Really existing Common Core

Part 1: Help Desk, Common Core edition

Our high school principal explains the centrality of modeling to high school math:

55:23 This is a very important slide and one that you’ll hear me talk about a number of times.

Because modeling, we really look at modeling as the way to really permeate through all of the different levels of mathematics at the high school level. And we really look at it from a standpoint of pedagogy. When we talk about modeling, what we’re really talking about is the conceptual side of mathematics. Recently, and there’s been a shift to a very computational format for teaching mathematics, especially at the high school level. And that’s where we would start to break things down and scaffold them into very fine points. But what we have found is mathematics teachers over the last 10, 15, 20 years, when this pattern was happening, was that students were starting to learn their broader understandings of mathematics. 56:19 There was a big need to pull back and get back to the point of teaching to deeper understanding and to the conceptualization of math, not just about being able to compute the correct answer. So modeling we really look at as the link to be able to do that. It’s the opportunity to create real-life problem-solving situations where students need to understand the conceptualization of what’s going on in the math as well as how it relates to the real world.

Geometry, obviously, is when we start talking about shapes and sizes and the relative position of objects, and statistics and probability gives us the opportunity to start looking at mathematics and creating analysis and really looking into the chances of opportunity and things occurring.

57:07 So again, as I mentioned, modeling becomes a real important focal point for us. And the phrase that we’ve been talking about is it becomes this umbrella for us. It’s the umbrella that brings the whole mathematics curriculum at the high school level together, and a way for us to keep progressing through and thinking about how it matches up. So when we think about constantly naming and reinforcing the work that the students are doing we want to constantly bring them back as well to these broader-scale concepts. 57:39 So this slide and the next slide starts to talk about that even within those conceptual designs that I mentioned before, even within algebra, there’s an aspect of modeling that’s critical and important for them to understand in the algebra as well as the other mathematical concepts within.

Similarly you have functions here, and again, there are pieces of it that we pull out and we understand how do we create real-life conceptualization and contextualization for our students so that when they’re working through this, they understand again not just the specific calculation of an equation or formula but what it really relates to.

Similarly we do the same things in geometry and we do the same things in statistics and probability. Again, for me, this is about teaching to big ideas and perspective. We’ve been talking at the school about deep understanding and I said that would be one of those shifts that we keep coming back to, and I think that that’s really one of the most important messages that we can deliver about the mathematics instruction and how the Common Core starts to create a shift for us.

Irvington UFSD School Board Meeting - February 11th, 2014

This strikes me as fundamentally wrong, but if you guys tell me it's sound, I'll have to revise my view.

My understanding of math, of what math is, is that …. mathematics is not essentially, or even first and foremost, a system for representing empirical reality. The fact that math so powerfully -- and so eternally -- does capture many aspects of empirical reality is, in my view, either a) beside the point, or b) creepy.

Math, as I think of math, has a mathiness that cannot be reduced to modeling; math is a thing unto itself and should be taught as a thing unto itself -- or, at least, students should be made aware of the fact that to a mathematician math is not just a code-writing tool.

(Again, setting aside the possibility that math is just a code-writing tool.)

They [ STILL! ] Do What They Do!! ;D

When I read this article, it made my blood boil! Amazing that this junk makes it into print! (Since it's Monday, you may want to put reading this one on hold...) Is Algebra Necessary? NYTimes Sunday Review, Opinion Pages I agree with rknop that "the core of his argument is the ultimate in anti-intellectualism"

a School to Watch

Seventh-grade math students at Decatur Middle School recently spread out in the classroom and hallways to create a blueprint for a rain forest area at a zoo.

"We're learning about volume, depth, cylinders and cubes," said Tayaba Nadeem, 12.

She and group members Emily Siegman, 12, and Molly Cooper, 13, researched mammals, fish, amphibians, birds and reptiles in the real-life application for math.

"It's a different way to do stuff without using the textbook," Emily said.

That's exactly the point, said Principal Mark Anderson. Getting kids who are used to talking, texting and watching videos engaged in their schoolwork should lead to better test scores, he said.

[snip]

In honor of their efforts, the Southwestside school has been named one of the state's first three "Schools to Watch."

The program, which was launched in 2002 by the National Forum to Accelerate Middle-Grades Reform, recognizes successful schools so that their efforts can be duplicated elsewhere. Every three years, schools must reapply to keep the distinction.

The title doesn't mean the school has soaring test scores. In fact, ISTEPscores at Decatur Middle School are flat, with about 60 percent of students passing each year, Anderson said.

"It's not about test scores," he said. "It's about what you're doing to help the kids."

Decatur Middle School started changing the way it teaches three years ago, including more project-based learning in anticipation that Indiana would become a Schools to Watch state, Anderson said.

Decatur Middle School's engaging approach puts it on a select list
by Gretchen Becker
March 11, 2010

Someone needs to make a video of these kids "learning about" volume, depth, cylinders and cubes.

How are they actually learning about volume, depth, cylinders and cubes while they're "researching" [Googling] mammals, fish, amphibians, birds and reptiles?

And how are they using the formulas?

What do they know about the formulas?

Do they remember the formulas?

If they happen to forget one of the formulas, and don't have access to Google, can they derive a more complicated formula from a simpler formula?

Could these kids figure out the formula for obtaining the surface area of cylinder by grasping the fact that the surface area of a cylinder is composed of two circles and a rectangle?

I bet they can't.

That's the problem with applying math to the real world.

Kids don't learn to apply math to math.

"Orton-Gillingham for Math": "Making Math Real" -- Introductory Post

Making Math Real

http://www.makingmathreal.org/

I just finished the 2-day, 14-hour introduction:

http://www.makingmathreal.org/index.php?option=com_content&task=view&id=38&Itemid=57

My brain is either fried or overloaded. Lots more sympathy for kids whose learning styles aren't supported in the classroom.

[Aside: hush!--already about the "learning styles". I agree that lots of the edu-babble about learning styles is content-free. However -- I sat, listened, and wrote for 120-minute blocks, about a subject that I am deeply committed to. I'm an adult with a well-honed capacity for taking in new information by listening, and retaining new information by writing. By minute 90, I was overloaded. You go shadow your kid throughout her school day and see how well you could keep up. /Aside]

Making Math Real (MMR) isn't a math curriculum, it is a specific, structured approach to math instruction.

A good analogy is:

Orton-Gillingham approaches to reading = MMR approach to arithmetic and mathematics.

The training is expensive.

Question: Is it worth it?
Answer: If your district is using Everyday Math (or other purely constructivist math curricula), it is definitely worth it to offset the fog of confusion EDM engenders in many kids, with or without LDs.

It may also be less expensive in the long run than putting your kids in Kumon, Sylvan, or other after-school remediation/tutoring programs.

Here's a description from the MMR website:

Multisensory structured methodologies deliver all instruction via the three processing modalities: visual, auditory and kinesthetic-motoric. Students who are struggling experience processing difficulties in either one or more of these processing modalities. Best instructional practices require linking all incoming information across the three channels to maximize successful processing.

Structured curriculum means starting with the simplest elemental foundation and building developmentally in an incremental and systematic progression from the concrete to the abstract. The most powerful aspect of a multisensory structured program is that each current activity and lesson builds the essential developmental tools for success at the next level thereby reaching the full diversity of learning styles and educational needs in all classrooms.

Schwablearning.com was a great source of discussion and information -sharing for non-standard kids. Here are links to previous discussions of Making Math Real on the parent-to-parent board (listed in chronological order):

• http://www.schwablearning.org/message_boards/view_d iscussion.aspx?thread=3601
• http://www.schwablearning.org/message_boards/view_d iscussion.aspx?thread=4982
• http://www.schwablearning.org/message_boards/view_d iscussion.aspx?thread=15320
• http://www.schwablearning.org/message_boards/view_discussion.aspx?thread=18313
• http://www.schwablearning.org/message_boards/view_d iscussion.aspx?thread=19498
• http://www.schwablearning.org/message_boards/view_d iscussion.aspx?thread=24091
  
• http://www.schwablearning.org/message_boards/view_d iscussion.aspx?thread=25871

BTW #1: , as part of the class, I am now "bombproof" on my 13 multiplication facts, thanks to the "nine lines". I'd lay it all out for you now...but I am totally used up, cognitively.

And actually, I'm kind of appreciative of that experience -- because, for some of our kids, they are "totally used up, cognitively" before the end of the school day. That doesn't happen so often for us as adults.

BTW #2 -- being "cognitively tapped-out" is why I think homework in k-3 is stupid a waste of the (a) teacher's, (b) student's (c) parent's time and energy.