We are all “Math People”!?

Consider, for a minute or two, that the beliefs that we are each either “a math person” or “not a math person” are holding back our potential achievements. Are there things you would do differently if you were a “math person”? Could you discover something new about mathematical relationships if you weren’t taking it for granted that you are a “math person”?

It seems that on either side of the math person belief system there are people who limit their understanding by holding fast to these ideas. The students who are “math people” tend to stop trying, they believe they already have it. When a new problem becomes challenging they tend to give up, and reconsider being “math people”? The students who are “not math people” believe they will never get it, so they do not even try. These beliefs are the accepted standard in our country. When I mention taking a math class to an acquaintance I undoubtedly receive an “I’m sorry” or “that stinks” response.

 

Now consider that these “math person” beliefs are not just holding back our academic potential, they are limiting our brain’s growth. Practice and hard work can actually  change our IQ scores, for a time. Research shows that problem solving increases connections in our brain, which improves brain function, ultimately increasing IQ scores. When we stop practicing (or using our mind power) these connections slowly weaken and IQ scores can go back down over time. So, keep your mind active! Just like other muscles in our bodies, our brain needs exercise. One way to exercise our grey matter is critical thinking about mathematical word problems. It is crucial that students are given complex problems, and time to develop solutions on their own.

This does not mean that teachers can hand out word problems and sit back while students “discover” the answer on their own. Before students can explore math problems through critical thinking, they must be taught how to do so. Fortunately George Polya developed a process with four easy to follow steps for this purpose.

 

Polya’s 4 Principles for Solving Problems:

  1. Understand the problem, consider the wording and information
  2. Devise a plan, choose an appropriate strategy
  3. Carryout the plan, be persistent and willing to redo work
  4. Look back, check your result, do other strategies work? does this apply to other problems?

 

A variation of Polya’s process named SQRQCQ was developed by Leslie Fay in 1965:

  • Survey. Read the problem quickly to get a general understanding of it.
  • Question. Ask what information the problem requires.
  • Read. Reread the problem to identify relevant information, facts, and details needed to solve it.
  • Question. Ask what operations must be performed, and in what order, to solve the problem.
  • Compute/Construct. Do the computations, or construct the solution.
  • Question. Ask whether the solution process seems correct and the answer reasonable.

Fay’s process, SQRQCQ, may be even easier for students to work with. I like how it clearly emphasizes questions in each step of the process. Reflecting on our progress by asking questions models the way we want students to be thinking. These processes are useful to all students, and are important in helping special ed students succeed in Math.

Finally, consider the empowerment that comes from an “I can do it” attitude. Show students that they can improve their math skills with practice. Talk to them about how our brains work, help them understand that intelligence is not something we are born with or without. Mathematical wisdom comes from experience, and it is worth working towards. Help to put an end to the “math people” myth.

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Math Literacy – beyond terminology

An important element of critical thinking on any topic is literacy, or competence. Math is no exception. In order for students to gain a deeper understanding of mathematical concepts, they must first become math literate. This means that students can apply mathematical reasoning skills to help them solve real world problems. It sounds like a daunting task, but it doesn’t have to be so grand. For young students math literacy involves knowing if they should use addition or subtraction to solve a word problem. This can transfer to the real world experience of biking to the corner store to purchase a treat, and making sure that the correct change was received. Older students will have more complex real world experiences, such as, earning enough money to purchase tickets for a concert. They can be encouraged to set up equations while problem solving.

Our job as teachers is to ensure that each student becomes math literate. The first step is to promote an expectation of success in math for all of our students. We have to believe that our students can do well, and then they will believe it too. Set up a culture of critical thinking on a variety of numerical topics. Invite students to create their own math problems, and to solve them. Set aside some class time for a discussion of thoughts about math. Tell students that there are no bad ideas, and watch the discussion grow. Even if no actual math computations are made, the discussion will reinforce the idea that math is important and that everyone can be good at it with practice.

Students need to understand that the mathematical language is important in conveying ideas, but math literacy goes beyond knowing terms. It involves a deeper thinking, the ability to view problems from multiple perspectives, and to apply previous knowledge to new situations. Giving our students the time and the skills to develop competence in math gives them the confidence for continued academic success.