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Not sure if this is the spot to post this, Tracy. Here is link to my math autobiography.
Tina Palmer
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Oh my goodness, Tina, what a courageous person you are! I was shaking with rage at the “D. As in dumb.” moment. OMG. I think it’s amazing that you worked your way back toward math education, led by your students. So beautiful and so brave. Thank you for sharing your story, from the bottom of my heart.
Tracy
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Horrible, how disrespectful those teachers were! And the unreflective nature of it too, the confidence that if a student gets a D in the test, it’s because they have a problem, rather than that there weren’t the right kind of lessons. There are a lot of people, as Tracy writes, who don’t get over that kind of thing.
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Simon, this is so fascinating to read. Your story is so unusual in that it seems like you’ve always seen the difference between school maths and mathematics. I’m amazed at the ways you fed your own curiosity throughout. I dream of a world where kids find the beauty you found outside of class in their classes. Thank you for sharing your story!
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I used to go to the local library too as a kid. I very rarely chose fiction. And the kind of kids’ maths books you get in the library, you know with pictures of toruses and klein bottles and hypercubes, and the number symbols they used in Egypt, that gives a very different kind of experience of what maths is – something more visual, conceptual, almost philosophical. There’s a need for more of that kind of thing in the classroom too!
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I see that link is just to my blog as a whole. The autobiography post is here:
http://followinglearning.blogspot.com/2017/01/my-maths-autobiography.html
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Here’s my (really, really long) story. More about my insecurities than true math autobiography, but seemed fitting-ish.
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Thanks for sharing, Casey. Your story is so personal and heart-wrenching, but I also know that you are able to support your students better because of your experiences. I love your student’s comment too! Your empathy for them will be a huge bonus in the long run. That said, that doesn’t mean you need to stay stuck in it. I wonder what it would do for you and your self-identity to take calculus somehow? Honestly, it’s pretty fun. 🙂
Thanks,
Tracy
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Casey and Tracy
I never took Calculus. There. I said it. In fact, if I am going to be really honest: I have actually lied and said that I have taken Calculus. I had too. After all, how can I be a K-12 math coach if I never took Calculus? Well, I am finally getting to a place where I can say that I can be a damn good math coach without ever having taken Calculus. How? Well, for one thing, I want to take Calculus. I
want needlovelive to learn. In fact, had I taken Calculus when I was in high school, I am not sure I would have gotten anything out of it because it probably would have been “heavy on algorithms, but devoid of stories”. Last year, I went to the NCSM annual conference with one of my favorite colleagues – she is a HS math teacher in our district – she teaches Calc. She used to be an engineer and switched careers. She is reflective and curious. On the plane ride, we did Calculus on cocktail napkins. I love love love Robyn because she lets me ask questions, make mistakes, and be so vulnerable. We laughed a lot. I was able to make some sense of Calculus – but I still had a lot of questions. Apparently it takes more than 5 hours to learn Calculus. 😉 This past January, I was at a professional development conference – without any of my colleagues – I took a risk and went by myself. Unfortunately, it was painful – wounds re-opened. I wrote about it here. Ironically, the last problem we did before I left the conference was to find the area under the curve without using Calculus. I did it!! I loved it. I owned it. I can do it again. I still have a lot of questions, but I made a lot of connections. I couldn’t wait to get back to Maine to tell Robyn. When I told her, she was so excited for me. I do want to take a Calculus class, but I will most certainly be very picky about who I take it with because I am trying to “break the cycle” and I can’t afford to waste time with people who don’t support me in that quest. Thanks Casey and Tracy for prompting me to continue the writing of my autobiography. -
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I think we’re all on the same road here Sarah. I tweeted about a quarter the cross, and Nat Banting tweeted https://twitter.com/FractionTalks/status/723132387375218688
Now I did “do” calculus (in a not very awe-inspiring way), I know what it does, but apart from that I can remember very little of how to do it. I looked up things on youtube, and examples on desmos, but couldn’t see how you would do it.
I think the thing is wanting to learn, and to learn in a way that’s alive and responsive and reflects the wonder of the subject.
But it must be like that for everyone. Even for professional mathematicians. None of them can know the whole subject. And since maths is still being explored there will be things not discovered yet, which no-one knows.
I remember reading that the prolific mathematician Paul Erdős (mentioned in Ch 2) didn’t get the Monty Hall problem right. In fact lots of mathematicians got it wrong when they first met it. There’s not-knowing and fallibility all the way through.
So to be a mathematician can’t be to have covered particular material, it must be a disposition towards mathematics and towards learning.
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Listening to Francis Su’s talk, I hear this, from Isaac Newton (inventor of calculus): “I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”
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Hi Sarah!
Your comment made me think of my own school experiences and my current learning ones.
I was actually a “good” math student in elementary, I enjoyed algebra in middle school…then with higher grades things gradually stopped making any sense. I remember the landslide of formulas and the feeling that there is no time to stop and think because then I’ll miss new dump of more formulas and theorems and rules that still make no sense.
I never took trigonometry or any other pre-calculus topics. I never felt an urge to. Until my teaching experiences in teaching elementary lured me into some topics where I wanted to learn more. I bought a lot of books. I downloaded a lot of videos. I made my way through pre-calculus with considerable effort but at my own pace, making sense and enjoying myself. I did enroll into online calculus course; it is pretty…uninspiring. But I have my books, I stop to make sense cause I’m not in a hurry. Join in, it would be nice to have a studying buddy!
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The ups and downs of my mathematical journey
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Jamie, your story is amazing and typical at the same time. The ups and downs are so striking! Your at-home play and Mr. Kuhl were so positive, and then 3rd grade and the gender stereotypes you inherited were so negative. I think it’s amazing that you were able to build on the good and learn from the bad as you developed as a teacher. You broke the cycle! I particularly love the story about the cumulative files. I’m right there with you on that. Awesome that you give students fresh starts and an open mind, rather than keeping them trapped in their little boxes.
Thank you for sharing your story!
Tracy
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I wrote mine up as a blogpost. Mostly out of guilt that I’m going to be asking my students to do so. It does help me realize how fortunate I’ve been in so many ways in my math journey. http://mathhombre.blogspot.com/2017/01/mathematical-autobiography.html
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Math got more and more boring as it went on into middle school, because there was so much repetition. I didn’t understand why we did the same ideas every year. The details were barely different, but the same ideas over and over.
John, I remember feeling exactly the same way! I didn’t see a big difference between adding two two-digit numbers and adding two three-digit numbers, but somehow it was a new unit and a big deal. I wonder if we’re making any progress on this front?
Thanks for sharing your memories!
Tracy
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Thanks for posting my math autobiography, Tracy! Decided to post it myself to practice using the forum. 🙂
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Revising my thinking. Might help if I posted the link… 🙂
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I blogged about my grandmother’s math class here: http://8ismyluckynumber.blogspot.com/2017/01/my-grandmothers-birthday.html
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Thanks for this conversation Tracy. Here’s my math autobiography: http://robertkaplinsky.com/my-math-story/. Sadly, it seems fairly inline with some of the other experiences I read.
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Here is the math autobiography I wrote a while ago for Justin Lanier’s sMOOC!
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On page 2 and in tears. I thought the memories, the names, the hurtful comments would never find me again. “Oh come on, you should know this.” “You should be done by now.” “I did not tell you to do it that way.” “Stop drawing on your paper.” “Do it like it says in the book.” “You cannot do math.” “She’s an idiot.” “Are you dumb?” “Where’s your brain?” As a learner, as a teacher, as a participant in a professional environment, I have struggled with the fear of what comment about my math ability is going to be slung at me next. I feel I am a math thinker, but thinking takes too much time. I learned that in elementary school. As a student, I was told, “Don’t think, just do, plug in the numbers.” As a young teacher, I was told to follow the curriculum and the teacher’s guide from pg 1-458. My job was threatened when I dared to listen to my students and change the path of our course. In the middle of my career I participated in a math session at a math educator conference. The presenter gave us problems to solve. I began thinking and drawing. The presenter walked around and collected participants’ work that she was going to share. I froze when she approached me. I was still working on the first problem of ten. “If you don’t know how to do the math, why are you here?” I slunk in my chair and apologized. In my mind, I was thinking. On my paper, I was drawing patterns. I was thinking about numbers and words to describe the patterns. But as before, I succumbed to that constant wound that keeps reopening and reiterating that I am not supposed to think, just do. I walked out of the session. As an older teacher, I have allowed myself to slowly let my thinking be visible. My students accept that I sometimes draw things out, in fact, they are starting to draw in their journals! I love learning. I am glad I found this book to help me along my learning journey. I want to become a better person, a better teacher. I am ready to read the next page.
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Goodness, Patricia. It is brave of you to share that story. My heart hurts for you. I am so glad that you walked out of that session, but I want to have some seriously stern words with that presenter. <angry face>
From my perspective as a university-level mathematician, taking time to explore ideas with different representations, finding ways to explain our thinking, and making new connections, are all vital parts of working mathematically. And *all* mathematicians, at all stages of their learning journeys, have more to discover. That’s the beauty of the infinite landscape of mathematics. I look forward to hearing more about yours.
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Patricia, I cried when I read your message. I am so sorry about what adults did to you when you were a child. And, like Amie, I am absolutely furious at that presenter!!! The thing is, I know that if she had gently encouraged you to talk about your thinking and your patterns, she might have learned some new mathematics herself! The creative process you’re describing is thinking mathematically. You are a mathematical thinker. She missed her opportunity to learn from someone who was thinking instead of just doing, and she doesn’t even know it.
I’m thrilled you’re here, beyond honored that this book is helping you on your journey, and so grateful that you posted. If you ever choose to come to another conference again to have some good experiences to replace that horrible one, please tell me. There’s no one else I’d rather sit next to and listen to, learn from, and support.
Tracy
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Patricia
I am so sorry this happened to you. I hope this person doesn’t approach their students with the same question, but I fear he/she probably does. He/she doesn’t need to say it out loud for the students to hear it.
Your tenacity to overcome such a hurtful statement is quite impressive. You kept learning. Wow. I am in awe. You inspire me to keep learning.
I am part of a collaborative K-12 group of incredible teachers. We were meeting yesterday and reflecting on how important our group is and how we have cultivated trust. One of my peers said, “It takes a lot of time to value the way other people think mathematically. I want to get what other people are thinking, but it takes time. The time we spend practicing and modeling the way we want our kids to engage in math is so important. We need to say, “help me understand” more – to each other and our kids. ” I wish more people felt this way. Clearly, you do and that is why the statements you described were so devastating, and yet, you persevered. Awesome. Thank you, Patricia.
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I don’t have a great place to park this so I hope you don’t mind me embedded some observations about my elementary math experience.
First: Overall I had a happy if odd Mathematics experience. This was the period in time when I decided that I really enjoyed Math. I’m noticing that the positive and negative accounts above seem to be following gender splits. I’d like to think that there are also women who fell into the same camp as me or at least going forward that becomes more the case.
I barely remember much of math in first and second grade. I’m sure we went over basic addition and multiplication tables. I’m a fairly good memorizer so these didn’t present much problem for me. I also don’t have any memory of timed tests or homework just occasional worksheets with sets of numerical problems on them. I’m fairly convinced that we didn’t spend as much time on Math as occurs today where you’ll receive instruction once a day.
In third grade in the last month of school as a preview, my teacher showed us the standard algorithm for division and multiplication over a few weeks. In retrospect, I suspect we probably didn’t reach our target for the year and she was cramming in the missing material. I remember just accepting the algorithms as fact. They seemed to make sense and again I didn’t need much repetition to master them.
Then what was probably a life changing experience occurred. My parents transferred me to a magnet school for Math where they were trying out an experimental curriculum. Instead of group instruction, this program was student directed. There were a series of worksheets color coded by topic (fractions, decimals, percentages etc.) For each unit you’d work through the sheets at your own pace. There were occasional manipulatives to try out or films to watch on an individual screening booth. In essence, this was Khan Academy without the computer. As I remember the teacher visited individual students and helped out or gave a lesson if necessary. For me this was ideal. Despite the worksheets often being repetitive, I went through 3 years of math by the end of fifth grade and had exhausted the program.
I knew at this point that the next milestone was Algebra even if I didn’t know what that entailed. And then life changed again. For sixth grade I transferred to a different elementary magnet school that focused on creative writing. My teacher who was actually fabulous at teaching writing really didn’t like Mathematics. We basically completely skipped doing any math for the entire year. Overall I had a lot of fun but I still remember occasional pangs of regret at the fact that Algebra was not possible.
So I’m not sure what the lesson of all this is but it probably still influences my view of what should happen or not with my own kids.
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Ben, I think you’re absolutely right. No matter whether you had positive or negative experiences, they do influence your teaching. For example, I could see the amount of repetition some students need coming as a surprise to you, because that’s different from how it was for you. What I’m saying is reflecting on your experiences is worthwhile and I’m glad you’re doing it!
Tracy
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Here’s mine:
http://sadarmadillo.blogspot.com/2014/11/school-math-and-me.html
I feel comparatively lucky, and even then I got bumped off the math track a couple of times.
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I published an abbreviated version of my math autobiography on my blog a while back because it partly explains why I became a math teacher. https://ispeakmath.org/2010/07/07/change-someones-math-care/
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9th grade Algebra 1 teacher gave me a great gift by being a sexist pig & being disappointed that I (a girl) was the only person to raise my hand in response to “Who’s thinking about a career in math?” His response: “Oh” with a big sigh. It was 1978, but still.
So, then I had to prove him wrong, and I have! But, have gotten so much push back from the way I teach high school mathematics. I have to know why things work & how they all connect together, so I encourage my students to investigate & explore, so they can find out, too. I get heat from parents, students, colleagues, but never from an administrator, thank God, in the 4 schools where I have worked. Takes about 3 weeks to win over the students & parents with my style. After a couple years at each school, I usually win over most of my colleagues. I just refuse to subject my students to the same boring & grueling process of note-taking & lectures that I was subjected to in hogh school AND at the university level.
The most appalling thing I have experienced in my teaching career was during an interview for Teacher-of-the-Year. When describing an investigation I designed for my AP Calculus students, a person from the community, that was on the panel, essentially said how dare I expect my students to figure out how things work and equated it to me dropping them off in the middle of nowhere without a map. No matter how patiently I tried to explain the richness of this investigation & the value in the journey, with me as a guide, of course, she ranted on & on, until the committee was embarrassed & I was fed up. I packed up my materials & left amidst apologetic looks from the other committee members. Each year, I get nominated by someone at my school, but I have explained to my administrator why I will not willingly go through that nonsense again.
Amazing what negative motivation does for my determination! 😜
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I’ve been trying and failing to write a maths autobiography, but while I was trying to write it I remembered that a few years ago I wrote something about one aspect of my maths journey: the freedom to enjoy maths. It’s called Elsa’s Freedom.
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I’ve written a couple more reflections on my mathematical experiences in the past. One on my experiences with maths and money https://blogs.adelaide.edu.au/maths-learning/2017/03/14/money-and-me/ and one on my earliest memories of maths and play http://blogs.adelaide.edu.au/maths-learning/2017/06/07/childhood-memories/.
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Thanks to everyone who has written up their stories so far. I really appreciated reading all of them, and feel like we all learn a lot from such accounts.
I’ve written up my autobiography here:
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Denis, I love this reflection and am so glad you’re getting so much out of the book and other people’s contributions. How wonderful that you and desmos found each other, and that you’re now able to take the time to discovering meaning and beauty and connections in the mathematics you were rushed through.
I think many of the feelings you describe are more common than we know. That feeling of being a fraud, for example, is something I’m sure many readers can relate to.
Thank you for writing about it all so beautifully! I hope you’ll continue to share your thinking as you read.
Tracy
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Thanks for the kind words, Tracy!
I take it as high praise coming from you, and will try to write more as I continue reading.
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As an elementary student,I enjoyed the idea of math but hated the idea of doing 20-30 math problems if instead knewn how to do the assignment. Combined with my father’ s belief that their was only one way to do any math problem. This led to a distaste for math that led through high school with the exception of geometry with Mrs. Jacobs. She made math interesting again but that feeling quickly faded by the end of high school. Math was a necessary evil in college but I never loved a math class.
Now as a 5th grade teacher, I work hard for my students to see the relevance and joy of math. My goal is for my students to leave my class with the idea that in math there is more than one way to solve a problem and to see the joy that math can bring when you allow them to be creative.
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I finally got around to writing a (long) maths autobiography. It’s here: https://amiealbrecht.com/2017/07/14/my-maths-autobiography/
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And now it’s a clickable link: https://amiealbrecht.com/2017/07/14/my-maths-autobiography/
(I hit Submit too quickly!)
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Finally wrote my math autobiography– it’s been a goal to write this over the summer, especially since I’m about to ask my math methods students to do the same. I learn so much by learning about other people’s math stories, and writing this was definitely helpful.
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Here is the link to my Mathography.
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Here is the link to my Math Autobiography!
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If I were to plot points on a plane to graphically represent my experiences with math throughout my education, the result would surely resemble an electrocardiograph: there were an assortment of highs, lows, negatives, positives, and of course unexpected parts of dull inactivity. The sum of me plus mathematics is lesser than or equal to a significant helping of frustration multiplied by weighty (but few) victories that still give me hope. In the seven hundred and sixty-one words that follow this sentence, I will attempt to capture shaping teachers, moments, bad decisions, and cases of hard work paid off. Simply put, math problems created problems for me by way of unfortunate miscalculations of my own abilities. Still, I am determined to ensure my future students’ early dealings with the world of numbers is welcoming, interesting and of course, applicable to their own realities or futures.
Truth be told, there were years I saw myself as a five-point math superstar. Measurements, word problems, and fractions boggled my brain in elementary school. But I truly found gold and a sparkly status as superstar when it came time to learn multiplication facts and dive into long division. Those two areas absolutely grew my math confidence exponentially. In fact, I remember so little about the teachers who taught me math early on. My childlike self was far more focused on the rewards for A’s and hitting milestones–ice-skating trips and ice-cream parties were great math motivators. I may have thought I found an answer to my number-woes, but as reflect, I find that memorization was my niche rather than the actual work required to fully comprehend concepts. After getting by and even maintaining top scores in my classes up until high school, it was crushing to receive red ball-point pen marked D’s and F’s. Algebra, Geometry, and Trigonometry had me looking like an out of control scatterplot with outliers everywhere. Just as I would get my footing with the quadratic formula, multivariable equations ripped me to shreds. Sadly, I started to internalize being horrible at math as part of my academic identity. No one showed me how to change my study methods and I refused to see the subject from a different, more positive angle. The single ray of hope shone out from my senior AP Statistics instructor, Mr. Ainley. Whether it was his dorky but genuine love for hypothesis testing, or the fact that this kind of math finally clicked, something shifted in my relationship with math.
Early in college, on an entirely fresh, unmarked plane, math became terrifying. In lecture halls of three-hundred students at a rigorous University of California campus, I drowned. By drowning I mean failed the same math course twice and continued a pattern of registering and dropping before the withdrawal deadline. Near the conclusion of my six-year undergraduate career, it was time to face my fear. Luckily, I landed an excellent professor in a community college summer school course featuring none other than my dearly beloved: statistics! Mrs. Cavalla immediately took interest in me and made me want to sit in the front row, ask questions, and go to her office hours. Her class was exciting and applicable. We calculated the likelihood that another student in the class would share our same birthday and we got our hands on some real data. This instructor redeemed my curiosity for math and instilled the belief that conquering math courses (or any other discipline) had very little to do with natural ability. I learned that it had but everything to do with practice, practice, and more practice. I worked harder than I ever had in a course and earned an A. At last, I felt a sense of congruency with math and thankfully graduated on time because I squared up and got to the root of the problem.
Even as I enter residency year with hesitation about teaching math, I recognize that my teaching and attitudes toward math are not valueless but valuable. The last thing I want to do is subtract confidence or dampen curiosity out of my own insecurities. For my first-graders at Sherwood Elementary who are forming ideas about their abilities, I want to make math lessons fascinating and tangible; in other words, more than just a multiple-choice problem to solve. A crucial denominator in my fraction of time with these kids will include mathematic examples that are meaningful to their lives all the while balancing the demand of state-set standards. Lastly, I hope to communicate to my students that math is everywhere. I needed it in my part-time job on the Santa Cruz Beach Boardwalk selling keychains, as an afterschool tutor, and as a social worker helping foster-care children understand budgeting or confusing financial aid breakdowns. Math has never and will never be irrelevant for any of us. Its uses are infinite. Even if my students go on to struggle with, check out, or drop math courses as I did, I believe I have the unique ability to encourage like Mr. Ainley or Mrs. Cavallo. Hopefully my students can sense that math is so much more than one-dimensional experiences and that they can just like I did. -
Mathorgraphy
Mkay Knox
Union University
Unfortunately, until my junior year of college, I never experienced a math class I enjoyed. In early elementary school, I began to struggle with math and this internalized into the belief I simply could not do math. My teachers in elementary school taught specific ways, which lead me to think math only worked out one way. So when I missed a problem, I figured my brain just did not work that way. This trend continued on into high-school where my teachers had clearly lost their passion for teaching. In my Algebra class, my teacher told us she did not know why she taught this class because you never used it in real life. As a result, I sat there wondering why I had to learn something “useless.”
Entering college, of course the idea of not taking math classes made me ecstatic. Finally, I could leave math behind. However, deciding to become a teacher required me to take at least two math classes-Mathematics for Children. This class changed everything. During this class, I experienced a teacher who not only loved the subject she taught but believed every single person could do the math. Her beliefs about us as future educators made this class a joy. I never thought I would not struggle in math until taking this class. I came out of the class with an appreciation for the subject, and even the slightest hope of maybe teaching it one day.
Now, I can say enjoy math. I do not believe I will ever enjoy it as much as I enjoy reading or history, but enjoying the subject at all is a step up from years of hating the subject. My hope of teaching the subject has increased; I long to teach math one day. I want to help those students who struggle with math as I did. I want to make math accessible to all students and help them see how enjoyable the subject can be. I cannot wait to begin this class. Even from the short lesson, we have seen, I know this class will deepen my understanding and love for the subject.
Nevertheless, teaching the subject still scares me. If I tried to explain math to someone who does not know anything about math, I would say math deals with different algorithms in which we use numbers to find the answers. I know this will probably not fully explain what exactly math is to someone, but it is the way I view the subject. I wish I had a better understanding of explaining math to people, but I have not had any opportunities to teach it. All of my undergraduate experience placed me in ELA classrooms. I look forward to being a part of this class and learning how to teach math!
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Math has always been so simple to me. You can only come up with one answer, and there is not much left to misinterpret. I currently consider myself a “math person.” I view all math problems as a challenge I must solve, and if I am not able to solve it immediately, I look it up online until I understand the process. Once I figure it out, I try to solve several problems by myself until I know I have mastered it. To me, math has always made sense. Although I have many experiences that fostered and challenged my love for math, there are still things about math that are scary to me.
I have had many experiences that fostered and challenged my love for math. Growing up, math was the only subject that I felt had only one answer. If I missed a question in math, there was a reason I missed that question. Although there are different ways to solve a math problem, there is always only one answer that makes sense. In reading and writing, there could be so many different answers that could make sense, which often left me confused. It was never like that with math. I do not have specific instances that made me love math. It just always felt like something my family and I were good at; however, in college, math started challenging me. I was taking elementary math classes, and they were trying to teach us the “common core” way of solving math problems. Simple addition problems became longer. For example, instead of just saying 8+7=15, we were taught to break the 7 into 2 and 5, and add the 2 to the 8 to make 10, then add the 10 to the 5 to make 15. This seemed so much harder because in my brain, I know 8+8=16, so I just subtract 1 since 7 is 1 less than 8, and I get my answer, which is 15. However, when I started tutoring an elementary school child in math, I realized that this method could be helpful for some students.
As I have said, I love math. I did my student teaching from 2016-2017 in a 4th grade math classroom, and I enjoyed it; however, the only fear I have about mathematics is failing my students and making them scared of math. I want my students to have the love and excitement I have for math. I do not want to make them hate math or feel like they are just not good at it. I want my kids to know math is everything that the do, from reading a clock, to go shopping, to going out of town, and even cooking.
In conclusion, my greatest hope is to be an elementary math teacher. I feel responsible for cultivating my students love and admiration for math, so they will never say they are not “math people.” I believe by introducing them to the fact they already do math every day, and the importance of math as they get older, they will understand how essential it iqs to feel confident about their math. By doing this, I may even be helping create a more financially literate generation.
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For me, math is like a distant relative, perhaps an uncle, that is in and out of jail. You have love for this relative because you both are kin and therefore supposed to love him. However, you haven’t seen this uncle since you were young, and you always hear about how terrible he is and how there is no point going upstate for visitation hours because you won’t be able to get through to him.
My whole life until very recently, I have had a math block. I have never had a fixed mindset about math. I’ve never felt like I cannot perform mathematics well, but I have felt that there is just a missing piece that is holding me back from fully accessing my “math brain.” And after careful evaluation of this missing piece, I believe it was just the lack of proper teaching. That is not to say that I never had a good math teacher, because indeed I had a few that I remember that really helped me understand some concepts that I still remember to this day. But I believe that I did not have enough good teachers because there are many concepts, which I am sure become simple with decent instruction and practice, that are like a foreign languages to me. However, in the very recent past, I have gained an insight into the world of mathematics that gives me hope for this class. So with this paper I will track my journey through some key math moments. I will reminiscently venture from 4th grade Douglas, who was seemingly hated by his math teacher, all the way to the confident, potential math teacher that stands before you as an MTR resident.
The grade was fourth, and though I do not remember her name, I remember the way this teacher made me feel about math. It seems like everyday I was chastised for my attempts at my math homework. I was made to read the problems out loud as an example of what not to do. This started me on a path of avoiding math, and that was not conducive to achieving in more advanced classes. The trend of negativity towards math continued throughout elementary school and middle school. Thus, I was tracked into remedial math for my freshman year of highschool. It went surprisingly well because I didn’t have to learn what we were being taught. So though I did not like math, I was able to succeed because the content was so basic.
And then I moved on to more difficult classes throughout the remaining years of high school. Needless to say, I was unprepared for the necessary arithmetic that I needed to learn. Sophomore year, I enjoyed geometry, and my teacher was a great guy; however, he did not care to structure the class and teach the content in a graspable manner. So I did not learn much there. The next year, my algebra 2 class was more of the same. The teacher was nice, but she was tough, but that helped me learn. Mrs. Spain set me on a path of how to properly learn math. So thanks, Mrs. Spain
It was perhaps this structural past that allowed me to succeed in college. I had to start with basic math, which I did well in. Then the next year I had to take statistics and probability. I’ve never had to work so hard to succeed in any class. Many sleepless nights were the only reason I learned in that class. The stats professor was not a good teacher. He was the typical college professor that is so focused on their own research they forget to teach. I essentially had to teach myself. However, after that class, it seemed I would be math free for the rest of my days.
Want to hear God laugh, tell him your plans. Enter the elementary Praxis exam needed for admission into MTR. As soon as I saw the math portion, I instantly felt like the fourth grader again. I just wanted to avoid it at all costs. But I knew that wasn’t possible. So I turned to something that has revolutionized the way I view math: Khan Academy. The concepts that I couldn’t understand as a youngster became so clear when I just sat down to watch those videos. Thanks to Mr. Khan, I passed the Praxis and have a new confidence for learning math.
So after reliving my mathematical journey from youth to elder, I realize that math can be fun. I truly enjoy sitting down to figure out problems that in the past eluded my understanding. I believe that I can succeed in this upcoming class, and with the knowledge gained, I will then bring my joy for math and instill it in my students.
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Mathematics was always my least favorite subject in school growing up, especially in high school. I cannot think of a single math teacher that I had by name, nor can I think of a single math class that left me feeling confident in my math skills. I felt as if staring at numbers for too long gave me a headache and only made them more confusing. I really started to feel this way when I was in the sixth grade. Before this point I liked math about as much as I liked any subject. This shift happened for me because my school decided to introduce Accelerated Math during my sixth grade year. We had to do math problems, mark our answers on a scantron, and scan in the answers everyday. When I got to seventh grade, Accelerated Math was no longer being used at my school. I do not feel like I learned any of the math that I was supposed to during my sixth grade year, and I was never really able to catch up after that. By the time I finally got the hang of a new math concept it was the end of the unit and we were taking the end of the unit test to make sure we learned the information. My grades on these test were never the best, but they weren’t bad either. My grades definitely did not reflecting mastery of the skill. Nonetheless, we just moved on to the next unit. By the time I got to high school, math just felt overwhelming to me and each math class was a real struggle. This is probably why during my time at the University of Memphis I only took the general education math course that was required and did not take another one.
Flashforward to today, math is actually no longer a grueling task for me anymore. It was not an easy journey to get to this point. I owe my new found math confidence to a book that I found on Amazon entitled, “All the Math You’ll Ever Need.” This book is a self-guided way to teach yourself about math. It walks you through how to do various types of math, from multiplication to complex Algebra, all while encouraging you to not use a calculator. I actually decided to complete this book in order to help me prepare for my Praxis exam, and I am very glad I did. In the beginning I would do my best to not use a calculator while completing a lesson in the book, but at times my self-discipline wavered and I’d end up pulling out my cell phone to help me along with a problem that was very difficult. Overtime, the frequency of me having to use my calculator became lower and lower, until eventually I was able to complete math problems in my head; I do admit that to this day that I will still check my work with a calculator just to be sure I am correct. Thanks to this book and myself, my math skills and my math confidence have both improved.
Going into the classroom, I know that the way I teach math will be greatly influenced by the book that I used. It was a very easy book to follow and helped me to understand math in a way that I had not experienced through my schooling. I hope to teach my students in a way similar to this book, so that way they leave my class feeling like not only can they do math, but they can also do it confidently without a calculator if need be. I hope I can help my students leaving my class feeling as if they are capable of doing math and not feeling intimidated by numbers.
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Hi guys, here’s my mathography.
https://docs.google.com/document/d/1exJlwngTV9UF7lHYMzcUDFtFIsYdNZ5Lopf0h3ewxYg/edit?usp=sharing
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For as long as I can remember, I have been “good at math” but I do not remember explicitly being told this in elementary school. As a child, I enjoyed challenges and puzzles and I saw mathematics as just that, another puzzle for me to solve. Because of this I was fully invested. When I got to middle school, I started to notice differences in attitudes towards math from my classmates. I thought math was easy and it just made sense. Thinking back, I do not feel like I put much effort into solving problems, I just kind of did it, and most of the time came out with the right answer. In middle school mathematics was very formula based and I was good at figuring out what formula I was supposed to use and what numbers went were in a formula. My career aspiration at the time was to become an actuary because I genuinely loved math. My 7th grade math teacher really helped to grow my love for math through her excitement for the subject.
It wasn’t until high school, when my brother was in elementary school doing mathematics the common core way, that I realized that my foundation for understanding the why behind math wasn’t very solid; I knew how to use formulas and algorithms to get a correct answer but I didn’t know why they worked. I still managed to continue onto more advance math in high school unfazed by the difficulty that everyone else said they were having with math. I ended up taking every math class my high school had to offer (discrete math honors, AP statistics, and AP calculus – just to name a few). My reasoning shifted from “I’m taking this class because I genuinely enjoy math” to “I’m taking this class because it’ll be an “easy A” for me” somewhere in the middle of my junior year but it didn’t keep me from taking the class. Sometime during my senior year I realized I didn’t actually enjoy math anymore, I was just doing it out of habit/comfort. I grew annoyed by people commenting on my “natural” math abilities, and wanted to be known for being good at something else, because at this point math was my only real strength.
On the other hand, when I attempted to help my brother with his elementary homework I came to the conclusion that I just wasn’t going to understand the common core way to do math because it had too many steps and therefore was too complicated; I gave up trying to learn the way he was learning. As a result of being in this mindset, it wasn’t until my junior year of college that I decided to take another look at elementary math. I finally decided to give it another chance because I realized I wanted to be a teacher and knew I had to understand the process and not give up when it got hard in order to be an effective math teacher. I did it with the mindset of “Surely, if elementary school children can understand this I can too”. I believe that it was the change of attitude that gave me patience to look fully through the process and have a greater understanding of foundational math and the how. I am now a full embracer of the discovery process of math and not just finding a solution, but knowing the reasoning behind the process.
When I got to college I remember being told that the only way I’d be required to take math classes in undergraduate was if I became a math or computer science major and I felt a sense of relief; I believe this is because I had some sort of resentment towards math. All of that was to say I went four years without learning any more advance math and it was the break that I needed. When I got into a classroom to provide targeted intervention for a math group (through City Year) I felt my love for math come back. I was excited about all the “new ways” students are learning to do math and I expressed my love for math to my students. Over the past two years I have come to know mathematics as a crucial part of our being. Math is a process to figuring out the world around us; math is in everything.
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I have had a very fickle relationship with Math throughout my life. Most events as a child resulted in me feeling unmotivated and defeated, however, as I learned how to teach math while in undergrad, I began to love learning the study of Mathematics. Currently, I enjoy teaching and learning math, especially since common core standards have been implemented.
As a child, I did not have very many happy experiences with math. I think my earliest memory with math was from second grade. I remember my teacher, Mrs. Brooks, writing a special note to my parents once I “mastered” my threes multiplication facts. I finally passed our weekly multiplication test that I studied really hard for; it felt good to be recognized for that.
I remember feeling confident in math that I could follow. I have always been a huge note taker, even as a child. I clung to procedural math because this required minimal creative thinking. I knew how to follow directions, so I knew this was the type of math I would succeed in. I vividly remember my fourth-grade teacher, Mrs. Perkins, teaching long division using PEMDAS (Please Excuse My Dear Aunt Sally) and feeling so capable. I knew I could simply follow directions to earn my A+. At the end of assessments, my teachers would always pose a bonus question that asked me to solve a problem using a different method or determine what was missing from the equation, and I rarely accepted the challenge. I did not feel intelligent enough to answer these question, I always assumed they were for the smart kids not the hard working kids like me.
Throughout junior and high school, math was usually horrible. Mrs. Butler, my tenth-grade Geometry teacher, made math accessible to me. She never appeared to be flustered when I did not understand something and always connected math to a real life experience. She held high expectations for me and made herself available for before and after school tutoring for those of us who needed help. I knew she loved math and wanted me to succeed. I earned a high B in her class. Eleventh and twelfth-grade math were very low points. I no longer made the real world connections and math became very boring. I wanted to think of math in steps and my teachers did not provide those for me. My note taking became ineffective and I was not able to apply what I already knew about math into my current math class. I felt disconnected and inadequate. This resulted in low grades in my math courses, which pulled down my GPA. I graduated high school with a 3.6 GPA and my lowest grades were from math courses.
In undergrad, I took a course on teaching elementary math during my sophomore year. In that course, we read a book by an Asian professor who shared what teaching mathematics in Asian countries was like. This book was so intriguing. My biggest takeaway was hearing how Asian teachers utilize textbooks. I learned their books are much thinner than American textbooks and are full of practice problems for students. Teachers used them as a resource, not a curriculum guides. This was a very different approach to math from how I had seen them used as a child. I decided then adopt the same idea about math textbook usage in my future classroom.
During my first few years as a classroom teacher, I taught my students the way I learned math. It was very procedural and focused on the fastest way to get to the answer. In hindsight, I realize this is not the best way to teach math and foster a growth mindset within students. I did, however, make it a point to consistently encourage my students to try their hardest. My classes were filled with students who had varied mindsets about math, I wanted all of my students to feel capable. It was not until my fifth year teaching that I chose to incorporate a learner centered approach in how I taught math. I gave my students opportunity to manipulate numbers and create problems on their own. I felt it more important to focus on their processing, as well as how they deliver the correct answer. I finally felt comfortable and capable enough to teach math.
Today I would define mathematics as the way in which numbers explain how the world works, it is everywhere! I am excited to learn more about alternative ways to think about math and ways to help the teachers I coach to provide the best math instruction to their students. I can not identify any worries, and I am very hopeful and eager for the challenge of thinking about math in new ways.
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Though many students first identified teacher is someone associated with the staff at the local school. My first teacher was my own mother, though she did not have a teaching degree, she was always resourceful. Her creativity and drive to not only prevent learning loss, but to set us up to be prepared for all the new math that we were going to learn, was uncanny. Reminiscing, I can almost be confident in saying that my mom gave me my zeal for learning and understanding- both in academics and spiritual life. From as young as 3, I can still remember how she somehow convinced my friends to join us early in the morning, which me and my brother did not understand because we could not go outside until we finished our lesson for the day, while they had the option, especially since it was the summer time! She would always come up with patterns and problems that made me think about whether something was true or not. She constantly pushed us to try to understand the concept of math, which is what initially sparked my love for math, early on. This early direction in the way of liking math caused for me to think in the means of an equation for almost everything in my life. Though my mother served as my first math teacher, she did not serve as the only teacher that nurtured that mathematical craving that I had throughout my early education years.
My love for math slowly became difficult to maintain after my parents got a divorce, as my mother was one of the main reasons me and my siblings did not lose information we had previously learned over the course of the summer. From the 6th grade on, I struggled with being interested in math, or any subject for that matter, as I was living with my father, who advocated for education, but did not have the time to invest in our homework as my mother did. However, I did have a teacher in the 8th grade that recaptured my flame with math. Her name was Mrs. Chaucer. Mrs. Chaucer, I felt, took liking to me because I was well mannered and behaved in class. She put an extra effort on making sure that I not only understood the lesson, but that I excelled, as she thought I could, in her class. She revived hope for me, and I began, once again, to look at the world through a mathematical lens. From sports to social life, everything was an equation that I sought out many variables to solve. As I progressed into high school, my love once again died, as I do not remember any of my high school math teachers. I do remember feeling as if I hated the math classes I did have, and disliking every moment I spent in those classes.
What excites me about math is the many ways that we can end up with the same answer. I look at all of life that way. So many different life paths, and yet 60 of us end up here, in Memphis, at MTR- that’s a math equation, probability! Math, to me, is a special science that affects everything that we do, like face to face interactions at the grocery store (prices) to typing wpm (words per minute) to food consumption (calories) and even scoring in sports. Math affects everything, and those who tend to find interest in it tend to be those who can think vastly about the many ways life ends up being what it is. There are so many things that can be explored through the eyes of math. What keeps me engaged in math is the grind that math is, having to find the right items to solve the problem. What usually tends to kill my excitement is being in the middle of a problem, stuck or unsure, on if I am even using the right information or strategy to solve it.
I would define math as a science that allows for us to explore the ins and outs of everything that we can see and why it may have ended up that way. Though many people simplify their definitions of math to just equations, math is much more than that. Math is science, the scientific method, and every conclusion that we come to in life. We often do not take the time to think much about it, but we process everything we engage mathematically, and that is why it is my favorite subject! -
Though many students first identified teacher is someone associated with the staff at the local school, my first teacher was my own mother, and though she did not have a teaching degree, she was always resourceful. Her creativity and drive to not only prevent learning loss, but to set us up to be prepared for all the new math that we were going to learn, was uncanny. Reminiscing, I can almost be confident in saying that my mom gave me my zeal for learning and understanding- both in academics and spiritual life. From as young as 3, I can still remember how she somehow convinced my friends to join us early in the morning, which me and my brother did not understand because we could not go outside until we finished our lesson for the day, while they had the option, especially since it was the summer time! She would always come up with patterns and problems that made me think about whether something was true or not. She constantly pushed us to try to understand the concept of math, which is what initially sparked my love for math, early on. This early direction in the way of liking math caused for me to think in the means of an equation for almost everything in my life. Though my mother served as my first math teacher, she did not serve as the only teacher that nurtured that mathematical craving that I had throughout my early education years.
My love for math slowly became difficult to maintain after my parents got a divorce, as my mother was one of the main reasons me and my siblings did not lose information we had previously learned over the course of the summer. From the 6th grade on, I struggled with being interested in math, or any subject for that matter, as I was living with my father, who advocated for education, but did not have the time to invest in our homework as my mother did. However, I did have a teacher in the 8th grade that recaptured my flame with math. Her name was Mrs. Chaucer. Mrs. Chaucer, I felt, took liking to me because I was well mannered and behaved in class. She put an extra effort on making sure that I not only understood the lesson, but that I excelled, as she thought I could, in her class. She revived hope for me, and I began, once again, to look at the world through a mathematical lens. From sports to social life, everything was an equation that I sought out many variables to solve. As I progressed into high school, my love once again died, as I do not remember any of my high school math teachers. I do remember feeling as if I hated the math classes I did have, and disliking every moment I spent in those classes.
What excites me about math is the many ways that we can end up with the same answer. I look at all of life that way. So many different life paths, and yet 60 of us end up here, in Memphis, at MTR- that’s a math equation, probability! Math, to me, is a special science that affects everything that we do, like face to face interactions at the grocery store (prices) to typing wpm (words per minute) to food consumption (calories) and even scoring in sports. Math affects everything, and those who tend to find interest in it tend to be those who can think vastly about the many ways life ends up being what it is. There are so many things that can be explored through the eyes of math. What keeps me engaged in math is the grind that math is, having to find the right items to solve the problem. What usually tends to kill my excitement is being in the middle of a problem, stuck or unsure, on if I am even using the right information or strategy to solve it.
I would define math as a science that allows for us to explore the ins and outs of everything that we can see and why it may have ended up that way. Though many people simplify their definitions of math to just equations, math is much more than that. Math is science, the scientific method, and every conclusion that we come to in life. We often do not take the time to think much about it, but we process everything we engage mathematically, and that is why it is my favorite subject! -
My math story started at the age of 5 at the kitchen table of my childhood home. My mom homeschooled my 4 siblings and myself, and I was the last one down the line. I can remember sitting at the table on multiple occasions with the colorful counter bears and coins that I had seen my brother, just two years older than me, use while he was beginning his math story. I always enjoyed math when I was a child. I loved getting the one-on-one time with my mom as she sat next to me at the kitchen table and we worked through math problems and concepts with me. As I got older, she would review the lesson with me and then send me off to do certain page in the textbook while she went over another siblings lesson with them. As a child I felt fairly confident and competent when it came to math.
The beginning of eighth grade I started my first year in public school. I had a math teacher named Mrs. Carter. She was young and the cheerleading coach for the eighth grade girls. I was very shy but I did well in her class. There wasn’t anything particularly special about the way she taught, but she was kind and I did well in her class. In 9th grade, I took Algebra 1. I didn’t do bad in the class but this was the point where I really began to not like math. My teacher taught purely lecture style for the whole hour and half everyday. My sophomore year I had Mr. Berry for geometry and I remember liking geometry way more than Algebra, but to be honest it may have just been the teacher. Mr. Berry was kind, funny, and an interesting teacher. He let us work in small group, partners, and he did whole group lecture during class. My junior year I took Algebra 2 with the girls basketball coach as my teacher. I did okay in his class but it was also a lecture style class much like my first Algebra class in high school. I was not very invested as a learner in either of my Algebra classes. My senior year I took statistic with Mr. Berry again and about 2 weeks in I was completely lost. I made my second C in my high school career in that class. Once I got lost I kind of gave up and I don’t remember Mr. Berry really trying to do anything to catch me up. I was pretty convinced at this point that I was not a math person and was absolutely not going to major in anything in college that required higher level math or science courses.
When I had to take statistics in college I was sure I was not going to do well. It was the class at ETSU that all majors had to take and it was also the class with the highest failure rate. When my professor walked in on the first day he didn’t bring up how easy it is to fail the class instead he said if everyone is willing to put in the effort in this class, everyone will pass my class. I went to every class and I made an A in the course. My identity as a math student shifted in that class. I saw the fruit of my effort and that when I applied myself I understood statistics.
My personal experience with math and what I observed many of my classmates experience is that once you fall behind you don’t catch back up. I saw this in highschool and I saw it in the first grade class I observed in last year. In many cases math feels like the rich get richer and the poor get poorer in math class. I don’t know what it looks like to differentiate in a math class but I have loved reading about how math can be learning through problem solving instead of for it. I feel that this approach can stop the epidemic in math courses of students who fall behind being left behind.
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As I prepare to enter the classroom as a new urban educator, it is only natural for me to carry my educational experiences with me. There was always something I could take away from every teacher that ever taught me—whether good or bad. Unfortunately, growing up I feel that I mostly did not have quality teachers even though I attended a small private Christian school. My school was a school for Missionary Kids in Madrid, Spain, where I grew up. More often than not, the school was understaffed. So many times, the only option was to place a warm body at the front of the classroom. Math seemed to be the hardest class to staff. It usually ended up being, “I took a math class in college, I guess I can teach Calculus!” Needless to say, I grew up mostly hating math—it was truly the one subject that I could not stand.
I walked into my first Algebra I class, my first day as a 9th grader and my teacher, Mrs. Anderson (who actually was not a teacher, but one of the parents who agreed to fill a staffing gap that year), asked us how we would rank our love of math on a scale of 1-10. I rolled my eyes and held up a “0.” However, throughout the course of that year, I developed a true sense of wonder in regard to mathematics. Mrs. Anderson exemplified her belief in growth-mindset. When I took the PSAT that spring, I scored in the 97% percentile in Algebra I—the year before, I was held back with half my class in Math 8 while the other half advanced into Algebra I. My teacher believed in me and had high expectations for me. She unlocked the initial mystery and prompted my curiosity about math and that made a big difference in the direction of my life.
Since the 9th grade, I have come a long way in my relationship with mathematics. I have developed a true appreciation for math because it is such a unique subject that demands exploration. It is a structured series of puzzles and patterns—a subject of infinite depth for every curiosity imaginable. By the age of 15, I was hooked. Eight years after Algebra I, I walked across the stage at the University of Kentucky to collect my B.S. in Mathematics. She believed in me and that made a difference; now here I am, hoping to be every bit of the teacher that she was to me.
Although I received my degree in math, it was not a cakewalk for me. I really struggled in upper-level mathematics. Partly, I believe, because I never fully received a strong foundation in math growing up. I always felt like I was playing catch-up in my classes. I had one professor, Dr. Coulliette, who specifically took the time to work with me outside of class. If it was not for him, I would not have made it. Most of the other professors that I had did not care if you got it or not. Procedures that came very naturally to my classmates were a struggle for me to fully comprehend. As a result, I was typically on the low end of the bell curve of grades in math in college.
I do, however, have a fierce respect for mathematics and I would love to teach it one day. However, the passion that I once felt for math has been somewhat shipwrecked along the way. Even still, I will always appreciate her simple beauty. Mathematics is a true study of balance in an abstract space. It is almost more philosophical than scientific. It is all about thinking and analyzing—questioning and defending. Truth becomes whatever we can deduce and define for ourselves logically. It is the study of numbers and space, and the space between numbers. “Math skills” are foundational in every facet of life, because it is all about problem-solving, cause and effect, and reason. These are highly coveted skills that translate between any career. Mathematics is a language—similar to poetry—that beckons investigation because there is always more depth that can be uncovered. It is an experience, an invitation, and a journey. Sometimes math does not even need to be taught—it only needs to be imagined.
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If I were to attempt to define my relationship with math simply, I would describe it as a voyage across a vast ocean. More specifically, like the voyage of Christopher Columbus in 1492. I knew I was trying to go somewhere, but not exactly sure where. There have been times of tumultuous weather, where I thought that that continuing was impossible. I often felt that there was no clear direction of the voyage and that I should just turn back. At other times, the proverbial winds were filling the sails, the weather was perfect, and reaching land seemed obtainable.
Most of the difficulty that I have had with math has been related to its seemingly abstract nature. Although math is incredibly relevant to everyday life, it was seldom presented to me as such. Being born in 1985, I spent the majority of my student career in the 1990’s. It may have been the specific set of teachers that I had; although, it seemed to me that math was taught only one way during this time period. As a young student I had some difficulty with attention and I processed things very slowly compared to my peers.
These issues, along with the narrow way in which math was presented to me, caused me to feel defeated in the subject early on. I struggled in math and failed to see its purpose. Math became something that I was told to do, but that was it. I put in just enough effort so that I could get through school, though I seldom found enjoyment out of it or made any sense of it. This is not something that I am proud of, but it is the truth. I hope that I can use the lessons I learn in this math class for good to keep young students from falling into the same hole that I was trapped in.
Luckily, not all of my experience with math have been unproductive. Because I had fallen so far behind in high school, I had to take some remedial math courses in college. This seemed like a terrible predicament in the moment; nevertheless, it turned out to be a powerful turning point in my understanding of math. Thankfully, I had a professor who noticed my struggles and made it her mission to help realize that math skills were not out of my reach. Not only did she take extra time to help me after class, she showed me how it was relevant in my life.
Learning the big picture of math’s relevance helped me understand why I needed to learn the little details. I began seeing that nearly everything I did had some element of math involved it. For me, this was like suddenly leaning the compass azimuth of my destination while on a voyage in uncharted waters. What really grabbed my attention was when I learned that math was related to a personal hobby of mine. I discovered music theory is based on mathematics. I found out that Pythagoras created the circle of fifths as a method to understand the relationship of tonal frequencies in music. Once I realized the importance of math, I was motivated to improve my math skills. My perception of math changed from something that was useless outside of school, to something that mattered in my everyday life.
I have to admit that I still struggle with math even though I have come to understand its value and have even begun to enjoy it. I look forward to learning more about how to make math fun, relatable, and digestible for my elementary students. I hope that my experience with math can fuel my ability to make a positive impact on my students’ perceptions so that they do not feel like a sailor lost at sea in an ocean of numbers.
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My journey with math over the years has been very interesting; I began in a place where I felt excited about math, then moved to a place of frustration and insecurity and finally back to excitement. Both the subject of math and the teachers I have had along the way have shaped how I view and experience mathematics.
My early experiences with math were very positive. My very favorite math experience in early education was when my 5th-grade class got to participate in a field trip to Exchange City, which was a fake indoor city for kids. I applied for, interviewed, and ended up landing the job of Bank President. This meant that I got to spend the day in charge of the Exchange City Bank. I dealt with and wrote checks, I counted money and distributed salaries, and most importantly, I was empowered. I had chaperones at my side supporting me when necessary, but for the most part, I did that job all on my own. It was an incredibly empowering and successful experience as a young girl.
Moving on from elementary school is when math became more of a challenge. Although I had very supportive and encouraging teachers who held me to high expectations, I at times felt inadequate in my Pre-AP math classes in middle school. I very much struggle with finding my identity in my grades, so when I did not pull out all A’s in my math classes, I was frustrated. I thought that my teachers thought less of me and viewed me as inadequate and even dumb for receiving B’s on quizzes and tests. This mindset of mine has changed incredibly over this summer as we have learned about high expectations.
This frustration continued to ring true in high school, but the teachers here are the ones that stick out the most when I think of math. I had teachers who were strict and showed no warmth, but I also had teachers who held me to high standards and were also warm and silly. They knew how to have fun in class and to also hold us to high standards. These were my favorite math teachers. One specific one was my sophomore Algebra II teacher. He loved Transformers and taught us in an understandable and patient way. My senior year AP Calculus teacher was colder. She had the strict part down but struggled to be warm with us. Because of this, it was obvious that there were certain students she favored and others she did not. All in all, there were plenty of nights where tears of frustration, inadequacy, and a fixed mindset towards myself reigned, but I think I came out on the other side as a better learner because of all those experiences.
I took a math methods course in college and although the teacher was not my favorite, it was such a growing and valuable class. I grew out of a frustration and dislike for math and towards one of appreciation and excitement. I began to learn what it looks like to teach elementary math, value all the different strategies my students will have in solving problems, how to break down math problems in different ways, and different strategies to teach math. That class also helped me brush up on basing computing skills since I had not taken a math since my senior year of high school.
I am excited to teach math to experience “ah-ha” moments with students. I love getting to see students confident in their ability when they have mastered a once tricky problem. This is a feeling that I also love to experience. I am not necessarily scared about teaching math, but eager to learn all that I can because there is so much to know!
Finally, I believe mathematics to be an exploration of numbers, statistics, shapes, lines, angles and so much more. Math is a way in which people can view the world. Math is everywhere, all around us, and is something we experience daily.
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Mathematics is the exploration of order and organization in God’s world. Studying math involves studying equations, distance, measurement, and the relationship between quantities. Numbers are key to the process of math, with letters also regularly inserted as variables. Some aspects of math in the world are evident on an everyday basis (such as time, temperature, and adding costs), while others are more conspicuous to the general population, utilized primarily by engineers or professional mathematicians. Math is valuable and important for success in our society and a broader understanding of God’s well-ordered creation.
Though I have always loved school, my relationship with math has been the rockiest over time. My early memories of math are vague, primarily consisting of worksheets, colorful plastic bears, and base ten blocks. I do not remember loving math in elementary school, but I certainly did not despise it. It was in middle school that my attitude towards math turned from neutral to negative. Suddenly, math was much harder and the expectations seemed higher. Pre-algebra in particular was the source of many tears in late middle school. With his math experience from being an accounting major, my dad would regularly sit with me at the kitchen table and explain concepts that I found confusing or had done incorrectly on tests. Unfortunately, my unrealistic perfectionist expectations at the time (such as starting a problem over when I made a minor mistake instead of just scratching it out) only compounded my frustration, resulting in many tearful nights, even as my dad sought to support me. Even during this time, I was blessed with a small class and an encouraging teacher, Mrs. Staley. She would spend time explaining concepts in various ways and letting students work together to enhance our learning opportunities.
Yet there was redemption in my math experience, transitioning my attitude towards math back to a more favorable position rather than the dread I experienced in middle school. This was primarily thanks to Mrs. Emery, my math teacher for Algebra 2, Geometry, and Precalculus. As a former math professor, she was passionate about math and shared that with her students. Her passion, combined with extremely evident love for her students, beneficially impacted my view of math and its importance in the world. Also, she allotted the bulk of each class period for us to work through problems with her, with other students, or on our own, rather than just having us listen to her lecture. Practicing concepts in class provided helpful opportunities to ask questions initially rather than experience challenges later in the homework.
At this point, I appreciate math for its importance in the world and reflection of God’s order and organization. Consequently, I am eager to share that appreciation with my students. Especially since math is a common subject of fear in school, I desire to change students’ perception of this valuable content area and part of life. However, one of my fears in teaching math is that I am more of a linguistic thinker rather than analytic thinker, i.e. not as “math-minded.” I doubt this will regularly present itself as a challenge, but am uncertain about my ability to explain math concepts in multiple different ways to students who are struggling to grasp the lesson.
In college, I had a wonderful Math for Educators professor, Dr. Donaldson, who helped us discover the “why” and “how” behind elementary math principles that we have known for many years but had not considered deeply past fifth grade. She was a tremendous guide in contemplating ways to explain math concepts to students using a wide variety of strategies and methods. I look forward to even more guidance this semester, particularly with an emphasis on how to benefit students who may be experiencing significant deficits in their math knowledge. -
Reflecting on my previous experience with Mathematics, my 5th grade teacher, Mrs. S, comes to mind. I remember Mrs. S and my 5th grade Math experience well because it involved many challenges. This was the start of learning algebra, geometry, and more complex Math concepts. Mrs. S was strict and very hard on her students, which often discouraged me and made me doubt my abilities. I quickly lost confidence and my view of Math started to become increasingly negative. The combination of my teacher, the content, and my own attitude, shaped my perceptions of Math throughout middle school and into high school. I went through periods of time when I enjoyed Math, but also others where I did not. My affection for Math started to grow in high school when I took Algebra II, Trigonometry, and Pre-Calc. My high school Math teachers impacted my growth for coming to enjoy Math more than I ever had in the past. Through learning and application I came to understand the importance of numbers and operations and how Math is used in everyday life. Math is a skill that can be taken with you wherever you go.
As an educator, I also recognize the importance of teaching children Math and giving them opportunities to love Math and grow in their understanding of it. In college I took two different Math courses for elementary school teachers. I thoroughly enjoyed these classes because they opened my eyes to the different methods that can be used to help students learn Math concepts. I absolutely loved my teacher for this course. She was really encouraging and helped us walk through the steps of the concepts that elementary teachers will cover. I am excited to take a course similar to my experience in undergrad to learn and practice teaching techniques and skills that will help benefit my students. I am excited to take things from this course into my own classroom and instill a love for Math within my second graders.
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When I think of math, I immediately think of equations and word problems. My next thought is that math is everywhere! I use math daily. I can remember learning about mental math with I was young and wondering when I was ever going to use mental math in real life. Now I understand! I use math to leave tips at restaurants, calculate time, and estimate how much I can spend at the grocery store. For someone who does not know anything about math, I would describe it as a complex system of numbers and figures that works itself together to help us make sense of the world. It is a logical system that helps us keep track of pretty much everything. Math is not just about numbers and shapes, but rather what numbers and shapes reveal to us. Math is logical and practical.
Growing up I liked math because there was always one correct answer. My brain did not do well with abstract thinking, so math was good and concrete. My first memories of math involve learning to tell time and count money. I can remember being so confused as to why the dime was worth more than the nickel even though the nickel was a bigger coin. We sang a song in my second grade class to remember whose face was on each coin. My mom used to make me count out the money at the grocery store to practice. I also remember not being allowed to have a digital watch. My mom and her friends bought us all analog watches, so we would learn how to read a clock. I remember having a hard time with fractions and being intimidated by long division, but I usually picked up on new math concepts quickly.
When I went to middle school, I had two subpar math teachers. I was put on the advanced math track, but my teachers for Algebra 1 and Geometry made me hate math. In high school pre-calculus, calculus and statistics made my life miserable. I had the same worn out teacher for pre-calculus and calculus. She was brilliant, but she was not good at explaining the process of solving problems. Word problems were always difficult for me and became increasingly more difficult in upper level math classes. I was in math tutoring sometimes three days a week my senior year just so I could pass AP Calculus. Thinking about trigonometry and proofs gives me anxiety to this day. I still enjoy problem solving, but I have nightmares to this day of the unit circle, degrees and radians. Because I took so many math classes in high school I did not have to take any math classes in college.
As I think about teaching math, I get excited. Teaching foundation level math is so fun. There are so many things you can do to make math come to life. I look forward to encouraging children to love math and believe that they are good at math even if they have believed otherwise in years past. I am nervous about teaching math because I know when I was learning math as a student I missed out on the “why” behind problem solving. I know how to line numbers up and regroup, but I cannot tell you why that works. From my undergrad math methods courses, I know that math is taught much differently than I was taught fifteen years ago. Regardless, I love being able to tackle a math problem and find the right answer. Solving math problems provides opportunities to celebrate little victories with my students all year.
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Math has always been my friend and foe. I have secretly enjoyed doing math because I enjoy solving problems and strategy, but it has been my foe because for much of the math I’ve learned I still don’t see much purpose for in everyday life. I now define mathematics as the use of numbers to solve real world problems. While math is for real life situations, it was difficult for me to understand the purpose for higher level math since I never planned on being a scientist or mathematician. Even when I was given word problems to solve they seemed abstract and didn’t relate to my real life experiences. I now understand that we can find math problems in almost all of our experiences, but this isn’t what I believed in my earlier years in education.
In my early years of elementary I had numerous people investing in my education from my teachers to my parents to friends. I feel like using numbers came naturally to me and people who noticed encouraged me to develop my math skills. I also enjoyed working through the details of math problems, as a result I could spend more time staying focused on my work than other students. I was excited when it was time to do math because people believed in me and thought I could get better at it over time. When I got to sixth grade I was placed in an advanced math section which at that point I didn’t like because I knew that meant harder homework, but it also made me feel good to be challenged. My teacher, Mr. Clevenger, worked really closely with the students in this section and encouraged us to continue working at a high level.
When I entered Junior High and High School I remained one class ahead of most of my other classmates. This made me feel confident in my ability to do math, yet the concepts I was beginning to learn became more unrelated to everyday life. I had excellent math teachers all the way through high school which helped me still enjoy it even though I thought I may never use what I was learning again. One of my favorite teachers who began to change my perception of math was my 11th grade statistics teacher Mrs. French. The first way she impacted me was that she was always excited to be teaching our class. Every day she would say how much she loved her job. This helped me realize there must be some value in mathematics. The second thing she did was make statistics relatable to my everyday life by doing hands on activities almost every class period.
I only took one math course in college which was another statistics class in my first year out of high school in 2011. Since then I have not had to use much math in my everyday life and have forgotten almost all of what I learned about math in the 13 years I spend in math classes. I now understand that there is value in math, but some of it still seems like there isn’t any use in learning unless I was going into a profession that will need it. That being said, the part of me that enjoys details and strategy still enjoys doing the math that I remember how to do. Even though I am teaching first grade I think there will be a lot I will need to review especially the strategies since so much of the curriculum has changed since I was in first grade. I am excited to help students develop their problem solving skills, but am nervous and scared to teach students who may struggle or don’t like math.
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I remember growing up in a home where reading was highly valued and books were a treasure. For the first 12 years of my life, I was required to read by myself for thirty minutes a day. However, I don’t recall my parents ever doing math problems or engaging in conversations with me about math, even when I had homework. In the third grade I began to get pulled out for academically gifted (AG) classes. Even though I don’t have vivid memories of math at this point in my life, I obviously was a high performing math student.
Fast forward to middle school, where I distinctly remember loving math because my teachers told me I was “good at it.” I was always getting called on in class and proudly shared my answers, making A’s in all three math classes I took in middle school. However, come high school, things shifted and my experiences with math became increasingly less pleasant. I remember being one of two freshmen in my Algebra 2 class and was always timid to ask questions in class. But I will never forget this embarrassing encounter I had with my teacher who told me that my way of doing math was stupid and it took too long. I can’t remember what problems we were solving or the context of the question but I will never forget how her words made me feel: “I was bad at math.”
Three years later I was taking an AP statistics class and struggling immensely. I worked really hard and even gave up my lunch periods to stay for tutoring (which was a huge deal as a high school senior). I was maintaining on average of a low B which was good for an advanced placement class. I vividly remember my teacher telling me that my intended profession of special education was a good choice for me because “people who struggle should help other people who struggle.” My teacher said this in front of other students and once again reiterating the belief that I was bad at math. After taking, and passing with a B, this defeating class, I ended up dropping my Intro to College Math class for the next semester to avoid taking math classes at all costs.
However, when I got to college I was required to take an introduction to teaching elementary mathematics class and ended up loving it. The material we covered was really surface level and just covered basic concepts of math. My teacher was passionate about us loving math so that one day our future students would learn to love math too. She left encouraging comments on all of our quizzes and let us share with the class how we solved problems. During my senior year of college, I was a student teacher in a third through fifth-grade special education resource room. I had the opportunity to work one on one with a fourth grader doing lower level mathematics such as multiplication tables, measurement, and place value. In a more intimidating manner, I also had the chance to teach group math to twelve-fifth graders out of their “Vmath” curriculum. Over the course of the semester, I became more confident in teaching mathematics and loved how engaged my students were, which was not always the case for these particular students. However, I found myself getting overwhelmed trying to differentiate instruction for my students who were on various levels, with varying needs and abilities. The hardest part was not being able to accurately convey ideas to students, however, it taught me about slowing down and thinking through the why behind the problems. I loved watching my kids light up when they got a math problem correct and watching them understand that what they already know about math is a foundation for what they are learning.
Right now, I am excited I get the privilege of teaching math to fourth graders. I am excited to learn how to teach alongside students. Hopefully, my mistakes will help them feel confident to make mistakes and together we can normalize error in math class. How my views about math have changed throughout the years will hopefully be an encouragement to my students. I can teach them that is okay to struggle and be confused but that math can be exciting and is everywhere in the world around us. If I had to describe mathematics to someone who didn’t know what mathematics is I would prepare them to work with numbers and to really expand their brain. I would tell them that it is more than just knowing numbers and facts about numbers but actually understanding the relationship between numbers. It would make them think and really make sense of the world around them. I would tell them to think about any time they had to interact with money or navigate a street or a baking a cake or if they are singing a song they have to count rhythm. A universal concept, I would be able to explain mathematics to someone who was not from the United States and use similar examples to get them to understand. -
Throughout elementary school, I loved the challenge of math. As a first grader, I begged my dad to write out math problems on this special yellow paper and reveled in the thinking it took to solve them. I am not sure if I actually got any of the work right, but it was more about enjoying the puzzle math offers. I had a third grade teacher who would create rewards for doing well on exit tickets, so I worked hard to get one hundred percent so that I could get a big candy bar or eat lunch with her. I also loved fractions–though I was lazy enough to hate finding the least common denominator–and would race through the speed fact quizzes, always trying to be the first to finish.
I maintained an appreciation for math in middle school and still performed well. I remember having a very hard time understanding negative numbers in sixth grade (how is it you could subtract a negative and have it turn into addition?) but overall enjoyed math class. In eighth grade, I was in honors and was asked to take a special math test for a competition; I do not remember why, only that I saw an f(x) function on the test and had no idea what in the world it was. Math was not my favorite subject, but I was always confident that I could do well and enjoyed the work once I actually sat down to do it.
In high school, I hated geometry at first. Proofs were difficult for me, but my teacher encouraged me well. I will never forget how motivating it was to hear her tell my mom at a soccer game how I was working hard and really beginning to get it. Looking at teaching this year, I am excited to be that voice of encouragement. While I do not remember loving Algebra II, I loved my teacher and did really well; pre-Cal the next year was more challenging but I still enjoyed the class and never felt incapable, even when the class was hard. Senior year, I took both Calculus AB and AP Physics, which included many principles from Calculus. While I did not like Physics because of the teacher, I loved calculus. The teacher was incredible and created a space to where I could ask any question and never feel worried about being dumb–so I would be persistent until I understood. Calculus made sense to me, and I enjoyed the organization and logic of the integrals and derivatives.
But in college, the only math I took was a statistics class my freshman year–and I got a fifty-five percent on the final, so it was not easy for me by any means. Reflecting on my past experiences with math, I actually wish I had taken more classes during my four years at school because I might have enjoyed it. I think I was scared off after my stats class, and while I loved studying history, it still jars me how I went from loving math senior year to never really taking it again. Thus, I am excited to get the chance to teach the foundations of math in first grade this year. Math is a way to understand the world around us with number and symbols; it is quantification, problem solving, logic, and order. Especially since math includes so many different ways of doing this (the functions of calculus are very different from the logic of proofs in geometry), I am confident that any child can be good at math with proper instruction and effort and hope to teach students to appreciate that rather than be scared of it.
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My mathematics journey has been something of a rollercoaster. When I was young, I struggled more in math than my brothers did and my parents started to reinforce the idea that math wasn’t my strong suit. I was given leniency and allowed to accept the idea that my math skills were limited and as long as I excelled everywhere else I was fine. As I grew up this deeply engrained the idea that I was inadequate. I only took as many classes as I was required and made sure they were the easiest available. This even affected my college placement exam because though I could have passed it easily, the pervasive idea that I’m not good at math let me give up early and forced me to take a class well below my ability level that I should have tested out of.
The experience was never helped by teachers who pushed me further than I did on my own. I never failed math classes, but my differing grades in every other class should have shown teachers I was fighting something. Never was the idea that I wasn’t good at math challenged. Teachers would just take my word and let me slide. In chemistry, when the math was more complicated and I was truly confused beyond belief, a teacher gave me pity grades because he was friends with my grandparents. All of this reinforced and internalized the idea that I was insufficient in all things related to math. It wasn’t until I returned to college for some post-baccalaureate work to earn my teaching certification that I started to change my relationship with math. I was forced to choose two minors and since my aversion to science is stronger than even math, I chose math and language arts. I took every class necessary for my math minor and began to recognize that I did not struggle once I removed the voices validating ideas that weren’t true. I really do enjoy math.
I like math because everything is fairly black and white. There is generally a right answer and a wrong answer, though not always just one way to get to that answer. If I understand the process, I will get the correct answer. It is comfortable and validating to truly engage with the material and come to understand it. I know that I can work hard and will see the payout that is not seen in every other academic pursuit. Because I have been on both sides of the line I can relate to students as they come to understand their story as it relates to math. I have hated it more than anything and have grown to look forward to how it intersects with my life. I have worked in retail where I’ve been forced to do the math on the fly to answer questions and accurately achieve sales. I love the idea of teaching math because I know how it has intersected so differently in my personal story. To me, math is where you use numbers and quantities to represent something that is known in order to find something that is unknown. Generally, there is a clear, finite answer to the question at hand. The actual applications for math in real life are innumerable though many will tell you that it is not. For me, my favorite thing is that math is a comfortable constant in a world that keeps changing.
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I’ve read the book, but finally just got around to writing my math autobiography! Here’s the link to it, apologies if it’s too long! Enjoy my journey!
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Over the years I have had multiple views and preconceptions about math. Most of my math experiences have caused me anxiety. I have always related my attitude with math based on my performance in the class that I was enrolled in at the time. Throughout this paper I plan to discuss my math experiences in elementary school, middle and high school, and college.
In elementary school, I do not remember math being a skill that teachers taught explicitly. In fact, the memory I have is in fourth grade memorizing multiplication tables. Those tests, gave me tons of anxiety and left me feeling constantly defeated. In fact, I still struggle with remembering those facts. Therefore, my attitude towards math in elementary school was mostly anxious and incompetent.
In middle school and high school, my math experiences are closely related with a seesaw. My experiences were based on the teachers that I had or my performance in the class. Therefore, i had some great math teachers and others that could care less about student’s understanding. The more encouraging or more explanation I received in math the more I enjoyed math. However, my math learning was procedural, and I could not explain my understanding until college.
In college, my math experiences began to improve, but my attitudes were not changed much. All of the math classes in college before my education math class were positive experiences but also procedural. Most of my experiences involved learning the math for the test then forgetting the steps and material. However, my elementary math class for grades 4-6 changed my life. This professor was so helpful and encouraging. He taught me how to do common core math as well as how to teach it. I remember as a college student being amazed at how much I understood the math. I was actually able to solve math problems and explain my thinking.
Therefore, overall, most of my math experiences involved anxiety due to only memorizing the procedure instead of understanding the math. I am excited to have more positive experiences in math to change my perception of math in general. I have learned that having a growth mindset toward math will change the way I view math. I am excited to having a new positive mindset about math so that I will be able to model a positive love for math for my students.
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Stared fashionable prepare:
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Here it is – finally!
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