I am not doing math - so I am happy!

Being chased by the ghosts of Math

The Tune that Sticks

What is 17 times 3?

I loved playing cards when I was young. Contract Bridge, ACOL system - in case you were interested. Inevitably, once in a while, we would be a partner short. So we would often play "Auction Bridge". If you have never heard of auction bridge before, here is an excerpt from Wikipedia:

[A]uction bridge [is] an invention of three members of the Indian Civil Service stationed at an isolated community, designed as a three-handed form of bridge to compensate the lack of a fourth player.

A deck has 52 cards, but 52 is not divisible by three. One logical solution is to use a "dummy" hand in each round, but a more interesting solution is to take away a single card and be left with 51 cards to deal amongst 3 people. Thus, 17 times 3 equals 51 gets etched in the mind of a young boy without having to memorize times tables.

... One Step Back ...

In a previous blog, I questioned the notion of math anxiety being more prevalent in girls than in boys. Some of the earlier papers, specially OG articles by Dreger and Aiken or by Richardson and Suinn, hint that math anxiety scores do not differ significantly for males and females. Nevertheless, the review article "Mathematics Anxiety: What Have We Learned in 60 Years?" by Dowker et. al paints a more complicated story.

The relationship between gender and mathematics anxiety has been studied widely. I plan to go through this topic in detail in a later post, but for now I will rely on some the snippets from the review article. The citations for the primary sources can be found in the article by Dowker et al, and are not explicitly mentioned in the points below.

1. Females tend to rate themselves higher for Math Anxiety. Males, on the other hand, show more confidence.
2. Girls show a relationship between math anxiety and performance even when general text anxiety has been accounted for, while for boys this relationship disappears after controlling for general test anxiety.
3. There are studies that suggest no gender differences exist in math anxiety and performance, although these studies do not account for general text anxiety.
4. Females are often being reminded of the sterotype that males are better at math than females, and due to these gender stereotypes, girls may expect to feel more math anxiety which results in avoiding math activities and courses.
5. There is a lot of room for further research on how the working memory of girls may be affected differently than that of boys by math anxiety.

Overall, the idea that math anxiety is more prevalent in girls than boys is more nuanced than I expected. The review article discusses this in more detail, and covers numerous other aspects of math anxiety. I am not a big fan of summarizing review articles, as that will just be a redundant summary of a summary. Therefore the reader is strongly recommended to read the review article themselves. What are your thoughts on providing key takeaways from review papers in learning blogs? Please let me know in the comments.

Why we do what we do.

Recently, a student dropped by my office to announce that she received a perfect score in her math test. Just a week earlier she had been suffering from severe math anxiety. I had no doubt in the student's math ability, but a single problem that she had trouble understanding was enough to derail an entire practice exam. It brought her to a near standstill, and led her to make mistakes in proceeding problems, problems that she could otherwise solve in her sleep. Thankfully, studying about math anxiety gave me some perspective on what she was facing. It also allowed me to empathize with her, and provide helpful suggestions on sidestepping her math anxiety. Her grades bore the fruit of her hard work and my understanding of math anxiety. Have you been able to help someone overcome their math anxiety? How did you do it?

Removing Math Anxiety

Throwing Caution to the Wind

"I am not doing math - so I am happy!" is a verbatim quote from an acquaintance of mine. How soul crushing would it be if that sentence were to be spoken in front of a group of strugggling students, who are all facing math anxiety to some degree? We really need to be mindful of projecting negative attitude towards math in front of others.

In fact, in their short paper "Math anxiety: who has it, why it develops, and how to guard against it", Beilock et al. list social influences as a cause for math anxiety. In particular, teachers with negative attitude towards math can pass it on to their students (specially female students). What's worse is that it can have a rolling snow-ball effect from one generation to another as the negative vibes keep getting transmitted from teachers to students.

Sale! Sale! Sale!

The images in this section look like typical sales in your neighborhood grocery chain. However, carefully reading the small text tells us that the Classico pasta sauce, if bought individually, is $1.99 each, while the PC Spinach and Cheese sauce can be purchased for $2.29 per single jar. Do you see what is wrong here? How often do you check whether the sale prices actually make sense?

It is imperative that we promote positive math vibes to those around us. We should be encouraging kids to play around with numbers in their heads, so that when they grow up, they are not intimidated to calculate whether they are getting a good deal at the grocery store. Let us tell the next generation how awesome it has been to do math without a calculator, so that they may find their way out of using AI to do all their math.

Courtesy of Reddit user u/dotdoth

Born with a Math Brain

     Make sure your baby is born with a math brain     

A Story for the Ages.

Sylvanna: Nice to meet you. What is your role at the college?

Me: I am a Math Consultant. I help students with math.

Sylvanna: Wow! I am so glad you are here. If students ever asked me a math question, I wouldn't know what to do; may be I would cry! I am so terrible at math...

Me: ... No at all. I am sure you use math everyday in some capacity! When  driving to Toronto from Waterloo, you are probably doing all sorts of complicated math in your head to see if you will arrive in time. However, you said you get worried when someone asks you a "math" question. There is a concept that fits well with what you described. It's called math anxiety, and I have just started learning about it ...

Math is not the Boogeyman

Sylvanna is not a real person, but the conversation above is very real. I have had very similar conversations with people from all facets of life. Cab drivers, librarians, even college biology professors have expressed to me that sometimes they just don't know what to do if someone asks them a math question. They feel worried, anxious - as if someone shone a spotlight on their unprepared self. They are just happy that the "math" people are available to help tackle these problems. Perhaps this is fine and fair; not everyone needs to an expert in math, just like how not everyone needs to be Picasso. However, each of us often handle fairly complicated arithmetic in our everyday life - the cab driver finds the shortest route to their next fare, the librarian knows how many copies of a book to order based on the popularity of the book, the biology professor has a fair idea on how the H-index of their recent publication is growing - so why do we get stuck, like a deer frozen in approaching headlights, if we have to suddenly do a "math problem"? Why do many say, with some pride, that they simply aren't a "math person"? Perhaps the root of problem lies with the society around us willing to accept this inability to do math as the norm, and individuals start wearing it as a badge of honour.

Beating the odds

I have studied mathematics for quite some time, and have been good at it most of my life. With a graduate degree in mathematics,  I am fairly confident in my math abilities. I have chosen mathematics teaching and consulting as a profession. However, this does not mean that I have a math brain. In fact, I don't have any natural talent when it comes to numbers or counting. Untalented people like us learn mathematics through dedication, grit, and striving for excellence. I learned math because I liked math, and enjoyed learning math. While preparing for my O-level math exam - where I stamped my first real success at being good at math - my first "mock" test received a score of 58%, the lowest amongst my peers. That was a good time as any to simply give up, to walk away saying that I am not a math person, to claim that I was not born with a math brain. Nevertheless, with a desire to learn from my mistakes, I accepted that I was unprepared for the test. I decided to make changes. Those changes led me to where I am today. The same changes that I now try to instill into struggling students.

Definitely happy to be a Master of Mathematics.

The Devil in the cogs of the Wheel of Anxiety

Last week, a student started his consultation by saying "I am really terrible at Math". However, by the end of the session, our (both the student's and mine) realization was that he was not bad at math at all. He was able to walk through all the difficult algebra and complicated rules of logarithms required to solve his problem. His struggle was with making connections between the steps. Simply trying to think about which rule to use to start solving the problem froze him in fear. A fear that is very real. An anxiety that led him to conclude that he is "terrible at math".

The science of learning is fascinating. Having studied memory curves, learning techniques, and good study habits in high school, I follow the techniques from those lessons to this day. As a math instructor, I learned about effective math teaching and learning techniques - enhancing the learning experience with fun math puzzles, revisiting concepts in a new context and challenging the students to rediscover them - which is incorporated in planning my lessons. With the right guidance, I believe everyone is capable of viewing math as a friend - as something to cherish and love - and not as a fearful entity.

Math consultants have to often convince students that they are not "terrible at math", and that there is no such thing as a math brain. This has led me to investigate why students feel anxious at math. Currently, I know very little about math anxiety. That is exactly why I decided to share my journey into studying math anxiety with everyone. Let us venture together, in no particular order, towards finding the answers to some burning questions about math anxiety.

• What is Math Anxiety?
• Who is affected by math anxiety?
• Do we know the causes of math anxiety (there may not be a definite answer to this)?
• What are some common triggers for math anxiety? What are some contributing factors?
• How do we overcome math anxiety? Can we get rid of our weakness(es) in math?
• Why is being bad at math often accepted socially? Are social expectations shaping how we view our math expertise?
• When and where is math anxiety more/less common? Is there a specific education level that sees a spike in math anxiety? Are there some cultures/countries that are nearly immune to it?
• Is there really such a thing as a "Math Brain"?

Welcome to My Jungle

I don't have the answers to many of these questions yet. My plan is to read academic books and articles on the topic and share my understanding with you through this blog. There will be some personal opinions and commentaries, but with an objective approach. Answering the above questions is just the beginning, let's see where that leads us to.

All readers of this blog are welcome to contribute. Please engage the discussion with comments, constructive criticisms, and suggestions. Feel free to provide expert opinions or contribute to the blog with your own post. There may be some subject matter experts in the audience - please let us know about good resources to learn about math anxiety or correct us if we misunderstand something. Just like a polymath project, let us all contribute, and make this blog a great resource for everyone to learn about math anxiety.