Why I Teach Students Multiple Strategies to Solve Math Problems
I am a big proponent of teaching students multiple strategies to solve problems and letting students choose the best strategy that works for them. I love it when students can take ownership of a certain way to solve a problem and find success. They really understand why it works and can then apply it to a variety of other problems. Here are some reasons why I teach multiple strategies to solve computation math problems.
Mathematical Thinkers Use Mental Math Strategies to Solve Problems
Skilled mathematical thinkers have a variety of problem-solving strategies in their toolbox and can access them quickly and efficiently. They understand that the same strategy doesn’t work for all problems and are able to apply the best, most effective strategy
I want all my students to become skilled mathematical thinkers who believe they are good at math.
Rote Math is Boring
When I was in school, I remember the teacher writing how to solve a problem on the overhead and we copied down how she did it in our notebooks. We were supposed to copy exactly how she solved the problem and apply it to all the problems on a page in our math books.
Do you remember being taught that way? Generally, there was only one right way to solve a problem. I wonder how much I was missing by being taught just one way. I did okay in math, but never really liked it. It was boring and mundane, and we did the same thing every day.
Fast forward to my first few years of teaching. I became involved with some professional development that taught me all about the different ways to solve multi-digit addition and subtraction problems as well as work with fractions.
My eyes were opened to a whole new world. I found out that I was good at math. I discovered, by being taught a few key foundational ideas, that I could approach a difficult problem and reason through it, figuring out my own way to do it. I loved math. That is what I want for my students.
Misconceptions about Teaching Multiple Strategies to Solve Math Problems
Whenever I post this photo on Facebook, it always gets a ton of attention, both positive and negative. I get the, “Why don’t you just teach them how to add” comments, the “What an awesome idea” comments, and everything in between.
I love using it to open up the conversation about teaching multiple strategies to solve problems. It is such a clear example of how to use 10 to solve addition facts.
You see teaching students how to solve problems using different strategies isn’t a new idea. Remember the new math in the 80s and early 90s? This was it. It came again in the early 2000s, too. Teachers have been teaching strategies to solve math problems for a long time.
However, the Common Core and many state standards have now made it more explicit, and in fact, encourage the use of multiple strategies before the traditional algorithm is taught. With new standards and professional development, the idea of teaching multiple strategies has come to the forefront again.
Should the traditional algorithm be taught? Yes. But, before it is given to students, they need to understand why the shortcut of the traditional algorithms works and what to do if it doesn’t (like figure out their mistake!).
It makes explicit what happens in our heads
It’s all about mental math. Most of us do it automatically at the grocery store when figuring out how much we want to spend. Although we can whip out our phones and use the calculator, it’s often faster to do it in our heads. Next time you figure out an addition problem in your head, think about how you solve the problem. Do you make a ten or round to the next friendly number? Do you estimate? Do you double or halve a number? How do you solve the problem?
I’ll bet you’re using some strategy that you’ve either invented or that someone taught you. You probably aren’t thinking about the traditional algorithm (although you might be if that’s all you’ve been taught).
I want all my students to become skilled mathematical thinkers who believe they are good at math.
Teaching students different strategies helps them transition between paper and pencil calculations and mental calculations. Most math problems can be figured out in our heads, even the really hard ones if we can hold all the numbers there. Students will find strategies that work for them. We just need to teach multiple strategies so students can find the ones that resonate with them.
That leads me to . . .
It helps students choose the most efficient strategy for themselves
Ideally, we want students to be flexible mathematical thinkers. We want them to be good at math and feel confident about their ability to “do” math. In order to do that, I teach students different ways to solve problems in the hope that one of the ways will resonate with each student.
Students are at different places in their mathematical journey. One of the best tools I have seen to explain this journey is Contexts for Learning. The Landscape for Learning outlines the pathways students can take to understand addition and subtraction and multiplication and division. Each pathway is different, but there are trends that occur.
There are a lot of words in these documents that you might have to look up, but the idea that I want to emphasize is that students are continually finding new ways to solve problems. Their mathematical thinking is not stagnant, but fluidly moving through different levels as they experience more and more problems. Teaching students different strategies to solve problems helps them see new, more efficient strategies that might resonate with them.
We want students to solve problems correctly and efficiently. Teaching different strategies will help them see different ways to solve problems and students will gravitate to the way that best meets where they’re at. Our job is to push them just a little bit further and become more and more efficient mathematical thinkers.
It provides scaffolding so that they can find a place that meets their needs
This is similar to the previous idea in that I want students to find strategies that work for them, but I also want to push students to experiment and look at new strategies that might be just beyond their reach.
In my blog posts all about different models and strategies for two-digit addition & subtraction, I go into more detail about different strategies for two-digit addition. These strategies scaffold learning for students so that they can transition from single-digit addition to multi-digit addition and deeply learn what happens to the place value when adding and subtracting.
Now there’s a fine line between scaffolding learning and providing a crutch. The key is always encouraging students to try something that is just outside their comfort level, which is called their zone of proximal development. We always want to push our students to go one step further, not too hard, but just enough that encourage them to learn more.
It motivates students to work at solving problems
Do you have those students who just don’t like math? Those who don’t think they’re good at math? That was me, as a kid.
I wasn’t motivated to work in math because it was boring. However, I have found that by teaching students multiple ways to approach problems, and then stepping away, just a little bit, my students will dive into the problems and start exploring. They are much more motivated to work during math than I ever was growing up. I have given students entry points into the problem and allowed them to approach it at their level, tackling it with the foundational skills that they know and understand.
I have empowered students to do math because I have taught them a variety of strategies to add to their toolboxes.
I teach multiple strategies to solve math problems because of it:
- makes explicit what happens in our heads
- helps students choose the most efficient strategy
- provides scaffolding so that students can find a place to enter into the problem-solving process
- motivates students to want to learn more.
What about you? Do you teach students multiple strategies to solve math problems? I’d love to hear your perspective on this topic in the comments below.
See the resources that I use in my classroom to teach students different strategies to solve math problems. Click on the image for a FREE sample of these resources.
Two-Digit Addition and Subtraction Products?
I also do this, despite the consistent negative feedback, the long term positive keeps me going. I am currently trying to put as much information and research together on the topic as I can find. I have found that this method really helps all of my students, especially my struggling ones that do not attach algorithms and equations to problems quickly, typically needing concrete introduction into a concept first. Great article!
Thank you so much! I too find that for my students who can’t remember an algorithm, this is quite effective because they can understand the math behind it all. I could always solve it via an algorithm, but never knew why it worked, nor did I understand that some problems were easier with a few changes (compensation). I wish I would have learned math this way in school.
Thanks for sharing this great article! I totally agree with teaching multiple strategies. Not all students will understand Math with just one method and you have to show them several ways so they can start to see what works best for them!
I completely agree with you! I live in Texas, we use the TEKS instead of Common Core. Our curriculum is also explicit in telling us to teach students multiple strategies. I’m a new Elementary Math Instructional coach, so I have parents and some teachers ask why we do this. I was in the classroom for 18 years and I saw the benefits of teaching multiple strategies. Before we taught multiple strategies, students were not taught to be thinkers. They just produced an answer after completing a series of steps, but didn’t know why. Now students are learning how numbers in math have connections and relationships. They are learning the why!!
Sorry, this is just a waste of time. This is going in reverse thinking, not forward progress. Students are getting bogged down in this nonsense. If I gave you directions from house A to house B, and it will take 10 minutes to arrive from A to B…why would you I give you a different set of directions from A to B, that still enabled you to get to A to B, just 15 minutes longer?
Writing ‘stories’ for division? This is absurd. Giving students multiple strategies? Why not just give them the one that is correct in the least amount of time. Having too many options in life is not always a good thing and can create doubt and confusion.
Complete waste of time in my opinion.
I truly appreciate you sharing your opinion. For some students the traditional algorithm makes sense and they understand the place value relationships of all of the numbers. Other students need to develop this understanding. Math isn’t about getting the right answer “in the least amount of time”. Yes, we want students to move toward efficiency and get to the point of using an algorithm, but until then, we teach and accept any strategy or pathway that students can explain. This also promotes flexible thinking, problem-solving, communication, and many other skills beyond just solving a problem to get an answer. Most of the time it’s not about the answer, but the process, especially in the younger grades.
I so agree with you. I find it confuses them even more.
I started doing this in my classes this school year. The first few months were a struggle. The kids are not used to “thinking”and they just want to learn the “technique”. But I held on to the success stories of other teachers I read and the evidence from various researches. Now, my students initiate in looking for “other ways” to solve a problem. They are now excited to share “their own strategy” that they have discovered themselves. And they become proud of each other when a student shares something that they have not predicted is possible. My students became addicted to multiple strategies! One time I introduced a problem on ratio and the students formulated ways on how to solve it beyond my imagination. Haha! This strategy works!!!
I teach 5th grade Math in the Philippines. 🙂
What do you do with the students who don’t want to learn multiple strategies but just beg you to “tell them what to do”? I have a son like that and their interest in learning math is zero. If there is even one moment of not understanding something he immediately gives up. He is not challenged by problem-solving but completely overwhelmed by it. Yesterday we were working on some homework from school on listing the factors of a number and then it asked to explain your thinking. He burst into tears and declared that he hates explaining his thinking, he just wants to write the answer and be done. Even my attempting to explain my thinking out loud stressed him out considerably. He actually is not too bad at math when he stays calm. But he hates problem solving and “strategies” with a burning passion!
This blog post is mainly written to classroom teachers who have students in their classroom at many different levels. Teaching multiple strategies helps all students learn. If your son isn’t struggling, he may not need an additional strategy to use. Perhaps putting him in a position of “helping others” might work as well. However, he should be able to explain his thinking. That’s different than teaching multiple strategies. He may not have the language or the words to explain his thinking. In that case, give him some of the vocabulary that he might need or some of the sentences and see if he can fill them in. Also, try to get him to explain his thinking in other contexts besides math homework.
Hey there! I am so sorry your son is having trouble explaining his thinking in math, but I am not surprised. Math in general has a language of its own, which makes it very challenging for many kids, when it comes to explaining their thinking. Math vocabulary is not part of our everyday language, but learning and practicing how to express mathematical thinking is important for deeper understanding and for language development, whether you speak English or are learning English as a second language.
ESOL teacher K-12
I am all for teaching students multiple strategies so they can find the way that works best for them. What I don’t understand is requiring students to demonstrate each method time and time again. If they find a strategy that works for them can’t they just use it? Requiring them to use strategies that don’t make sense to them makes them feel like they don’t understand math.