How
often have you started your year with students saying that they hate math? I don’t know
about you, but I find that it happens every year…and when I ask why, students often can’t say....so,
I don't necessarily believe that it's math that students "hate" (though they think so). Instead,
I believe it's something that happens or has happened in math classes that they dislike.
My
goal is to help students like math class enough that they’ll open their minds to the possibility that math
can be fun, interesting, and even helpful. This can be a challenge when some of them have had a negative math mindset for years.
I’ve
found that a few simple actions/habits on my part seem to lead to improved student attitudes
and the mindset that math might actually be a “likeable” subject. It's not necessarily the way I explain concepts (although I like to think I do that well:-), but more my attitude of acceptance that I think helps to change their attitudes.
Here
are a few ideas I believe have helped my students develop a like (if not a love) of math.
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| Using Pentominoes |
1)
Encourage students to ask questions and then be willing to take the time to answer
them. Students often hesitate to ask questions, especially in front of the
whole class, and especially at the beginning of the year. I start my year with
an activity that encourages students to work together right from the start, to
try to foster a comfort level that will encourage them to ask questions in
class.
I constantly remind students to ask questions when we introduce and
discuss concepts.
At
the beginning of the year, students will typically start asking
questions during group work time, and I take the time to answer, even if it
takes me a little longer to get to other students. As the year progresses, and
students see that I really do want questions and that I really will answer
those questions, they become more comfortable asking questions in class. The
more they ask, the more they learn. Yes, it takes extra time sometimes, but
it’s worth it to me….I want them to develop deeper understandings and that happens
through questioning.
2)
Allow students to talk to each other about math. We know that many students
love to talk! Why not encourage them to talk about math? Students often come to
my class having had very little chance to talk about math with others, and they
are surprised at how often I ask them to do so. They always have a
talking purpose – often it’s discussion of the warm-ups they did for
homework….what were the answers, how did they solve, why do they have different
answers? Other times they work on problem solving together….what do they know,
how would they approach the problem, where are they stuck? Talking about math
is so important and they come understand that they can share their ideas freely.
3)Ask
why. I ask why all the time. To begin with, students often think that me asking
why means they are wrong, so they change their answers. But it doesn’t….it just
means I want to know why they think what they’re thinking....I think this makes them feel valued. The more I ask them to justify their
thinking, the more able they are to do so, and the more they like to explain….even if it’s not “right”- they know I'm not judging, I'm just listening. I love
having them go to the board to illustrate their "whys." Some of them are
super willing to do so at the start of the year, while others take a while. But
by the end of the year, they feel comfortable explaining their whys.
4)
Tell stories about math in real life.
Last year, I told my students about the night my son (who was working as a
server in a restaurant) got a $60 tip. I knew the total of the bill, and we
were working on percents at the time, so we figured out
what percent tip that was….I think it was somewhere around 50%! They were so
interested, because it was about a real person. It was a short story, but those little tidbits
really add to"math interest."
5)
Be accepting of students’ thinking, explanations, and mistakes. This might be
the most important thing you can do. Sometimes students are on the right track,
and sometimes they aren’t....but making mistakes helps to grow the brain, so it's ok if they aren't on the right track. Yes, some math problems have one
right answer, but when students are simply told “No, that’s not right,” they
may shut down and tune out….feeling embarrassed about making a mistake or sharing "wrong" thinking. Peter Sims, writer for the New York
Times, says that successful people “feel comfortable being wrong.” Students
need to realize that they ARE doing some correct, valid thinking even if it leads them to the wrong answer. It can sometimes be challenging to take time
in class to find the parts of student thinking that can be built on, to lead to
the right answer. But as a math teacher, that’s part of my purpose…take students
from where they are, ask them questions, share thoughts, accept their mistakes, understand what they’re
thinking....and expand it or redirect it to help grow the concept in their minds.
According to Jo Boaler, “One of the most powerful moves a
teacher or parent can make is in changing the message they give about mistakes
and wrong answers in mathematics.” When students observe you accepting and
building from others' mistakes, they become comfortable sharing their own ideas.
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| Making Triangles |
6)
Let them explore math concepts! I know it’s hard to take time to explore,
especially when your math periods are short and you may feel pressure to
“cover” material within a certain amount of time. But letting students explore
math and play with math is so valuable! In Jo Boaler’s book, Mathematical Mindsets, she
references brain research and the idea that, “If you learn something deeply, the
synaptic activity will create lasting connections in your brain, forming
structural pathways, but if you visit an idea only once or in a superficial
way, the synaptic connections can “wash away” like pathways made in the sand.”
She also references a Park & Brannon study that found that “...the most
powerful learning occurs when we use different pathways in the brain...” Giving
students time to explore math allows them to explore those pathways and think more deeply. This can only benefit them and build their
foundation for the topics you'll teach.
At
some point during the year, most of my “haters” stop hating math. They realize
that maybe it’s not so bad, and they become willing to have conversations about math topics. They become willing to ask those questions in front of the class and
explain their thinking about those tricky problems - even when they don’t know if they’re
correct. They become willing to take risks because they know they won’t be
judged or harshly told “sorry, that’s wrong.” And when they learn that their
thinking wasn’t quite on track, they
don’t feel judged or stupid...and their minds stay open to the learning.
For me, one
of the best parts of teaching math is watching the metamorphosis of a child, from one who “hates” math to one who willingly goes to the front of the class to illustrate and explain
his or her math thinking.
This week's math dates are pictured here!
How
often have you started your year with students saying that they hate math? I don’t know
about you, but I find that it happens every year…and when I ask why, students often can’t say....so, 
This is just a quick post to share what I'm planning with "math dates" this year. Last year, I got such a positive response when I posted ways to write the dates as mathematical expressions. So I decided to get a little more organized with it this year, and plan the week of dates on Sundays, instead of thinking of them one day at a time.
I loved using expressions as the dates last year - it kept students fresh with their exponents/exponent rules, exposed them to roots (we don't really study these yet in 6th grade), and encouraged them to figure out their own expressions. 
The "butterfly method" for comparing, adding, and subtracting fractions -WHY teach this? I don't 
I used to have students come to me, having learned the butterfly method for comparing fractions.....they often had no idea why it worked....they
knew the trick better than they knew how to find a common
denominator...they didn't seem to understand that the products from the
cross-multiplying were the actual numerators they would get if they made certain equivalent fractions (figure 1); they just knew it worked.This bothered me, because I believe they should understand why things work. So I always made sure to explain why the method worked.
In the problem solving, students had to add 5/6, 2/3, 7/12, and 7/10. And here's where the butterfly method totally fails the students who have learned to rely on it, not only because they don't understand why it works, but because it becomes so cumbersome! They couldn't use the butterfly method to add 3 or 4 fractions at a time, so they added two fractions at a time. Instead of finding a common denominator for all 4 fractions, they found a new common denominator each time they added on the next fraction. For example, they added 5/6 and 2/3, getting a denominator of 18, as in figure 2. Then they added 27/18 and 7/12, as in figure 3, getting a denominator of 216. From there, they added 450/216 and 7/10, shown in figure 4. They ended up with a HUGE denominator that they then had to work really hard to reduce! It might seem crazy that they continued this process to get such huge numbers, but some of them did, because this was the method they learned. I was so shocked to see this....and this is the first year I saw this method used in this way. 
