Recently, I have been thinking a lot about what causes math anxiety for students. As a high school math teacher, it was common for students to enter my classroom on the first day and announce that they were either not good at math or they didn’t like math. Sadly, these feelings were much more common than those that exhibited great (or any) enthusiasm for math. I would respond with “You aren’t good at math yet!” or “Maybe you’ve never been taught so that the math made sense.” Eye rolls and snarky laughs were a typical response from the students.
So where does all this anxiety and hatred for such a
beautiful, exciting and useful subject come from? Of course, like everything in
life, the answer is complex and involves many variables. I do believe that some
of this math anxiety comes from how we treat math facts. If you have spent much
time around an elementary classroom or have children of your own, more than
likely you have seen the infamous “Mad Minute” sheets. Regretfully, I am guilty
of using these with high school students who were in my Title I classes.
(Shakes head in regret.)
While I understand the intent of these timed test, I think
the un-intended consequences, leave lasting negative impressions for many
students. I will offer some alternative ways for students to learn facts that
don’t include memorization and drill type activities. First, I would like to
point out some reasons why we need to reconsider using Mad Minute type activities.
Math Anxiety
Below is a portion of an article that appeared on Edutopia
titled “Tips
for Tackling Timed Tests and Math Anxiety” by Youki Terada.
For many, taking math as a child was a dreadful experience.
“Timed tests were the horror of my primary schooling,” Rawini Ngaamo recalled.
“All I learned from them is that I was stupid and slow. I still hate maths even
now because of the way it was taught.” Dozens of people agreed, recalling their
own personal experiences or sharing those of their students or children.
The effects appear to be long-lasting, haunting some of the
commenters for decades: “As a 57-year-old, I can still recall the anxiety of
timed tests,” said Debbie Denmead Cassady, before suggesting that teachers
“forget them” in the future. And the post brought back vivid, unpleasant
memories of elementary school for Adina Thuransky: “In second grade, our
teacher timed us on math facts (times tables)... it freaked me out so much I
can still remember how much anxiety I felt!”
It is clear from these examples that timed test have the
potential to cause long lasting, negative attitudes toward mathematics.
Emphasizing Understanding
Perhaps the most important expectations in the Arizona Math
Standards, is to teach with a balance of conceptual understanding, application
and procedural skill and fluency. Traditionally, there has been a disproportionate
emphasis on procedural skill with students reproducing memorized procedures
with little on no attention paid to why they work or when they might be useful.
If reproducing the procedure is the goal, arguably the “drill and kill” method
can prove useful. However, this leads students to believe that math is a
disjointed subject where procedures have little or no connection to one
another. Memorizing multiplication facts does little to help students
understand how the numbers are related to one another, the patterns that exists
within multiplication tables, the relationship of multiplication to other
operations or even the relationship to area. These connections are what make
math interesting and useful.
Effective Teaching Strategies
Teaching of mathematics often goes something like this. The
teacher puts a problem on the board, then the teacher solves the problem while
the students observe. Next, the students solve a problem while the teacher
solves the same problem on the board using the same strategy that was used to
solve the first problem. Then the students practice on another problem similar
to the first two individually. While there are variations of this process, the
steps are basically the same and are often referred to as “I do, you do, we do.”
John Hattie has done extensive work evaluating teaching and
learning. “Through the Visible Learning research, John Hattie has
identified more than 250 factors that influence student achievement. He then
set about calculating a score or “effect size” for each, according to its
bearing on student achievement. The average effect size of these 250 factors was
0.4, a marker that can be shown to represents an (average) year’s growth per
year of schooling for a student. Any factor that has an effect size above 0.4
has an even greater positive effect on student learning.”” (“About
MetaX.” Corwin Visible Learning Plus, www.visiblelearningmetax.com/research_methodology.)
Hattie identifies worked examples (I do, we do, you do) as
having an effect size of .37. Thus, this is a very average strategy to use in
terms of students learning over the course of a year. An alternative to using
worked examples might be the use of Math Talks where students engage in sharing
of ideas through discussion. Hattie rates classroom discussion with an effect
size of .82. From a teacher perspective, it is often times much quicker for students
to get the “right” answer when we show them how to complete a problem rather
than discuss, share ideas, make mistakes, discuss, rethink and reflect. However,
research is clear. Learning involves confusion, mistakes, discussion and time.
Messaging – Math is About Answer Getting
When we ask students to answer 100 math fact questions in 1
minute, the message we are sending is that math is about getting the answer as
quickly as possible, often from memory. This is the wrong message. Math is
about using what we know and applying it to learn more about an idea or a
problem. Teaching students to use what they know and understand to approach a
new problem seems a much better life lesson to teach than the alternative. When
facts are taught in a “memory dependent, speed is important” way we paralyze
students. With this approach if you do not know the answer there is not an
alternative. This is not how we solve problems in our lives. We might do
research about the problem, talk to a friend or mentor, try an approach that
has worked before or a combination of all these strategies.
So what instead?
I encourage all teachers that are using timed activities to “teach”
facts to reconsider how to incorporate different approaches and strategies.
I will start with a simple change to the timed test approach
that I incorporated. Students seemed to find the strategy more engaging and useful
as well. Instead of timing students on the Mad Minute, I asked them to find 10 facts
that they could answer easily and write their answers in red. I would then ask
them to find 5 more problems that they could answer by using a strategy that makes
sense for them. For multiplication this might be skip counting, related facts, drawing
a visual model etc. Finally, I would ask them to pick 3 that were the most
difficult for them and find a partner who could help them understand how to
find the answer. I had moderate success with this. I never felt it was perfect,
but it was better than just doing the regular 1-minute timed test.
Another approach that I highly recommend is Number Talks.
You can find lots of information regarding Number Talks with a simple search. Basically,
students are presented with an expression that they are asked to independently
find the answer for. The work is done mentally without paper and pencil. The
teacher solicits all answers and then facilitates a discussion where students
consider and share strategies. The routine takes approximately 10 minutes once
students and teacher are familiar with it. It is a great way to build
understanding of numbers and relationships and empowers students to think about
the math that makes sense to them.
How are you addressing math facts in your classroom? What do
you agree with? What do you disagree with? Share your ideas so that others can consider,
and we can all get better together.
Resources
YouCubed
– Jo Boaler shares ways to help students improve their number sense and the more
about the damage done by using timed test.
Number
Talks – The Dana Center has a library of videos that show Number Talks
being used in classroom with students. There are a variety of topics and grade
levels.
Visible
Learning MetaX – An interactive database that organizes and explains the
work of John Hattie. Learn which influences are most effective in impacting
students learning.
