Visual Models vs Algorithms

There has been a substantial increase in the use of visual models in my class compared to last year. As a beginner teacher with no experience, I taught like how I was taught. This year however, I understand how important conceptual knowledge can be, and what a better way than to visualize it. It's the reason why some of the weaker classes can keep up. Visual models are good for everyone. Just because a student is in the algorithmic stage (as in, they can solve a problem algorithmically), doesn't mean that they have the conceptual knowledge.

I have been wondering lately though, when should I take students off of visual models and move them onto the division w/ fraction algorithm? Some higher level students are annoyed with drawing models, but I want them to understand that this is a tool they have in their disposal at any point in time, not something that's disposable just because there is a faster way.

We have been doing a lot of division with fractions lately, and we've gone as far as division with fractions with uncommon denominators. And I must say, it did occur to me that the model for division with fractions is a piece of extra work when the algorithm is so easy to follow.

VS.

 

The downside to the algorithm is that it literally conveys no conceptual knowledge at all. I want to make sure students have a solid foundation of what division is before moving onto the next topics (long division/GCF/LCM). In the long run, I'd rather be safe than sorry. I think when students have shown that they can compute or solve word problems fluently with the visual model, then I can teach the algorithm and we can move on.

Congratulations to Class 604!

I wanted to give a special shot-out to class 604 on the blog! Their math skills have been on such a SHARP increase lately! They are experts at Mathematical Practice #1:

Because this class NEVER gives up when given a problem, we have been able to struggle for some time, and learn new math. I am very impressed by their ability to try their hardest and to ask questions. They will become expert mathematicians in no time!!! In addition to coming so far with math, they are also now an ALL gold token class! Congratulations 604, I am proud of you all.

Signed,

Mr. E

The 8 Mathematical Practices

I remember weeks ago when I made the following post: MP Posters. I found a sweet post on another blog that actually broke down the 8 mathematical practices into kid friendly language! You can check that blog here: MP.

Really awesome and helpful for students to refer to at any point of a lesson. I decided to use the same words but make/decorate my own posters using Word 2010. Here is the final product:

Hoping that staples did them correctly and that I can pick up the order tomorrow and have them up by the middle of next week!

A Mathematician's Wish

Perhaps the biggest thing I wish I could do right now is create small posters for each of the MP standards and hang them around my room. What I want to do is break each one down into kid-friendly language so students can actually understand what they mean. This way, the students and I can refer to them before, during, or after each lesson and recap which, when, and how they were used.

Problem: I am completely clueless when it comes to things like this and I haven't the first clue of how or where to get something like this done. I am terrible at decorating or making things look nice (unless it's on a computer). When I actually do have materials, I try way too hard and end up epically failing anyway. I almost ruined my room with acrylic paint last week.

Lost cause? I have some small poster paper in my room that I'll try to use tomorrow and see what happens.