Help grow your students into strong math thinkers who are able to persevere in problem solving using the tips included here. Plus, grab a free printable poster set for your classroom!
Today is the start of a short series here that I’m calling, “Build Math Habits.” Although we certainly want to teach the math content and cover all the necessary skills, there are other aspects of our math teaching to consider, not in addition to the content, but alongside the content we’re already teaching. These are called the “Standards for Mathematical Practice” and I believe helping kids develop these habits as they explore, learn and grow as mathematicians will help them become strong thinkers and problem solvers.
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I’m excited to explore these standards a bit and think about how we can help students to develop these habits in the math classroom. I am addressing these standards because I believe that developing these practices in our students is what will lead to deep understanding (so they are not just doing math, but understanding math).
Now, today I want to focus on the first two math practice standards-what they mean and how we can foster these practices in our students.
1. Make sense of problems and persevere in solving them and
2. Reason abstractly and quantitatively.
There are SO many things we could discuss and unpack in those two short sentences, but today I want to focus on perseverance.
First, let’s consider what perseverance means. That’s a pretty big ask for kids–to persevere in solving a math problem even when they don’t understand, even when they feel stuck and even when they think they don’t have any strategies left to try.
But I would suggest that all the other mathematical practices flow out of an attitude of perseverance. A willingness to press on and not give up, even when it’s hard.
So how do we foster a classroom culture where kids are ready and willing to persevere? Where they know and feel comfortable making mistakes because they’d rather make a mistake than quit completely?
As with all of these mathematical practices, this is not something that can happen overnight. You can’t just tell kids to persevere or to keep trying and expect a complete change of attitude. But you can certainly be consistent in how you present problems and how you support students so that there’s so much excitement and internal motivation that perseverance begins to happen on its own.
Start With the Right Problems
I think it begins with what problems you present to students and when/how you present them. If you give students an interesting problem that is just a little beyond their ability (something related to what they already know, but hasn’t been explicitly taught yet), you draw them in and provide an opportunity for productive struggle.
This will get them interested, because rather than telling them “this is what you do…” you’re asking them, “how could YOU solve this?” and you’re putting the ball in their court. You’re building their self-esteem by showing them you have confidence that they can figure it out.
And if they get stuck? Provide just a little support to nudge them in the right direction, or ask just the right question to spur them on.
For example, if you’re teaching first grade and your students are comfortable adding within 20, you might begin class by asking them to solve the problem 36 + 21. How might they use what they know to figure it out? What tools could they use to help them?
Or if you teach fourth grade, and your students have already been introduced to fractions, but you want them to think more deeply about how they relate to other fractions and whole numbers, you might ask a series of “which is greater?” problems. For instance, which is greater, 1/2 or 1/4? Which is greater, 3/4 or 1? Which is greater, 1/3 or 2/6? Knowing how to represent each of these fractions, how can they justify their answers?
Having opportunities to engage with new and interesting problems will not only help kids to persevere, but all the other mathematical practices begin to flow out of that perseverance.
By being challenged with a new or interesting problem, over time kids will learn to make sense of the situation and use what they know to think about it. They will learn to reason abstractly about the problem, discuss it in mathematical terms and justify their thinking. They will begin to notice patterns and increase in fluency and flexibility with numbers.
So how do you choose good, interesting problems? This doesn’t have to be time consuming or require tons of prep and research. It might just be choosing a problem from the next chapter of the textbook. It might be choosing a relevant word problem that relates to their everyday life. Or it might be more of an open ended challenge that has multiple possibilities.
Challenge Your Advanced Learners
And if you have kids who don’t need help persevering because they are a math whiz and the first one finished everyday? Ask a simple question to remind them they are never finished learning and exploring: How else could you solve that problem?
This will push them to persevere in seeing the problem a different way–to look for a different strategy, a new visual or apply a different tool to solve it, which will in turn give them a deeper understanding of the concepts.
Resources to Help You Get Started:
Ready to get started? The following resources will help you find rich tasks and problem sets for your students, and the word problem templates will help kids to make sense of the situation in word problems.
- Explore rich math tasks here
- Grab the word problem solving templates here
- Try an open ended challenge such as this set of Which One Doesn’t Belong?
- Read the book, “Productive Math Struggle: A 6 Point Action Plan for Fostering Perseverance” (I just discovered this gem of a book today…I’ve already started reading and it is so good!)
One helpful quote that I will leave you with today:
“Navigating productive struggle is hard and complex. It takes time. Student struggle is not something that can be ‘fixed’ by the teacher. It is a process that is facilitated by the teacher.”
Ready to Dig Deeper?
If you are loving this conversation and want to learn even more about choosing rich tasks, teaching through problem solving and inquiry and helping your students to make sense of word problems in meaningful ways, I go into much more depth than I had time for here in my courses, Problem Solved: Teaching Math Through Inquiry and Problem Solving and Making Sense of Word Problems.
Although all of my courses are available separately, they are truly designed to work together to provide a foundation for math teaching in K-8. All together, the 6 courses include 8 hours of professional development, which you have lifetime access to. If you work through one course per week, you could easily complete all of them.
FREE Math Practice Standards Poster Set
Want to explain these math habits to your students? This fun and free set of posters provides a springboard for discussion as well as a visual reminder all year long.
There are two versions included in this pdf file. One includes a cursive font and the other includes only manuscript fonts so you can use these with younger students.
I’ve also adjusted the wording of some of the standards so that is uses more kid friendly language.
Grab this free poster set by entering your email below!
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