Week 2: The "Problem" with Math
The Problem with Math
What is a
problem? Just the word has a negative connotation. You think of something that
causes distress. Problems usually are uncomfortable. Some people procrastinate and
don’t want to deal with the problem right away. We have to change our mindset
about math “problems” – perhaps we should use words such as “question,” “challenge,”
or even “riddle” instead of the word “problem.”
Students
must believe that they are “math people” and that they are capable of learning math.
Have a look at this inspiring article about how a teacher empowers inter city
students to free their minds and to keep asking questions until they truly
understand the concepts - http://bit.ly/2O1Xjze
So, what
is the issue?
Dan Meyer’s video “The Math Makeover” provided an excellent
analysis of the current state of most math classrooms as students:
- Lack initiative
- Lack
perseverance
- Lack
retention
- Have
an aversion to word problems
- Are eager to use formulas
Students want a fast and easy way out. Just plug some
numbers into a formula and presto, there is the answer. They didn’t really
understand the problem even though they got the answer. When they can’t solve
the problem, they display “impatience with irresolution.” I found this to be
the case with students during my block. They did not like to persist and gave
up much too early!
The Difference Between Knowing and Understanding
Understanding the problem is an obstacle many students
encounter. Students demonstrate knowledge when they can compute an answer as
they understand and follow a procedure. However, can they explain the math? Can
they make connections to demonstrate true understanding?
Sometimes students don’t know even where to start. George
Polya wrote a best-selling guide “How to Solve It” in which he detailed 4 steps
to solve a problem. How do you get to Step #4 when you are stuck at Step #1?
Source: https://binged.it/2DePnGy
Step #1 Understanding the problem or the analysis of the
problem is key to problem solving. You need to understand the meaning of the
problem. What is being asked? Can you rephrase the problem using your own
words? Do you really understand everything in the question? Do you need
additional details?
Sometimes, there is too much information and you need to
extract what is not important in the problem.
Let the students build the problem!
I really agree with Meyer’s comment about having students
actively involved in the design of a problem instead of just giving them a problem
to solve. The process is so important yet often overlooked.
For example, Dan Meyer demonstrated a word problem
involving a water tank. The following is a typical textbook problem:
Source: https://binged.it/2POgk5q
The problem was then altered – all the previous details such as
dimensions were omitted and the students only had a video showing the tank
being filled and the question: How long will it take to fill the water tank? Everyone
is on a level playing field because they only see a video and numbers and
formulas are absent. This is so powerful! They can talk about the problem and
share ideas. They can guess. Everyone can be engaged. They can redefine the
problem and discover what is important. The problem is more authentic as it was
a video of a water tank being filled.
Source: https://binged.it/2NXFkK7
Other tips
Meyer had some additional recommendations that I will use
in my teaching such as:
- Using multimedia
to add a real-world experience (and really reinforce that math is everywhere)
- Encouraging
student intuition (and emphasize the process, not the answer)
- Asking
the shortest questions possible
- Letting
students build the problem
- Being
less helpful (they have to persist and keep trying!)
I also thought that our in-class discussion regarding centers
or stations was great! I never thought about using stations in math but it
makes so much sense as it is a great way to differentiate abilities and student
interests and give teachers some time for 1:1 and/or small group support.
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