Guest Post: Math Anxiety

Kramer McCausland is an instructor at AcerPlacer. He is working on a double bachelors in math and philosophy.

Math anxiety is wildly prevalent. Official studies vary a lot in their reporting of math anxiety, but in my personal work with students, I’ve found as much as 50% report some degree of math anxiety. Everything from mild dread when faced with a math problem to near terror at the sight of numbers. The art and practice of manipulating numbers is often portrayed as dull work, but for those with math anxiety, it can feel like an adrenaline-pumping fight for their lives. OK, maybe I’m exaggerating a bit, but I do have a lot of respect for students who, even though math is a source of major anxiety, choose to fight that good fight every day. I’ve compiled a list of some of the best tips I’ve found for combating math anxiety:

1) Stay organized, stay calm

Doing a complicated math problem can sometimes feel like heading down a rabbit hole. It can be full of twists and turns and dead-ends, and the sheer complexity of looking at that on a piece of paper can worry us. It is hugely important, as you head into these more complicated math problems, that you develop a step-by-step way of writing out your work. If you can’t look back at what you’ve written down and describe what you’re doing between each line of work, then you’re not being organized enough. Don’t be afraid to use scratch paper if you need it. Number your steps so you can see them clearly. Use colored pens or pencils to tell the difference between each new step. Clarity is your friend.

2) Keep your notes handy

First, take good notes. Well-written and organized notes are your greatest homework ally. As you work through your math homework, think of your notes as a leg up. Keep them nearby, but not visible. You want to challenge yourself to complete the hard work of mathematics without looking at your notes, but never feel ashamed if you have to pull them out every few problems (or even on every problem). As we learn math (especially if we’re preparing for a no-notes test), we need to train our brain to find the right answer without help, but it will help us avoid anxiety if we know we have somewhere to turn to when we’re stuck. If you get anxious about taking notes in class, ask your instructor if they have a printed copy of the notes. This way, you can dedicate yourself fully to paying attention instead of worrying about keeping up with what the instructor writes on the board.

3) Know your limit

In a perfect world, we would study math (and all of the beautiful things) simply because we enjoy it. But, for many of us, we’re studying math as a requirement for a high school or college level class. That means that we probably have a time constraint and will feel pressured to work ourselves into exhaustion. Now, a little bit of pressure is good, it will keep you motivated and focused, but know that you are going to have an upper limit. At some point, continuing to study will not yield additional knowledge. Do some amount of math every day as you prepare, but don’t burn yourself out by doing an outrageous cram session that you can’t remember the next day.

4) Test-taking: A breathing technique

A big part of math anxiety boils down to math test anxiety. There is no denying that taking a big math test can be scary, but keeping in mind a few test-taking tips can help us relax. Other than being prepared (which I hope you are), you should also learn a couple breathing and relaxation techniques to avoid psyching yourself out. To help you relax, close your eyes and try breathing in through your nose for 5 counts, holding for 2 counts, breathing out through your nose for 5 counts, holding for 2 counts, and repeat. As you breathe, just take a moment to notice where in your body you feel the breath moving in and out of your body. Maybe you feel the air traveling past your nostrils, expanding/contracting your chest, or as an up and down motion in your abdomen. The goal here is to just give your mind and body a break right at the beginning or in the middle of the test if you start to feel out of sorts. If you run into a hard problem, try to do 3 or 4 cycles of this breathing technique and then come back to it.

5) Test-taking: Relaxation technique

If the breathing trick isn’t your cup of tea, you can also find some peace of mind by trying some visualization. This takes some practice, and it may feel silly the first time you do it, so you should practice this a bit at home before test day. The goal is to be able to travel in your mind to your own personal “happy place”. I use this all the time as a mini-vacation I give myself during difficult tests or while doing my homework to relax. Start by closing your eyes and picturing a place, either real or imagined, that is calming to you. For me, I close my eyes and see the shores of a lake I used to go to as a kid. The details don’t have to be perfect, but throw in some small details to draw you in. For me, I’m sitting on a canvas chair, looking out at the blue water. I’m alone, and I have a book in my hand. But I’m not reading, I’m just looking out on the water and feeling the sand under my feet. Your happy place might be leagues different than mine, or might be pretty similar. Give this a try and see if it helps you keep a cool head when the going gets tough.

“Almost everything in life will work again if you unplug it for a few minutes, including you.”

— Anne Lamott

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Guest Post: F.A.T. City

Our guest author today is Stacie Leavitt, an instructor at AcerPlacer who recently got a degree in math education from Weber State University. She will begin teaching for the Weber County School District this Fall.

It’s a bit of a weird title, isn’t it? Let me explain. F.A.T. City is a workshop done by Richard Lavoie in order for adults to understand what having a learning disability feels like. F.A.T stands for Frustration, Anxiety, and Tension, three things that are extremely common among students with learning disabilities. Though we may think that in today’s world we are well aware of disabilities and that the fight has already been fought to gain rights for students with disabilities, we still sorely lack education for teachers in how to best help these students. This is especially important for the not-so-apparent learning disabilities. There are many students with dyslexia or processing deficits who either never get diagnosed or struggle getting the help they need. As teachers, this will be what we unknowingly need the most help on. In the words of Richard Lavoie himself, “I came to recognize — for the first time — the great irony of the teaching profession: Those of us who teach school usually did well in school ourselves and enjoyed the experience — why else would we return to the classroom to make our living? Therefore, the kid whom we can best understand — to whom we can relate most — is the one who does well in school and enjoys being there… Conversely, the kids whom we understand the least are the kids who need us the most. The struggler, the special-education student, the failure.”

Now as teachers in education, we need to look at what aspects of our behavior can be causing students with learning disabilities to experience frustration, anxiety, and tension and then avoid these as much as we can. It has been showed in many studies that if the negative affect is high in among learners then their ability to learn diminishes. So we as teachers need to make sure we are not instigating situations in our classroom that could cause unneeded anxiety or tension. Here are some common situations we create in our classrooms that we may not be aware of.

For the sake of time teachers will often demand answers quickly, and since they may not be giving sufficient time to students, this can cause them to freeze or become anxious. In essence, the student becomes a deer in the headlights and we as teachers may assume a number of things from them being stupid to thinking that they just haven’t been listening. Now teachers may not always be conscious that they’re doing this. Oftentimes teachers get caught up in the need to cover all the material, they feel rushed, and then they consequently rush the students which really just makes things worse overall. Another tactic that teachers use both consciously and subconsciously is using sarcasm to demean the student when they don’t answer correctly or quick enough. Imagine this, say student Jimmy has dyslexia and it takes him twice as long as the other students to figure out an answer. You’ve asked the class what 2+2 is, they’ve answered and then you ask Jimmy what 2+3 is and he says 4. You tartly reply, “why yes Jimmy, 2+3 is 4”, the class laughs and you move on not thinking much of it. But what does it feel like to be Jimmy? He had just barely figured out your first question and bravely put forward his answer and in return he got laughed at. Now rarely do teachers intend to tear students down, but they can do it unintentionally if they aren’t careful. Haven’t we all let out a quick retort without thinking? As such, sarcasm should never be used to negate wrong answers given by a student who took a risk by answering.
Other things to avoid are telling students to “try harder”. How does one just try harder? And teachers often state this as if students with learning disabilities are not already trying their hardest. We as teachers often see things as being easy because we’re coming from a higher vantage point of already knowing the answer. Take the picture below; do you see the image in the picture?

FAT City 1

Why don’t you see it? Well look harder! Now, it doesn’t make much sense to tell you to look harder, does it? Rather you might need me to give some structure to help you see where the eyes, ears, and nose of the animal are in the photo and then you’ll be able to see that it’s a cow.

FAT City 2

Similarly, it doesn’t help to tell students to try harder. Instead, if they have a learning disability and are not understanding we need to give more structure and guidelines to help them to see the overall picture we’re trying to show.
All in all, we must be careful to try and make our classrooms low in frustration, anxiety, and tension especially for students with learning disabilities. While some nerves can help heighten ability, too much can inhibit learning in many students. This responsibility lies mostly on us as teachers and we need to be educating ourselves in how we can best help students with learning disabilities in order to give them just as many opportunities to learn as everyone else.

Guest Post: Reformers in Math Education

Today’s guest post comes from Madison Hodson, an instructor at AcerPlacer who studies mathematics/statistics education at Utah State University.

In this article I would like to highlight a few educational reformers. I would also like to discuss a brief history of education and the impact that it had on mathematics and mathematics education.

Johann Pestalozzi was an educational reformer of his time. He believed that all children deserved a fair chance to attend school and be educated. He tailored the curriculum to meet the needs of each of his students, especially the underprivileged and poor children. Johann’s influence was not limited to the 1700’s alone; today we have education and teaching criteria similar to Johann’s approach to education. Examples of Johann’s influence in today’s education include: an emphasis in children taking an active role in their learning, having a well-rounded education system, and a student-centered teaching approach. Johann also emphasized that school and home are both places for learning to take place and that parents and teachers must work together to make that happen. He also introduced the focus on not only what subject is being taught, but how that subject is being taught. These are just of few of the valuable contributions made by Johann that influence our educational system today.

Another reformer that I would like to mention is Franz Gall. Prior to Franz Gall’s work, the world believed that the intellect and all learning came through the heart and the soul. Franz Gall changed that belief to the knowledge that is still held today- that learning and intellect stems from the brain. With this newfound discovery, Gall divided and categorized the brain into separate sections that each serve a specific purpose. Gall’s findings are helpful in teaching mathematics because we can target specific concepts or learning ideas that engage various parts of the brain. We can also recognize that everyone’s brain works a little differently, meaning that individuals learn differently. As math teachers, there are many methods and examples that we can use to convey the same concept to our students. We have the resources and knowledge available to us to target specific teaching methods that will yield the best long term results.

As educators, we have the responsibility to not only help our students understand how to solve complex math problems, but also to teach them how these concepts can be useful and applied to real-life problems. Critical thinking and problem solving skills are indispensable assets that all individuals must learn in order to succeed. Math teachers are fortunate because we can combine our curriculum with applicable examples that will give students useful skills for life.

Math Movie Night: Probability and Gambling

This week we talked about probability (specifically Bayes’ theorem) and how it could help you in everyday life. What if I told you that probability could even make you a better gambler?

Probability and gambling have always had a symbiotic relationship; studies of gambling improve probability, and probability improves the ability of people to gamble. Even if you aren’t a gambler at heart, very similar mechanics permeate many types of games today, making it an interesting study.

Without further ado, our feature presentation: How Science is Taking the Luck Out of Gambling!

 

Cancer Scares and Polygraphs: What Can Bayes Do For You?

How many times have you seen a TV talk show mention how someone failed a polygraph, so they must have cheated! Lie detectors don’t lie, right? How many times have you had a friend get bad news on a medical test and see that emotional toll that took on them?

What could these two have in common? They could both be helped by Bayes’ theorem.

Bayes’ theorem is an idea in statistics that allows us to update the probability of something happening based on new evidence. You can see what it looks like in the featured image above. However, the best explanation I have ever seen comes from this image:

Let’s go through each part of this image individually:

  • H: This is our hypothesis, or what we think is true. In the talk show example, this could be “I think my man is cheating on me.”
  • D: This is our new information. For the talk show, it’d be the results of our polygraph test.
  • P(H|D): This is the likelihood that the hypothesis is true given our new information. “What are the odds that my man is lying about cheating on me if the polygraph says he’s a liar?”
  • P(D|H): This is the odds of seeing the new information if the hypothesis is true. Here, it’d be the odds that the polygraph would say someone was lying when they were lying. This turns out to be 88% (Rice, 2007).
  • P(H): This was the probability that the hypothesis was true before the new information. For example, 22% of men say that they have cheated on a significant other.
  • P(D): This the odds of the test saying the person was lying in every outcome. Here, you’d use the 88% it says someone is lying when they are, and multiply the odds that your man is lying (22%). You’d also have to add the odds the test says they are lying when they are not (false positive), about 14% (Rice, 2007), multiplied by the 78% chance your man isn’t a cheater.

This gives us the following result:

CodeCogsEqn(1),

or 63.9%. This means that less than two out of three of those polygraph results are actually accurate. This low success rate, by the way, is one of the reasons most states don’t allow polygraphs in court.

But what about the bad medical test? How could it help us there? In statistics circles, the common example is the case of mammogram result that comes back positive for cancer. For our purposes, we’ll use numbers used by The New Yorker when they talked about this problem in this article from 2013. The numbers they quote are as follows:

  • The chances that a women in her forties has breast cancer is 1.4% (meaning 98.6% don’t).
  • The chances that a mammogram comes back positive when the woman has cancer is 75%.
  • The chances that the mammogram comes back positive when the woman doesn’t have cancer is 10%.

Let’s imagine your friend in her 40s gets a positive result back on a mammogram. What are the odds that she actually has cancer? Bayes’ theorem tells us the probability would be

CodeCogsEqn(2),

or only 9.6%. If that seems low to you, don’t worry: one study showed that 95% of physicians given similar numbers incorrectly estimated the likelihood to be about 75% (Rice, 2007). Your friend should be concerned and have further work done, but you can comfort her by saying that there is an over 90% chance it is a false positive for her.

What can Bayes’ do for you? It can help make talk shows more laughable, and it can help bring comfort when tests go south. It helps to give perspective and a more realistic view of the world. As it turns out, it’s pretty useful.

We’ll continue to explore these ideas in movie night this week with some videos that give even more examples about how Bayes’ theorem can help you every day.

The odds that those will be entertaining? 100%.

Math Movie Night: Math and Music

Last time, we mentioned a speaker by the name of David Kung and his work comparing music and math. While I have not been able to find the lecture referenced in that podcast, I did find one that seemed to be fairly similar. While it is a bit long, it makes for fantastic listening as he has two other musicians on stage with him. His main point? “Math helps us understand music. Music helps us understand math.” If you’d rather not listen to the whole thing, I’d listen to the final portion of the presentation (starting at about 59:00) where he discusses how Bach used several math concepts in his music that were well ahead of the mathematicians of his day.

Now sit back, relax, grab some popcorn, and enjoy tonight’s feature math film, Symphonic Equations: A Mathematical Exploration of Music!