As teachers, we know that not every math problem-solving method/strategy speaks to every learner. Introducing a variety of problem-solving strategies and tools, and allowing learners ample time to grapple with them is paramount to math success. It's this grappling or "productive struggle" that encourages learners to attack a problem in a way that makes sense to them; it allows them to build perseverance through trial and error and practice using a variety of strategies. As each learner attempts to solve a problem or learn a new strategy, they ask themselves questions like: What is the problem asking me to do? What information is provided? What part do I understand and what part is giving me trouble? It's these types of questions that engage learners and provide an opportunity to gain a deeper understanding of the structure of a problem because they're given the opportunity to attack it on their own. Productive struggle helps learners develop important learning habits, including but not limited to perseverance and flexible thinking. Teaching learners to embrace the process of working through a problem, thinking outside the box, and not getting discouraged when they initially fail is essential to their success as a math learner.
When learners understand the purpose behind the struggle and embrace the idea that their efforts must be focused and working toward achieving a goal, it can change feelings of hopelessness to empowerment. This week's guest bloggers reflect on the successes of their own productive struggles.
I really struggled with adding and subtracting like and unlike fractions. I think I knew how to do it all along, but my brain just blanked out at so much information, I couldn't pick out the parts of it that I understood and which parts I didn't quite understand. I got through this struggle when I gave myself some time and put some thought into really focusing on just one part of a problem at a time. After a while, everything just came to me, like I switched on the lightbulb in my brain. It felt so good to finally understand something I wasn't able to understand for so long. If my peers were struggling with something in math, the advice I would give them is to not expect to understand everything right away. I would tell them to slow down and take the time to realize that it's totally okay to struggle with something that your classmates or friends aren't. Everyone's brains learn differently and work at a different pace. - "Glisten"
Something I really struggled with in math was when we were adding fractions. I wasn't sure how to get the same denominator. I got through it by practicing, not wasting time, and working with others. Now it's easy to add fractions with unlike denominators! Some advice I would give to someone who is struggling with fractions would be to not give up. - "Cat"
I was struggling with comparing and adding fractions a lot, so I started to use the rectangle fraction manipulatives to help me make sense of fractions. After a couple of weeks, I didn't really need the manipulatives anymore and now I can do it on my own. If a classmate of mine was struggling with fractions, I would try to teach them the strategy that worked for me, and if they are still struggling, I would have them try a different strategy. - "Clover"
Struggle time in math is really helpful, especially when we were learning about division. I was trying to find a good strategy that I could understand and had spent a week trying to figure out the strategy that made sense to me. I finally discovered the magical strategy of the Big 7 Method! From then on, I could solve any division problem. If you are struggling with division, it's okay. You will figure it out at some point, as long as you try new methods and don't ever give up. - "Dune"
The advice I would give to my peers who are struggling with something in math is to ask for help from a teacher, focus on what is being reviewed, and to participate even if you are not sure if you have the right answer. - "Aloha"
In math, I struggled with fractions for so long. I got through it by working on fractions and practicing with them almost every day until I got better. My advice to someone who is struggling with fractions is to never give up because you will eventually get it. - "Yah"
Something I really struggled with in math was double-digit multiplication. I kept messing up when I was adding up the numbers, so I would get the answer wrong. I got through it by asking the teacher for help if I couldn't figure out the answer myself or if I knew the answer was wrong. My advice to my classmates would be to never be afraid to ask for help because that's what I did and my teachers really helped me to find out how to fix my mistakes. - "Rianna"
In math, I was struggling with double-digit multiplication because I kept forgetting to drop the zero. I helped myself by spacing everything out correctly and then adding the zero. My advice to someone who is having trouble in math is to take it easy on yourself and take whatever time you need to figure things out. Don't rush. - "Lize"
Something I really struggled with in math was division. I really just did not understand how it worked. When we learned the Big 7 method, I could not figure out how to do it on my own. Ms. Davis and my dad both tried to help teach me the method, but when we had a division problem for our math warm-up, I would always get it wrong. I could not remember how to do it. Finally, I was introduced to the box method and it made much more sense to me. Now, I always get my math division warm-ups right! The advice I would give to my peers who are struggling with something in math is to be patient and try new strategies. Eventually, you will have success. - "Ritzi"
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