The Reflective Educator

Education ∪ Math ∪ Technology

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Day: July 5, 2013

Students who are uninterested in math

Results of the NCTM survey on why math is hard to teach

Source: NCTM Smartbrief

 

It seems to me that "students who are uninterested" is a problem of pedagogy. If that is what is holding students back from learning mathematics, then you should make your lessons more interesting. "Students who are disruptive" seems like another way of phrasing the first problem, but having worked in a challenging school myself, I do remember students who were challenging no matter how much I stood on my head to make my lesson interesting. That being said, both of these challenges are significantly less with good teaching. Students who are uninterested in what you teach are a sign that you should change your approach.

"Students with diverse academic abilities" is a serious problem, but it is (at least in part, see below) solvable. The basic trick is this, don’t teach everyone the same thing at exactly the same time. I would approach this particular issue with low-entry / high ceiling problem solving activities in small groups and then I workshop solutions with individual groups as I move around the classroom.

"Lack of a parental involvement" is definitely a huge issue. I think if you have interesting lessons and develop positive relationships with your students though you can mostly counteract the effects of parental apathy. My objective here is to set high standards for my students and their relationship with math like what I have for my own son.

"Lack of teaching resources." Uh… Have you heard of the Internet? Being a part of the Math Twitter Blogosphere means that lack of resources is never a problem. In fact, more resources than I can possibly use is more frequently the problem. Edit: It occurred to me that this may mean lack of physical resources, like pencils and paper, etc… in which case someone, somewhere, needs to rethink the priorities for their schools. Teachers and students should not lack for basic supplies.

For me the "students with special needs" problem can partially be addressed with using a problem solving approach with media that asks questions (like what Dan Meyer is curating with 101qs.com) for students for whom literacy is their barrier to mathematics. However, students with dyscalculia or who are many, many grade levels behind in their understanding of mathematics probably need more support. Having worked in a school that had minimal support for students with special needs many years ago, I definitely empathize with people who see this as a problem. 

The thing is about all of these responses is that not one of them is how I would answer this problem. For me, the things that I feel impose the greatest limitations on how I would teach (and most importantly, what I would teach) are the standards we are assigned to teach and the way students will be eventually externally assessed on those standards. I can certainly still teach in a creative way given these limitations, but they definitely place limitations on how I teach.

Designing open-ended tasks – Part 1

Designing an interesting and open-ended task is relatively easy. The challenging part comes when you attempt to use the task and learn something as a teacher about what your students understand.
 

Graph of inverse relationship between open-ended tasks and formative assessment tasks
This graph represents the main issue that comes up when designing open-ended tasks for students to use; the more open-ended a task is, the less information you are likely to be able to gain from using the task. You can gain insight into what your students are thinking when they are working on an open-ended task, but chances are much greater that they have a much wider variety of insights and misconceptions that will come up during their time working on the task.

If we define "formative assessment" as "any tool used by teachers to gain insight into their student’s thinking and use that information for future planning of teaching and learning activities," then the open nature of these tasks helps with gaining insight into student thinking, but it makes planning future activities more challenging since we could potentially end up with much more information about what each student knows how to do, but potentially less information about what each student does not know how to do.

The very task that gives students the freedom to try many different potentially successful mathematics techniques to solve the problem unfortunately also limits how much of what we know of those paths that students chose not to follow. Did a student not use an algebraic approach because they don’t know algebra? Or did they use a non-algebraic approach because they didn’t think of an algebraic technique? Did they use a table to solve the problem because they love using tables? We have no time-efficient way of answering these questions.

One possible solution is to make sure that each time students work on a task, they have the opportunity to share their different solutions with each other. This way students who tend to use graphs to solve problems will see algebraic solutions to those same problems. Students who generally solve a problem using a table of values will see how other students used a diagram instead. By sharing different solutions created from the students amongst your class, students may be able to add to their own toolbox of methods they can use to approach problems.

The problem with this last solution is that this only works when the students are working on essentially the same problem; it will fail to work when the task is so open-ended that students have sufficient influence over the questions they ask. Maybe there are some other solutions to this problem?

In a future post, I will take a task and create different versions of it, sliding along the scale of open-endedness, and hopefully this will lead to some insights as to the challenge involved in open-ended tasks.