What does it mean for students to have a choice in math? After my last post about struggling students, it was interesting to see that the aspect of ‘choice’ was what really resonated, and was shared here in Aviva Dunsiger’s blog, and here on VoicEd Radio. This really got me thinking deeper about ‘choice’ in math.
The word ‘choice’ can be difficult in math because it is often laden with differing expectations and pre-conceived notions. Are we talking about students choosing the math problem? Choosing the type of problem? Choosing the strategy? Choosing the right numbers? The right operations? We can apply student choice in so many ways.
I wanted to investigate the aspect of choice in math. More specifically, how students come to select a mathematical strategy.
For the purposes of this blog post, when I discuss choice here, I am thinking about how we help students understand and make choices about where and when to use the most appropriate strategies. I also think that it is important to draw the distinction between helping students to execute a strategy correctly, versus selecting a strategy to implement. There are strategies that students will execute very well, and will be able to use to obtain the correct answer. However, it is the latter that I wish to focus on here, because I think it is imperative that before we help students to solve correctly, we want them to be able to select a strategy. And if students are proficient with using strategies, we want to push them even more with math problems that force them to dig deep and consider what strategies they need to use.
When we talk about selecting a strategy to use in math, we hope that students can develop along a continuum of strategies ranging from inefficient to efficient that can help them solve a math problem in a timely fashion. There are many trajectories and continua of math development, my favourite is the Lawson Continuum.
Efficiency is important. If students are unable to use a strategy efficiently, then they are more likely to choose a strategy that is NOT going to work for them. Therefore, it becomes very important that we help students not just learn the strategies, but also become efficient in them, and understanding how they help in solving different types of math problems.
Some strategies will be more efficient than others, and depending on what strategy a student chooses, this will tell us a lot about where a student is developmentally. When we know this, we can make sure that we implement the opportunities and next steps needed to continue to develop.
Sometimes, however, we will learn that a student is developmentally unable to choose. There are several variables that can affect the ability to choose an appropriate strategy.
The first issue surrounding student choice includes their ability to:
- read and understand the problem, and
- implement a strategy.
In order for students even start with being able to select a strategy, they need the ability to read and understand the information in the math problem, THEN they need to develop the ability to implement various strategies. Therefore, students might need different interventions and scaffolds to first understand the math problem, then they will need a repertoire that they could try to implement BEFORE they are able to make a selection. Their ability to implement a strategy will depend on what they have learned, practiced, and their mathematical mindset.
What can we do to build this repertoire of strategies that they can regularly practice?
Number Talks are just one way that students can learn about mathematical strategies. The power behind Number Talks lies in the visual representation of student thinking. This paired with the ability to help students listen, and engage in productive discourse helps them to make explicit connections with strategies. This modelling and practice will help students to become aware of the choices available, while at the same time allowing them to understand how other students think mathematically. Other ways to help students become aware of strategies include mini-lessons, and guided practice of strategies applied to various problem structures. (You may have great ideas yourself that I hope you will share here.)
However, some students will continue to struggle in their ability to choose an effective strategy. Math anxiety is a factor for some students that limits their ability to choose.
Math anxiety is another factor that can negatively diminish the ability to choose an appropriate strategy. We all either know first hand, and / or have witnessed the effects of anxiety in our students when it comes to math. I know that when I feel anxious, I become concerned about how others are evaluating my choices. Other intrusive thoughts may accompany anxiety, and this greatly reduces working memory for students. They may also feel like they have to choose the same strategy as their friends – or choose the one that their teacher is looking for. These types of intrusive thoughts greatly reduce the ability for a student to process the math problem at hand and make the best choices.
But perhaps choice is best discussed in terms of how strategy selection occurs at different developmental stages in math. Some students may be developmentally ready to recognize a strategy that is right for them, and educators can track this and assess student progress and decide upon the next steps to become more efficient.
However, other students will need extra support. They are our struggling students.
While many students are able to choose the most efficient strategy, others will need the strategy to be chosen for them – e.g., like the student who has a learning disability in visual-spatial/visual-motor skills who needs explicit visuals and precise strategies chosen for them for a while to help them learn the strategy to solve a particular math problem. Why not modify a math problem, or provide a visual of the strategy that a student should use, until they are able to commit the strategy to memory and decide how to use it in a problem situation on their own.
My question becomes, how do you teach strategies, and how do you help your students choose which ones to use, and use them efficiently?