Bottoms Up to Conceptually Understanding Numbers

This is just awesome! I am working my way down to the younger grades, and learning about this foundational pieces has been an eye opening experiences. I do not know if it is the length of time since I was this age, or the lack of experience in teaching these grades, but these are pieces that I just assumed we came equipped with. Learning that it is both purposeful and intentional to give students this experience plays out in so many fundamental ways, it also helps me think of the students I had in high school and college that did not experience this earlier success.

As I grow in my understanding of how students (and all peoples for that matter) learn and acquire mathematical knowledge, the more important these foundational pieces become. Funny how something as seemingly simple as an inversion to the number line creates understanding, like vertical number lines, these are difficulties we need to attend to, and we need to be careful how we accomplish these tasks.

All that to say, this is a great read and I am reblogging, more for personal reference than anything else, it acts as a reminder for that which I discussed above.

Questioning My Metacognition

The concept of 10 more/less is a beast in the primary grades.  Last week I realized that I’ve been feeding the monster that I’m continually trying to defeat. Almost every day, in every K-2 classroom across the United States students encounter this guy:

Screen Shot 2014-10-10 at 11.56.05 AM

I made a conscious effort to pop my head in every K-2 classroom in the schools I visited this week.  It was great to see that every classroom had a traditional 0-99 or hundreds chart posted like one above. 

While visiting, one of the teachers asked if I could come back today and model a lesson using a 0-99 chart because her students “just weren’t getting it.”  I gladly accepted her invitation and showed up with this guy:

Screen Shot 2014-10-10 at 11.52.19 AM

I didn’t use manipulatives for this lesson because I was specifically focusing on the rote counting process which precedes one-to-one cardinality when counting by ones OR tens.

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