For a while, a long while, I let this math blog just sit. I didn’t want to delete it. I spent too much time on it and I knew it was full of great stuff that was still being used. But I wasn’t in love with writing on it.
In my lethargy, the hackers and jerks managed to infiltrate and completely take it down. That was on October 23, 2025.
Today is December 30, 2025. I rescued all the posts and will gradually get all the good ones reposted. But I have to start over, creating the whole website from scratch.
Luckily the wayback machine (internet archive) has a nice snapshot of the images and layout. It’ll take me a while, but I’ll get it all back up. Maybe even with some improvements!
If you are looking for a specific post – something you remember from long ago or something you want to know about – leave it in the comments. I’ll hunt it down and get it posted.
I’m looking forward to having all those great math stories, thoughts and tips live again – I hope you are too.
I was labeled an “airhead” in high school. Until today, I’ve avoided telling people that. The moniker had a real negative effect on me.
I was known as the kid who asks dumb questions. If my peers wanted to waste the last five minutes of class and not have to start another topic, they’d whisper at me, “Ask one of your dumb questions.”
“There are no dumb questions.”
If you’ve never said these words, email me now and I’ll send you $10.
You’ve said them, haven’t you?
Yup — we all have.
The fact is that every question is a dumb question. Because someone else knows the answer.
And the more people who know the answer, the dumber the question is. And the more valuable it is to ask it.
Just because everyone knows the answer to a question, doesn’t mean it’s the right answer. It’s just the safe answer.
I asked a question with an obvious answer.
The story of how I earned my “airhead” nickname is a rather curious one. It happened like this:
We had a guest speaker, a grownup, in our debate class. He was explaining details of the debate topic, which involved transporting water across some distance.
He drew a series of pumps and downward sloping pipes on the chalk board. He explained that water had to be pumped up every so many feet so it could continue traveling the decline.
I watched and listened. I wondered why they didn’t just pump the water straight through a horizontal pipe.
I asked, “So why do the pipes have to be tilted?”
The grownup responded with a snicker, “Because water runs downhill.”
In retrospect, it is clear to me that I was dealing with an idiot. He lacked the novel thought, as well as nurturing behavior, to wonder what a 14 year old might be thinking when she asked the question.
My classmates joined in on the grownup’s joke. “Wow, you don’t know that water runs downhill,” they jeered, “What an airhead!”
Who knows what would have happened…
Suppose that grownup would have encouraged my line of questioning.
“The pipes have to be tilted because we let gravity do most of the work.”
“But why can’t we just pump it straight through horizontal pipes?”
“It’s not efficient to do it that way.”
“What does it mean to be efficient? Do we have numbers on that?”
“I’m not sure. Maybe that bears some investigation.”
Perhaps I would have proposed that we create a pumping system so powerful, and efficient, that we didn’t need thousands of pumping stations? That might have led to other innovations.
There’s no telling.
And yet his snide remark, which gave the other students encouragement to be mean, shut down all routes of novel thinking for me.
At least in that class.
The airhead learns best.
Novel thought — creative thought — is the foundation of innovation. It’s the foundation of learning.
In math, thinking outside the proverbial box is an efficient way for a student to learn. Asking crazy, airheaded, dumb questions gets a student thinking about all sorts of things.
The effort put into this novel thinking to solve a math problem will seem high. But the depth and breadth of a student’s understanding when they do this is incredible.
And that understanding will carry to other things — decreasing the effort to learn even more!
So why not be an airhead?
Kids start out being airheads — thinking novelly and creatively. And grownups (like the guest speaker in the debate class) have an uncanny knack for destroying it.
When your kids ask a dumb question, refrain from being a grownup. Ignore the fact that everyone knows the answer to that. See what happens.
Encourage your kids to ask dumb questions. Give prizes for the most dumb question of the day — the one that sparks the most novel and innovative thinking.
Epi-blog
By the way, my peers continued this nonsense for years. It might be easy for me to say that I stopped wasting my dumb questions on those idiots. But in fact, they were just as squashed as I was.
They were covertly given permission to do it by our teachers (except for Mr. Berkebile), therefore they continued.
Forget it. If they don’t want to pay attention and learn, so be it.
Perhaps you’ve heard others say this, or felt it yourself. It can be extremely frustrating trying to teach a child something who just doesn’t get it, doesn’t pay attention, doesn’t seem to care or who doesn’t seem to want to learn.
There is an alternative.
However, if we consider the bigger picture, we see another possibility. Much of a student’s behavior can be a protective front to keep them from feeling like a failure – after all, who likes that?
Perhaps they act this way because the material is unfamiliar and therefore they don’t know if they can understand it. The uncertainty is a bit scary.
“Well they don’t have to be scared,” we say.
But they are. So… if they pretend they don’t care, and if they don’t try or if they hold back on really applying themselves, they can’t fail. Problem solved.
What does this have to do with me?
Those students who experience these negative feelings can exhibit behavior that can make it seem as if they don’t care. And then we take it personally. “They’re just really ungrateful of everything I do.”
It’s our job to meet them where they are — in their distraction, interest, frustration, intimidated state, excitement, fear, wonderment, avoidance, etc. But if we are burned-out, frustrated, or feel unappreciated, it’s hard to do that.
So how do I get there?
Adjusting just a few assumptions can put us in a more relaxed, sustainable place to offer reassurance and hope to kids who feel this uncertainty. Doing this is just as much for our self-care as it is for their education.
Use these statements to reset your assumptions.
These guidelines are designed to help us “reset” our assumptions in the service of positively impacting our approach to students.
1. It’s about them, not us.
When kids avoid or check-out, most of the time they aren’t doing it to “get back” at us. They do it to avoid the concern they feel about whether they’ll be able to meet a challenge. Or because they’re worried about looking incompetent in front of their peers.
They may even act out to divert attention away from their academic ability. This is another protective feature — again, not about us.
Adjusting this assumption can free up the compulsion to defend ourselves. It can also allow for more time and energy for them.
2. Kids have different levels of abilities. Period.
If we assume this, all of a sudden we aren’t expecting Joe to perform as well as Roger, or vice versa. This allows us to determine, without judgment, where Joe and Roger are with their abilities and to ask independent, non-comparative questions.
“What does Joe need to further his learning and education.”
And completely separately…
“What does Roger need to further his learning and education.”
3. They ARE trying.
There’s an assumption that all students CAN understand “if they just try” hard enough.
When we take this into the classroom, it’s easy to become frustrated (All they have to do is…), become resentful (I am so tired of busting my tail and they’re not caring) or even retaliate (If they don’t want to work in class, I’m just gonna load them up with a ton of homework. That’ll teach ’em!).
Assume that they ARE trying and ARE understanding as much as they possibly can. Doing this rids us of the temptation of doing things such as shaming and scolding — which has been shown to be counterproductive to learning.
It also puts us in a “glass half full” position of recognizing what they DO learn, rather than focusing on what they don’t. (Half cup of motivational praise, anyone?)
Keep these statements handy.
Write the above sentences down and keep them nearby. Read them at the beginning of every day, or every lesson or class even. It helps to have brief, yet constant reminders.
After a couple of weeks, see if you can tell a difference in how you feel, your stress level, and the reaction of your students.
Try them out and share know how it goes in the comments or on twitter/x. Did you come up with some of your own assumption adjustments?
Update: The That’s Math! membership site is no longer available. However, this post still has useful and entertaining information.
While developing the That’s Math! membership site, that launches today, we’ve had some interesting discussions about wording. Because of our different backgrounds, we’ve had to have some lengthy clarifications. Bon, with her technical math info, and myself, with ethical/credible research wording.
Below is a rough “transcript” sample compiled from a couple of discussions.
Bon: Math anxiety makes it so that kids lock up – they’re paralyzed with fear and then can’t do math.
Wil: Well, actually, the anxiety they experience doesn’t prevent them from doing math. It just makes it much more difficult.
Bon: And That’s Math! will fix that.
Wil: No. We aren’t trying to “fix” anything. Just help parents with positive math exposure.
Bon: And the research proves that the parents talking about math in front of kids will take care of that. Got it.
Wil: You have to be careful with that word “prove”. We have to say the research suggests that kids who have a supportive environment are more likely to engage in math exercises and homework. Part of that support is talking about math in a positive way.
Bon: Great! So we support the parents by helping them discover math that happens in their environment.
Wil: Right. And the exercises we’ve designed help parents to practice saying that math in front of their kids. When the kids hear Mom and Dad talk about math, the kids learn to be not so scared of it.
Bon: We act just like we see our role models act. Mom says “hey, there’s math” instead of “I was never good at math, it’s so hard!”
Wil: Right. It’s called social modeling. We pick up on what other people do, whatever it is. There’s all kinds of research to support that social modeling is how we learn how to act.
Bon: So “social modeling” is doing stuff where kids see it. And if parents use that for math specifically…
Wil: Exactly and…
Bon: …and BAM! Their kids will love math and be geniuses!!!
Wil: It doesn’t mean they’ll love math or be geniuses!
Bon: But it will get them closer to being geniuses.
Wil: Well, there’s research that supports that they are likely to engage more, so I guess you could say they’re getting closer to being geniuses.
Bon: Virtually proving that using positive math talk like we teach in That’s Math! will improve your kids’ grades.
Wil: Dude. You’re killin’ me. But I like the enthusiasm.
Are you ready to positively influence your kids in math? Learn more about the That’s Math! membership website now!
Who said it first? Maybe Jerry Mortensen. Maybe George Phillips.
But hundreds, maybe thousands, of math teachers have said it and put it on their syllabus.
Because it’s true.
But does this mean that students have to “practice, practice, practice”?
And what exactly does that mean?
Say to me “practice, practice, practice,” and I’ll growl at you.
You’d might as well say to me, “I don’t know squat about your learning style and aren’t interested in finding out. But I know that you’d better do all 50 problems or you’ll lose points on your homework grade.”
So I prefer to think of this triad mantra in three phases: Practice Phase 1, Practice Phase 2 and Practice Phase 3…
Practice Phase 1 is isolated practice.
When a student learns a new math concept, he or she should apply it a few times, by itself. This is what’s offered in the problem sets of textbooks: isolated practice of the new math skill.
This practice is also an assessment phase. At many points here, the student can ask, “Can I do this? Do I understand this?”
Regardless of the answer, the student can proceed to Practice 2.
Why “regardless of the answer”?
Practice phase 1 is what’s commonly referred to when grownups say “practice, practice, practice.” But over practicing can be detrimental.
Some kids need to nail the isolated practice before moving on.
Some kids.
And some kids will become annoyed with it and need to move on to see the value of the skill.
Refrain from giving 50 problems just because “practice makes perfect.” It doesn’t. Practice sometimes makes frustration.
Let your child move on to practice phase 2. You can even let them skip assigned problems. She or he may return to the isolated practice in phase 1 later or mentally isolate the skill within the “bigger picture” in phase 2 or 3.
Practice Phase 2 is “big picture” practice.
This practice phase helps solidify the math skill. It should teach the integration of the skill into the full toolbox of math skills.
The math skills ancillary to the main skill being practiced, are themselves being practiced (hopefully in phase 2 or 3). How fluent a student is in these ancillary skills has an impact on his or her perception of achievement of the main skill.
Textbooks offer a problem set for this phase, but it’s often disguised. It just looks like harder problems.
It’s helpful to point out the ancillary skills being practiced. This helps affirm how much a child is learning and aids in building confidence.
Practice Phase 3 is ongoing.
Real skill is realized when it’s integrated without thought. For me this was always at least six months after first learning a skill. Sometimes it happened years later.
And there are some things I didn’t “get” until decades later.
Which means that practicing a skill must be continuous – even if a student doesn’t fully understand the logic underlying the process.
Of course this phase is subtle if not completely invisible. But instructors can point out when the “old skills” come into play long after they are learned.
Example: Factoring
Skill: Use the distributive property to remove a common factor from an expression.
Practice Phase 1 – Isolated
\(3x + 3y = 3(x + y)\)
Or with letters:
\(xy + xz = x(y + z)\)
Practice Phase 2 – Big Picture
Here the skill is integrated with factoring numbers:
At some point a student might notice that combining like terms is equivalent to factoring the common term then combining the numbers, like this:
\(3x + 5x = (3 + 5)x = (8)x = 8x\)
So, really – how much practice and when?
A student should practice in phase 1 until he or she is comfortable. Remember, over practice can be annoying and seem punitive.
And punitive math is never effective.
A student should practice in phase 2 based on his or her comfort level. This is a great time for parents/instructors to notice weaknesses in other skills, too.
Practice phase 3 is, well, ongoing.
It’s really helpful to note, out loud, where old math skills come into play. Instructors should always be on the lookout for ways to do this.
Even things like long division show up in the more advanced skill of polynomial division.
Pay attention to your student.
Some kids may respond to the “practice, practice, practice” mantra. Some may get annoyed at it (like me). If your child needs and wants more top-down learning, allow it.
Don’t force phase 1 practice – offer it.
And if you see a deficiency in an ancillary skill in phase 2, bring them back to phase 1 on that one.
Math really isn’t a spectator sport. But that doesn’t mean you have to drill like crazy on it. Adjust the teaching and practicing according to the child.
We don’t teach each new math skill just to have something to do during the next math lesson. And yet textbooks make it look like we do.
Math skills are presented in bubbles called sections. The section doesn’t show how the math rule being taught connects to past or future lessons. Nor does it point out what previously learned skills or rules are currently being employed.
Okay, it might note that this section is similar to the others in the chapter. But how often do you see a section point out how you’re going to use the skills you learned in a previous course?
Kids rarely understand that each level of math is taught so that the tool that’s being practiced can be used later – in another math lesson or math situation.
They don’t see the long term growth of math skills and math maturity – their math toolbox.
Math skills are tools.
Take a look in any man’s garage and you’ll see a plethora of tools.
Point one out and ask the owner these things:
What is this?
Under which situations will it function (and under which won’t it)?
In what situations would it be helpful to use?
Do you have the confidence and ability to use it when you need to?
Have you ever used it when there was something else that would’ve worked better?
Chance are, he’ll have thorough answers for 1, 2 and 3. And for number 4 – he’ll look at you like you’re nuts and say, “Well, yeah!”
For number 5, he’ll say, “Well, of course. Sometimes I’m not sure what will work best, so I just pick a tool that I know can work. If it turns out to not be the best tool for the job, it’s no big deal. It might have taken a little longer, but it still got the job done.”
Tools accumulate – and add to each other.
Mr. Garage Owner didn’t collect a whole bunch of tools that he’s clueless about. He likely wanted to build one thing and realized a tool could help. So he bought it.
He learned how to use it, then hung it on the wall. Probably on a pegboard with the shape of the tool outlined.
Then he wanted to fix something else. He could have used his tool, but if he had another tool as well, it would make it even easier.
So he bought another tool.
Together with the first tool, he fixed his gadget then hung the new tool on the wall.
He continued this way until his pegboard was full and he was building more tool storage space in the back yard.
Now he knows each tool, when and how to use them, and confidently pulls them out each time it’s necessary.
And if he chooses the wrong tool for the job, he gets over it quickly.
Teach math like the kids are accumulating tools.
When you start a new section in your math lesson, review the math rules that they previously learned. Show how the newest problems may (or may not) be solved with the old math skills alone.
Present the new skill or math rule thoroughly. Be clear on what it is, how it can be used and under what circumstances. Also point out where it can’t ever be used. Like “adding to both sides” can’t work when there’s no equal sign.
Point out some areas where the new math rule might be helpful. Point out some areas where the new rule might not be the best for the job, but it would still work.
Show how to use the new math rule along with the old rules (pointing them out everywhere) to achieve results.
Have them make a list of all the math skills they’ve learned – a pegboard outline – so they can be kept handy.
Let them play.
Math is typically thought of as the subject where “there’s only one way to do it.”
BAH!
Just like Mr. Garage Owner, using the non-optimal tool for the job still gets the job done. As long as it works (can’t run an electric drill in the rain, after all).
So let them play. Turn your math lesson into a time where they can use any math rule they want. Let them discover their own confidence in choosing tools.
And let them try out tools that might not be the best for the job.
As they grow their math toolbox, they’ll grow in math maturity and confidence!
This is the 3rd in the draft purge series where I’m throwing stuff out. I’m down to 56 drafts – down from 70! (not factorial)
I’ve taught in the classroom for over 17 years. I never hesitated to give my phone number out. In all those years, with all those kiddos, I got one drunk call. And that was an accident – he meant to call Ben and not Bon.
It was a good idea. And I’ve had good results.
So why should you do it?
To show you’re human.
If you teach math, you just might be viewed as supernatural. Or inhuman, depending on the student. Famous, important or supernatural people don’t just give out their phone numbers willy-nilly.
If you give yours, you’re showing your human side. You have to keep the authority, but you can give a little. Let them in.
To offer a ray of hope.
They will probably be nervous about calling, but they’ll text. And they’ll understand if it takes you a while to get back to them. If they have this lifeline, they won’t lose the confidence
they have gained in your presence.
I’ve heard hundreds of students say, “I was doing okay in class, but when I got home, I just couldn’t understand what I’d been doing.”
There’s a magic of the teacher standing there. It’s a safety net. And it gives many students the confidence they need to keep going.
It’s a fake net, but it works.
If they know they can text you, they maintain this safety net at home.
To show trust.
For some reason, classrooms have gotten into the “us vs. them” mentality. Teachers are the bad guys to the students. Teachers may label kids unfairly, too.
Show your students you’re not a label maker. Let them know that you have trust and faith in them. Give them your number!
Will you do it?
How do you show you’re human? How do you give hope and show trust? Will you try the phone number sharing?
Let me know in the comments and don’t forget to share this on twitter!
There are a number of ways to be an education advocate. Facilitating or encouraging change is definitely one of them.
Communicating, getting support for change, and making that change happen can be a bit of an art. Especially because we’re asking others to be part of it.
Here are some ways to make this easier.
Get their ear.
Communicating is perhaps the most important tool in advocacy. It’s more than just having a voice and speaking up.
As parents and education advocates, we must let others know what’s important to us and why – AND be ready to listen to the their concerns.
It’s a conversation.
Use “We” instead of “You.”
If we’re wanting change, we can’t just criticize. We need to offer ideas of what that change could look like.
The difference between being an advocate for change and being a complainer is this:
Complainer – “I don’t like this. YOU need to do something about it.”
Change advocate – “I have concerns about this. This is why. I think these changes may help. I think this is a way we might be able to make that happen. What do you think?”
Being an advocate comes with having ideas of what TO DO and HOW to change, rather than just criticizing what IS.
Be an advocate (and not a complainer).
It’s important to know what we want before talking to others about it. Being unhappy with what is currently happening in education is the first step.
From there, ask yourself what specifically you don’t like. What could replace this that would be more effective, appropriate, or helpful? How could that transition occur? Who’s involved and what will that change look like for them? How will they handle the transition to this change?
You don’t need to completely answer all these before starting a conversation about educational change. But keep those questions in mind. Be willing to offer ideas on them.
It can go a long way in getting others to listen.
Be patient with the process of change.
Many parents and teachers know the benefit of shifting the focus in the schools. They want to get away from memorization and performance on standardized tests. They want to move toward learning ideas and understanding concepts.
But that’s a tall order.
For a broad change like this to occur, there must be (near) unanimous support. There must be a sense that this change is not only helpful, but is needed and required.
Convincing people who are married to the “traditional” way of the teaching/learning method can take time.
Make the change easier for others.
Advocating for change isn’t just pushing for it or convincing others that it needs to happen. It is important to support those who will be a part of that change.
Help teachers and administrators understand you’ll be around to support those changes. Let them know you don’t expect them to do all the work. Then they’ll be more willing to support and make those changes happen.
Talk to everyone.
You never know where you’re going to find the ally – or someone ready to consider something new.
And start here. What do you think? How will you start the conversation?
Leave your thoughts in the comments. And share this post on twitter!
I just learned what the phrase “differentiated instruction” means. Jeanette Stein told me on #MathChat that for her, differentiated instruction is
Meeting kids where they are at to take them where they can go.
I love it!
So I read the article Jeanette shared from Teach-ology. Seems differentiated instruction is a fancy term for focusing on the individual students rather than the teacher.
I’ve been doing it for years!
The first few semesters I taught math (back in 1996), I would lecture. I mean straight up, lecture. But soon I learned that it wasn’t about me.
Over the next 16 years I watched the students. I quit spending so much time and energy on preparing lectures and much more time and energy thinking about the comments and questions I got from the students.
I learned that many of the “math rules” were merely tricks some clever person thought of as a mnemonic device. And that if these tricks are forced on certain students, they’ll likely never understand what’s really happening.
And most importantly, I’ve learned that creating a safe and inquiry based learning environment is the key to differentiated learning.
And there’s more!
In considering my classroom experiences, I’m finding many other instances and examples of differentiated instruction. So this is the first in a series on tactics to improve your own differentiated classroom. Here are the proposed topics/titles:
Eliminating the Fear – How to Engage Students without Calling on Them
Show Your Work! – What’s up with that?
Grading in a Differentiated Classroom – Why Teaching Math Is Harder than Giving Birth
“It’s Your Education!” – How to Empower Your Students
If Shakespeare Taught Math – How to Use Metaphors to Teach Math
If Picasso Taught Math – How to Use Drawings to Teach Math
How to Teach Your Students to Think Like a Mathematician
Wow – that’s rather ambitious of me, isn’t it?
I’ll shoot for these once a week and you can find a link to the series (this article) in the sidebar under “Quick References.”
If you have any requests or ideas, let me know in the comments. And don’t forget to share this series with your PLN on twitter!
I am attending the Offshore Technology Conference this week, meeting old friends and looking for great math to talk about. Yesterday, while relaxing at the Oil States booth, I explained my goal of finding math at a trade show.
Amber, a subsea and pipeline engineer (i.e. super math girl) started throwing out ideas.
She saw the ratio of bolts in a flange connection to the size. She mentioned gear ratios and the number of turns it takes to open and close valves.
And then things took a strange turn.
Amber jumped outside the box with both feet: “How many CEOs does it take to change a light bulb?” I wrote down the joke.
Feeling comfortable with getting a little math-crazy, she unleashed her creativity.
She suggested that thread size, shape and spacing on bolts was like the binding on spiral notebooks – both good places where math is used. She pondered the statistics of letter frequency in the names of different nationalities of people.
And she noticed that the distance between the signs hanging from the rafters, and the tops of the booths must have been calculated or they would be smacking into each other.
“I love thinking outside the box,” she gleefully exclaimed.
And then she told a story of creativity destroyed.
As a child, she had drawn the famous Ferdinand the Bull under his favorite tree, smelling the flowers.
And her teacher told her it sucked.
“I never did art again,” she confessed to me.
Heartbreaking – especially since I’ve heard a version of this story hundreds of times. I never thought that I would ever hear it told with drawing, though.
A few words can destroy creativity.
It’s normal and healthy to know our strengths and weaknesses. But we each have a right to discover our own weaknesses. Having someone declare our weaknesses is a violation.
Amber does very well as an engineer. But how different would her life look like now if she had continued to draw?
Maybe none. Maybe she would have drawn for years, enjoying it. Perhaps she would have eventually discovered that she was much better suited to engineering.
But maybe she would have become a Picasso.
Be careful what you say.
If a child is giving it their best shot and you meet them with criticism, you might shut down their creativity for life. And it’s easy to do this with math – there are so many ways for a kid to do things “wrong.”
But try to treat math learning like learning to create art. Regardless of how much the drawing sucks, be encouraging.
If a child is adding denominators instead of finding a common one, discuss what the answer looks like. Give them the right, and the power, to see where they went wrong.
Foster each child like they’re a budding Picasso and Pythagoras, regardless of how little talent you may see in them. Let them do things their way.
You just might be surprised at what they end up doing.
Do you have a story of creativity destroyed? Share it in the comments. And don’t forget to share Amber’s story on twitter.
