Monday, July 28, 2014

Five steps for eliminating math anxiety

Five steps to eliminate math anxiety

When I meet someone new at a party and we exchange the customary small talk ("What about this weather?" or "How about those Giants?"), inevitably the question of what I do for a living comes up. Even before I share that I have been a middle school math teacher for 25 years, I can pretty much be certain that the response will be something along the lines of "Oh, math...I never understood algebra" or "I hated math in high teacher was the worst". What a buzz kill.

It doesn't take much of a detective to figure out that ours is a nation filled with mathphobics, or at least math-haters. There is plenty of evidence that babies do not come out of the womb hating math. So what happened between the time babies are born loving math and the time they become adults practically bragging that they can’t do math? SCHOOL.

School causes math anxiety. More accurately, the traditional instructional practices commonly used by math teachers - although it makes them highly regarded by their colleagues - are the very causes of the math anxiety experienced by our nation. I understand that there are other genuine causes of math anxiety that have nothing to do with schools, but for the purposes of this essay, I’ll only focus on math anxiety that is the direct result of our suck pedagogical practices in mathematics.

Five Steps
  1. Eliminate timed tests
  2. Provide students with a choice for assessing understanding
  3. Let students invent their initial understanding of the mathematics
  4. Teach multiple solution methods
  5. Encourage lots of student collaboration
It doesn’t have to be that way. Mathematics is an inherently interesting and beautiful and creative topic. So what can be done to keep our students thinking that is truly awesome? Here are my five steps for teaching math in a way that reduces the chance that students will develop math anxiety:

  1. Eliminate timed tests
  2. Provide students with a choice for assessing understanding
  3. Let students invent their initial understanding of the mathematics
  4. Teach multiple solution methods
  5. Encourage lots of student collaboration

Let’s take a brief look at each one.

1. Eliminate timed tests

It’s bad enough that math has the reputation for being a black-and-white, right-or-wrong subject, but the practically religious zeal with which teachers use timed tests is about the worst thing we can do in a math classroom. We know that when children are put under math stress they are less able to correctly solve problems. Timed tests also give students the idea that mathematical success is somehow connected to speed rather than critical thinking.

It is true that the Common Core State Standards of Mathematics uses the word fluency throughout the standards. Rather than using timed tests to teach (or measure) fluency, however, we should embed fluency building opportunities within number sense building activities. When students learn how to be flexible with numbers and quantities THIS is when fluency will naturally develop. Fluency, thus, can be developed in our students without causing fear and anxiety.

2. Provide students with a choice for assessing understanding

Since we know that students are less able to perform mathematical calculations when under stress, why do we continue to use stressful tests to measure student achievement? In a way, math tests are just longer versions of the timed tests that we already know are bad for students. Let’s seek methods of assessing our students without causing fear and anxiety.

Start by assessing students formatively and informally on a daily basis. As students are working in class, the teacher should wander around the room noting which students are confidently and competently solving the problems, and then record that with a clipboard and checklist. Why should the teacher bother with a stressful test if she has already personally observed students successfully solving the problems?

If an actual assessment activity is necessary, we should provide students with a choice in how they demonstrate their understanding. Students who like taking tests can take one. Students who would prefer an alternative can demonstrate their understanding by
  • making a video with screencasting software
  • performing a skit
  • standing at the whiteboard and solving problems
Giving students a voice in how they are assessed means students can choose the assessment method that they are the most comfortable with, thereby reducing math anxiety.

3. Let students invent their initial understanding of the mathematics

In a traditional classroom the teacher leads the discussion and shows students step-by-step how to solve the problem. Then students practice some problems in the classroom. Finally students go home to practice problems on their own. We in the ed biz call this the “gradual release” model.

This model of teaching leads students to believe that mathematics is not something discovered, but a fixed set of skills that is handed down from generation to generation. Since math is viewed as a fixed set of rules, a student who can’t immediately come up with the proper solution method is left only with the assumption that he is incompetent.

Instead, we need to foster an environment where students see mathematics as the creative endeavor that it is. Students should be empowered to create their own solution method or algorithm when necessary. We know that invention activities lead to deeper understanding in mathematics. Therefore, prior to teaching a particular content, students should be given the opportunity to use their natural number sense to invent their own solution method prior to being taught the “official” method.

4. Teach multiple solution methods

I have observed many of my Algebra students get stuck on a math problem that could easily be solved arithmetically or by guess-and-check. When I ask why they didn’t use one of the simple solution methods, students usually say that those are the “wrong” methods to use in an algebra class. Not only is math a bunch of rules, students also feel that there exists the added layer of complexity of using the “right” method.

As a direct result of #3, we need to teach students a variety of solution methods whenever possible. The very nature of mathematics is to find as many ways to solve a problem as possible. If this was not the case, the first time the Pythagorean Theorem was proven would have been enough for the mathematics community. Instead, the theorem has been proved over 300 different ways! We need to allow students to hunt for many different solution methods for a single problem, rather than forcing students to use one method to solve 30 problems. Students thrive when given the opportunity to re-create their own Pythagorean scenarios in class.

As students solve a single problem in multiple ways, they have the opportunity to compare and contrast the methods, see the connections between seeming unrelated methods, and develop a deeper understanding of the number sense that is inherent in that problem.

5. Encourage lots of student collaboration

Misery loves company? There’s safety in numbers? Two heads are better than one? Whatever meme you want to use, students thrive when given the opportunity to work with one another. We know that student discourse improves achievement. Let students talk, so they can learn! Math anxiety will not rear its ugly head when two students are talking to one another in their own kid-friendly language. While students are collaborating, the teacher should be grazing around the room collecting formative assessment data: who is using which technique, who invented something novel, who is struggling, etc?

Collaboration only makes sense! Imagine The Beatles trying to learn how to be a band together without being allowed to talk with one another. That is exactly what we do in class! Students are seated in rows, often with seating charts specifically designed to discourage talking.

While it’s no guarantee, my 25 years of experience says that implementing these five easy steps will go a long, long way towards preventing schools from causing math anxiety in our students! Reducing the math anxiety amongst our teachers...that's a story for another day.

Do you have anything you'd like to add to the list?

Tuesday, July 1, 2014

Is Math Anxiety Just Another Name for 'Bad at Math'?

This came through my inbox today. I wanted to share it with everyone.

Is Math Anxiety Just Another Name for ‘Bad At Math’?

            “To many people, ‘math’ is a scary four-letter word,” say Sian Beilock (University of Chicago) and Daniel Willingham (University of Virginia) in this article in American Educator. “They don’t like it, they don’t feel like they are very good at it, and they just want to stay away from it.” Math anxiety is associated with poor performance in schools and colleges – and with on-the-job errors by nurses, financial planners, and many others around the world. When does math anxiety get started, where does it come from, and what can be done about it?
            Beilock and Willingham report on research showing that math anxiety emerges early, affecting as many as 50 percent of first and second graders, is directly related to math performance (the more anxiety, the less well students do on math assessments), and is not correlated with performance on reading assessments. So is math anxiety just a manifestation of being bad at math? The authors think not. People with math anxiety would do better at math if they weren’t so anxious. That’s because anxious thoughts (fear of making a mistake, looking stupid in front of other students, displeasing the teacher) impair their working memory, or their mental “scratch pad,” and this means they’re less able to keep several things in mind at the same time – essential to manipulating numbers and solving problems. Brain scans have found this effect when highly math-anxious people even thought about doing math.
            What kicks off math anxiety? Beilock and Willingham say it is associated with children’s math abilities when they first enter school – for example, counting objects, deciding which of two numbers represents the larger quantity, and mentally rotating three-dimensional objects. Having difficulty with these basic skills starts a self-reinforcing cascade of anxiety and poor performance. Oddly, it’s students with the best working memory who are most impaired by anxiety, perhaps because they’ve come to rely on working memory in other areas and it’s shut down by anxiety.
A second source of math anxiety is the signals students get from home, the classroom, and society in general. Children can pick up signals from adults that math is, indeed, something to be worried about. Those students who enter school with math skill deficits are especially susceptible to a teacher’s or parent’s negative comments about the subject. Two studies have shown a direct correlation between female primary-grade teachers’ level of math anxiety and their students’ math performance at the end of the year: the more anxious the teachers were, the worse their students did, especially girls.
There’s a lot more research to be done, but given what we know so far, what can be done? Beilock and Willingham have these suggestions:   
• Ensure fundamental skills. Parents can build their children’s basic counting and spatial skills, and for students who enter school without them, teachers need to diagnose weaknesses and work quickly to improve them before anxiety sets in.
• Focus on teacher training. Building elementary teachers’ confidence and knowledge is essential to reducing their math-anxious vibes. Researchers have found that it’s more effective to teach teachers how to teach math concepts than focusing on the math concepts themselves.
• Don’t use timed math assessments. Racing the clock heightens anxiety; the simple remedy of untimed tests makes it possible for many students to do better work. [See Marshall Memo 538 for an article about timed tests.]
• Get students to write about their feelings. Studies have shown that having students write freely about their emotions about a specific situation (like a looming test) for about 10 minutes can help boost performance. The student thinks, “Oh, maybe this math test isn’t really that big of a deal” and working memory is freed up to focus on the math. Here is the actual prompt that was used in one such situation (students were assured that their writing was anonymous and would not be seen by their teacher): Take the next several minutes to write as openly as possible about your thoughts and feelings regarding the exam you are about to take. In your writing, really let yourself go and explore your emotions and thoughts as you are getting ready to start the exam. You might relate your current thoughts to the way you have felt during other similar situations at school or in other situations in your life. Please try to be as open as possible as you write about your thoughts at this time.
• Think carefully about what to say when students are having difficulty. If we say, “It’s okay, not everyone can be good at these types of problems,” students may interpret that to mean that the work is too hard for them and there’s no hope. “Consolation sends a subtle message that validates the student’s opinion that he’s not good at math, and can lower a student’s motivations and expectations for future performances,” say Beilock and Willingham. A better statement would be, “Yes, this work is challenging, but I know that with hard work you can do it!” Following up with specific study strategies and assistance adds to the power of that statement.

“Ask the Cognitive Scientist – Math Anxiety: Can Teachers Help Students Reduce It?” by Sian Beilock and Daniel Willingham in American Educator, Summer 2014 (Vol. 38, #2, p. 28-32, 43),