Strategy #3: Be More Prince – Discussion

[Maggie Moor]

I hadn’t thought of this before, but I think I can use those interlocking blocks to teach multi-variable algebra. Hmm. HMMM!

I am guilty of rushing my students into an algorithm. Then again, it is not always easy to judge who is ready to make that transition and who is still leagues behind. I have a grade 8 student who has made it this far with (seemingly) no conceptual understanding of multiplication or division. She can do it with a calculator or table, but she has a hard time understanding that multiplication and division are effectively opposites. I wonder how I can support students like this in the same room as students who are roaring ahead at lightning pace.

[Kyle Pearce]

Ohhhh I KNOW you can! There is so much that can be done when we ask ourselves “how” or “why does this REALLY work?”

I’m excited to hear what you come up with!

[Amy Kopcznski]

The Prince reference really hit the nail on the head for me regarding the amount of time it takes for concepts to build and progress through concrete to visual to abstract. I also appreciated the separation within concrete of using the actual objects and then manipulatives as well as using symbolic prior to operations and numbers within abstract.

The math department at my school really dug into using algebra tiles in all three grade levels this year. Prior to us working at home, sixth grade was able to see how they could be used when working with the distributive property, seventh and eighth grade was able to use them when solving equations. Now that we are all working at home and not able to access these manipulative that are in our classrooms, how can we continue this exploration and discovery through manipulatives with our students virtually?

[George Garza]

I think in high school math I have trouble seeing how to make some of these ideas concrete so they can be modeled with blocks or tiles. I know putting in the time and effort to do so will really help students understand.

There’s a scene in the movie stand and deliver where Mr. Escalante announces that they are going to start learning about fractions, and he puts on an apron, pulls out an apple and a big knife. That would be a memorable moment that he started with a concrete example. I need to do likewise for my math kids.

[Kyle Pearce]

It is definitely more challenging as we move through the grades. Keep in mind that “concrete” doesn’t always mean math manipulatives.

A great start is algebra tiles, in my opinion. Have you used them for like terms? Solving equations? Expanding? Factoring? All great ways to help kids experience math!

[Valerie Silver]

I tried Algebra tiles and the didn’t get how to use them! Guess I didn’t do it right.

[Kyle Pearce]

It is definitely a progression. If students haven’t used base 10 blocks for multiplication and division, then they will try to proceduralize the use of the algebra tiles which isn’t helpful. Ensuring there is a clear understanding for multiplication of whole numbers to expanding with algebraic terms is so important.

[Nicolette Kranz]

The power of manipulatives, it is so easy to go straight to abstract.

[Kyle Pearce]

So true! We always have to remind ourselves to slow down!

[Debra]

I am guilty of guiding my students to the abstract too early. I see the value in focusing on the concrete first (manipulatives), which leads to the visual representations in drawings and diagrams to the abstract (symbolic).

[Kyle Pearce]

Awesome to hear. Something else I’ve come to realize is that all three should be used interchangeably throughout the process so connections can be made. I often thought that after some time, we’d move on to the abstract and not go back to the visual or concrete.

[Kristin Priola]

I like the Cuisenaire Rods to show relationships. I love how you can stack them and show them what multiplication really looks like! They can also get very complex when making equivalent snakes. They are amazing!

[Mereana Povey]

Hi,

I see the value from taking the students from concrete to abstract. Visual is most value to put in front of them first, then breaking it down to the abstract as they progress.😀

Thanks!

• This reply was modified 1 year, 2 months ago by  Mereana Povey.

[Kyle Pearce]

So glad to hear it! Go be more Prince 🙂

[Rebecca Hyde]

I have a lot of very low students in my classes. On a particular test we use statewide, they core below 10% of the State average for their grade. Most are below the 50% mark. These students are generally ESL and likely lost the opportunity to learn many basic skills in lower grades than 7th grade that I teach. As I listened to the presentation, it occurred to me that they may still be in the concrete area for learning. Giving them concrete examples just may be the boost they need to bridge over to the abstract understanding of the concepts I am teaching. Thanks!

[Kyle Pearce]

Give this a shot and keep us posted on your updates. You may be surprised at how much support they may require to get over some of their barriers.

[Michael Scott]

The CRA model is something in which something I strongly believe but did not enough of it in the classroom. I am tried to do as much visual teaching as I could because that is how I learn. Some concepts are difficult at least for me to teach visually with discovery to spark the curiosity. I am very interested in learning how to do this.

[Bryce Boudreau]

I have found algebra tiles to be effective in teaching the distributive property, as well as factoring quadratics.

[Nancy Yamagata]

I appreciate the idea of going from concrete to abstract…I get that this is an introduction – I’m looking forward to the “How to Teach Algebra” for specific examples/strategies that use this idea in the lesson. I use area models extensively but (I’m a HS teacher) but, many of my students did/do not know how to find the area of a rectangle…which made this tool a little more challenging to use.