads together and come up with a better method for that student. Now, I know there's no way on earth I am going to be a math teacher (no offense, Amber), so I am trying to extend this thought process to my subject area too.

The bottom line is that I want to encourage them to think outside the box, to go beyond what their classmates are using, what they've always been forcefed, and really apply themselves however they want to (within reason..). That is a lesson they will carry outside of my class. If a student invents their own method that no one else has thought of or put in a book, I want to express to them how amazing and smart (careful...) that is (but not in a way that sets them apart from or above other class members) . When one-on-one with a student, I could be more freely honest with a student about their intelligence. I really want to try to get on my student's level (see below). I don't want to be stooping above them, or seem like I'm on a pedestal of knowledge and experience (even though I am..just kidding!) I want to listen to them, try to understand them, before I give any advice or impart any wisdom. This is a personal goal of mine, hence this categorization. I want to set up my priorities and rank the importance of how I react to my students, and being humble is way up there in the top 4.