Math is a verb!!!

Problem solving and getting kids to think is really what the whole school day is about. Though we break it into subjects and time slots, the process is all about doing those two things. It just so happens that math is often thought about as only procedures. It's like knowing the alphabet and being able to make words, but never putting words into anything more complex than a few sentences.
 Words are the things we recognize as the symbols for oral and written communication. In this same way, the symbols in the language of math communicate ideas and the ideas get more and more complex. And that is because the problems become more complex.

The idea is to remember that the real mathematical purpose behind symbols is to communicate tangible concepts (or intangible concepts as the math become theoretical).

For adults, think of how signs on the road are a part of driving. Driving is complicated by many variables and reasons, tasks, and material. Signs are essential, but more needs to be known to drive.




The pictures in this post were from last week as the kids moved through timed stations with an unknown dividend/product and to figure out the multiples. It was a way to assess their strategies. By the 3rd move, the partners were able to find the factors or non factors for the mound of "gold nuggets." They had 10 minutes per station. On Tuesday, we went over the numbers and wondered about the process. And, that just knowing the math facts is essential, and a tool.

Are there remainders, what does that mean?

This week using their thinking in solving real word problems has been hard and interesting. 4th graders are really learning that thinking is problem solving and the first step is figuring out the problem and what to solve for, whether you are doing some math thinking, writing a narrative, or driving a car. (These are just a few of the metaphors that are probably popping into your mind.)

How do you want to group? Why?

Prime or not? Why?

 
 Using any type of manipulative to make a number have real value is key.

 Cooperation of how to figure out the process was a large part of this activity. Checking and keeping record. Counting by multiples, noticing patterns and having a game atmosphere because of a time limit kept it lighthearted. There were no creepers though. Next time. :)

 If students were counting by ones, I stepped in to remind them to use a more efficient method. Often, the students rely on what is comfortable--just like us--so getting thinking to move is the support I provide.

Friday night and into late Saturday this past weekend, I got to do some great Professional Development in CDA working with other math teachers throughout the region. We work on what we attend to when working with students, crafting questions for interpretation, and helping to respond to needs. The goal is to have kids think deeply by helping them develop their number sense to apply, analyze, and communicate their thinking. We dissect video footage of kids doing math. It is fascinating and  a time of great reflection for what I get to do each day!

 Every pair was matched by how easily they worked together. These partners also share where they are as math thinkers. By partnering the kids in this way, this time, was to allow them to learn together and not have one person lead while the other listened. Participation is key to individual growth. When kids work cooperatively and then have time to go back over the work, as we did, they create connections and make analytical leaps in their problem solving and content knowledge.

Focused and Fun, Engaged and Interactive, Supportive and Logical Thinking