Even if I wasn't using computers and iPads in my classroom, my teaching would still be completely different from what it was five to ten years ago. Way back when, I started learning about teaching for true understanding, critical analysis, and creative creation. These ideas was alluded to in my teacher training, but that was so long ago they were just in their infancy for most of the teaching community. Working with manipulatives and understanding the concepts and patterns of math BEFORE showing how to record them with arithmetic algorithms was just the first step. Now I ask students to use what they know to solve problems well above their grade level using teamwork and critical thinking skills. Being smart is using what you know to figure out what you don't know. Even after this arduous process I won't check students' work because that's not how it works in the real world. Mathematicians and scientists don't have anyone to tell them if their theories and calculations are correct. They compare results with their peers, so that is what my students do. Storytelling has changed as well. No longer do I accept just regular writing. I want exciting and precise vocabulary, proper organization, and exactness of detail. And the excuse, but they are just first graders won't fly with me. They aren't JUST first graders, they are FIRST GRADERS! Empower the students, teach them foundational skills, get out of their way, and they will amaze you. Now, add in to this the use of computers and iPads and the revolution grows. Geography takes on true meaning when you are in the midst of a mystery location call, bloggers have a world wide audience, your partner on that last project was not your buddy from class but your buddy from across the world. My students have close to the sum of human knowledge at their fingertips. But as Harold Wheeler says, they need to develop their crap detectors, because let's face it, there is a lot of crap on the internet. My kiddos don't me to teach them details, they need me to teach them how to find the accurate information they need in order to solve problems. If you can be replaced by a video, you should be! So, with the switch to the "new" common core I wonder what is "new" about any of it. Assessing the processing of information, critical thinking, and problem solving skills of students is nothing new at all. It is just so much more exciting and customizable with technology.
Are you cringing already? I know, many adults say they "aren't math people." But you are wrong. You might not be fast at your reasoning and calculating, but that doesn't mean you can solve mathematical problems logically. Really, anyone can do it. My first graders are proof. What was this problem they worked on for so long you wonder. Well, here's the best part, some of the kiddos needed more time the next day in order to finish. Whaaaatt? Yes, my little kiddos were figuring out how many stripes we needed in order for every student in the class to make an American flag. How man red stripes, how many white, and how many in total. Yes, first graders were working on this problem. I figure if they can add 7+7 to figure out how many stripes on two flags, why not three, or seven, or sixteen? And they did it! Even better, they did it with a sense of excitement and enthusiasm.
Some used blocks, made piles, rearranged them into groups of tens and counted. Some drew arrays of squares, colored in groups of ten and counted that way. Some used multiplication to figure out the number of red stripes, then subtracted sixteen to find the number of white stripes. And here's the kicker... I refused to check their answers. I'm training these kids to be mathematicians, not to fill out a worksheet. How often in your adult life do you fill out worksheets? This means the kiddos have to find an answer, and solve the problem in at least one more way where they will hopefully get the same answer. Then they need to check their work against that of fellow mathematicians (classmates) to see if the results can be replicated. This is how mathematicians work in the real world, so this is how the mathematicians in my class work. We call this comparing of strategies and answers Math Conferences. I go to teacher math conferences to learn from and teach other teachers, so my students go to student math conferences to learn from and teach other students. Now this work ethic didn't magically implant itself in the brains of my students, we trained for this. We do work on daily math lessons with instruction and practice, and we start the year with simple math problems. But just like training for a marathon, you build strength and stamina until you are a finely trained athlete. The same is true for becoming a mathematician. All it takes is training, practice, and perseverance. Working persistently, and for great lengths of time, in order to solve something that needs to be solved is a skill that will serve these children well in their lives. Careers, relationships, life traumas and emergencies... all of these require hard work, not giving up, and finding that solution that works. So, I hope that my little mathematicians, unlike most Americans, will retain and foster these skills, and grow up to say, "I AM a math person." 
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