# Do you think teaching math causes you to over think??? Almost like “going insane “…NaNa Dunn from a post on Visual Math’s FB page

Oh yeah! I used to dream about my lessons… over and over during the night. I’d wake exhausted. Here’s an example of what I do now…

When you realize the students can’t ‘see’ the thing you are teaching them

My kiddos are learning to write quadratic equations. This requires them seeing patterns of growth. The first lesson in this series was to help them see the growth in a pattern of cubes. I used a YouCubed lesson that involved coloring each growth step. Just that. This exposed several issues. The lesson with numbers was the next day, and I was pleased by the intensity of their interest, but here’s why I think that happened: I had prepared them for what they were looking for.

Quotes taken from the original FB post…

Beth Hanna McManus writes “My 8th graders… totally missed the concept that the altitude to the base of the triangle goes through the vertex and hits the base at a 90 degree angle. I explained this in mathematical terms, in layman’s terms, using words like straight to the base, “shortest distance”, had them draw them on the white boards (checking and helping each drawing) multiple times, had them label triangles. When it came time for homework, no one knew what to do. I flipped out and spent the rest of the day in a dither wondering what is wrong with me that I can’t communicate with these kids…”

When I plan a learning experience, I look for the base skill/image/idea a child needs to be able to have to participate in a lesson. It may be a simple warmup – for the triangle problem above, after realizing they didn’t get it, I might have them draw the altitude, pointing out the way the angle looks, and how it starts in the vertex, in several different triangles. Just that. No math, just letting them learn to see what they are looking for.

Starla Adams writes, “Yes, yes, and yes….says the teacher who is out of strategies to teach long division after Friday. I actually thought I was going a little bit insane for an entire hour.”

Teaching long division is challenging. I’ve worked with 9th graders who do not understand what dividing does. If they don’t have an understanding of partitioning and regrouping, long division is just a nonsensical set of steps that they must follow – and memorize. A warmup using manipulatives (coins buttons beads) to set the stage for dividing into groups would help them understand what they are looking for. Then long division can be taught as a routine to get there.

Another common student skill gap with division is poor factoring skills. A warmup (or preview lesson the day before) with a factoring math problem string like this video from Pam Harris, might help strengthen their math fact fluency.

While working on any new skill that requires factoring, try giving students a factor chart. They won’t be using all their working memory on remembering number facts, but on learning the process of the task at hand.

Learning plans should empower students…

I realized that my 9th graders didn’t yet know that they had the power to create their own understanding. They were waiting for me to tell them what to do. Danielle Love and Kay Butler point out ways to shift the heavy lifting (and learning!) to the students!

As teachers, we spend lots of time creating learning plans. Many of us already know what misconceptions kids have, and what errors are going to get made. So lets plan ahead to expose -and remediate and preview- so that these issues don’t cause student failure during the learning of new material. These little discovery sessions and warmups are critical to building understanding and are often worth every minute of time we spend on them!

By all means, overthink and go crazy, in a most productive way! Math teachers, you rock!! I would love to hear how other teachers prepare for these misconceptions and gaps!

(And no, I don’t have those recurring math dreams nearly as often anymore!😂)

Thanks to Shana McKay of Scaffolded Math and Science, and and this really interesting thread on her fantastic FB Visual Math!

# Do You Speak Words of Life or Death?

“Thoughts become words, and words have the power of life and death. Think to speak life giving words to yourself and others.” Joseph Prince

These words put me in mind of how we as teachers have the power to create hope or plant failure in the minds of our students. Our students believe us. For good or ill, we hold all the answers (even when we don’t).

We can use that belief to inspire our students, to enable them to reach beyond anything they might be willing to do on their own. Here is one way:

Fixed vs Growth Mindset

Do your students have a Fixed Mindset or a Growth Mindset? Do they eagerly tackle problems, curiously start investigating the challenge placed before them, generate ideas for possible solutions?
If you give students a choice of assignments, do they pick the easy ones or the hard ones?
Do your best students want class discussion, or do they just want you to show them how to work the problem, so they can do their work and keep their A?

It breaks my heart when a student walks into class and says ‘I’m not good at math. Don’t expect much from me.’
Or the kid who told me, ‘whenever I’ve done enough to pass, I’ve been told that I usually quit trying.’ Or the A student who is afraid to try the problem until you have shown them how they are supposed to think about it. These students are exhibiting Fixed Mindsets. They have been given the idea, by teachers or parents or grouping or grades that they are dumb or smart or not good at math, or science, or too smart to fail at math, or science, or any other subject. Girls, especially, tend to get the message: math is not your ‘thing’; children are grouped by what teachers believe they can do: advanced, remedial or in-between – all a form of ‘silent’ stereotyping, as deadly as anything we say out loud. What message am I sending when I too quickly provide an answer, instead of asking good thought-provoking questions? How can I encourage a growth mindset?

What is a growth mindset, and how does it benefit our kids?

A growth mindset is the ability to see possibilities. It is a confidence in one’s ability. It is the MacGyver in all of us, to use a modern example. And it can be taught!!!

Teachers can encourage a growth mindset by changing the messages they give to their students:

“I believe in you”

Don’t let grades define your student. Instead of a grade, give specific feedback on problem areas. Tell them – put it in writing – that you are giving them the feedback because you believe in their ability to fix their mistakes.

Celebrate mistakes!

Your students are scared to death of making a mistake, getting it wrong, so they sit on their hands in class. Am I right? How frustrating is it to ask a question about the material and be greeted with blank stares?

It is time to celebrate (maybe even reward) mistakes. Sounds crazy, I know, but hear me out…

Tell the kids that every time they make a mistake and struggle with fixing it, their brain gets smarter. (Don’t worry, it’s true, check out this link: Brainology)

Reinforce the message:
Give them a picture of their head in profile with a brain drawn in it. Make sure the brain has lots of little empty spaces in it, like the one I’ve posted below (or break out the projector and let the kids make their own personal profiles on blank paper).

Tell them that each time they find a mistake, they get to color in a section of their brain. Celebrate the fact that their brain has grown! (Younger students like stickers; older students may want stickers, too! It doesn’t have to be anything huge.) I would even keep a big poster of a brain on the wall- on a really tough day, where the kids have made it through with lots of effort, color in a space on the class brain- they have become collectively smarter! This is also a great community builder. It’s like those scaling a wall, walking on ropes exercises where you can’t make it without everybody pulling together – without the parental permission forms!

And for those of you who aren’t sure whether you have a fixed mindset or a growth mindset, here’s a link to a great article, with a short mindset assessment at the end. Growth Mindset

And don’t worry if it tells you that you have a Fixed Mindset- it is only temporary!!

What did my results say? What do you think? Am I a Fixed or Growth mindset kind of person? I can’t wait to hear what you think!