I'm Bon Crowder and the photos above are both of me - in 1989 and today. I'm a Generation X mom of Generation Z kids.

I began peer tutoring in high school in 1984. MathFour.com is the 2015 version of me helping peers be comfortable in math.

If you're a Gen-X parent, you're in the right place!

# Category Archives: Cognition

### Teaching Math to Special Needs Children

I’m out of my depth.

Like 3 bazillion leagues out of my depth.

I took a math teaching position at a school for kids with neurological differences. I knew it would be hard. But I didn’t think it would be this hard.

### Lesson 1: Everything you know is wrong.

It’s a Weird Al song, but it also applies to teaching kids with special needs.

I gave this great math artwork activity that I thought would be perfect. My students are all 12-19 years old. They can communicate, be polite and follow instructions. And they are all listed as over 2nd grade in abilities.

So this should have be a perfect activity. Or so I thought.

The idea was to color each of the one hundred squares one of 6 colors. Then fill in a chart with the percent, decimal and fractional amount for each color.

Pretty cool and fairly simple. At least from the coloring perspective.

Oh, but with this population, everything I know is wrong.

One kid spent all 45 minutes coloring 6 squares. I had to encourage him to move to the next one each time.

One student decided that my 6 colors were severely insufficient. When I realized what he was doing, he’d already colored 30 squares 30 different colors.

There were a handful of students that nailed it. But only a handful.

### Lesson 2: Don’t bother expecting the unexpected.

I was working on an activity for the folks over at cwist using LEGOs. I thought I’d try it with my students to see how it would go.

The instructions: Build a structure that touches both floor and ceiling (simultaneously) and uses only LEGO brand items.

After 45 minutes and multiple reminders of “we’re building UP!” here’re some of the things I got:

• A five inch tall stack of red LEGOs (all red)
• A four inch tall structure made of thin LEGO plates
• A three inch by 24 inch platform
• Two cars

Again only a couple of students built up. But they lost interest after about 10 inches of bricks.

It might be that you should expect the unexpected. But with these kids, you can’t even fathom the unexpected.

### Lesson 3: Changing the rules is essential.

So I’m done giving “traditional” (yet creative) assignments. For the next couple of weeks I’m going to try something new.

I’m going to put out a box of LEGOs with new instructions: Play.

And I’m going to watch.

I’ll make notes in Evernote for each student. I’ll use the bricks to see who can count, who can subitize and who can categorize.

I’ll find out who can do one-to-one correspondence of the studs to match one size brick with another of equal size.

I’ll use the arrangement of the studs on the bricks to see who can multiply and divide. I’ll learn who can factor and see that a 2×6 brick has the same number of studs as a 3×4 plate.

And I’ll figure out how to create activities that are meaningful to each student.

We won’t get a lot of math done, necessarily. But we’ll be laying the foundation for appropriate math learning.

### Wish me luck.

I’ll need it. Plus any advice you have… share it in the comments.

Thanks,

### 11 Responses to Teaching Math to Special Needs Children

1. I like your plan B. Will be interested to hear how it comes out.

• Bon says:

So far it’s going well!

2. Jayne says:

Hey Bon! I always felt out of my depth there too, but I am such a better teacher and thinker for it! Love your new idea! Can’t wait to read how it pans out. Best of luck

• Bon says:

Thanks, Jayne. It means a lot!

3. Amber says:

I like your plane B, you may not be teaching math in the traditional way but it is still a way that they can learn and grow.

• Bon says:

I sure hope so, Amber. Thanks for stopping by!

4. Abby says:

Hi Bon, I am only a freshman in college studying to be a special education teacher. I know it will be very difficult at times and reading this post definitely reiterated that for me. But I do have to say that it will definitely be rewarding in the long run. I think that your plan B will work really well for your students. I may have to keep that non traditional of teaching math in mind when I have my own classroom some day. Good luck I hope it works!

• Bon says:

Thanks for the support, Abby. I’m keeping track of things so I can report back, too.

You’re likely to be well qualified and have more ideas because of your training. The rub for me is that I have no SpEd training and very little experience with it. But it seems that a good heart, creative mind and a willingness to keep trying is what the admins think it takes.

I hope they’re right!

#confident

5. I blog at http://www.mathnook.com on neural nerd issues related to math education. I have looked into subitizing before, and I understand it to be a foundational skill – you gotta have it to move on. I had a special ed tutee who couldn’t seem to handle this, so we locked in to making one-to-one correspondences (I called them “amount matches” to keep the language simple. We eventually laid the foundation for multiplication and division by using 1cm cubes, grouping, and factoring. I think your idea with the Legos lays the same kind of foundational understanding that I was going for – and neurologically reorganizes the brain to think in sets and groups.

Hope this helps. Special ed opens your mind up to another human mind in a way that’s almost like falling in love.

• Bon says:

Ron, thank you SO much for taking the time to share that! I haven’t tried the subitizing thing, but perhaps that’s next. I can find out who can and can’t do it and then take things from there.

I totally love the “amount matches.” That’s simple enough for them to understand at any level.

6. Melissa says:

Your idea is brilliant and it will work. I have been at this for some years after raising two brilliant but unusual son’s who have never done things in the conventional way.I provide materials and I sit back and observe…I have learned so,much this way! I love teaching this population.they are so outside the box…stratosphere etc.enjoy your adventure!

### Confidence is More Important than Knowledge

Do your students have confidence? It’s the best route to knowledge! Continue Reading

### Use Your Experiences in Math – For Math!

Don’t be a blind chicken when it comes to crossing the math road. Use your experiences in math! Continue Reading

### 3 Responses to Teaching Processes Destroys a Growth Mindset

1. Very well said. I just covered solving equations and inequalities, and the whole time the process was thought about in terms of figuring out what was happening to the variable and what should be done to get it by itself.

What frustrated me to no end was to hear students recite rules related to graphing in equalities on a number line that did not work when the variable is on the right.

Thanks.

• Bon says:

Chris – it sounds like you are doing sort of what I was doing! I did a short video of it here.

When they start spouting rules senselessly just kills me!

I look forward to hearing how your transition goes – please share anything, as I’m in that transition too.

2. Cory says:

This is actually something I’ve been struggling with lately…
Perhaps a year ago, I would have responded to this post with an enthusiastic “yes”, but right now, a year into grad school, I’m a little less sure.

I’ve always learned by intuition, and rarely proceed with something until I “understand” it, even if I “know the process”, but lately I’ve seen that sometimes I just need work through something blindly, before going back and understanding what’s “really” going on.

A particular example is something called “path induction” (or “identity elimination”) in type theory–it’s a notoriously difficult concept (amongst type theorists, anyway), and I beat my head against it for over a month. I then worked through about a dozen exercises and simple proofs blindly using the rule, and then went back to try to understand what it meant, and suddenly, it was almost completely clear.

Certainly, at school, process is (devastatingly) over-emphasized, but I’m less sure that teaching process is necessarily bad–it has routinely helped me gain intuition for concepts I’m struggling with.

### Why Math Isn’t Fun

Math isn’t fun! Not because it can’t be, but because we train kids (and grownups) to always search for the right answer – instead of exploring, learning and enjoying. Continue Reading

### 4 Responses to Why Math Isn’t Fun

1. Great post – and I love Brene Brown’s work. I’ve learned so much from her!

I’m a former math teacher who banished the right answer police from my classroom and made math fun (accessible might be a better word) for my students. I totally understand where you’re coming from – if our students go into a classroom where getting the right answer is paramount, they may develop math anxiety (I had it in college, one reason why I tried to teach math differently) and not enjoy the challenge of working through a problem.

I always told my kids that it’s good when they don’t know something or make a mistake, because that’s how I knew what to teach them. This was really hard to do if the teachers above/below my grade, the administration, and parents weren’t supportive, but I wanted my students to love math and relish the challenge, so I persisted.

I can’t wait to see what you do with this topic!

• Bon says:

It’s weird in a college class, too, Kelly. I have students asking, “Well, which is right?”

So I’ve had to constantly say, “We have no right or wrong answers in here.” Or even, “We’re not going to play make-right or make-wrong.”

Today I had a student put a problem on the board and when he saw an error (in the middle of our discussion) he tried to approach the board to fix it. I told him to sit down – we need his error to see how thinking happens.

He was quite annoyed, but sat down anyway.

2. Frank says:

If getting the right answer isn’t the goal, what is? Sure, I may have liked math class (and all my classes in high school) more if I didn’t have to worry about getting it right, but I don’t know if I’d have learned anything.

• Bon says:

Frank, in the long run, yes – the right answer is the goal. However, getting the right answer doesn’t move you to learning. And worrying about getting it right sets you back even more.

### Where is Math's Magical Place?

Your best work, and studying, happens in a place where you are at peace and enjoy working. Help your students find a good place to study math! Continue Reading

### Teaching Intuition in Math

Do you teach intuition in math? Do your students understand what you’re doing or are they confused with your teaching style? Continue Reading

### One Response to Teaching Intuition in Math

1. I think this has always been my problem with math. I was never taught to use my gut with it, and that’s what I do with just about everything. As an adult I’ve learned, what I like to call, work arounds that make math easier for me, and when I think about them they are all gut things that I do.

### A Different Way to Teach College Algebra

If your sense of number doesn’t get established, your brain can’t compress math learning. I’m thinking about using this principle to teach college algebra. What do you think? Continue Reading

### 4 Responses to A Different Way to Teach College Algebra

1. I’ve often thought the key to math is doing a lot of it until it becomes second nature. I tell my students to compare it to learning to walk. Watch a toddler and see how much effort it takes to learn, but you haven’t given it a thought in years.

How do you get that number sense? With our games we try to have lots of different activities of different types, so that students see the same concept over and over but in different situations.

However you do it, I agree, number sense is a foundation too many people do not have, and just like in construction, you can’t build very high without a foundation.

• Bon says:

Repetition is important, but only if the foundation gives you the ability to make it compress. Otherwise you’re just trying to be a computer running a gazillion subroutines!

2. suehellman says:

Great illustration, Bon. The only thing I’d suggest is to replace is the “younger” vs “older” labels in your comparison with “novice” vs “expert”.

Have you read any of David Tall’s stuff about mathematical thinking (http://homepages.warwick.ac.uk/staff/David.Tall/themes/three-worlds.html) ? He says that as expertise in math develops, processes become encapuslated (aka: compressed) into what he calls “procepts” — “thinkable concepts” or hybrids of process + object which can be manipulated in their own right.

Working memory (WM) is known to have a very limited capacity (newer research has lowered this from 7 plus/minus 2 items to 3 plus/minus 1). Without encapsulization/compression, WM fills to capacity with the calculations and single steps which all must be juggled individually and sort of held in suspension there until they can be assembled into a problem solution.

When students have to deliberately recall and then ‘drive’ each little step in a more complex process, WM capacity is exceeded and cognitive overload ensues. Some of the little pieces may be displaced by other little pieces which need attention. Unable to recall how the individual steps contribute to the solution, the student may become lost inside the bigger process. Unable to ‘see’ a solution taking shape, the student may shut down.

Developing fluidity is essential, and facility in fractions especially is now seen a sort of bellwether of future success in math.

• Bon says:

Very nicely articulated Sue!

I had no idea that working memory was so small. I was still back on the 7.

My brain just realized that it can’t take much more and is wanting to shut down. Time for coffee!

When you struggle to remember things, do you reach for google? Or do you strain your brain? Could the strain be helping you build math skills? Continue Reading

### Math and Vulnerability – A Series Inspired by Brene’ Brown

Based on Brene’ Brown’s definition of vulnerability (and her work in the area), it’s clear that doing math is vulnerable.

This is the first in the series. Continue Reading

# MathFour.com

Calming generation X in math since 1985.

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