Tests and Revisions

Students have test anxiety and math anxiety. Two ways that I alleviate this for my students are

1. For tests, I allow students to talk for 5 minutes while holding the test, without writing utensils.

2. I allow students to revise anything that they submit (except for the final, for time constraints).

The purpose of the 5 minute talk is that I believe in testing the way I teach. The class is highly collaborative and students admit that they aren’t as stressed about tests because of the ability to bounce some ideas off each other for a couple minutes. An added bonus to this is that when you walk around the room, you hear some of the RICHEST mathematical conversations. (I am not exaggerating when I say that I almost got teary-eyed during a final several semesters ago because I heard great conversations coming from students who said they felt weak in math earlier in the semester). For students who have disabilities and need to take their tests in a different room, I allow them to come to class for the first 5 minutes and after the collaboration is over, they walk to their testing room.

For revisions, I tell students to not erase anything and to write revisions on a separate sheet of paper, as seeing their mistakes help them remember not to make those same mistakes again. They have to have these sentence starters:

  1. I got this (partially) incorrect because…
  2. I now know…

and then they do the problem again.

I have them do this because I strongly believe that reflection is a huge part of learning. They should reflect on what was incorrect on their first attempt and they should reflect on what is correct and why it is correct.

Study Guides

For study guides, I put a couple exercises for each topic on a Google Slide and give students commenting privileges. They spend the period on their laptops/devices choosing what exercises they want to do and then they are to comment their solutions with explanation. I highly encourage my students to have mathematical conversations in the comments section.

I used to do review sessions where I would do some problems on the board that students needed assistance on, but I realized that I wasn’t reaching all my students. I needed to think of a way to have students practice problems that they individually needed help on. Then I realized putting exercises on Google Slides would help with that.

I think there are 3 major benefits to this: 1. Students can work remotely while helping each other out 2. Students can also see other students’ solutions to verify if their solution is correct 3. This frees up my time so I can go around the room helping individuals. The drawback to using Google Slides however, is that not everyone has internet access at home.

Thank You Cards

For the past couple semesters, I gave personalized thank you cards to all ~180 of my students. I’m a pretty sentimental person and I hate things ending, so writing them a thank you card for being a good student and wishing them the best in the rest of their educational career is the least I can do. I also like this because it challenges me to really get to know every single student throughout the semester and to find at least one of their strengths.


I’ll be honest in that even though I have a bachelor’s and master’s in math, I have probably only heard of two non-white mathematicians in all of my math classes. It’s not like only white males can do mathematics. This is why I will add notable mathematicians on here frequently to have a little collection that teachers can use to expand the idea that anyone can look like a mathematician.

Yang Hui

In 1275, he described patterns in what is now known as Pascal’s Triangle. In Asia, they name that triangle after him (rightfully so, since Pascal didn’t come until 300+ years later). Hui also worked with magic squares and magic circles.

Source: https://www.britannica.com/biography/Yang-Hui

Benjamin Banneker (b. 1731)

Banneker made predictions on solar eclipses, surveyed Washington D.C., published his own almanac, and even made a completely wooden clock that was precise for decades. He wrote to Thomas Jefferson saying that one race is not superior to another.

Source: http://www.americaslibrary.gov/jb/colonial/jb_colonial_banneker_1.html, https://www.britannica.com/biography/Benjamin-Banneker

Zu Chongzhi (429-500)

You know the volume formula of a sphere? He and his son derived it using dissection! He also approximated pi to 6 digits using the fraction 355/113 ~1100 years before Europeans achieved this!

Source: The Volume of a Sphere: A Chinese Derivation Author(s): Frank J. Swetz Source: The Mathematics Teacher, Vol. 88, No. 2 (FEBRUARY 1995), pp. 142-145 Published by: National Council of Teachers of Mathematics

Sonia/Sofia Kovalevsky (1850-1891)

Every year, the Fresno State math department would host a Sonia Kovalevsky Day where we would invite 7th-12th grade girls to our campus to show that they can be mathematicians as well. Kovalevsky’s dad would use his old calculus notes as her wallpaper and she was fascinated by it and wanted to study it more. Being from Russia at that time, she was unable to go to college without permission from her dad or her husband. Because of that, she got a fake marriage and went to study under Weierstrass in Germany at the University of Göttingen, where her specialities included partial differential equations, elliptical curves, and the dynamics of Saturn’s rings. In 1874, she became the first woman to receive a PhD in math.

Source: https://www.britannica.com/biography/Sofya-Vasilyevna-Kovalevskaya

Draw a Mathematician

Imagine what a mathematician looks like. Draw the mathematician that is in your mind. What do they look like? What are they doing? Picker and Berry (2000) conducted a study where they asked 12-13 year olds from 5 countries (USA, UK, Finland, Sweden, and Romania) to draw a mathematician. Both males and females drew mostly males, with the exception of females from the UK as seen from the table below.

(Table from Picker and Berry 2000)

Already, before these students reach high school, a lot of females see mathematicians as a male-dominated field. Not only this, but quite a handful have negative connotations to the role, as seen in these examples:


Though this article is from 2000, the idea is still important and relevant. I have asked students from my classes to draw a mathematician and though about 90% of my students are female, the majority drew a male mathematician teaching. Not only do we have to show that mathematicians can look like anyone, but we have to expand their minds on what a mathematician does.

Knowing this, I spend the first couple days of school strictly on mindset. Students may come into class already hating math so it is important to establish the idea that everyone can be good at math and everyone is a mathematician.

10/8/18: Monday Motivation – Elissa Miller

Every Monday, I will highlight someone who has motivated me to become a better educator and this week goes to Elissa Miller!

I listened to Elissa’s Global Math Project talk and I loved her idea of “Two Nice Things.” If you are unfamiliar with it, the rule is, whenever you say something negative to another person, you have to immediately follow it up with saying two nice things about that person.

What struck me was when she said that this rule pertains to yourself as well. If you say something bad about yourself, you have to say two nice things about yourself too and I love that. I have problems with self worth and doing this for the past week outside of the classroom made me happier with who I am.

I told all of my students this idea, so Elissa, you’re popular to all 180 of my students, and I hope that they will bring your idea to their classrooms.

Above all else, it is important for students to see that they are valuable, and Elissa is doing a great job providing an environment for her students to see that for themselves. I intend to focus more on this idea this semester. Thank you for being my motivation Elissa!

10/1/18: Monday Motivation – Diana Herrington

Every Monday, I will highlight one person who has motivated me to become a better educator and this week goes to Diana Herrington.

Diana unfortunately passed away May 17, 2018 but I am forever grateful that I had the opportunity to co-teach classes with her for a year during my master’s program. She completely opened my mind to what a math classroom could look like.

Here are just a few ways she has helped me:

  • She introduced me to Jo Boaler’s Mathematical Mindsets
  • She really pushed the idea that the process is just as important as the final answer
  • She gave me the idea that students should be able to buy back points for assessments
  • She showed me how to use tech effectively in the classroom
  • She came up with the “5 minutes of discussing” before tests
  • She had projects that really looked for math outside of the classroom
  • She had the idea of having students do Digital Portfolios to really show off what they learned throughout the semester
  • She taught me to bring real-world objects into the classroom. Ex: We brought in pine cones, tree branches, shells, etc. when we were discovering the Fibonacci sequence.
  • She showed that there should be personal stories behind your math exercises.

I learned so much in that one year of co-teaching with her. After I graduated from the master’s program, we still shared the same office and collaborated even more. What I love about her was that she never pulled the experience card. She has worked in a high school setting for over 30 years, but she was open to suggestions from a newer teacher like me. I loved that she was always learning to improve, even after all her experience.

She was so selfless too. She bought SO many items for her students and even gave away $1,000 a year to students who used mathematical modeling in their Science Fair project through the M-power award.

There are too many wonderful things to say about Diana so I’ll split them up into separate blog posts.

I am the educator I am because of Diana Herrington. Just like Sir Issac Newton said, “If I have seen further it is by standing on ye shoulders of Giants.” Diana was, and will always be, my Giant.

Thank you for reading.

9/24/18: Monday Motivation – Christopher Danielson

Every Monday, I will highlight someone who motivates me to become a better educator and this week goes to Christopher Danielson!

I’ve only known Chris online but he is an integral part of my Twitter community.

I *think* my first interaction with him was in this tweet: https://twitter.com/Trianglemancsd/status/927233326997561344


He is an expert in math, but he doesn’t make others feel intimidated. I’m trying hard to follow Max Ray-Riek’s idea of “listening to” rather than “listening for” and I can totally see that Christopher does this, as seen in this example:

I love that he has Math on a Stick to show the general public how fun math can be. A lot of math educators do a good job showing how math is fun within the classroom, but I love how Christopher extends that to everyone.

Lastly, I love that he supports the LGBT community. I posted my “Just married” photo a couple months ago, mentioned that I always lose followers whenever I mention being gay, and he says:  

I know it’s 2018, but I am still amazed at all the people who support our community. Thank you Christopher. I don’t take your support for granted.

Christopher is a wonderful educator and human being. I strongly believe that the way you live your life is a vote for what you want society to look like, and the world would be a better place if we had more Christophers. Thank you for enriching my Twitter experience and I cannot wait to finally see you in 2 weeks!

9/18/18: The People I met at Math Unleashed

Rather than a Monday Motivation, I’m going to highlight the great people I met at Math Unleashed this past Saturday:

(Pre-conference dinner including Carole Pryor, Casey McCormick, Chrissy Newell, Devin Rossiter, Heidi, Kathy Henderson, Allison Krasnow, and Sarah Galasso)

Chrissy Newell

Though she didn’t go to Math Unleashed, it was awesome that she was coincidentally in Sacramento when we were. I sat next to her at the dinner and I loved how the conversations just felt like we’ve been friends forever. I’ll always admire how knowledgeable she is with math ed and I’m excited that I get to see her a couple more times this semester.

Kathy, Casey, and Allison


I’ve met Casey before, but I’ve been waiting a while to see Kathy and Allison. Looking around at the dinner the night before the conference, I was on the verge of being teary-eyed because I’ve finally met them. I will never not be amazed at the relationships built with someone that we haven’t met in person. They are all super kind and I cannot wait to see them next month at Taste of TMC NorCal (which you should go to, too).

Devin Rossiter (pictured at the dinner)

Devin drove all the way from Bakersfield for this! Such commitment. At the dinner, he said that he wants to present in as many conferences as he can and that takes the courage that I’m still learning to build. From starting with Sports Broadcasting, I’m glad he made his way to the math field. We really need him and his ideas.

Sarah (pictured at the dinner)

Sarah is doing great things with Carnegie Learning, traveling all around California and Nevada giving PD. She is super approachable and kind and I’m sure I’ll see her at a conference soon.

Heidi (pictured at the dinner)

Heidi was SUCH a fun person to hang out with. The night before, she said she would come to my session even though we just met. After the session, she even nudged Carole to make me the keynote next year (jokingly of course). Thanks for being my cheerleader for the weekend!


Demetrius came up to me towards the end of the day to shake my hand saying that he follows me and I wish he did so earlier! I talked to him later and he has wonderful ideas and passions, such as wanting to use tech to make teaching easier. I hope I get to see him at another conference.


This was the first time I ever talked to Fawn in person and it feels like we’ve known each other for a long time. She is one of those people that can talk for 3 hours and I would not get bored. I loved the math problems she gave us, including the 25 mice race, Conway tangles, and the host/handshake problem. She deserves the world and I am so honored to have her as a friend.

Ed Campos Jr.

Ed is a treat to watch. Hilarious and loves to give shout outs to other educators. I met him before very briefly at CMC Central but this was the first time I watched him present. If you haven’t yet, you absolutely need to.

Carole Pryor (pictured at the dinner)

Carole, thank you for letting me present at your conference. It was my very first conference talk so Math Unleashed will have a special place in my heart. The entire time, you were all smiles and warm-hearted. The people you work with are so lucky to have you.

Debbie Hurtado (not pictured 🙁 )

Debbie came up to me at the very end of the conference to say hi to me and I wish she did sooner. I hope to see her at another conference soon so we could have a more proper chat!

People at my session

I remember most but unfortunately not all of their names (Nicole, Colby, Syndi, Herman, Heidi, Andrea, Katie, Fawn,…), but I was so grateful that they all had a good time during the presentation, especially since I had a dream a couple nights prior where a guy said “yeah…you shouldn’t be presenting.” I saw Heidi’s friend Andrea write “Great energy!” on her notebook just minutes in and that made my day. From someone who has pretty low self-esteem, it’s unreal that people would use my ideas, so thank you for validating that my ideas *are* good and that other teachers will implement them in their classroom.

Aside from the travel, Math Unleashed was a great experience. This is my first of 6 conferences that I’ll be attending this Fall and if this was any indication of how the others will turn out, it’s going to be a great semester.

Thanks for reading.

9/10/18: Monday Motivation – Robert Kaplinsky

Every Monday, I will highlight an educator who has inspired me to be better, and this week goes to Robert Kaplinsky.

If you’re a math educator, there’s a very high chance that you know of Robert.

I saw him at CMC South last year and he said something that I think about at least once a week. It was something along the lines of “Well, we were taught procedurally and we came out fine, so why is it important to change how we are teaching?” To be completely honest, I forgot what he said after that and I didn’t write it down in my notes, but I’d like to answer that with “Because our students deserve it.” (Robert, if you’re reading this, I would like to know what you really said).

I love that he emphasizes DOK levels and Open Middle. Those are my go-to’s for low floor, high ceiling activities. I love it so much that I’m making it into a project for my future elementary school teachers. Also, it is awesome that he is giving free live webinars next week! So selfless!

I also love that Robert is really interested in meeting other educators. I’m not going to lie that I freaked out when I saw that he DMed me about going to the CMC South dinner. Fawn tried to ruin it saying that it was a mass DM, but it still counts even if it was a mass DM. =P

I have much more respect for Robert after reading his math story (https://bit.ly/2dDfoNR). It is obvious that he reflects on his past experiences to drive his motivation today. Also, I cannot imagine going through his experiences with math and getting to the point to where he is today, so mad props to him on that. His heart is definitely in the right place. By the way, after reading his math story, I finally understand why he said “You know how marijuana is a gateway drug? Pre-algebra is the gateway to math.” during his talk at CMC South.

Thank you Robert for inspiring and helping many math educators. Your purpose is sincere and you are moving mountains. I hope to be as impactful as you one day. 

Thank you for reading.