Monthly Archives: January 2019

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.

Mathematicians

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.