The “One Size Fits All” Approach to Teaching Mathematics

This is just another post about grades, feedback and “good” math questions. I’m at a loss, so feel free to dive in. The context of this post is about providing students with one or two rich open ended math problems instead of quantities of more of the same. You know, textbook work. Please consider the following (sings Bill Nye theme):

So I wonder: until we have a major assessment and evaluation reform, prompting math questions will not be the norm as prompting questions are difficult to evaluate? When I say “prompting” I mean rich, open ended math tasks instead of the quantities of repetitive questions where a small number has changed but the procedure has not.

The math lesson formula – Question, Example, Solution, Practice, Practice, Practice – where we tell students what strategies to use – is quite structured and easily falls into a rubric category. It’s a safe go to, parents understand it and we can quantify it with a numerical value. Besides, the textbook follows this procedure. I am curious about the use of levelled rubrics when so many teachers have to assign actual percentages come report card time.

I also wonder why we look to changing math questions first, rather than how to evaluate them. If we never give a primary student a level 2, will they always approach rich tasks with an open mind rather than the “I’m no good at that” mindset? After all, can’t we “assess” without giving a grade?

Why is it OK to give one open ended prompt in English class?

“Why do you think_____. Use details from the text and your own ideas to support your answer for a final mark out of 30.”

Could you imagine:  “What is the surface area of this bizarre meteor. Explain your mathematical reasoning and thinking to justify your answer for a final mark out of 30.”

How can we move away from teaching strands in isolation to giving rich problems? I’m all for the “Rich Problem” instead of “Math Topic” approach but this requires the teacher to have an incredibly firm understanding of their curriculum so they can assess and evaluate it when they see it which isn’t always easy.

Markbooks are in structured rows and columns and gaps provide levels of discomfort. Isn’t it much easier to teach isolated strands and “tedious” math questions? I’m not sure we have evolved passed the “fill the mark book” mindset. If that’s the goal, how many rich probing math questions will teachers give?

If we continue to provide rubrics, even great ones, won’t there always be minimum and maximum limits to learning?

If we have to provide grades, won’t we always need concrete evidence on a levelled numerical scale rather than an open ended unbiased solution?

If we focus strictly on feedback and provide open ended problems with various methods of solving them, will we improve the mathematical “literacy” of our students? Don’t they need some fundamental understanding of “tedious” math in order to solve rich tasks?

Without a general consensus, are we failing our students when they progress from grade to grade and from teacher to teacher?

Whose job is it to “prepare” students for what comes next?

Are we doing our best to prepare for the kinds of students coming to us?

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3 Responses for this post

1. Kendra Grant
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Great questions. Given the name of the presenter I thought you might sing “Hip to be Square” 🙂
I really like this TedTalk “Math class needs a makeover” by Ted Meyer. You may have already seen these resources – there is some great content. http://www.curriculum.org/k-12/en/projects/leaders-in-educational-thought-special-edition-on-mathematics I also like Dr. Christine Suurtamm – A Balanced Approach video that talks about the myth that Ontario is all about “discovery math”.

2. Nicole Beuckelare
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Some great points were brought up in your post. There is no denying that many parts to this system has some flaws, some gaps and some room for improvement. Although, in the defense of where we are at…change is a slow process. We can’t expect to take a teaching strategy or topic and expect full implementation, understanding and change without some much needed time to review, experiment and reflect on the process.

I feel confident saying that over the last few years there has been a conscious shift in the way we approach teaching mathematics in general. Although I’m not convinced that some of these strategies are new and upcoming. I have a feeling that maybe the role technology, sharing and being more open about our teaching triumphs and struggles has just made these wonderings more open and public. Regardless of the reason, I think that many educators struggle with the same questions you have.

I’ve argued this point before, that until there is widespread change in practice when it comes to the need for grades, grades will always be a driving factor for the majority of our students. Students need good grades to get into post-secondary education, they need passing grades to achieve that secondary school diploma necessary for the majority of jobs in our society. Until we create a system that allows for succession and entrance into programs based on related skill demonstrations or demonstration of learning, marks will stand in the way.

Personally, I would rather teach, work with or employ an individual who can demonstrate their learning, work thru problems and communicate clearly over an individual who has good marks and no team skills. The process an individual goes thru to achieve a goal and to experience success means more to me than the result they get on a test or assignment given to them at a moment in time under varying degrees of pressure.

In my math class, this means allowing students time to retry, to communicate their thinking and to be able to demonstrate their learning in various ways. This proves to be a very tricky task. The structure of our reporting systems and the prior understanding of parents makes it difficult to report on student achievement and to get buy in that tests and quizzes are not the most effective way of assessing how a student learns. Rigid reporting timelines restrict the ability for students to continue working on topics and strands they need more time to grasp. The structure of our resources don’t lend well to the idea of a spiralled curriculum either.

I personally think there is a balance between having students learn fundamental mathematical principles and having a chance to work with them repetitively, and creating an inquiry based model for applying their knowledge and skills. I know that there are some structures and topics that students need to master before it is possible for them to apply that learning to broader questioning and probing. I also know that we need to offer more opportunity for students to communicate their math knowledge at a young age.

I question how we can retain the sense of wonder, questioning and learning that children naturally show at young ages. How do we get them to keep that inhibited desire to know, to learn and to question as they move thru the school system? I want my secondary students to ask questions like my 6 year old does. Natural curiosity exists…how do we build an educational environment to sustain it in the majority of children, not just a few?

The one thing I do know, there are many educators who are very vocal, public and dedicated to helping create resources, discussions and debates to encourage a shift in the way we teach and assess math. I’m sorry I don’t have the answers for you Brian…but I do know that there are good things happening in classrooms all over the globe. The more we share, question and learn, the better things will be for our students.