## Saturday, July 6, 2013

### Saturday Sayings: It Makes Sense

First graders don't dabble too much in algorithms.  I suppose the double digit addition algorithm might be taught in some first grade classrooms towards the end of the year, but I've never been one to teach it that way.  In the past few years though, I've found that the quote above is true.  I don't have to teach to specific problem solving strategies or even algorithms for that matter.  When given the chance, kids can and do solve problems in ways that make sense to them.  They surprise me with the solutions they come up with, but most importantly, they understand what they're doing and can teach each other as well.  If math is supposed to make sense,  then allowing each individual to solve challenging problems in a way that makes sense to them, well, kind of makes sense.

(By no means am I an expert, but I hear there's a place for algorithms in the upper elementary grades but only after the kids have first been allowed to explore and invent their own strategies.  Once they have done so, the algorithms are more likely to make sense.)

1. I wholeheartedly agree, Tammy! I've taught both primary and intermediate grades and see the importance of letting kids explore in the younger years and then introduce the standard algorithms in the older grades.

1. Keri, it does seem to make sense, huh? They need to explore and understand what they're doing.

2. This is a good point, Tammy. I wavered back and forth last year, as I struggled to teach my lowest math kids how to "do" double digit subtraction. I started with just having them figure it out themselves - but then felt I "should" teach them the algorithm. Maybe for some kids that is just too much of a struggle for the end of 2nd grade, and they need to do it however it works for them.
Something for me to think about - when I start thinking about school - after another week :)

1. Sara, it's definitely a different way of going about things, but it's rewarding to see them explore the possibilities with confidence. Yes, something to think, but first enjoy summer! :)

3. I love that you have your students explore and explain how they came to their solutions. Building understanding rather than just memorizing is so helpful as they build toward more difficult tasks. Another great Saturday Saying, Tammy!
Lori
Conversations in Literacy

1. Lori, they sure do learn more when they investigate rather than memorize. It's pretty cool to watch.

4. Good thoughts. If it doesn't make sense to them...it isn't going to help them. Last year I was finally confident enough in my teaching to introduce a method of solving the problems from the manual, then saying "if that confuses you, don't do it that way!"

Crystal
Teaching Little Miracles

1. Crystal, it does take a leap of faith, but it's been sure lots of fun to see them grow into problem solvers.

5. OK, I'm gonna be honest here ... I had to ask my husband what an algorithm is. I've heard the word but don't really understand it myself ... so it was surprising to hear you talk about it in relation to first graders. What I do know is that when kids come to my counseling office with a problem, I'll typically ask them how they think they could solve it and ... voila ... they usually have something in mind. So it must follow with math and other subjects.

If only I knew when I started 28 years ago what we know now .....

Thanks, Tammy!

Barbara

1. Barbara, I love your honesty! I couldn't define the word until a few years ago, so don't feel bad. :) You've made a great connection to problem solving in general. The book I've been reading says that children are natural problem solvers.

6. I wish I had this to show my dad when I was a kid. One of the reasons I think I hated math so much growing up was having a Virginia Tech grad in engineering for a father! :) He had so many different algorithms to show me how to do one problem and I know I had my own methods of doing it that probably would have worked just as well-I just ended up very confused. So suffice it to say, I do agree with this quote! We let the kids play with words and come up with their own ideas, we should do the same for math.

NotJustChild'sPlay

1. Miss Trayers, I memorized algorithms when I was in school. I pulled it off and got great grades, but I didn't necessarily understand what I was doing. I bet I would have been better off making up my own strategies too. :)

7. The math series our district uses teaches the kids all kinds of ways to figure out answers. For some kids, it's not a big deal. I have had some of my lower kids that knew how to do the skill but totally bombed at the skill when I taught it a new way and even got confused on the way they knew. i don't have a lot of options, we are supposed to be using the series "with fidelity".
Kelly

1. Kelly, "fidelity" is one of my least favorite educational words. I don't think I do anything with fidelity. :)

8. Sometimes I think I learn more from my students than they learn from me. Just taking the time to listen to how students process information on their own is fascinating. Thanks for Saturday Sayings...It wouldn't be Saturday without them!!
Jenny

1. Jenny, that's the sweetest thing to say about Saturday Sayings. Thank you. I agree that their processing is fascinating. I'm so glad I've learned to let them do their thing and listen.

9. Love that quote. I love to watch my first graders as they process information. They amaze me how they arrive at some of their answers! :-)

1. Barb, they are so amazing, huh? They learn to be confident risk-takers too.

10. Hi Tammy!
Love this post! I have always "taught" the standard algorithm for double digit addition and subtraction to kids at the end of second grade. However, this past school year, I had a very low group of second graders and we spent extra time on conceptual development and having students develop their own strategies. I never "taught" the algorithm and kids had a much better understanding of multi-digit computation than ever before. The kids think so flexibly and compute so efficiently it is amazing!

Tara
The Math Maniac

1. Tara, that's really cool to hear. It's amazing how much math makes sense to them when they do discover their own strategies. Thank you for sharing.

11. Great post, Tammy. In BC we're not supposed to introduce algorithms until the higher grades for all the reasons you mentioned. Makes good sense.