I originally wrote the text below as part of a UCLA class I taught for in-service math teachers. Many of them were going through what I had also gone through: the uncomfortable feeling of realizing that you are finally making sense of math combined with the reality that for so many years you hadn’t. I always wanted to share this online but never did because I didn’t know what people would think. I came across it again recently and realized that it was hypocritical of me to encourage people to be vulnerable and go outside of their comfort zone during trainings, yet not do the same myself.
So, here it goes…
My first memories of learning math in a classroom are from the second grade. I was at a private school in a 2/3 combo class. I remember learning my multiplication table. I recall being proud of knowing 9 x 8 and 9 x 9 but having trouble with my 6’s, 7’s, and 8’s. I also remember using the standard algorithm for long division in second grade.
After second grade I left private school and attended a Los Angeles Unified School District public school for third grade. I recall being bored and confused as to why I was doing addition problems and was supposed to “learn” about multiplication soon. I also recall answering every question and contributing more than my share to the classroom conversation. Accordingly, I was given a desk of my own far away from everyone else in the back of the class. At the time I thought it was a great reward but I now better understand what it meant. Apparently my teacher had enough of me and I was skipped to fourth grade.
In fourth grade we were going over multiplication and I don’t recall much other than feeling like I wasn’t challenged. The next school year, my mom sent me to a gifted magnet school. The problem though was that in addition to being immature for my age, I was also a full year younger. As such, my mom made me repeat fourth grade at the new school.
I remember at the new school feeling more challenged but I was still doing multiplication and division. I was doing timed multiplication tests where you were given a ten by ten grid and with randomly placed factors from 0 to 9 on the outside and had to fill out the answers as quickly as possible. I recall that while I knew all my facts, I wasn’t as fast as other students at completing the chart. Clearly I must have been learning other concepts as well, but in retrospect, these feel like wasted years.
In fifth grade I remember learning about the coordinate plane and doing coordinate plane drawings. I also remember the first time a teacher said she was wrong about something. She had said that anything to the zeroth power was zero but days later told us that she talked to another teacher and anything to the zeroth power was really 1.
I don’t remember anything about 6th grade math, and I went to junior high for math in the 7th grade. At this junior high, the brightest 7th graders took a class called Logic. At the time I recall liking it and we learned about things like if P => Q and Q => R, then P => R. However, when I went to eighth grade and took Algebra, I was not prepared at all. In retrospect, I really wish someone had put me in a Pre-Algebra class.
My first memories of not having a clue about what was going on in math come from Algebra. I recall trying to factor polynomials and just guessing until I got it. I don’t think I had any idea about anything I was doing. I must have had some procedural understanding but certainly little to no conceptual understanding. I think I got a C in that class.
In Geometry in 9th grade, I was doing so-so, but then a series of life changes happened (I talk about those life changes in this 10-minute #ShadowCon16 video) and I wound up missing a month of the second semester and also changed schools. I was able to finish Geometry at the new school but after missing a month of school I had only a vague understanding of what was going on at that time.
During these years, you could still take summer school to get ahead, and I was made to do just that. I wound up taking all of Algebra 2 during the summer at a nearby high school. I do recall learning a lot and enjoying my teacher, but really, how much can you learn when you fit a whole year’s worth of material into 5 weeks?
The next year I was now a 10th grader entering high school. I was the only 10th grader taking Trigonometry / Math Analysis. I was very poorly prepared and also had one of the worst teachers of my K-12 experiences. I don’t recall understanding much of anything.
In 11th grade I took Calculus AB. Similarly, I was the only 11th grader in the class. My teacher did a great job, but at this point I was damaged goods. I had no foundation and did not understand anything. I wound up having to have a tutor every day after school just to avoid a D. I think I pulled off a C- for the first semester and then a B in the second semester. Amazingly, I barely passed the AP Calculus test with a 3.
In 12th grade I did not take math as there was no Calculus BC class at my school and I couldn’t get to a community college in time.
When I got to UCLA, I realized that I wanted to do a major related to computers or something in math / science. All of those majors required many math classes. I decided that either I was going to make a change now or have it catch up to me later. As a result, I took the same Calculus class that I already passed via the AP Calculus test. Between being a couple years older, receiving additional tutoring in college, having a great professor, and having another chance to see the material, I wound up getting an A-. I would take other classes but kept coming back to math. I wound up majoring in math and finding varying levels of success in all of my classes… except for one. I did have to repeat one math class, Math 151A: Applied numerical methods. I was thrilled when I got a C- the second time and knew I would graduate.
The next time math made a major appearance in my life was years later when I went into teaching after the dot com crash ended my programming career. I actually had no intentions of being a teacher at that point but had been unemployed for a year. I was helping a teacher friend chaperone a field trip and it came up that I was a math major. They were looking to replace a teacher and hired me as the third teacher of the year for a bunch of unruly 7th graders. I honestly had no business being a classroom teacher. I had never taken an education class or student taught.
I remember that one of my first lessons was on the Order of Operations. I didn’t recall ever hearing about it. After being told what that meant, I realized that I knew which operations came before others, but I had no idea how I knew and even less of an idea about how to explain it to someone else.
I also remember the first time I did not know how to do something in math… and I didn’t realize that I didn’t know until I was in front of the class and trying to do it! I had no idea how to use the standard algorithm to divide decimals. I hadn’t tried to divide decimals without a calculator in so long that I was clueless. I remember that moment of panic at not knowing what to do. I recall asking the student, “So, how do you do this?” “Now, what do you think the next step is?” Fortunately I was able to figure it out based on how they responded.
It should be little surprise that I was a pretty awful teacher during my first years. I had plenty of heart and enthusiasm, but I had no idea what I was doing and was Mr. Worksheet every single day. I do vaguely recall going to various math conferences and having my first realization that I could do math yet not understand it. I also recall thinking that it wasn’t such a bad thing to get an answer without understanding what I was doing. I wasn’t sure if it really mattered if I understood why as long as I could get an answer. I also didn’t really want to think about all the other things I probably did not understand. It was something of a Pandora’s Box and I didn’t want to deal with all the realities this implied.
My next big moment in my math education came during my first year in Downey Unified School District in 2005 where I still work full time. I was selected to implement a very conceptual curriculum provided by UCLA. Before we were expected to teach the lessons, we were given many full days of training where we got to do the same lessons we were supposed to do with our students. I recall using manipulatives for what might have been the first time in a decade, my first experiences with integer tiles, and of trying to make sense of zero pairs. I remember many moments of being happily surprised at realizing that I finally understood something. It was very enlightening.
That being said, I still wasn’t in a place where I realized that it was essential that I teach students conceptually as well. I certainly tried to connect all topics to real life applications, but I still taught the topics mainly procedurally. My students were getting higher and higher test scores each year so I figured I was doing something right. My reality check came during my first year as math coach.
I got an opportunity to teach or observe many classes at the Downey high schools. Many of my former middle school students were there, unfortunately relearning many of the things I had already “taught” them. It was honestly hard to acknowledge at first, but I had to accept that what I taught them or how I taught them did not prepare them for success in future math classes. I was doing to them the same things that I was bitter about other teachers doing to me: teaching procedural knowledge without any conceptual understanding.
I will be spending the rest of my career working on ways to improve my own understandings and providing resources and tools that will help others ensure that my experience becomes the exception and not the rule.
Thank you very much for making it this far in a lengthy blog post. I hope that by sharing my experiences, it gives you better perspective into who I am and why I do what I do. I’d love to read more about your own story or what resonated with you about what I wrote. Please let me know in the comments.
It’s fascinating to see how choppy your math experience was and yet how resilient you were to press on. Your line about feeling like “damaged goods” is tragically so prevalent among students today. No student should be bored and confused! That’s a recipe for wanting to quit. The system failed you as a whole, Robert. I guess now YOU are the agent of change – so other students experience less of what you did and more of what they deserve. It makes me wonder, how does a student connect all the separate dots (some forgettable and some not) of their math experience into a meaningful picture? Or might it be easier, and quite popular, to dismiss the picture all together as many do? Thanks for your persistence, Robert. Your reach as a teacher leader has been far reaching.
Thank you John. Yes, you can see that my own experience is my main drive to make sure it never happens again. In some ways it failed me, but at the same time, those experiences led me to where I am today, so somehow it worked out.
This makes me feel so much better about pursing math teaching! I can do it procedurally, but I am still learning all I can about how to teach conceptually and with real understanding. I have to relearn math conceptually myself. This gives me hope that I don’t have to completely redo all that before I can begin to teach somewhere! There’s hope!
If someone asked me, “What comment would you want to read that would make sharing this blog post worthwhile?” I would have basically stated what you just wrote. Everyone has to realize that virtually everyone else feels the way you feel and that we gain nothing by not admitting it. We have to begin by being honest about where we’re at and working on improving our situations. Thank you Shelley.
Your welcome and thanks again! I’m getting more and more sure of my direction and desire to do high school math.
I love this, Robert!!! Thank you so much for sharing. I wish I had such clear recollections to share. In this crazy blog world we live in, I always feel somewhat helpless that I don’t know as much as others and am intimidated at the very mention of calculus. It’s reassuring to know that others’ paths were not paved quite so evenly as I would assume!
Thanks Casey. Yeah, I felt like it was worth sharing because people need to realize that they are not alone, even though it may feel like that. Perhaps one potential pitfall of the way people use social media is that more good things are shared than challenges. This may lead others to have a less balanced perspective on what’s really happening and consequently incorrectly evaluate where they are at in relation.
I’m glad this resonated with you.
As I read your math story, I was also flashing back on my own. I feel compelled to put it down on paper. It’s crazy to me how many math stories are littered with wasted years. No wonder so many people have such a bad attitude about math. I was the kid who could easily pick up the prodedures, but was totally annoyed/frustrated until I figured out the why behind the steps.
In my position, I also see students across several years of their math education. I feel like if all teachers could view students’ math progression in the way we are able to, they would be more likely to embrace teaching conceptual understanding.
Interesting Lori. Honestly, I don’t remember ever feeling frustrated about not understanding why. I honestly think I accepted that there was no reason why and that it didn’t occur to me that math could make sense. So, I had sort of a sad blissful ignorance.
Gives us a lot to think about moving forward.
This resonated with me so much. I always did well in math because I was an excellent memorizer, but I always knew secretly that I was a fraud, because when it came to problems that required anything outside of using a memorized formula, I was in trouble.
I am currently a math coach, and I am about to complete an MAT, partially because of my continual need to understand what I’m doing.I still have my moments of feeling like a fraud, but I am realizing that nobody knows it all, and the important thing is to keep questing for understanding.
Thanks for sharing this Wendy. There is something liberating about being able to openly acknowledge gaps and then work on filling them. I am looking forward to a 2-day training I’ll be attending to improve my conceptual understanding of stats.
I hope you find a way to share this with the people you coach. My experience has been that most respect me for my honesty and are willing to be more vulnerable around me.
I was Dux of my high school and top students in both Maths courses and I felt I understood what I was doing. I didn’t realise how much I didn’t understand until I had to lead students and explain why. I am a secondary teacher and have been for thirty years, but one of the best things I ever did was primary school numeracy training in the form of The First Steps program. It allowed to me to make connections for secondary students who were not at the expected standard for high school and I can see how many errors are based in the misunderstandings developed before I ever meet my students. I see many teachers who know the content but can’t explain it or who believe all students have to do is remember it, they don’t have to understand to pass. Thanks for sharing your story.
Thanks for sharing this. Your comment of “I didn’t realise how much I didn’t understand until I had to lead students and explain why.” really rings true with me (and likely many others). I remember an interaction like this that happened once:
Student: “Where does pi come from?”
Me: “It’s just a number that has to do with a circle.”
I seriously didn’t realize where it came from (and what a ridiculous answer I gave) for many years. It’s definitely a challenge to first realize that’s a problem and then do something about it.
Thank you for sharing this. It strikes a chord with me as I’m sure it does many others. I was a great “answer getter” until I got to Algebra. Then I hit a wall! I taught elementary school (mainly 4th grade) and I taught how To get correct answers. It’s all I knew! After taking a job as a state K-6 Mathematics Specialist, I began to realize how much I didn’t know! In the last 10 years in that position my mission is to help elementary teachers grow in their conceptual knowledge and encourage them to teach in ways that grow that same understanding in kids. Again, thank you for sharing.
Thanks Heather. I appreciate your kind words. It felt a little scary to share this, but I felt like it needed to be done so that others would not feel alone. Glad it resonated with you and that you realize that your experience is, sadly, not uncommon.
Hi Robert! Great post. I love the vulnerability for the greater good. It seems you and I have been the developing the same idea independently… #MyMathStory !!! Here is what I wrote this weekend:
https://changingmathattitudes.wordpress.com/2016/11/14/mymathstory-the-most-significant-post-i-have-written-week-7/
Let’s keep in touch and coordinate our efforts!
Wow. Small world Adam! Thanks for letting me know that you were up to the same thing. Definitely worth normalizing some of our experiences.
Hi Robert,
Like the others have expressed, what a GREAT post. I fully relate to your experiences, as I actually have ZERO recollection of ever even learning math! I remember being pretty good with fractions in the 7th grade, but have no memory of the learning process. My only stand out memories are a boy named “Steven” constantly getting in trouble for not staying on task, being awarded a 7th Grade Math Trophy, and “earning” my first D, and later F in algebra (as a freshman in high school), which was–not coincidentally–taught by the driest, most disconnected teacher I have ever encountered.
Your story brings to light the importance for us to be “present” as teachers, ever improving on the teaching practices that will make us more effective, than those of our experienced past.
Thank you for sharing, Robert!
What a nice comment! Clearly it appears that this story resonates with most people as they have sadly had similar experiences. It’s interesting how you broke your memories into doing math and the learning process. I guess I don’t have a lot of (or maybe any???) memories of the actual learning. I just recall watching my teacher do math and me repeating what they did. Not ideal but something to build from.
Thanks again.
I shared your story with my 16 year old, as it is very similar to her current experience in math. Thank you for giving us hope!
Thanks Stacey. As painful as it is to write down, so many of the bad experiences students have with mathematics don’t come from factors the student can control. That often isn’t the message students receive, however.
Robert, thank you for all you do to improve math education. Your line “I was doing to them the same things that I was bitter about other teachers doing to me: teaching procedural knowledge without any conceptual understanding” rings true in many areas of life. People tend to teach the way they were taught, coach the way they were coached, parent the way they were parented, etc.
I had a different, but is some ways similar, experience as you. I took Pre-Calculus as a senior in high school and, after switching majors in college, took Calculus two years later. I was rusty with algebra and got by without fully understanding everything that was being taught. Taking Calculus 2 twice was humbling but helpful. Finally in Calculus 3 the light bulb went on and everything made sense again.
Getting a M.A. in Math Education after teaching for six years was a powerful experience. Much of the content from the undergrad program was repeated. However, technology had changed since the undergrad days and we looked at things differently – more conceptually and with more applications. Even though there was not much new content, my background in math was greatly strengthened and my understanding had increased tremendously. It was liberating to truly understand topics/concepts that I had “gotten by with” previously.
You are an inspirational educator Robert – keep up the good work.
Thank you Jim. It is still humbling to me that so many people hear their own experiences with math resonating in my story. It’s further humbling that despite those experiences, it sure is hard to make the changes that will prevent history from repeating itself.
I’m glad you found a path that took you where you want to be.
Having only met you fairly recently, it is wonderfully encouraging to read this story. I, too, was a math monkey all through school. I struggled through my college calculus classes, earning progressively lower grades, and just scraping out the 5 semesters I needed to get my engineering degree. My first years as a teacher (which I never intended to be) were spent modeling algorithms that students would mimic for no reason other than my say-so.
I am so pleased that I was unhappy with that method of teaching and searching for something better when I attended the in-service you did at Kinkaid. As Dan Meyer would put it, I had a headache and you had the aspirin. Otherwise, that in-service might have just been another wasted day. Instead, it was a turning point for me and for all my future students.
Wow Kathy. This was so nice to read. I believe every person who does professional development HOPES that what they do makes a difference. So, it sure does feel good to realize that it did for you. I love the connection too, to Dan’s metaphor. I use that headache and aspirin one all the time.
I graduated from college with an Elementary Education degree and a subject focus area in Math. I had to take the highest level math courses and without tutoring the way through I don’t think I would have made it (and I thought I was good at math). I became an elementary math coach 5 years ago and instantly panicked when I had to work with anyone above 2nd grade. I learned in a procedural manner and, like you, had no idea how to approach teaching conceptually when I didn’t know myself!! I have since been taking elementary math apart from K-5 and have developed a passion I didn’t know i had. Thank you for sharing your story. You definitely are not alone :))
Thanks Laura. Your experiences are fairly common, as you might imagine. One piece of perspective I might add is that the issue is not really a “math from higher grade levels is harder” issue but rather “anything I’m not familiar with is harder”. I remember going to teach my wife’s 3rd grade class subtraction once. I figured, “I got this. How hard could it be?”
It wasn’t until the middle of the lesson that I realized, “Um, I don’t think I understand this as well as I thought.” Specifically, I knew the procedure, but technically, you’re not borrowing a 1, it’s a 10 or 100. So, in that moment I realized that there was more than I knew.
Anyway, I’m glad you developed your passion and now can share it with others.
As for I know having lived in four continent and grew up in India and UK US is the only country that imparts degree in Mathematics education or Chemistry education or Physics education. Most nations Japan, India, UK Germany, Russia (many mathematics professors at US universities are Russians) one has to take a degree with combination as Mathematics major, subsidiaries Physics and Statistics or Mathematics Major, subsidiaries Physics and Chemistry or Mathematics Major with computer science and statistics as subsidiaries. In a coin if two sides are physics and chemistry mathematics interface (the edge). Thus with a major degree in mathematics one sees the connection of the interdisciplinary subjects. I have come across in the US teachers with mathematics and concentrations in PE and Spanish or any of the irrelevant subjects. This is one reason why we are in short of Computer scientists different from IT. Computer science is like Quantuum mechanics in physics.
I am a retired professor of engineering mechanics at Berkeley/Princeton. Taught in high school after retiring AP physics, AP chemistry and AP Math/statistics.
Interesting. I didn’t realize that majoring just in mathematics was so unique. I appreciate you sharing this perspective.
Sad story with a happy ending.
My story is not at all like that one, because even when my teachers didn’t understand, my mom would always show me the concepts and the reasons of doing a procedure.
I did find boring some years. Math was not my favorite time at school. I was frustrated with some teachers that kept on inventing impossible figures and situations. I liked explaining homework to my classmates.
I entered the math olympics when I discovered there were such things, the last year I could compete. After being chosen with other 16 students in my state, we were given a fabulous summer full of problems to solve. I saw how other students knew things I didn’t learn in regular lessons. At first I felt inferior, but that was so challenging and fun, that I was chosen to go to the national contest, the best and most meaningful experience of my life (I even found a husband there).
I agree that, while teaching, is the time when you get the most interesting doubts about what you know. That division of fractions (we solve it with the “candy method”) is always the first one to arise. It was fun to prove it for the first time “on the air” in front of the students. Sorry for writing this much on your blog, but your posts are so inspirational…
My Alg 1 class is testing today for a unit on statistics. I mentioned that the goal was to score 100 on the test. The disbelief, the comments! ‘I’ll be happy with just not failing!’ Said more than one. My students do not see this as possible at all. On the other side of that, however, is that they’ve been given the ‘shortcuts’ for so long, they are not of a mindset (yet!) to struggle with the concepts. There is a pattern of trying to remember the how, then incompletely or incorrectly applying it, not being able to successfully complete the problem. They then stop out of frustration. My goal is to teach and share the why as well as the how….
That certainly is disappointing (though not surprising) to read how students feel that way. I’m glad that they have someone like you to help them develop deeper understandings. I also liked your #growthmindset “yet!” comment.
The more ‘Math People’ I get to know, the more I realize there is no such thing as a math person. I am a fairly new teacher. I taught 5th grade all subjects for two years and just math for three years.
If you follow the link and go to my first post – Believe, you will find my story.
Unlike you, I was really good in Algebra. It probably had something to do with the fact that every time I moved, I was placed in another Algebra class. When you move a couple of times a year – the admin understands there will be gaps so they put you in only classes required for graduation…
https://nerdymathteacher.wordpress.com/blog/page/2/
Can you please send me that link again. I can’t figure out which one it was.
Not sure how it took so long for me to see this, but I’m so glad I was able to read your math biography. I was seen as gifted from an early age, and loved those times tests because I did so well. I was fortunate to have learned a lot algebra from my father, and developed a reputation as “the math guy” in high school, which allowed me to get away with so many people student skills throughout high school. I was the captain the math team, so didn’t need to do homework. That hurt me so much in college. I did well in some classes, but prolly in others. I even found I understood much of my Abstract Algebra class, but never bothered to turn in my homework. Eventually I found my place, and scored quite well on the Putnam exam, and even was a fairly successful mathematician in the dot com era before switching to a teaching career. My first few years, I was enthusiastic, but had much to learn as a teacher. Still, I was well liked and respected by most students and parents and administrators. I struggled in grad school for many reasons, mostly personal (death of my father and a difficult divorce during the birth of my first child), but some other reasons. Still, though I’d been teaching for teen years, grad school did give me some validation that I’d done a lot of things right. Now I’m in a school where many (~30%) are on full scholarship, and nobody is well served my their local public school system, and I’m proud the work I’m able to do. I have to take to heart the last conversation I had with my father, in which he told me, “You can’t save everyone, but you can save one kid at a time.” Wise words that have helped me throughout my career.
Wow Ethan. Thanks for sharing such a powerful and personal reflection. It’s amazing how we all come to the classroom with our own challenging experiences. I’m sure all of this has given you even more perspective about what you’re trying to accomplish… and avoid.
I feel like I had a good understanding of number sense early on because I loved sports and kept a lot of stats and scores. I was really good at following procedures and I had a good memory, too. This helped me be very “successful” in mathematics throughout school. So, I decided to be a math major at Indiana University. I to an A in Calculus I as a first-semester freshman. Then, I took Calculus II during the second semester. I had a very difficult time understanding the professor and thought I had hit my math wall (which I know now is a myth). I changed majors and along a different path I found my way to education anyway. I found a passion for early literacy and early numeracy and I now teach kindergarten. I am working hard to help students build a solid foundation of understanding and a belief that they are mathematicians. I hope this foundation allows them to go as far as they want in learning mathematics.
Thanks for sharing this Kenny. I’ve had similar realizations… and I think they are accurate (but could be me just passing blame elsewhere). While I loved UCLA and my time there, I felt that many of the math professors were not good instructors. Most felt like they viewed teaching as a requirement for them to stay at the university. Lecture did not work well for me and I did not understand as much as I wished I had.
Back then I thought it was just me. Now I think differently.
I was good at maths because I had a good memory which worked until year 12 (final year of high school in Australia) when I almost failed. I remember my maths teacher saying to me “don’t become a maths teacher!” I didn’t start teaching until I was 35 (10 years ago and I honestly think it has only been the past handful of years where I really get it). I started teaching the same way I was taught. I know that’s not good enough anymore. Robert, you are certainly not the only one by a long stretch! Thanks for sharing.
(PS I lost to P.K. in Year 5 times tables races – 7×7 scarred for life!! 🙂
Thanks for sharing your story, Christine. One part of what you wrote stands out to me: “I was good at maths because I had a good memory” I simultaneously completely understand what you mean but am also saddened that we’ve had to experience math as something where being a good memorizer matters and forgetting means you are no longer good at math.
We clearly have a long way to go in math(s) education still.
Thanks for being vulnerable enough to share this publicly, Robert. I resonate with much of what you shared. I, too, was identified as “gifted” in math at a very young age, and was pushed ahead quickly. For me, realizing I was far enough ahead in HS that I could “quit” math was a relief, because what was the point? I signed up for College Algebra as an undergrad because I refused to subject myself to calculus. I went to 3 days of class before the prof offered to let me test out of the class by exam. I did well enough on the department exam that I “earned” my college math credit and vowed never to take another math class again.
But then I got to a “Math for Elementary Teachers” course in my teacher ed program and suddenly we were exploring concepts, ideas, patterns, and meanings behind elementary mathematics. I was intrigued. Like you, I remember the moment I realized that I had never truly understood math, despite being extremely successful at it by most traditional standards. Yours was with middle school level math, dividing decimals. Mine was with first grade level subtraction. The idea that “5 – 2 = 3” had more meanings than I had ever dreamed of was mind-blowing to me, and started me on a new journey of learning elementary school math right alongside my students. This journey has been more exciting, fulfilling, and empowering to me than I ever dreamed possible.
Now, I’m watching my own children run the gauntlet of school mathematics, and unfortunately, too little has changed. Like many of us, my 10th grade daughter is now “damaged goods,” despite being a straight-A student with her eyes set on a STEM degree at Stanford and a career in science. As a math educator and a mother, this is heartbreaking to me. But what gives me hope is stories like yours and mine that tell me that “damaged” isn’t a permanent state. You and I didn’t begin to repair that damage until we were adults. My hope for my daughter is that she’ll have just one teacher in high school or college who will help open her eyes to the beauty of mathematics and her own capacity to make sense of it. Perhaps if she gets into Stanford, she can take Jo’s course. 🙂
What a great story, Karen. Yeah, it is humbling to be so entrenched in math education yet have so little ability to help influence what happens to my own son. I hadn’t thought about your final part about what gives you hope, so I guess that is a plus for sure.
Thanks for sharing this.
I was not a confident math student. Math scared me. I wasn’t good at it and I didn’t understand it. I distinctly remember cutting out pie pieces (fractions! AHHH!) with my dad and crying because I couldn’t understand how 1/3 is bigger than 1/4 if 3 is less than 4?? My anxiety continued into high school when I had to take geometry with Mr. Lord. The same Mr. Lord who taught my PARENTS. He was old school and would have us answer problems out loud in numerical order – but he didn’t always start at 1. I would count ahead and see what problem I was going to get and then try to solve it in advance. By the time he called on me I was shaking and ready to cry. Ugh. I hated math. I was a strong ELA student, combined with music, so I continued on that path. I became a Public Relations Major in college and had a very successful fundraising career in nonprofits, which I loved. However, my life took a left turn after starting my family, and a little teaching seed that had been planted years ago finally sprouted. I went back to school and got my teaching certification – and started teaching elementary school at age 38. I was in a team teaching situation and naturally I taught ELA. Until….the year my principal came to me and asked me to teach MATH only. WHAT? ARE YOU INSANE? I actually said that to her. But something in me said “Do IT!” and in my heart I wanted to make sure that no child, especially a GIRL, ever had a math experience like mine. So I dove in, learned all I could about math best practices, wove in growth mindset, and created a classroom where it is safe to make and analyze mistakes and where we celebrate all things math. I tell my students all the time – “If I had a math teacher as cool as I am, then I would have loved math.” We talk about math anxiety, we use our problem solving strategies and guess what – I freakin’ LOVE teaching math! LOVE, LOVE, LOVE it! I will never go back! One of my best student stories is when one of my anxiety driven 3rd graders went on to 4th grade. On the first day, her new teacher asked the kids to describe themselves. She proudly announced “I am a mathematician!” I cried when I heard that. Now I am the gifted & talented MATH teacher for the entire district grades 2-8. I have found my calling and my niche and I am forever grateful for the opportunity.
WHAT A WONDERFUL STORY!!! I think that people who struggled with math as students often make the best math teachers. Partly it’s because you can empathize with students’ experience and partly it’s because you realize the importance of learning so many different methods for making sense.
Thanks for taking the time to share such a transformational journey.
Hi Robert,
I attended your workshop today in Stockton and was thrilled to see you validate what I have been learning through my credentialing program. I was loud guy with the loud red velour sweater on. I usually freeze in that building. Anyway your personal story brought tears to my eyes. To make it out of the foster system and into UCLA is a true story of empowerment. Like the resilient research asserts it only takes one positive adult relationship to motivate a child to be successful. I look forward to meeting you again. I thoroughly enjoyed your workshop and admirer your authenticity.
Thanks for taking the time to check in Willie. Your enthusiasm was very helpful yesterday. I appreciate you reading some of my other posts to learn more about my story. For as much as it was a challenge being that child, it’s given me much greater perspective as to what’s important in life and that I need to do everything I can do empower others.
I do hope to see you again soon.
My math story does not have an ending (Yay!) … and yet the beginning was not pretty or fun (Boo!). I remember growing up not liking math, feeling stupid in math, never understanding why my teachers told me to do certain steps, but, I was good at memorizing (learned my facts quickly) and I could follow directions (as long as a problem followed the steps the teacher showed I was good to go). However, I remember failing algebra (which I took in 9th grade-as back in the day it wasn’t offered in junior high). Things got worse from there. In college, I avoided math and took the necessary requirements (College Algebra and Teaching Children Mathematics). As an elementary teacher, I made math the shortest part of my day (I didn’t like it and I made sure that I passed that down to my students … SO SORRY!). However, in my third year of teaching things started to change. I was asked to teach math to gifted/talented students. In order to do this, I needed to learn the math, understand the math, immerse in the math, and converse about the math. During this time I must say that I became vulnerable with my students. I learned so many strategies and methods for approaching problems from them. And so….. my math journey/story continues. I eventually became a middle school mathematics teacher (went back to school and took all those math classes I had avoided) and taught Algebra, Algebra Honors and Geometry. Then, I became a Secondary Mathematics Curriculum Specialist and an Elementary Mathematics Curriculum Specialist. My heart still pounds when someone gives me a problem cold to solve. Everyday I learn more about math, how to teach it for understanding, how to question and discuss what students are doing and why. My math story hasn’t ended….
What a great story, Dottie! My working hypothesis is that people who struggled mightily with mathematics wind up being better instructors because they understand why just knowing the procedures is not enough and value having multiple approaches (as well as understanding how those approaches connect to one another).
I’m so happy that you’ve come so far. Great job!
Hey! Great story. I was a memorizer. Appeared to be a good student but was going through the motions. I became a math teacher because I wanted to work with high school students, but had to figure out how to best do that. When the Chicago series books came out as well as the TI 81, the data did it for me! I finally started to understand how everything fit together. I am in my 28th year, I have taught everything from pre Algebra through Calc BC and I can spot a memorizer a mile away! I am constantly asking them why..so they do not leave my classroom as mystified as I left my high school classrooms. Thank you for your story and your perseverance.
This is beautiful, Christine. How much I wish I understood “why” math worked at the highest levels of high school and in college. Thank you for what you do.
Robert,
I loved your story. It is funny how we all can relate to your story in some way. I can remember in 4th and 5th grade being so proud because I was good at beating other students when we practiced multiplication/division flash cards. How little did I know that wasn’t the what I really needed to know about math. Thanks for your continued work in making teaching math better for those of us who know that there needs to be more than procedures.
Carol Jones
Thank you Carol. My hope is that if we as math educators can be more transparent about where we’ve come from, then we can take another step towards making positive changes.
I learned procedurally as well. I was good at math and always made straight A’s until I got to High School. In High School I had a geometry teacher who really didn’t teach us anything. Her teaching method was to do problems on the board and hope we absorbed the information. Although I didn’t understand a thing, I still got an A. That changed when I went to live in a group home for a year. At that school I failed Geometry. It was the first class in my entire life in which I mad less than an A and my grade was an F.
After I returned home to live with my aunt, I graduated early (I wasn’t required to go my senior year because I already had enough credits). I still loved math, but never thought about becoming a teacher. I got married and began to have children. After a few years, my husband and I divorced and I was a single mom working as a janitor in a lot cal factory. I knew I was smarter than that and got up the nerve to ask him for a promotion. He basically told me that I was where he wanted me to be and I got angry, but it also motivated me to go back to school.
I enrolled in the local college where my only options for a four year degree were nursing or teaching. I thought that if I got my degree in teaching, that I could use those skills anywhere, so I went for it. When I graduated, I still didn’t know what I wanted to do. After several years and several different jobs, one day I decided to use my teaching degree and began teaching.
I started in third grade and would consistently see the same kids staying in at recess because they were practicing the standard division algorithm. It was then that I decided to do something about it. I decided to learn the whys of mathematics and learned conceptual understanding of math. It was enlightening. I began fighting the battle of trying to get other teachers on board before conceptual understanding was a thing. Sadly, I’m still fighting that battle. Despite the changes in standards, most math teachers that I know are still teaching math the way they learned it: procedurally. I’m still plugging away though.
I currently teach 7th grade math and am more determined than ever to teach conceptual understanding to my students. It is very difficult to be the only teacher in the building who teaches the way I do. I don’t have a lot of support.
I appreciate the resources you provide. They are very meaningful and helpful. My students enjoy them as well. A huge thank you from Georgia.
Thank you for taking the time to share your story. I believe that people who started out as math robots where we could do math without understanding why it worked are also the ones who most appreciate the value of conceptual understanding and passing it along to our students.
Hi. I know I am still in the 10th grade, but I have always loved math. I want to teach math when I get old enough. Do you have any tip for me Mr. Robert Kaplinsky?
Just Call Me cole
Hi Cole. That’s great that you’ve already figured out what you want to be when you grow up. Besides the obvious advice of going to college, you might consider attending one that offers a program where you can graduate with your teaching credential and possibly a Master’s degree.
Other than that, I’d continue to focus on school and try as much as you can to understand why math works. For example, you probably know that when you divide fractions, you change the sign to multiplication and do the reciprocal of the fraction on the right. Why does that work though?
Similarly, why do we bring down a zero when we multiply or borrow a one when we subtract? The more you can understand why what we do works, the better prepared you will be.
Just call me Robert.
I was a great ‘memorizer’ and so did fine in school, but I remember being in “Math for the Grades” education class in college and being handed base-10 blocks. It was like a light from heaven and the Hallelujah Chorus all at once! It drives my students crazy that I make them explain WHY procedures work, but I am convinced that it is essential 🙂
Hi Shaanti. Yes, the more I have learned, the more I have realized how much I don’t actually know.
I remember when my math train fell off of the tracks in fourth grade. I remember what the room looked like. I remember coming home and crying because for some reason I went from being “smart” to feeling completely stupid. All of this was over the long division algorithm. Prior to fourth grade, math had been incredibly easy for me because it was all very basic and the rules were easy and the answers were simple. As soon as math became complicated, that part of my brain went dark. I was alone in a foreign land with no one to translate for me. This continued year after year through high school. In high school, I took Algebra I and II, Geometry, Advanced Senior Math, and Trigonometry. I was always “awarded” a B or a C for effort I assume. I remember none of it and it was all a fog of stress and frustration. I never understood ANY OF IT. When I started college, I specifically scoured course catalogs looking for majors with the fewest number of math courses – finally settling in Journalism. I changed majors at some point to Communication and oh – the dread… A new math course to take – Finite Mathematics. I remember purchasing the textbook and CRYING. It looked like it was written in Sanskrit. I approached the professor on the first day and explained that I “just needed to pass the class” by any means possible. I did. I passed with a C by 1 point – again probably a gift. Life took a few twists and turns and I ended up in education. I received a transitional certificate, because I already had a degree. My transitional training program was bare bones. During my first two years teaching, I taught fourth grade beginning on page 1 of the text and so on. My intervention method was “if at first you don’t succeed – try, try, again.” Because – seriously – that had worked SO WELL for me as a student… I muddled my way through a few years of third grade math instruction and then needed to fulfill the requirement of rank change. I chose a rank change portfolio program that allowed me to self improve, as opposed to a “one size fits all” masters program. This was the beginning of my metamorphosis. I knew I needed to become a better math teacher. When I looked in the mirror, I saw all of the mistakes I had lived through as a student coming out through my instruction. I reached out to local math organizations in Kentucky (where I live). At first, I thought they might kick me out when they realized I was not a “math person.” On the contrary, I was embraced and supported. I realized that there was a far better way of teaching math that I had never known as a student or teacher. I was introduced to the concept of sense-making and the use of visual models and that there was MORE THAN ONE WAY. It was a magical transformation for me. I am still only comfortable with math up to about fourth grade. I hope some day to retake Algebra from someone who can teach “someone like me.” I love seeing kids LOVE math in a way that was never accessible to me. It is now my mission. I was a math intervention teacher for two years. I now teach first grade, but hope to focus strictly on math again in the near future. I also started a Facebook group called Math Intervention Matters to connect people like me to resources and support. Foundational math is my passion. Improving math instruction is my mission. Connecting people with resources (both human and otherwise) is my jam! Thank you for sharing your story.
Thank you so much for sharing this Amy. One sentence really resonated with me more than anything else: “I remember what the room looked like.” It’s been my experience that when something really traumatic happens, somehow I can remember all these details: where I was standing, where other people were standing, what was in the room, etc.
I’m sorry that you had such a traumatic memory so early on.
I’m happy though that you ultimately had your magical transformation and realized that it was never a measure of you but rather how we teach (or have taught) math. I wish it wasn’t such a common experience though.
Thanks again.
Math. It never ever made sense to me. Basic subtraction still confounds me. My academic and personal lives have been filled with anxiety. It wasn’t until I was in college that an observant prof watched me trying to solve basic arithmetic problems and suggested I make my way to the special ed department where, after a series of tests, I was relieved to find out I have a math LD. The funny thing is, as much as math eludes me, I still like it. It’s like this puzzle I need to solve, and I keep working at it. I think all of this serves me well as a teacher, as I can empathize with those for whom Math does not come easy. I have a notebook full of drawings my profs helped me create to help me recall how to solve math up to about the 5th or 6th grade, and the irony is that I pull that notebook out daily and use the strategies in it to help kids in study hall. We draw pictures, we count with counters, and I tell them whatever works to help them “see” what is happening is what they need to do. And do again and again. So why do I follow the blogs of math teachers? Because there’s so much for me to learn- or relearn. And there’s this puzzle to solve, with so many lovely numbers and angles and symmetry and fractals and…..
Thank you for sharing this personal experience, Nancy. It’s really hard to navigate these waters and hold on to your sanity. I appreciate you sharing how you overcame your hurdle or at least realized that there was even a hurdle to begin with.
Thank you for sharing! Your resilience is inspiring!
Thank you Roberta.
I had an easier time with math, but your comments around being able to be procedurally competent with no real understanding strongly mirror my own experience. I scored oodles of perfect scores in high school, but I operated on pure instinct, mimicry and a great memory for algorithms (and natural aptitude that was never really developed in a deeply blue collar school district). I distinctly remember meeting with my third year Calculus professor about something unrelated and admitting to him that I really had no idea what I was doing in his class. His look of stunned horror when he protested that I was one of the top students in his class has always stuck with me. Eventually I became a pension actuary, so procedural competence took me pretty far, but I wonder how much of our “only special people do math” mythos comes from mistaking poor procedural memory for a lack of actual mathematical ability.
Thanks Victoria. I imagine it was both validating and horrifying to realize that you are not alone in feeling the way you have.
All the information mention above is true. Life is a mathematical problem. To pick up the most, you need to realize how to change over negatives into positives. Loved the information and thank you for sharing it.
Thanks Jerry.
Your story is so true for so many educators, including me. As a math educator in today’s world, I am having to dig deeper into the content to understand the ‘why?’ I was never given the opportunity to just explore/discover math and make those connections or even feel vulnerable enough to try other strategies. Now, as a continue to be better for my students, I realize that conceptual understanding starts with multiple entry tasks that allow students to discover the ‘why’ and apply to new ideas in math.
Thanks for sharing this, Jennifer. You’re certainly not alone.
Like many here, I had an amazing memory as a child. In addition, I had a solid base of understanding throughout elementary that was due to a combination of my dad’s (a farmer) influence, and a gift for questioning and those “Aha” moments. My trouble came in algebra, where I received my first C. No one ever explained why those letters had invaded my math world or what practical application this had in life. I was now stuck in a world of “guess-and-check” that was frustrating and time-consuming. An even worse experience in Algebra 2 convinced me that I no longer liked or was good at math. Geometry proofs rebuilt my confidence, as they relied on visuals and my ability to memorize theorems and postulates. Trigonometry was a nightmare (fortunately only a trimester), but Calculus made sense.
As a teacher, I taught a combination of my training and my “aha” moments, and my elementary students achieved high test scores, but I knew something was missing. I had a student teacher who was teaching kindergarten. Having started my career in kindergarten, I saw what she was doing and longed to return. I wanted to use 10-frames and rekenreks to create those visuals to lay a solid groundwork for my students. I discovered Christina Tondevold’s work and my mind was blown. I set about changing my own teaching, and tried to transform the teaching of those around me.
I was determined to do better with teaching algebra to the students I tutor, so I consulted my friends in the Build Math Minds group for guidance. They suggested the Hands-On Equations program, and I was elated! I finally saw what I had missed in algebra as a child; it made sense! Sadly, I have had little impact on the skill set of those around me, as I discovered that so few elementary teachers like math or feel that they understand it well. I retire next month, and I will miss having conversations with other teachers to try to transform their math minds, but I will continue my own journey and that of the students I tutor.
It can be really challenging to be making your own breakthroughs, realize how powerful they are, and not be able to convince others to come on the journey with you. My best advice is to keep investing in yourself and your journey. The more you grow and have success, the harder it will be for others to deny that what they’re doing is just as good as what you’re doing.
“I will be spending the rest of my career working on ways to improve my own understandings and providing resources and tools that will help others ensure that my experience becomes the exception and not the rule.”
WELL…you REALLY meant that and I so appreciate the amazing resources you kindly and willingly share to make all of us better math teachers. I use the resources and suggestions you offer rather than the curriculum we have been using that has still not improved test scores. Student engagement has never been higher since I’ve started implementing your ideas. I can honestly say that my students are finally mathematical thinkers and they understand and value meaningful learning experiences that are relevant to their lives. I am sorry your own experience wasn’t great, however, great things came out of it for the rest of us because we get to get to learn from you – the BEST PART of it all is that we are making a difference in the lives of the children we teach every day. Thank you!
Thank you so much for making time to write this, Alexis. This is so touching and is the fuel I could use right now to remind me why we do what we do. Truly, thank you.
My story is different than yours, but your story resonates with me because while I was “good” at math, I had a SEVERE case of imposter syndrome. I figured i was always just moments away from being found out that I actually understood nothing. Even in college, as a math major, I remember hoping I would not get called on because if I did, I would just have to guess. To me, a lot of my insecurity stemmed from using the textbook or other resources as examples and then just trying to squish the currently problem I was working on into the model. I was never encouraged to think or try on my own when I was younger, therefore, as I got older, I didn’t really know how to think and try. Remembering this has helped me a lot in my teaching. Kids love looking at example problems, and I often have to stick to my principles about not just teaching this way (because it seems much easier in the moment). But I see such growth in kids (middle school) when you really push them to wrestle with problems often and fail a lot. By this time of the year (minus the pandemic) they often do not want to see examples, instead opting to try out some things on their own first. Finally, one of my greatest joys of teaching is when I discover something in Prealgebra or Algebra that I didn’t know before…and it happens all the time! I really liked your fraction example, I love talking about fraction division with kids (and. parents) as an example of how the math doesn’t have to be “hard” in order to invite interesting investigations. Love your posts and thanks for the inspiration!
Thanks for unpacking this for all of us, Paula. I’m sure many can relate. I imagine that this is a source of power and inspiration for you as a teacher. I see it in your comment about experiencing joy from new learnings. I hope you also share this with your students so that they realize they’re not alone.
Thanks so much for sharing! I was not nearly as proficient in math as you were going through school. I was a pretty good rule follower and just followed the rules that were taught in math class as well as I could. After that, I just learned how to dodge the classes that became too difficult (which means I didn’t get past Geometry.) Then my own two sons came along and began school and I had to deal with how to help them with math homework. Having to teach someone else, I realized that I knew rules but not why. This became even more apparent during my student teaching when I had to teach 5th grade math concepts I couldn’t explain. Fortunately, I had a fantastic teacher in my credential program that opened my eyes to the conceptual side of learning. He introduced manipulatives that I had never seen or used before. Today, I still feel I am on a journey to gain conceptual understanding, but because of enlightened and generous sharers such as yourself, I feel excited about the prospects.
Just so you hear this from someone, I am so damn proud of you, Jill, and you should be proud of yourself too. I hope that what you’re realizing is that it is was never about you not being a good student, but rather it was about you not having the right teacher for you.
The sad reality is that your teachers probably never had someone teach them conceptually either, so (at best) robotic understandings were all people had to pass down. Great job and all your students will benefit from what you’ve done.
It’s funny, I went to UCLA for Theater, and one thing I was thrilled about was that I didn’t have to take any math classes! My last math class was at the local JC between my junior and senior year of high school, and I felt I’d put academic math behind me.
Fast forward to now, and I’m teaching freshman integrated math at a public school. I have the “Wow, I don’t know what this is!” moment all the time, but since I wasn’t really rooted in math, I’ve been looking at it with a mind that isn’t rooted in the algorithms and methods I was taught and no longer remember. I’m finding myself figuring out these concepts with my students, and regularly stumbling into places where we are all suddenly having the light dawn on us, “Oh, that’s why this works!” I have really been emphasizing number sense and an understanding of the structure and function of mathematical operations, and it’s been a great experience. At the same time, I also know there is NO WAY I should be put into a higher math class, because I just don’t have the rock-solid background to make it work. In a few years? Who knows.
There is so much great about your reply. Similarly, I was going to pick Computer Science at UCLA because there was no language requirement. Yet here I am, able to speak Spanish fluently now.
One thing I want you to realize is that ALL of your colleagues have gaps in their understanding. They might be more experienced or better robots who can replicate practices, but if you asked them WHY the math works, many of them would not know either. So, while you’ll be even better with more experience, everyone is benefiting from you continuing to explore the “why”.
VERY similar experience! Here is a link to my Math Efficacy statement that I wrote years ago while working on my teaching certification.
https://docs.google.com/document/d/1J4NI1W7vd6k_mEevodJq5le2RCVmgtN5/edit?usp=sharing&ouid=104782885218948946611&rtpof=true&sd=true
I love this part: “On the day that I received my Bachelor of Science degree in Mathematics, my parents confided that I had been evaluated in school as “learning-disabled” in math. Yet, if that was the case, I had just accomplished a nearly impossible goal. How could that be? Perhaps, I considered, the schools themselves had been “teaching-disabled” in mathematics all along.”
Absolutely. I’ve found that more often than not, our concepts of “high” and “low” students say much more about our own teaching ability than students’ ability to learn. Thanks for sharing.
I majored in music education (choral and general music) the first time around and was hired as a Junior High music teacher. I had a hole in my schedule 2nd semester and was asked to teach an “academic” class by my principal. I had taken 3 quarters of Calculus in college (just for fun…), so picked up a 7th grade math class. I was told that a class was too large and that I had been given “the best” kids in the class. It was mostly boys and no one told me that it was a “low level” class. Some of the parents told me that they were impressed with what I was doing because their child suddenly was enjoying math for the first time. But, it was challenging for me because I knew how to do all of the topics (like fractions, decimals, etc.) but had absolutely no idea how I had learned to do the math or how to teach it! So, I went back (nights and summers) to pick up a math degree, one class at a time. Eventually, I started teaching math full time (no more music) and really enjoyed it. I always thought that I brought a completely different perspective to teaching math (sort of an outsider’s creative view). Somehow, math just always seemed to relate to everything else in life that I was interested in, so projects and labs and activities became an important part of my classroom. I still have a bumper sticker from the show, “Numbers” that says, “We All Use Math Everyday”. I retired after teaching for 34 years (a year in Staff Development and 3 years as a math coach). I am still involved in tutoring, math ed organizations, and math conferences.
I loved math class as a student and saw it as my strongest subject. I eventually went on to become a special education teacher and it wasn’t until about my 8th year of teaching, when I found myself pushing into a “regular education” math class that I realized I had very little conceptual understanding. This happened when I had the pleasure of observing a fantastic teacher who used base ten blocks and cubes to show WHY we “carry,” in addition. It was a skill that I had “learned,” and mastered at an early age was not something I ever questioned. But it was in that moment of observation, watching kids get the “why,” behind a procedure, that my own light bulb went off. I was blown away that I had never truly understood this skill, which in turn made me ill-equipped to teach it. Since then, I have again tapped into my love of math and try to actively seek out the “why,” before attempting to teach a concept to my students. I love your resources and am grateful for your work. Thanks for sharing your story!
Thanks for sharing your story! My math experience was similar in that I also got good grades and could do the math, but really did not understand why. I ended up majoring in Math because after 2 years at Cal, I couldn’t think of majoring in anything else. I always was taking a Math class. Upper division math was tough, but I did persevere and graduated. After working for various businesses in a tech capacity, I took time off to raise my kids. I slowly started working again by working at my kid’s school in the front office handling financial issues. Eventually I started helping with Math intervention and enrichment which led me to pursue a teaching credential for math. I saw so many ways to help the small groups to not fear Math, and appreciated my Master’s program. However, now as a middle school teacher I still struggle on how to teach without relying on just procedural efforts like I had experienced in middle school. Thanks for your frank and honest story and your reasoning on why you are so passionate about your work and sharing your finding and resources!
Yes, our stories were VERY similar. I believe that our shared struggles will also be the source of our strength, passion, and inspiration. Thanks for reading this.
I am a product of the late 80’s early 90’s timed test movement…I was stifled by having to be fast and it crippled me. Because I wasn’t fast and had zero strategy besides memorization, I was constantly told I wasn’t good at math, “but that’s ok…you’re a girl and that’s just the way it is.” . Fast forward to collage; math methods course proved to be zero help. Fast forward to my entry into elementary teacher. I often had to get help from my teammate to solve some of the fifth grade math. Especially fractions. My kids always did ok, but I shoved procedures down their throat. If they would just memorize it, they’d be ok. In 2018, I went to a training called OGAP and my mind was blown!!! Between this training and the use of Bridges Math, I learned elementary math 14 years into my career. Now I’m a pre-K -5 math coach and math is now my favorite thing in the world. I’m just sad it took me this long to become a solid math teacher. #MyMathStory
I wish this wasn’t such a relatable story, Summer. Better to have this awakening later than never, I guess. Congrats.
Thank you for your honesty! My journey was different. Public school in MA, I was slow at the start (3rd grade and multiplication I recall- I’m still not the best at memorizing), but got in a gifted program by fifth grade. My confidence grew, and I stayed in the honors track. School was my happy place, home not so much. In 7th I had a phenomenal teacher who was all about conceptual learning. I still remember how he explained visualizing area of a circle by turning it into a rectangle. In 9th and again in 11th I had another brilliant math teacher who I am proud to say became my future dept head when I returned to teach at my old HS. He taught me so much about conceptual learning and teaching. (Deriving the quadratic formula- so cool!) In college I was an elementary ed major- I loved the idea of giving young kids a solid math foundation. Well, those jobs are really hard to find so I took a high school math teacher job and haven’t looked back! 13 years in
This is a wonderful story, Vivi. Congratulations.
Thank you for your post. We moved often when I was young so I missed multiplication in school but my Dad worked with me over the summer. I was always the annoying kid who asked why we did each step in math. I also wanted to know why it worked. I would do some research on my own, but didn’t have the access we have today, so often I just learned the algorithms. I could figure out how to do the math just by looking at examples in the textbook but did not always understand why it worked. That was especially true for me in college during 4 semesters of calculus. It wasn’t until I started teaching and having to answer to the same kind of questions I asked that I learned why different things worked. I now use some investigation learning to try to help my students understand why the shortcuts work. I explain to them that everything could be figured out with arithmetic but the higher maths are shortcuts to a much longer way but we have to understand that way before we can understand the shorter way. I often give multiple ways to get to an answer. I tell them to choose the method that makes sense to them.