hi

Dr. Foss: What are you in for?

Veteran Teacher (aka me): I think I messed up.

Dr. Foss: You did. Now what?

Part I: Excuses are like… well, you know.

I have a confession.

For too many years I allowed my white privilege and implicit biases to infiltrate my classroom and impact my students. Yes, my intentions were good and no, I didn’t know any better, but neither of those excuses will cut it.

You see, I thought I was doing the right thing. I thought I was giving every student “what they needed”, when in reality I was making assumptions that led to low expectations and sent harmful messages to the students I claimed to care about. I believed that I was differentiating and that students would benefit from these accommodations. Little did I know that my students knew better, they had learned the rules to a game that I didn’t even realize existed.

Looking back, I believe that many of my students knew I expected less of them so that is what they gave me. They knew I would make excuses for them so they responded accordingly. Even though it was not my intention, and even though I was blissfully unaware, they got the message loud and clear.

Selfishly, I have thought about reaching out to these students. Finding them on Social Media and apologizing, even if it meant creating a TikTok account. Thankfully, I have learned some lessons along the way and I know better.  What would apologizing do, make me feel better? Oh how very white of me. They deserve better than that. They deserve more than I was ready or able to give them, they deserve everything, and they are definitely not responsible for mending my broken ego. Good intentions are no excuse for inequity.

Dr. Foss: What are you in for today?

Student: I have detention because I didn’t do my homework.

Dr. Foss: Why didn’t you do your homework?

Student: Because I didn’t understand it at school … how am I supposed to understand it at home by myself?

Dr. Foss: You pose an excellent question.

FYI: Fairy tales can be scary.

Don’t believe me? Check out the history behind Hansel and Gretel and try sleeping tonight. This one won’t be as bad.

A Math “Fairy Tale”

Once upon a time there was a school where students were punished for not understanding. Made to go without socialization, eat by themselves, face public shame and embarrassment, even wake up early and work on their days off! Wait a minute… I feel like I’ve heard this story before. You?

There is a common misconception that the teacher-student relationship is transactional. The teacher gives information and the student receives. If a student does not receive what the teacher has given, then it must be the fault of the student. And there WILL be consequences. 

Seems kinda ridiculous when you think about it right? Punishing students for not understanding what was taught? You have probably experienced this strange phenomenon without even realizing it. Did you ever have detention because you didn’t do your homework? Ever have to miss recess because you got caught cheating? Ever been kept from a field trip or other “fun” school event because of your grades? If not, chances are you know someone who has. 

Consider this:

Students have just taken a test on previously taught content.

Zach gets an “A” 

Slater gets an “F”

What assumptions did you just make about student Zach? Are they a “good” student? Supportive parents maybe? Motivated? Attentive? Hard working? 

What assumptions did you make about Slater? Are they a slacker? No support at home? Defiant? Lazy? 

Now consider this: 

Zach is an auditory learner, able to take in and process what the teacher says quickly. He is able to memorize material and regurgitate it with speed and accuracy. Zach is healthy, gets a good amount of sleep, and eats 3 square meals a day. Zach’s only responsibility when he gets home from school is to do his homework (if he didn’t already finish it in class).

Slater is a visual learner and gets lost easily during lecture based instruction. He has a difficult time memorizing information out of context and processes new information too slowly participate in class discussions. Zach suffers from undiagnosed depression and anxiety, dad is out of the picture and mom works nights. After school he is responsible for taking care of his much younger siblings.

Is Zach more capable than Slater? Maybe, but most likely not. 

Is Slater given the same opportunities to succeed in math as Zach? I would argue no.

So, why is it, that to be successful in mathematics you have to come with a certain set of privileges? Fair is not equal. Let me say it again. Fair is NOT equal. Giving ALL students what they need to succeed. That is equity.

For many students, this means the “traditional” math classroom will not work for them. I challenge you, as a parent, an educator, a member of society… before you decide that you are “good” or “bad” at math, consider the opportunities that you have been given to experience math in a way that makes sense to you. Then reconsider your mindset.

Dr. Foss: What are you in for?

Teacher: I have to teach math.

Dr. Foss: Ok, so what’s the problem?

Teacher: I’ve never experienced learning math in the way I’m expected to teach it.

Math Rehab 101

I spent the last two weeks preparing for and presenting at professional conferences for math teachers. I took a risk with the title of my session: Math Rehab, hoping that people would feel comfortable enough sharing their stories. Teachers are not a group that likes to admit defeat, especially in front of their peers. Admitting that you struggled learning math is risky business in a room of math educators. I wasn’t sure anyone would even show up.

I took my chances and am glad I did. I didn’t get as many participants as I would have liked, but the conversations we had were real and the stories shared were all too familiar. We need to pay more attention to teachers experiences as students. Were they positive? Negative? Traumatizing? Frustrating? These experiences, if not understood, will most definetly impact their students.

An Impossible Job

Imagine this: you go your whole life visiting doctor’s offices, watching doctors portrayed in movies and on TV. You go to school to become a doctor, go through residency, pass all the tests, and are finally given the piece of paper you need to do the job. All of your experience has led you to believe you are fully prepared. Then, on your first day on the job, you are asked to practice medicine TOTALLY DIFFERENT than you have ever experienced. You are expected to treat your patients differently than you were treated by your own doctors, differently than you were taught in med school, differently than the other doctors during your residency, oh, and you are expected to do this with very minimal training and support, if any at all. Good luck! Remember, you didn’t get into this line of work for the money… oh wait, maybe you did.

Seems silly right? Welllll…. you probably know where I am going with this. Insert math teacher into the scenario above and you have the true story of millions of K-12 math teachers across the country.

Math teachers are expected to teach math for understanding, allowing students to construct their own understanding and make real mathematical connections that will stick. Sounds great, right? Sure would be, but if you were educated in the U.S. and experienced a traditional math classroom then you most likely have no idea what this would be like.

Don’t get me wrong, most teachers are totally on board, after all, we didn’t get into this line of work for the money. Whatever is best for students is what we want to do. If you have ever tried to do something new with little training and little support then you know what a difficult ask this is. If you have ever tried to change a habit, perspective, or belief, then you know how impossible it can seem. Yet, we persist. Despite the challenge, despite the pressure to perform, despite the constant barrage of criticism from misinformed leaders, co-workers, and parents, despite all the political BS that infests education… despite all that. We continue to teach, we continue to learn, we make and re-make commitments to ourselves and our students to be the best we can be. Every. Damn. Day.

So, before you open your mouth about anything related to math education, educators, or the subject in general, do your research. Ask the right people the right questions. Be patient with our profession as we continue to do the impossible job of preparing the next generation for whatever dumpster fires lie ahead. Have grace. For students, for teachers, and for yourself. Learning new things is hard, but refusing to do so is harder.

In light of the recent decision by the Supreme Court I would like to shed a little math on the subject.

Disclaimer: The math in this post does not necessarily represent my personal opinions. You can’t argue with math. Therefore, don’t argue with me. *

Thank you, internet for the inspiration.

Part I: If one male human can impregnate 9 female humans EVERYDAY for 9 MONTHS, how many potential pregnancies will that one male be responsible for? I’ll wait…

Answer: 2,430 pregnancies

Part II: If one female human can get pregnant only once within a 9 month period… even is she (like her male counterpart) is with 9 partners a day for 9 months, how many potential pregnancies will that one female be responsible for? I’ll wait… oh, done already?

Answer: 1 pregnancy

Part III: 88% of female humans use some form of birth control and 45% of male humans regularly use condoms…

Answer:

*Disclaimer to the disclaimer: Its very unlike me not to share my personal opinion, so if you want it, read below. If not, thats cool.

Opinion: ALL humans deserve the right to bodily autonomy. Therefore, no other human has the right to tell another human, of any gender what to do with said humans body.

Dr. Foss: What are you in for

Student: I need the key to this gate

Dr. Foss: Oh, you mean the gate that only opens if you fit all of the ridiculous criteria and come from a place of privilege?

Student: Yes! I need to get through! Can’t you see the opportunity waiting over there?

Dr. Foss: Yeah…sorry, can’t help you. I don’t have the key either.

Gate Keepers Gonna Keep

At what point in your math education did you know where you fit?

You know what I mean. Was it in elementary school when you won the flashcard race? Or in middle school when you were publicly shamed for not knowing an answer? Did you skate through high school thanks to the answers in the back of the book or did you have to hide your love for math to keep your social status?

The subject of math is often considered a “gate keeper.” Only letting through the students who are most “qualified” and leaving the rest of us on the other side of the gate wondering why we aren’t good enough.

The Math Gate Keepers Start Early

Can’t count to 10? Not ready for Kindergarten.

Didn’t pass the state standardized test in 3rd grade? Retention.

Struggle to understand fractions in 5th grade? Below Level Instruction.

Didn’t understand your homework in middle school? Lunch Detention.

Below average in 8th grade math? Remediation course as a Freshman.

Oh, you still don’t understand? All aboard the low track train for the rest of your life.

The Math Gate Keepers Are Liars

Some people make it through a gate or two. Feeling pretty good about themselves they confidently sprint toward the next gate (insert middle school, geometry, calculus, etc…) only to be clotheslined. Stunned and embarrassed they stand up, turn around, and walk in the other direction assuming that they aren’t “good at math” after all.

Others breeze through every gate and continue to believe the lies. They have found the keys and continue to believe that math must be about getting the right answers. They get the right answer so that must mean they are smart. Those who don’t make it through? Well, maybe they aren’t smart? No, no, that would be unkind to say. Maybe they just aren’t a “math person”. Lies. All lies.

Too many of us are stopped at the gate early in life. Fed the lies about what it means to be “good at math” and over time come to terms with the fact that it is just not for us. We are just not good enough, smart enough, enough enough. We are limited by the lies we believe about our own ability.

The sky is the limit! Really? We all do live under the same sky, correct? So, if the sky really is the limit why is it so much lower for some? The Math Gatekeepers determine the limits of your sky. Yeah, I know. Rude. As a student I learned very early that my limits were low. I struggled HARD in math. I learned that understanding math was synonymous with being smart and drew my own conclusions. I failed my Kindergarten screening, was almost retained in 8th grade, sat through all of my high school courses with underclassmen, and didn’t make it into my college of choice. I ended up needing to buy my way into a private college (still paying those loans btw) and ended up at the top of my class, graduating with a 4.0 in Elementary Education. Ha! I had tricked them. Those damn math gatekeepers couldn’t keep me down! Or could they? Despite my success as an undergrad I was secretly terrified to teach above 2nd grade. The fractions! The multiplication facts! The horror!

Fast forward 18 years and I somehow managed to become a Doctor of Education (long story) and have dedicated my career to (of all things) MATH! That being said, the ghosts of those gatekeepers still haunt me. Not a day goes by where I don’t wonder when I am going to be found out. When I don’t worry that my colleagues are going to realize how unqualified I am. Even after 10 years of math coaching and curriculum writing I still start to sweat when asked to “math” in public and will never be able to remember the answer to 6×8 without a minor panic attack (even though now I know I can use 6×6 + 6×2 instead).

Moral of the story is this: Math can either limit us or make our options limitless. Remove the gates. Remove the stigma. Remove the false narratives. Let’s stop using math as one more way to segregate and separate. Let’s stop using math as a measure of how white and male someone is. Let’s stop using math to determine students worth, ability, and future.

Math for everyone. Period.

Sorry to break it to you Will but pizza boxes aren’t squares, pizzas aren’t circles, and a slice of pizza is most definitely NOT a triangle.

Did you like Geometry? You probably remember it as a subject in high school but did you know that geometric concepts begin at birth? Infants begin to notice shapes in their environment as soon as they can see and by the time they are 18 months old they are able to match basic shapes, even if they aren’t talking yet!

But we don’t need to go that far back. I’m sure you learned your shapes in kindergarten. Something like this:

Seems simple, right? Watch Sesame Street, color in a few worksheets and you have all you need to know. Until, that is, you are asked to write proofs in high school Geometry. Maybe you remember writing proofs as a high school student. Or, maybe you are like me and have no idea if you even attempted it. Either way, I’ll bet that up until that point you had never been asked to justify your thinking in math, never had to prove why a square is a square… or even question it! If this seems familiar, keep reading.

PSA- IF YOU KNOW OR EVER WILL KNOW A YOUNG CHILD: Please be aware that elementary school students will be expected to not only name shapes, but also define, compare, classify, sort, compose, decompose… oh, and prove and justify their reasoning. This may be difficult because there are a number of lies about geometry that students need to unlearn (see below) but relax. All children are capable of these things when given the opportunity to do so.

FYI- THINGS MOST PEOPLE THINK ARE TRUE BUT ARE NOT:

Lie #1: Pizza is a triangle

Truth: A triangle is 2 dimensional (length and width = two dimensions). Pizza is just delicious. Triangles are FLAT (no, thin crust doesn’t count).

Lie # 2: A rectangle has two short sides and two long sides

Truth: It might… but it might also have 4 sides that are all the same length. In that case it is a SQUARE rectangle. That’s right folks, a square is a rectangle with a special name (a square is also a rhombus, paralellogram, and quadrilateral… don’t trust a square).

Lie #3: Diamond is a shape (despite what all the children’s books say)

Truth: According to Britannca, a diamond is “a mineral made of pure carbon”. Not a shape. The RHOMBUS might look like a diamond to some but I don’t see the resemblance.

The lies do not stop there, but I will.

Now, go find all the children’s books about shapes and cross out diamond and write rhombus (use Sharpie).

Thanks.

PS- None of these are triangles

Let’s take a break from math for a minute.

So…I just sat and stared at the screen for a solid 8 minutes trying to figure out where to begin. Although I have a quite a few “dads” in my life that is not a title that I have used for anyone.

My biological peaced out early, I am sure he had good reason and hope to someday get up the courage to ask. I am a lot like him… I think. Weird how a person can add so much to your life without being a part of it. My freckles, sense of humor, appetite, last name, messed up teeth, gypsy soul … all from him. Thank you Dad. For most of it.

My step dad has been in my life for as long as I can remember, yet I don’t call him dad either. Growing up, I was my mothers child and although I know he loved me, he left all of parenting up to her. He taught me how to hit a ball (kind of), helped me memorize my 9s facts (which I forgive him for), and brought me with him to the bar (relax, he was a bartender). At the bar I would roll change and drink my weight in Shirley Temples. He always saved the boot for me. We would drive around town doing errands, listening to Wham!, Madonna, and the Beatles. He shared his Orange Crush, bought me 5th Avenue Bars at the bottle depot and was always a reliable source of entertainment. He took me under his wing and called me “Tiny Whiny” a name that now belongs to my 4 year old. Thank you, Dad.

My moms dad worked at the paper mill. When I was young, he would make me mayonnaise sandwiches and we would watch the Dating Game and Star Search together. I always guessed the winner. At age 3 I told him to stop smoking, so he did. Cold turkey. Thank you, Grandpa.

In my twenties, single and broke, I lived with my best friend and her boyfriend. He would always ask where I was going, who I was going with, and when I would be home. Picked me up when I couldn’t drive and made me dinner that wasn’t frozen waffles and peanut butter. Thank you Dad.

While planning my wedding, the Father Daughter Dance was a constant source of anxiety. Should I ask my step dad and risk hurting my mother? Ask my biological and risk hurting my step dad? Say F it and skipping the dumb tradition all together? I opted to dance with my step dad and keep my fingers crossed that he would stay sober long enough to avoid embarrassing me. I asked my sister to dance with my biological and avoided making eye contact with my mom. Everyone was happy. Except me.

Now that I am parent I understand how difficult it is. And although I know they are only human appreciate everything my dads have ever done for me, I don’t feel bad saying that it was not enough.

The best dad I have ever known belongs to my boys. The way that my husband loves our sons is everything that either of us ever wanted from our own fathers. Our babies don’t know and probably never will know how lucky they are to have him. But I do. I know how hard he works, how fiercely he loves, and how much he sacrifices. Thank you will never be enough.

Happy Fathers Day to everyone who has ever taken on the role. It not an easy gig.

Dr. Foss: What seems to be bothering you? 

Female student: Well, I want to be a (fill in the blank with pretty much any profession) but I’m just no good at math. 

Only 1 out of 4 people entering a math related field (think physics, computer science, engineering, etc..) are women (Cimpian, 2020). What’s up with that?

I grew up understanding that I was just not “a math person.” I knew who the math people were… and it wasn’t me. I mean, I am a girl, so what should I expect right? I guess that means I have to be good at reading then… YIKES. 

Needless to say, not feeling very good at either can leave a girl feeling pretty useless. “Smart” is not a word I would have used to describe myself for most of my life. I had come to peace with it, I had lost the reproductive organ lottery. Oh well. 

Consider this:

My husband is a much better cook than I am. What if he had grown up believing that due to his gender he would never be a good cook? I’ll tell you what would happen. He would be forced to eat frozen waffles 5 nights a week and live by the belief that “when pizza’s on a bagel, you can eat pizza anytime.” It would have robbed him of something that he truly enjoys AND excels at… and would have robbed me of his pistachio crusted salmon. Phew, dodged a bullet on that one.

In 2013 I accidentally found myself teaching 8th grade Algebra I. That’s a different story… anyway, the whole first week of school went by and NONE of the girls in my class would speak up. So, one day when the lunch bell rang I told the girls to stay behind. I shut the door and asked my girls what the deal was.

I bet you can guess the answer.

Yep, they didn’t want to look stupid in front of the boys (insert eye roll/vomit emojis). What if they said something wrong? What if they embarrassed themselves? What would that mean for their reputation? For their lives? For the lives of their friends and families?

You think I’m exaggerating here, I am not. These are the questions that young girls are plagued with on a daily basis.

So, I basically told them that they deserved their voice to be heard and that my expectation was that they would stop doubting themselves and start speaking their mathematical minds. It worked. Not for all of them, but for most. The girls showed up, started to take risks, and didn’t die upon failure.

What I am trying to get across here is that the common narrative that boys are “better at math” than girls is LUDACRIS. 

So MOVE boys, get out the way… (sorry, my love for Luda runs deep).

Dr. Foss: Welcome to Math Rehab, what seems to be the problem?

Student: I can’t answer questions fast enough.

Dr. Foss: Fast enough for who? For what?

Student: Hmmm… I don’t know…

One more thing about learning multiplication. No need for speed. 

Somewhere along the line speed became synonymous with smart. Not in other subjects though, just math.

Finished reading that novel already? Read it again.

You can spit historical facts out faster than your peers? No one cares.

Rush through a science lab? Not safe!

Win a flash card game? Genius (insert sarcasm here)!

Anyone play “Around the World” in math class? I did… If by play you mean anxiously waiting for the game to be over or the school to catch fire, whichever comes first. The game  should really be called “You are inadequate  so stop embarrassing yourself and sit down.”  

Ok, ok, I might be bitter, and yeah, maybe I blame my elementary math experiences for most of my adult insecurities. Nothing 20 years of therapy can’t solve. Let me explain. 

The game starts with everyone sitting down. One student starts the game by choosing a classmate to compete with. The choser and the chosen stand next to each other and asked to quickly spit out the answer to a math question, typically, a multiplication fact. Everyone else just watches, breathing a sigh of relief that it’s not them. It’s a duel to the death and someone has to be Hamilton. The person who says the answer first gets to stay standing and choose a new victim. The other student sits down, defeated, embarrassed, and one step closer to hating math. 

The thing is, with this game and others like it,  EVERYONE  loses. The student that wasn’t fast enough equates that with not being good enough. The speedy student gains a false sense of being better than their peers, and the teacher thinks they are helping students “have fun” with math. And just like that 30 minutes of instructional time goes up in flames.

So please, adults of the world, STOP MAKING MATH A RACE. You don’t have to take my word for it, take it from Ice Cube “Math ain’t a track meet, it’s a marathon.” At the very least, let’s stop publicly shaming students for not meeting antiquated and unrealistic standards. K? K.

Dr. Foss: What are you in for?

Parent/any teacher 4th grade and up: My child/student can’t memorize their times tables.

QUICK! 7 x 8 = ?

What just went through your head? Did you know the answer right away? If so, how? Did you “just know it” or did you have to do some type or calculation in your head or on your fingers? 

Maybe your brain shut down or you broke into a sweat. If so, you aren’t alone. 

Do you remember “learning” your multiplication facts? Which ones were easy to remember? Why? Which were harder to remember? Why? My guess is x2 and x5 were easy and x7 was more difficult.

Ready to get your mind blown?

7 is the SAME and 2 + 5.

Why does that matter? 

Well, if you were a kid struggling to learn their “7s” you could just use your “2s” and “5s”. 

Back to 7 x 8… if you broke out into a sweat over this one just think of the 7 as a 2 and 5. 

Do you know 2 x 8 easily? What about 5 x 8? 

2 x 8 = 16

5 x 8 = 40 

Soooo….. do you see where this is going? 

7 x 8 is the SAME as 2 x 8 and 5 x 8 together (16 + 40)

When I  started teaching I wanted to teach 1st or 2nd grade because I was afraid of math. If I didn’t understand it how was I supposed to teach it?

Well, let me tell you, when I started reading through my teacher’s edition I was PISSED. You mean to tell me that NO ONE ever thought to tell me that multiplication can be thought of as ADDING equal groups? That information would have been helpful while I was sitting at the kitchen counter crying over my math homework. 

I was never taught what multiplication LOOKED like. Had I known that 3 x 4 means “three groups of four” it probably would have made more sense to me.

When you say “three TIMES four” what do you see in your head? The numbers? 

When you say “three GROUPS OF four” what do you see in your head? Something like this?

**** **** ****

Make. Math. Visual. 

That is all.