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One of the most important

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One of the most important components of being able to teach "HOW" is that the students have suffient "mental reserve" to be able to hold the necessary content in short term memory. This is only possible if the students have acquired basic number skills and are capable of performing them automatically. In other words they have acquired "automaticity'

I have a simple test I give to all of my middle school students to find out which need more basic work so that they can learn the "how" of advanced concepts. I call it the 100 addition facts.
I provide a test all of the addition facts from 0 to 9 randomly listed on one sheet of paper. ie 1+3, 0+6 etc. It is a timed test in which students are not allowed to skip questions. They are given 60 sec from the time they turn the paper over. Each should be able to write 60 answers in 60 sec --- if they have automaticity. I have had several 8th graders who answered less than 20. Try it on your class. I hope you are pleasantly surprised.

Middle school math teacher and coach

Thanks, Paul. An honest

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Thanks, Paul. An honest mistake, but one I caught only after submitting. As you alluded to, though, the point still stands: it's about the how and the what.

Middle school math teacher and coach

Science teacher, the point of

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Science teacher, the point of that paragraph, nay, the entire piece is that we must pay attention to both sides of this thing we call math. 32 years of experience might have also taught you that having a clear sense of approach (and not just procedure) actually helps students become better mathematicians. Hope that helps the understanding.

Middle school math teacher and coach

Well said, Ms. Garcia. Having

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Well said, Ms. Garcia. Having some sort of connection matters lots.

High School English Teacher from Navajo Nation

I went to a training this

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I went to a training this past Saturday on CCS for Math, and I discretely asked my favorite math teacher at my school what a quadratic equation actually does. I told her I could solve for x, but I had no idea why I'd ever use it. After talking, we started to share ideas on how to make our content more real for our students. As masters in our own content, it can be difficult to see how the "other side" thinks and reach all of our students.

I always loved the math teachers who explained the WHY and the HOW of each equation.

Math teacher

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Teaching Honors, and Concepts classes are two different things. Honors students have no problem following along as demonstrations are done in front of the class. However Concept students, or divergent students is completely different, and they need alternative methods of instruction. It is difficult to keep them interested in the topics, and frequently their fundamental knowledge is so weak that they need remediation in even the most basic areas.

Would you rather your

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Would you rather your students know how to find the slope of a linear relationship or that they can make sense of the answer once they find it? You want both. If they don't make sense of the answer, they won't remember how to find it after the test. I know this from experience, because as a high school science teacher, the slopes of many graphs are important, and I know that middle school math teachers went through the motions of teaching what slope is, but I always have to reteach it before we begin to interpret the data that is graphed after lab. If you teach the thinking and analysis part, their standardized test scores won't go down...they will actually go up. 32 years of experience has taught me that.

Math Teacher

Jose, you have stated very

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Jose, you have stated very well the change that, difficult as it may be, we must pursue if we are ever to improve our student's math proficiency. However, one minor note - there are eight mathematical in the CCSSM, not seven. These are closely aligned with the Process Standards that NCTM has been advocating for over 20 years.
If the CCSSM are to be implemented properly, then it is really about how we teach math as much as the what.

Constructing Arguments

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I like how you describe some of the practices as 'soft skills'. I believe you are absolutely correct in stating that the practices are as important or more important than individual content topics, and agree that if a student can't make sense of a slope that they are unable to know if they are correct or not.

Thanks for sharing your post. I will be forwarding this on!

Educational Consultant/Author, Southern California

Thank you for your candor.

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Thank you for your candor. Each class of students is unique, as each child is unique, and I appreciate your thoughts on helping kids develop rather than just help kids test.

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