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I would like for my students to say they learned how to share their thinking and learned from each other. Also how the process of what they did was very beneficial to them learning how to solve math problems.

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I realize now that all the those games we played in math were actually teaching us something.

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I would hope they would say the class was super fun and engaging! I would want them to love it so much that they couldn't wait to come back everyday or make it so memorable that they have something to say about it 20 years from now. I would want them to be great mathematicians since they are learning for understanding instead of just to learn it.

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My fourth grade year of mathematics was a year of learning and exploring. My teacher often didn't even know the answers.  We talked a lot about math and did many group projects.

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That my teacher would bring back the content to the real world to make it more relevant.

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I hope my class would talk about the math conversations/discussions we had and supported our answers. Our conversations got rather "lively" at times. I want them to be able to back up and support their answers and use reasoning skills(justify). I hope they became good problems solvers and were able to apply strategies to use in every day real life.
I hope they love math and are able to better understand it! I hope they learned work through a productive struggle.

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20 years from now, my current math students would probably be saying they wished they had paid attention better as they help their own kids with homework! Seriously, I would hope that most students would talk about the time in class we took to discover and talk about mathematics. I would hope they remember the struggles  and how most of the time these turned into productive struggles.

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my students will found math interesting and challenging.  Math can be   applied throughout their day. Students will see the fun in math and continue to have a playful attitude towards it.  They will see it's application daily.

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my students will found math interesting and challenging.  Math can be   applied throughout their day. Students will see the fun in math and continue to have a playful attitude towards it.  They will see it's application daily.

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I was diagnosed with dyslexia and dyscalcula when I was in 7 th grade. Until then... math was terrible. I was told be teachers that I did not try. That I was not listening, stubborn. You name it, it was told to me. So long story short I hated math!

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Let's just say I've always been more fluent with words than numbers....

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Loved math all my life.  I won a crown for being thefirst  to know all their multiplication facts in third grade.
My students would say it was frustrating never knowing if they were correct. Always figuring things out on their own.

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Every week, my geometry teacher sat us by our weekly test scores. I never got out of the first row all year! 😢 Side note- I knew all my facts!

I think my students saw me as a "hands off" teacher. Part of that was due to me not having taught math for over 15 years and therefore, being immersed in a "alien" world myself! I was treading water all year, trying to learn the"floor" yet trying to challenge my 17 gifted kids to scale the ceiling! There was much discussion and reflection not because of me but for my own personal growth. Mutualism was alive and well in Room 21! 😁

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I wanted to be in the “high” math group. I wasn’t and I decided that I was awful in math. That followed me through my school career.

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I was ‘that kid ‘ in elementary school...didn’t like math and made to feel very inferior in comparison to peers. One time had to sit by the teacher as tests handed back because ‘evidently I needed extra help’. Truly believe this helped me want to make math a much better experience for my students.

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Growing up in the 60's and early 70's math was the most painful part of my schooling. Everyone was doing the same thing and we were never encouraged to talk, think outside the box, collaborate, or think with others. I am so thankful that I became a teacher and could experience math in new way. Now I absolutely love math.
Fast forward 20 years:
I think most of my kids would say that hey haves loved math and appreciated that the classroom was an open place for all of them as learners. A few other would say that they got tired of me always making everything I did related to math! Haha

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I remember wanting to know the why behind the content that we were learning and being told to just memorize it. After that I decided I wasn’t good at math and didn’t ask any more questions.
That influenced my teaching by always ensuring that my students are making connections no matter what area we are working on.

20 year student reflection
My students will remember that we spent a long time on one concept and explored it in many different ways.

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I remember always being interested in math but never really excelling at it. The older teaching methods were not effective for me. Learning from text books or written procedures were lost on me because of my ability to remember the procedure.
When I began teaching, I found math to be the most difficult to teach because of my understanding of the material. And I remember trying to teach procedure and not really getting it myself. After many classes of learning these more effective methods, I found my math abilities to grow as well as my passion for teaching math has returned.

Fast forward...

I believe my students will have decent memories of math class. One of my goals for students is to not consider themselves "good" or "bad" at math. So I'm hoping that during the rest of their academic career they are more willing to take risks and attempt to solve problems rather than defer to someone else.

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When I was in 6th grade I wasn’t in the “high” math group for fractions. I really wanted to be with my friends. I then decided I was bad at math/fractions.This stuck with me through the rest of my school career.

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I love doing mental math. In first grade one of my classmates and I were always
competing for Around the World champion. Instead of bedtime stories, my dad would give me multi-step word problems at night and I loved the challenge.

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I remember doing a LOT of math problems from a textbook. It was a great day when the teacher only assigned the “odds” ! I remember
having timed multiplication facts tests. I feel like I learned “how” not the “why”. I am trying to teach the “ why” and have students engaged in real life math problems. I want to foster an environment that promotes risk taking and perseverance.

Now...
I believe ( I hope) that my students would say that they felt that math time was a fun experience. I try to provide opportunities for students to collaborate and problem solve real world situations. This past November, students used the iPad as a resource to plan a Thanksgiving meal. Students enjoyed figuring out how much a turkey would cost per pound and how to plan the food portions/recipes for the amount of people. I feel my students will remember activities like that instead of my memories of textbook learning.

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HMy memories of math class are mixed. I feel like they went through extremes: either I picked up concepts right away and applied them successfully or I didn’t get them and was devastated. In elementary school, I do remember fact exercises most vividly—timed tests, around the world, tables, flash cards. We also had workbooks we worked from I’m assuming from a purchased curriculum program.

In middle school, I was on the college-bound track, starting pre-algebra in 7th grade. I was a strong student because I could get work done quickly, took good notes, and my photographic memory served me well during practice. I remember doing many practice problems for homework each night. I remember working through text books from middle school forward, but we did do some project based work, specifically designing a golf course and a school mascot image from bricks. In high school I finished in AP calculus, but ended up having to take calculus again as a freshman in college. I remember my college experience being far more terrifying than my high school experience.

As a teacher, my perspective on teaching mathematics is so different. The mathematical practices help me target going deeper into the math and beyond getting the correct answer. I still cringe when it comes to timed tests, and I remember crying when I didn’t understand long division on the state math proficiency test. I consider the anxiety I felt as a kid in mathematics; looking back, I realize I was a high-achieving, mostly successful math student, but I wouldn’t say that my perception was that I was “good at math.” For my students, I want them to each feel they have an entry point and that nobody is “bad at math.” I want to give them rich experiences to extend their understanding, practice and become engaged without fear of failure, and become real-life mathematicians in as many ways as possible.

Fast Forward 20 Years...
If I were to step into my students’s shoes 20 years from now, I would like to think they look back on math as a positive memory. At least more positive than the way I recall math back in my time. I think the anxiety around testing would be less, however, the productive struggle may be something some students feel less comfortable with. I think its not a warm and fuzzy feeling to go through that struggle, but hopefully they’ll have learned the reward that comes with sticking with it and persevering. I fear that there is still some negative mindset around math, adopted from parent feelings and cultural norms, but I hope we are on the way to eradicating that. I do still see students who avoid the math, feel unsuccessful, and struggle to enter math tasks. I hope they will remember the community of learning, working together to problem solve, freedom to share ideas flexibly, and playing fun games. At a minimum, I hope each left my classroom with the belief they had some strengths in math, and lots of room to discover and grow. I hope they will see me as a teacher who worked hard to support them and guide through through math.

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I remember having a chart on the wall for all to see with star stickers for every level you passed. I remember being embarrassed by this when I was not at the top with some of my friends. I also remember sitting in individual desks in rows and being assigned pages 21-26 all the odd problems. If you finished then you got free time, and I never got to the free time. My worst memory was when I was an entering freshman into college and the councilor helping me register for classes did not want to let me take a specific course and when I asked why not she said, “Let’s face it, you’re not the brightest student.” All of this was because I did not do well on standardized timed tests, but academically in my classes did very well.  This really scarred me. Now I always try to take into account my students self confidence and reflection of themselves and learners and how important this is in their math history. Number sense, problem solving, strategies etc. are so much more important than a score on one timed test at one point in their life.

In 20 years I think my students math store about me would be that I made them really think. They had to figure things out on their own and they were forced to actively struggle and develop problem solving strategies.  It was about the process and not the answer.

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I remember starting to "fear" math in the sixth grade with Mrs. Thompson. I can still hear her walking behind me, looking over my head, her shoes creaking along the wood floors as she moved closer toward me. The anxiety was at an all time high. It took several years after sixth grade math to overcome those irrational fears. It took the help of a high school math teacher, Mrs. Miracle (ironically) to turn those fears into productive challenges with an emphasis on it being okay to make mistakes. This made me realize, as a teacher, that we have the power to influence a students' attitude toward math. We have the power to make them either love or hate it. It's all about how the content is presented.

Fast Forward 20 Years...

I often try to share my sixth grade experience with my students each year. I tell them that if they EVER begin to have fears similar to mine own, to come and talk to me. School should be a place that they WANT to be, not a place where they feel they NEED to be. And within our community, they should feel safe and comfortable. I hope my students look back at their math experience and reflect on a community of learners who felt safe to make mistakes, whose mistakes were treasured and shared with an opportunity for growth, who experienced successes both big and small while feeling celebrated along the way!

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Math came easily for me, well memorizing facts did. It wasn’t until teaching that I learned how I can use numbers flexibly. I did have one experience in 6th grade that I recall enjoying. My teacher introduced the game, 24, and each card had 4 numbers that you needed to manipulate by using the 4 operations to get to 24. I remember that it challenged my competitive spirit and motivated me to get creative with numbers.

Fast Forward:

I want to provide meaningful opportunities for students to engage in problem solving that they will remember for years to come. I want them to love math and to think about numbers flexibly. They should be able to tackle any problem and love challenges.

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Elementary math was ok...I honestly don't remember especially positive or negative feelings. I do remember feeling frustrated by my seventh grade math teacher because we would have homework but then never go over it the next day. In high school I avoided anything super challenging and got through fine. I came from a "math minded" family and enjoy math as an adult. As a teacher I try to bring a fairly relaxed atmosphere and work to balance problem solving and number sense.

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I don't remember a lot of my elementary math, but remember a bit of my high school. Most of high school was about memorizing formulas. I can't say I was really great at it. I remember for finals being able to use a notecard and writing as small as I could and as much as I could! I remember working problems out on the board in front of the whole class.

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I did not feel passionate about math because I needed to know all my facts quickly and I hardly ever won when playing around the world. In math everything was isolated and we could not collaborate or share our thinking. There were never opportunities to revise our thinking because either you were right or wrong. Math seemed hard and boring and I always dreaded that time of the day. My anxiety of math stayed with me all through high school and into my adulthood. Luckily, reading Jo Boaler helped me shift my beliefs about mathematics. It has also helped me develop a growth mindset which I am still working on each day.

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I feel like I really don’t have “ math memories” from elementary... I remember geometry and being completely lost. After that experience, I stopped taking math courses. I do enjoy teaching math!

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I feel like I really don’t have “ math memories” from elementary... I remember geometry and being completely lost. After that experience, I stopped taking math courses. I do enjoy teaching math!

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I think my kids would say math was fun...we played a lot of games. I believe a few would say it was hard, but I had the gifted cluster and needed to push through a little faster. I’m still trying to figure out the correct approach with the all the different levels.

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I loved math class and being challenged. I remember getting a lot of satisfaction out of solving a really tough problems. Although times tests cause anxiety among many students and I recognize that as a teacher, I loved the competition of them as a student. It was a strong motivator for me, but I realize that’s not the case for everyone.

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My outlook on math throughout school was mostly negative. When I think back to my math experience the first thing that comes to mind we’re timed tests. These brought a lot of nervousness and anxiety that made me feel like I couldn’t do math. From this I work to incorporate ways to help my students feel successful in math and comfortable with making attempts and making mistakes.

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I was never “fast” with math and could never get “answers” quick. I however always found different ways to explain my answers. I was never able to be validating in my explanation or answer because no one else was on the same wavelength. I love teaching math and love hearing all different answers and strategies.

20 years from now I think my students will remember getting satisfaction from perserving through hard problems. They will remember not being “told from the teacher” but instead hear from their classmates. They will remember completing challenges with me and discovering math together.

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I realized taking my college methods classes that I was taught to be a math robot. I memorized well and learned the shortcuts. I always got As in math. But it was in my methods courses where we learned the WHY.  I had no idea why math worked. My students challenged me during student teaching when they asked WHY. I realize now that I had no math sense. I find that today as I can no longer help my own kids with high school math because I have forgotten the formulas. If I had been taught math sense, I could still do HS math.  How sad!! I do struggle letting go with memorizing facts though! I want my students to understand math but I feel it’s easier in the long run if they’ve mastered their facts while doing longer mult/div problems and fractions if they have that base.

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Math was never my thing.  I was ok, but never felt like I excelled at it.  I had a HS math teacher tell me math didn’t really matter, even when I tried to get help, because I was “probably just going to raise babies.”   This stuck with me & gave me the fire to prove him wrong.  HS math really solidified my efforts to avoid math in college.  Ironically I really love teaching math now.  I feel I can identify with the struggling kids & empathize with their struggle.  

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Math was never my thing.  I was ok, but never felt like I excelled at it.  I had a HS math teacher tell me math didn’t really matter, even when I tried to get help, because I was “probably just going to raise babies.”   This stuck with me & gave me the fire to prove him wrong.  HS math really solidified my efforts to avoid math in college.  Ironically I really love teaching math now.  I feel I can identify with the struggling kids & empathize with their struggle.  

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I think they would say I made them think.

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So many different memories.....I remember in 1st grade I had to write the numbers 1-100 in order. If I missed any, I would have to start over. Throughout the rest of my school career, I remember having books or workbooks. You would go through the lessons with the teacher demonstrating how to solve the problems and then you would mimic. I struggled with this because if the problem was written any different than what was shown, I could not apply my understanding, if I truly really understood. I remember being able to solve basic facts in my head or other problems, similar to what we have our kids do in number talks, but would not use those strategies because I thought they were wrong and I needed to memorize facts. For me, I have always felt Math was my worst subject, I had a teacher in middle school who tried to convince my mom not to allow me to take Algebra A, to encourage me to only take basic math. (I took Algebra A, taught by her husband, as well as Allegra B and on). I may not always understand how students solve their problems, but math is actually my favorite to teach. I guess I feel like I am getting a chance to show my understanding in a way that in the past I felt I couldn’t .

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I think I had good number sense and was taught strategies that eventually led to memorization. Memorization may been been stressed in those days, but it was the memorization of certain math facts that allowed me to build on: Example: I knew 3x8 was 24 because I knew 2 is were 16 and I added 8. When I got to 6x8 I knew that was 3x8 twice, and I could add 24 + 24 in my head which led to the memorization of 48. I was a good math student until high school and hypothesis. Forget Trigonometry and calculus.

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I was a not a good memorizer. I struggled and had major anxiety towards math because of it. I feel that the article brings up some good points with math facts and memorization and how it isn’t helpful.

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I am a memorizer so looking back I do not have any negative feelings or remember any bad experiences with math in elementary school. I remember worksheets, which I always enjoyed doing, and remember playing around the world with multiplication facts. Since I was a memorizer I always would go far in the game so it was an activity I always enjoyed. I do remember spending a lot of time working with the metric system because at that point the country was going to switch over to the metric system. Not many memories with secondary math, but I remember struggling with geometry and getting extra help from the teacher.
They would say it was a noisy class, used the calendar for helping with math concepts, some whole group, some partner, some team, and some individual work. Had free math choice, variety of iPad activities/projects, hands on activities.
Some would say they remember parts of math class and others would say they don't remember a thing.

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I was a superior memorized, which means that I am a low achieving mathematician. My experience included feeling very confident about my Math skills, until I had to solve large story problems that involved reasoning. I would over think/reread/struggle with ideas, but laboriously resort to “
calculating” the numbers in the problem in the way I thought the teacher wanted me to based on the lesson.  If we were dividing, that must mean that the problem wanted us to divide, etc. It wasn't until college when the professor asked our class to count to 100 in Base 2 that I started reasoning with numbers. I wasn’t alone in our class, because the entire class minus 2-3 students were greatly struggling with this task.

Student Autobiography in 20 yrs.

I always felt I didn’t get enough time to practice! I often listened to my teacher’s lessons, but I also had a lot of people sharing their experiences with the lesson with each other at the table. I got confused really fast, but tried to make sure that I worked the problems like the teacher showed me on the board. Sometimes my teacher would do “My Favorite No”, and I never wanted to be her favorite “no”. No one would know it was me, but I would! I always liked playing the games that we got to do at the end of Math class. Those were always fun, I got to play with a friend(s), and it didn’t seem as hard as the lessons in class.

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I remember worksheets and rows of solving math facts.  I used math workbooks.  I also remember timed tests.
I know I did not have number sense. As an educator, I realized that I learned math through memorization and not number sense.
I remember math being an individual activity. I do not remember collaborating with others and solving problems with a partner or small group.
I remember thinking there was only one way to find an answer.
I did not feel I was good at math.

Student Biographies
I think my students would say they mostly enjoyed my instruction. Most students love participating and sharing their work. I gave many opportunities for
Students to share their strategies by displaying their math using the ELMO. Students would also say that math is a collaborative time in our classroom. They spent so much time having opportunities to work with partners or small groups on math tasks. They would say we used a variety of materials to show our thinking such as paper, iPads, manipulatives, chart paper, etc.

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I do remember a lot of memorizing. In later elementary I was placed in a higher math group. We worked independently on the regular classroom work and then worked through extensions.  All the extension work was group work.  To be placed in this group you had to do well on a placement test.  I did not do as well on that test but through in class discussions I was placed in it anyways.

Today, I like to use math extensions to push my higher kids. I do use unit pretests to help decide who would benefit most for each unit.  I do make changes to these groups within a unit based on need.  This groups changes for each unit.

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Memories of math class- I don’t remember much from elementary school, except basic tests. I remember being scolded for using my fingers and actually created my own dot system for addition and subtraction where I tapped number amounts. I remember doing lots of math to get it back all red and being like 1 number off!  I also remember being removed from the class in 5th grade to be worked with in math and it was all basic calculations. The basic facts were of upmost importance, in my elementary brain larger than anything else.

Middle school/ High School I loved math and was surprised when teachers praised my effort. I was not used to that in math. I started to feel like a math student and it was shocking.

I wish I had learned math like we teach, the visual component would have made it all make sense.

Fast Forward 20 years later
My students from this year would say that I valued mistakes and that mistakes lead us to knowledge/ misconceptions. They would say that we would have “problems” to which they would work with their partners and determine an answer- and then the work began. They would prove their thinking, ask questions and multiple students would share their work.

They would say, I value explaining your thinking and explaining what others have done. I love strategies, different ways to get an “answer”. The learning pit- you have to get back up again and keep working.

Most of all, I hope they would say it was fun! We learned alongside each other shared, disagreed and debated.

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I loved math! I had teachers who made math a fun experience. We did have to memorize our times tables. In 4th grade, we had to stand up infront of the class and the teacher would fire multiplication facts at us. We only had so long to answer. If we could not answer or provided the incorrect answer, we sat down and did not earn a sticker for that fact family. Due to this activity, I worked super hard to know my facts quickly. However this was not true for some students. It caused great stress to my younger sibling. I do not want to have students but discouraged by math. So providing multiple ways for students to show their understanding is how I hope to eliminate a bad taste for math. Hands on experiences and applying math skills to real life help students them see the purpose for the instruction.
Math Biography for current students
I think that my students would share my love of math. I really try to create an environment that promotes acceptance. We celebrate everyone's thinking: right or incorrect. I tell my students that sometimes adult "language" is boring and hard to understand. Therefore they are able to help teach one another by sharing their thinking and working through a problem. We use all kinds of manipulative to make math fun and enjoyable.

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My memories of math include worksheets filled with rows of problems to solve. When I became an educator, I wanted students to see the patterns and real world connections in math.

"Math is purposeful! I see the value of sharing our mathematical thinking because it challenges us to see different perspectives of how we think about numbers. Math makes sense to us because we see the real world connections.”

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I always liked math because my teachers were willing to take time and help me. I had some teachers who created a game atmosphere and that was fun. We had opportunities to work together.

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I never felt like a smart math student. I memorized facts and did time tests. I always completed my pages of homework. I don't have great memories of activities, but I definitely hated story problems the most!!!

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My memories of math include the teacher assigning problems one day, and the next day giving us the answers and assigning a new set of problems. There was no talk of how we solved the problem or explaining it. This led to math anxiety for me. As a teacher I want to allow time for discussion and reflection so my students come to an understanding themselves

20 years later...
I hope my students are making their own discoveries about math. My students would be explorers, given a choice of tools to solve real life problems and making connections. My students would consider themselves students who reflect on their work willingly give and receive feedback.

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Math class was all memorization of facts and was not my favorite subject. We used flash cards often. It’s almost like learning math all over again with how it is taught today. Much more useful for kids! I hope that my students will remember math as “discovery” and fun learning. They will be confident and know that understanding the process was much more important than getting the right answer all the time. I want them to remember math class as being a safe and comfortable environment where understanding that “making mistakes is how we learn.”

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I remember sitting in rows, watching the teacher solving problems, then we were given a worksheet to practice. I was stressed and scared to ask questions because I felt when I continued to ask questions the teachers got more frustrated with me. I knew I never wanted to make kids feel the same way that I felt!! I want to provide a classroom where their thoughts and questions are valued and mistakes are the pathway to learning.