This week, I read "Beliefs about word problems" by Greer, Verschaffel, and De Corte. In this article, the authors argue that word problems should not have a bijective relationship with arithmetic computations, but be thought of as exercises in mathematical modeling. The article presents a number of empirical examples of students and student teachers engaging with mathematical word problems that are firmly based in the real world. That is, the problems require the participant to think realistically, rather than simply mapping the problem to an arithmetic computation. They found that only a very small percentage of students and about half of student teachers placed the problems within a real world context. Why it is "ok" to disconnect mathematical word problems from reality, the authors suggest, is due to the beliefs surrounding word problems. They state that although beliefs about word problems are most prevalent in the classroom setting, a broader perspective that includes the school, the education system, and society in general is necessary to understand how beliefs shape mathematical practice. The authors provide the following illustration:
As you can see, I was wondering how and where parents fit into this picture. Just the other day, I came across a friend's post on Facebook which was a video of a mother complaining about the common core standards and advocating for a "just teach the algorithm approach". My friend said something along the lines of "this is stupid and makes me contemplate homeschooling." Of course, I felt that I should at least chime in from a neutral standpoint addressing the pros, cons, and overall intent of the standards. Then, someone replied to me saying "You
say the intention is to create independent math thinkers. .... but by
frustrating children to the point if tears.... how about we take that
money we are spending on this foolish frustrating system.... and we
reduce class sizes so teachers can effectively. ... oh I don't know..
TEACH." I gave this woman a well-informed response, but she hasn't said anything back yet. :P
This dialogue was running through my head the entire time that I was reading this article. If parents are so convinced of what constitutes mathematical reasoning and the doing of mathematics, in what ways does this affect the classroom? Moreover, where does the unwillingness to accept that mathematics might be more than plug and chug stem from? How can teachers (who understand and appreciate the new standards) convince parents otherwise?

Vanessa,
ReplyDeleteI just had discussion just yesterday with a colleague on a similar topic. He has two children just beginning elementary school, and has taken it upon himself to try and help other parents with the fact that they might not immediately recognize the math their kids were learning. His approach was to draw a parallel to music: many kids have parents who are not musicians, but still think that music class is valuable - you need to trust your kids (and their teachers) that they will figure it out.
Perhaps it is because the perceived stakes are higher. We don't get to leave math class behind; it follows us to high school. When I run into such arguments typically try to point out that the `old' algorithm way is what left so many of our current adult population with a poor relationship with math - don't they want better for others? I suppose if children are crying in frustration that might be a difficult point to make...
I often wonder why there is this consistent negativity/struggle associated with mathematics. Is it because in other subjects, subjectivity plays a larger role? In English, for example, you can struggle through writing a paper knowing that it's not the best, but it's not the worst. In math, if you're struggling to solve a problem you may get it wrong. So often on math tests, and other forms of assessment, students simply receive x's and checks with little to no other feedback.
ReplyDeleteIn response to your question, parents have a HUGE impact on their child's understanding and enjoyment of math. If a parent works with a child on a math problem in a positive manner, their child will see that even if someone doesn't understand something, they can still work at it and revel in the eventual (hopeful) understanding. If a parent sits down with their kid and says, "What is this new math?!? This is ridiculous!" clearly that same attitude will present itself in the classroom.