I’m pretty stoked for a new blog hope idea that has been created by a pretty awesome group of mathematics educators (thanks Brandi from The Researched Based Classroom for organizing!.  The plan is to bring you multiple perspectives on a joint topic every couple of months.  This month there are 15 of us teaming up to bring you our thoughts on place value.  Make sure to ‘hop’ through all 15 posts to pick up some ideas about how you can use place value in your classroom!  You may even find a freebie, or product along the way that will help out as well.  Many perspectives and grade levels are covered.  I do hope you will enjoy our new endeavor!

This past week I attended a state level mathematics supervision meeting  and had the pleasure of hearing Dr. Sherry Parrish speak.  Dr. Parrish, or Sherry as she told me to call her (say what?!) is the author of the book Number Talks

If you are not familiar with Sherry’s work, you may want to check out this NCTM article from October 2011.  She also has a fabulous video of one of her talks on YouTube

Now, I’m not expecting you to look at the entire video right now (though, if you have the time it is ABSOLUTELY worth watching in entirety), I would, however like you to watch the first 8 minutes, paying close attention around from about 3:30 to around 7:00.

Did you hear what the student’s responded to Sherry?  Okay… so there’s an issue!  The kids know the algorithm, they know how to get the “right answer” but they clearly have no conception of what their numbers mean.  They have not made the connection between place value and their algorithms.

So, what can we as teachers students see the place value connections?

Personally, I think we teach alternate algorithms FIRST and then we start helping the students make the connections to the ‘more efficient’ traditional algorithm.  Let’s look at a example traditional problems and then look at some alternatives:

Pro : Efficient

Con:   What does that little 2 stand for? Why do we shift the second line or add a zero? Is it 5×2 or is it 5×20.  Little to no connection to what is happening.

Lattice method

Pro: Easy for students who aren’t great at multiplying.  Organizes information easily

Con: If taught rotely and procedurally, makes as little connection to place value as the traditional method. Students needs to see the connection between the diagonals and place value.

Area method

Pro: Easy to set up, helps students with decomposition, instant link to place value, direct connection to multiplying polynomials using manipulatives in higher grades, helps students “see” why the traditional works when placed side-by-side,  helps with mental math

Con: can be cumbersome to draw out with 3,4,5 digit numbers.

Partial Products

Pro: helps students with decomposition, direct link to place value, helps students “see” why the traditional works when placed side-by-side, instant link to place value, helps with mental math

Con: can be cumbersome with 2,3,4 digit multiplication.

Donna from Math Coach’s Corner has a great blog post on using partial and area methods that you should also check out!

Okay, so you’ve seen some alternatives now.  I don’t think that any of them is necessarily better than the other, but I DO think, that using the three alternatives FIRST is a great idea.  Get the students to have a conceptual idea of the place value.  Have them work fluently between the methods.  Then, once they have a grasp of what is going on, see how they do with the traditional method.   And, if a student prefers an alternate method… that’s okay!

Have you used alternate methods in your classroom?  What are your thoughts? How can you help parents transition to one of these methods?  I’d love to hear your thoughts!

Leave me a message letting me know your opinion and then head on over to Mr. Elementary Math by clicking on his icon to see what he has to say about place value

1. This post on alternative methods for multiplication is so important! In our school we teach these alternative models prior to standards because when students know alternative methods, especially partial products and the area model, they can better evaluate if their answer “makes sense”. If a student makes an error in the traditional algorithm, it is so difficult for a student to notice and self correct because the place value sense of “about” what an answer should be is not there. Thank you for a great post!

The Math Spot

2. Jamie,

I love this post. As a middle school teacher I am constatly hearing how “alternative methods do not work…why do they teach them.”

Here is my 2 cents (no pun intended). I love the idea of alternative methods….However you hit hte nail on the head when you said you have to ensure that eventually students go to the algorythm once they have the conceptual idea get them going on the more abstract. We do this in upper grades as well when we are introducing a new concept. Concrete-Representational-Abstract. I get tired of upper grades “blaming” lower education for “providing stupid ways.” I have about had it with the blame game. What we really need is to do is spend some time teaching the alternative (first as you said) and then allow students to try the other models and see how they connect.

Thanks for this post. As a fellow teacher of those middles…your honest opinon of the alternative methods is needed more in this world!

Cheers,
J.

3. I can’t believe it, but you just blogged about a method I’ve never seen! I’m in the middle of a math endorsement and all we talk about are student solutions and the lattice method is still totally new. Given enough time and practice, the students will develop the standard algorithm and when they discover it themselves, it will be because they have the conceptual understanding that allows them to make a generalization. Thanks for emphasizing that there are many ways to solve a problem.

4. I love how you have laid out all the methods with their pros and cons! I just got the Number Talks book and I can’t wait to apply what I am learning in the classroom. There is nothing like a really good teacher book to make you feel motivated and rejuvenated!

Tara
The Math Maniac

5. I like the way you compared the different methods. I like the Area Method that you showed, because it does translate into polynomials. This method makes it easy to see the place values, whereas the lattice method could get confusing if a student doesn’t get the order of the lattice.
Thank you for explaining them so well.

6. What a great post outlining the benefits and drawbacks of different methods. So important for teachers AND students to understand. Thanks so much for sharing!

Smiles,
Sarah