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Post date: May 1, 2013 6:10:03 PM

Can some students not learn Algebra? posted 11/26/2011 by Rebecca

Dan Meyer posted an interesting and highly commented on blog post this week: .

"Last April, fourteen of Palo Alto High School's twenty math teachers petitioned their school board [pdf] against raising graduation requirements to include Algebra II:

We live in an affluent community. Most of our students are fortunate to come from families where education matters and parents have the means and will to support and guide their children in tandem with us, their teachers. Not all of them. [..] We are concerned about the others who, for reasons that are often objective (poor math background, lack of support at home, low retention rate, lack of maturity, etc) can't pass our Algebra II regular lane course. Many of these are [Voluntary Transfer Program] students or under-represented minorities."

Many of the comments to this blog post talk about the usefulness of Algebra and specifically Algebra II. As it is taught currently, I would tend to agree that's it's abstractness is not necessarily used on a daily basis. I do, though, believe that if algebra were more easily understood, it could be applied in more situations in order to increase successful outcomes.

This is where DR comes in! We are needed now more than ever.

Brain Calisthenics for Abstract Ideas posted 6/10/2011 by Rebecca

I read a fantastic NYTimes article this week:

It talks about how our intuition is underused and that the human eye can recognize patterns quickly in our subconscious even before we understand it ourselves: perceptual training. Quoted studies include:

1) Matching equations to graphs (quickly)

2) Liking a better deck of cards when gambling

3) Distinguishing painting styles [I like this one the best!]*

4) Fraction building (quickly - repetition)

5) Slime-mold for global warming experiment

Patterns, patterns, patterns....they are what life is all about. It is so nice to find research that is, yet again, substantiating the direction of Dream Realizations.

*3) Distinguishing painting styles [I like this one the best!] Seeing multiple painting styles instead of just concentrating on one artist alone allows the eye to pick up the pattern naturally. I relate this to base systems: if we teach all base systems, then the eye can pick up the patterns for itself and focus is off the single painter (base 10). The world has opened up with possibilities!!

Definitely worth the read!

DR is developing a public grant to bring subQuan to the iPad posted 4/9/2011 by Cooper

I believe the touch interface will enable the creation of an intuitive and very real graphical user interface (GUI). This GUI allows us to build seamless transitions in the user input screen based on the level of knowledge and special needs of the user. This is ideal for young students learning numerical values, words, and symbols. I also believe this might provide a solution to a problem dyslexics have with numbers.

Replies to This Discussion

Reply by Rebecca Reiniger on April 12, 2011 at 9:49pm

Just got intel on this website today: . This may be a way to get our programming publicly funded. We will need to dive deeper into the ramifications and upfront costs of such an endeavor.

Math Visualization posted 12/4/2010 by Rebecca

What does "math visualization" conjure up in your mind? Is it only physical manipulatives? Or is it drawing out a word problem into pictures? We regularly step back from math and try to visualize its usage, but have we stepped back far enough to see the patterns? Just a few random thoughts to start off a Saturday morning. Happy weekending, all!

Replies to This Discussion

Reply by Alexsis Kamala on December 4, 2010 at 2:51pm

Seeing the patterns of numbers takes looking at the shapes numbers make, not at the symbols such as 1, 2, 3 etc. These symbols don't have the beautiful patterns that subquanning makes. When the numbers are all laid out in subquan sheets, the patterns become very apparent. It makes the other things we do in math seem so easy.

Reply by Maria Droujkova on December 11, 2010 at 7:13am

For me, visualization means RE-presenting. That is, the action of constructing, making, building, growing a visual representation of mathematical ideas based on some other representation: words, formulas, tables and so on.

One of my favorite math visualization activities is storytelling - where visualization happens in people's minds. Some math storytelling is assisted by pictures, for example, the Sona (Africa) sand drawings. We did a math club activity about them.

Reply by Maria Droujkova on January 8, 2011 at 6:17pm


I usually invite kids to talk and draw their visual and sound synesthesias. Some have very particular colors for their numbers, and also piano notes.

Smell and taste are harder to represent. You can use consistently smelling substances such as coffee and chocolate, I guess. We will try some of this when my math club resumes. This will be good "apple math" activity - that's what we call snack time math.

Reply by Maria Droujkova on January 9, 2011 at 2:26am

Cute name :-)

This discussion reminds me of the phonics article Alexander recently linked at Math Future:

He advocates for made-up systems for learning English reading. My daughter, as his son, is English-Russian bilingual, and I can only agree! And we may need a similar made-up system for learning math reading. I know many people who used such private languages with their kids. Imagine groups of parents using the same language, much like "Baby Sign" movement. Won't that be powerful?

Reply by Rebecca Reiniger on January 12, 2011 at 8:01pm

That was a fantastic video, JayCee. I watched the second (47 min) as the first didn't allow me to view for some reason. The human brain is really amazing. I don't think we've even scraped the surface of our own capabilities and with neurological research coming to the fore, I don't think it will be too long before we make some huge discoveries thanks to PET and fMRI technology.

Thanks so much for posting this one!

Jonathan Crabtree said:

I taught mathematics using creative visualisation more than 20 years ago. Right brain learning is an excellent way to pre-process information before the left brain processes the symbols.

However I am now wanting to explore the development of multi-sensory learning of mathematics.

So has anybody else created a 10 value musical scale or associated quantities with tastes yet? I'm also keen to know if anybody else uses a 10 point color scale based on our visible spectrum.

Here is a short video of Daniel Tammit with David Letterman.

In his book 'Born on a blue day' Daniel talks about synaesthesia. If there is a way we can help children retain this ability, we will go a long way to helping them enjoy numbers.

Thank you for watching!

Reply by Cooper Macbeth on January 15, 2011 at 5:37am

Thanks for sharing this. I have seen other presentations on BBC and also read his book. It was disturbing to see how much we had in common as he has been diagnosed with autism and that is not what one seeks. Mais, c'est la vie. I do not know how much of subQuanning is related to his ability but I do know the wonders that are coming out of it. We have 40+ year-olds who hated math, didn't really understand Algebra and within 30 minutes they are looking at subQuan metapatterns and telling us the equations, like 3x^3+2x^2+6x+5 in less than 30 seconds. To be honest, we have no idea how far subQuanning is going to take us but it definitely get the response, "Oh my God", a lot. Sorry for my delay in replying, since we are still building the website to replace this Ning as fast as we can, I haven't checked it much. Please forgive me....Cooper

Brains vs. Computers posted 12/4/2012 by Rebecca

The brain can be compared to computer hardware. Graphics Processing Units (GPUs) have become more widely useful in computer and video processing. “Using GPUs … gives the computer a processing capacity that competes with supercomputers over twice its size” ( , paragraph 2). The vector (3D) graphics implementation in computer hardware has increased capacity and facilitated a greater speed in computing. "GPUs are redefining high performance computing," said Jen-Hsun Huang, president and CEO of NVIDIA. "With the Tianhe-1A, GPUs now power two of the top three fastest computers in the world today. These GPU supercomputers are essential tools for scientists looking to turbocharge their rate of discovery" ( , paragraph 7). Designers are finding in the computer industry that graphics give computers a stronger foundation for processing.

Dehaene (Jossey-Bass, 2008) describes a major upheaval in the mental arithmetic system during the preschool years when “progressing in math means storing a wealth of numerical knowledge in memory” (p. 281). This storage of numbers in the brain is different than the storage of vocabulary. Verbal memory can be powerful with its cohesiveness and connectedness. Humans possess associative brains; we can open a memory from a vague recollection, something computers have yet to master, which makes learning vocabulary easier than learning the multiplication table. Each calculation within the multiplication table hangs independent of the other multiples when memorizing and that’s where the brain’s associative nature fumbles and numbers jumble inside our head, resulting in mistaken memories, which correlates to wrong answers. So, why are we still relying on this outdated practice of memorization?

Jossey-Bass, I. (2008). The Jossey-Bass reader on the brain and learning. San Francisco: Jossey-Bass.

Virtual Worlds and Mathematics posted 12/4/2010 by Rebecca

How can we incorporate what has been done in the past with virtual worlds, how the brain learns, and using this 3-D environment to tap into the instincts with which individuals were born and see mathematics as we have never seen it before: patterns unrecognizable without the advancement of technology?