Whether you're talking state tests or just meeting with your team to plan the next math unit, the conversation inevitably turns to word problems. But it can be hard to know how to build math problem solving skills without resorting to pages of boring story problem practice.
These days word problems aren't the basic one-step wonders that many of us dealt with as students. Instead, multi-step story problems that require students to apply multiple concepts and skills are incorporated into instruction and state assessments.
Understanding brain research can help simply the process of teaching this challenging format of math problem solving to students, including those that struggle.
What research says about building master problem solvers in math
Have you seen how many math skills we are required to teach these days? No teacher truly has enough time to build the critical math skills AND effectively teach problem-solving…or do they?
Research would argue, we are going about these tasks all wrong. Instead here's what the brain research says about the must have elements for word problem mastery.
Finding #1: Becoming a master problem solver requires repetition.
Duh, right? Any good teacher knows this…but what's the best recipe for repetition if you want students to master word problems? How much practice? How often?
Let's start with the concept of mastery.
What it takes to become an expert
In the 1990's, Anders Ericsson studied experts to explore what made some people excel. Findings showed a positive correlation between the amount of deliberate practice (activities that require a high level of concentration and aren't necessarily inherently fun) and skill level.
In other words, the more practice someone gets the more they improve. This became the basis of Malcolm Gladwell's 10,000-hour rule, which stated that it takes 10,000 hours to make you an expert in a field.
But what should that practice look like? Is it better to have a long, deep dive into word problem or do short bursts of practice do more for long-term understanding?
Building better word problem practice
We can look at Ebbinghaus' work on memory & retention to answer that. He found spacing practice over time decreased the number of exposures needed. In other words, small amounts of practice over several days, weeks, or even months actually means you need LESS practice than if you try to cram it all in at once.
For over 80 years, this finding has stood the test of time. While research has shown that students who engage in mass practice (lots of practice all at once) might do better on an assessment that takes place tomorrow, students who engage in repeated practice over a period of time retain more skills long-term (Bloom & Shuell, 1981; Rea & Modigliani, 1985).
And how long does research say you should spend reviewing?
How long should problem solving practice really be?
Shorter is actually better. As discussed earlier, peak attention required for deliberate practice can only be maintained for so long. And the majority of research supports 8-10 minutes as the ideal lesson length (Robertson, 2010).
This means practice needs to be focused so that during those minutes of discussion, you can dive deep – breaking down the word problem and discussing methods to solve.
Applying this finding to your classroom
Less is actually more as long as you plan to practice regularly. While students may need a great deal of practice to master word problems, ideally this practice should be provided in short, regular intervals with no more than 8-10 minutes spent in whole group discussion.
Here are a few simple steps to apply these findings to your math classroom:
- Find 8-12 minutes in your daily schedule to focus on problem-solving – consider this time sacred & only for problem-solving.
- Select only 1-2 word problems per day.
Finding #2: Students who are challenged & supported have better outcomes.
Productive struggle, as it is called in the research, focuses on the effortful practice that builds long-term understanding.
Important to this process are opportunities for choice, collaboration, and the use of materials or topics of interest (which will be discussed later).
This productive struggle also helps students build flexible thinking so that they are able to apply previously learned skills to new or unfamiliar tasks (Bransford, Brown, & Cocking, 2000).
“Meaningful learning tasks need to challenge ever student in some way. It is crucial that no student be able to coast to success time after time; this experience can create the belief that you are smart only if you can succeed without effort.”
It is also critical to provide support and feedback during the challenging task (Cimpian, Arce, Markman, & Dweck, 2007). This prevents frustration and fear of failure when the goal seems out of reach or when a particularly challenging task arises.
Simple ways to build productive struggle into your math classroom
Giving students a chance to struggle with challenging word problems is critical to building both their confidence and skills. However, this challenge must be reasonable or the learner's self-esteem will falter, and students need support and regular feedback to achieve their potential.
Here are a few simple things to try:
- Select problems that are just at the edge of students Zone of Proximal Development.
- Scaffold or model with more challenging problems to support risk taking.
- Give regular feedback & support – go over the work and discuss daily.
Finding #3: Novelty & variation are keys to engagement.
When it comes to standardized testing (and life in general), problems that arise don't come already labeled with the skills and strategies required to solve them.
This makes it important to provide mixed practice opportunities so students are focused to ask themselves questions about what the problem is asking and what they are trying to find.
This type of variation not only supports a deeper level of engagement, it also support the metacognitive strategies needed to analyze and develop a strategy to solve (Rohrer & Taylor, 2014).
The benefits of novelty in learning
A 2013 study supports the importance of novelty in supporting reinforcement learning (aka review) as well. The findings suggested that when task variation was provided for an already familiar skill it offered the following benefits:
- reduced errors due to lack of focus
- helped learners maintain attention to task
- motivated and engaged student
Using variety to build connections & deepen understanding
In addition, by providing variations in practice we can also help learners understand the skills and strategies they are using on a deeper level.
When students are forced to apply their toolbox of strategies to novel problem formats, they begin to have to analyze and observe patterns in how problems are structured and the meaning that brings.
This requires much more engagement than being handed a sheet full of multiplication story problems, where students can pull the numbers and compute with little focus on understanding.
Designing word problems that incorporate variety & novelty
Don't be afraid to shake things up!
Giving students practice opportunities with different skills or problem formats mixed in is a great way to boost engagement and develop meta-cognitive skills.
Here's a few tips for trying it out in the classroom:
- Change it up! Word problem practice doesn't have to match the day's math lesson.
- Give opportunities to practice the same skill or strategy in via different formats.
- Adjust the wording and/or topic in word problems to help students generalize skills.
Finding #4: Interest and emotion increase retention and skill development.
Attention and emotion are huge for learning. We've all seen it in our classroom.
Those magical lessons that hook learners are the ones that stick with them for years to come, but what does the research say?
The science behind emotion & learning
Neuroscientists have shown that emotions create connections among different sections of the brain (Immordino-Yang, 2016) . This supports long-term retrieval of the skills taught and a deeper connection to the learning.
This means if you can connect problem solving with a scenario or a feeling your students will be more likely to internalize the skills being practiced. Whether this is by “wowing” them with a little known fact or solving real-world problems, the emotional trigger can be huge for learning.
What about incorporating student interests?
As for student interests, there is a long line of research supporting the benefits of using these to increase educational outcomes and student motivation (Chen, 2001; Chen & Ennis, 2004; Solomon, 1996).
Connecting classwork with student interests has been shown to increase students' intentions to participate in future learning endeavors (Chen, 2001).
And interests don't just mean that love of Pokemon!
It means giving social butterflies the opportunity to work collaboratively.
Providing students with opportunities to manipulate real objects or create models.
Allowing kids to be their authentic selves while digging in and developing the skills they need to master their learning objectives.
What this looks like in a math class
Whenever possible, evoke emotion and use student interests to engage the brain in deep, long-lasting learning.
This will not only help with today's learning but will also promote long-term engagement, even when later practice might not be as interesting.
Here's how to start applying this research today:
- Find word problems that match student interests.
- Connect real-life situations and emotions to story problem practice.
- Consider a weekly theme to connect practice throughout the week.
Finding #5: Student autonomy builds confidence & independence.
Autonomy is a student's ability to be in control of their learning. In other words, it is their ability to take ownership over what the learning process looks like and how they demonstrate mastery.
Why students need to control their learning
Research shows that providing students a sense of control and supporting their choices is way to help engage learners and build independent thinking. It has also been shown to increase intrinsic motivation (Reeve, Nix, & Hamm, 2003).
However, this doesn't mean we just set kids loose to learn on their own. Clearly, some things require repeated guidance and modeling. Finding small ways that students can take control of the learning process is much better in these instances.
We know that giving at least partial autonomy has been linked to numerous positive learning outcomes for students (Wielenga-Meijer, Taris, Widboldus, & Kompier, 2011).
But how can we foster this independence and autonomy, especially with those students who struggle to self-regulate behavior?
Fostering independence in students who struggle to stay on task
Well the research says there are several conditions that support building toward independence.
The first (and often neglected) is to explain unappealing choices and why they are one of the options.
When it comes to word problems, this might include explaining the rationale behind one of the strategies that appears to be a lot more work than the others.
It is also important to acknowledge the negative feelings students might have about a task or their ability to complete it. While we want them to be able to build independence, we don't want them to drown in overwhelm.
By providing emotional supports, we can help determine whether a student is stuck with the learning or with the emotions that come from the cognitive challenge.
Finally, giving choices is recommended. Identifying choices that both you and the student can live with is an important step.
Whether this is working in partners, trying an alternative method, or skipping a problem and coming back, students need to feel like they have some ownership over the challenge they are working through.
By building in opportunities for autonomy, and choice, teachers help students build a sense of self-efficacy and confidence in their ability to be successful learners across a variety of contexts (McCombs, 2002,2006).
We know this leads to numerous positive outcomes and has even been linked to drop-out prevention (Christenson & Thurlow, 2004).
Fostering autonomy in your classroom
You're not going to be able to hold their hands forever.
Giving opportunities to work through challenges independently and to feel ownership for their choices will help build both confidence and skills.
Here's how to get started letting go:
- Give students time to tackle the problem independently (or in partners).
- Don't get hyper-focused on a single method to solve – give opportunities to share & learn together.
- Provide appropriate supports (where needed) to build autonomy for all learners – like reading the problem orally.
Finding #6: Students need to be taught how to fail & recover from it.
Despite Ericsson's findings discussed early on in this post, talent does matter and it is important to teach students to recover from failure because those are the moments when they learn the most.
A 2014 study by Brooke Macnamara analyzed 88 studies to determine how talent factored into deliberate practice.
Her findings show what we (as teachers) already know, students may require different amounts of practice to reach the same skill level…but how do we keep those struggling students from keeping up?
Growth mindset research gives us some insight into some ways to support and encourage these students when it comes to math problem-solving and includes harnessing the power of failure through “yet”.
You might not be able to do something yet, but if you keep trying you will. This opens the door for multiple practice opportunities where students learn from each one along the way.
And what about the advanced students?
Many of these students have not experienced failure, but when it comes to complex word problems they may have met their match.
To support these students, who may be experiencing their first true challenge, we need to have high standards and provide constructive, supportive feedback on how to grow.
Then we need to give them space to try again.
There is a great power in allowing students to revise and try again, but many times our grading system discourages being comfortable with failure.
Building the confidence to fail in your classroom
Many students feel the pressure to always have the right answer. Giving students the opportunity to fail safely means you can help them learn from these failures so they don't make the same mistake twice.
Here's how you can safely foster growth through failure in your classroom:
- Build in time to analyze errors & reflect.
- Reward effort & growth as much as, if not more than, accuracy.
- At least initially, skip the grading so students aren't afraid to be wrong.
Getting started with brain-based problem solving
The brain research is clear.
Spending 45 minutes focused on a sheet of word problems that all follow the same format isn't the answer.
By implementing this research, you can actually save yourself time and the frustration that comes from a disengaged class.
I've created my Daily Problem Solving bundles based on this research to save you time.You can get each month separately or buy the full year bundle at major discount.
Currently I offer bundles for:
- 2nd Grade
- 3rd Grade
- 4th Grade
- 5th Grade
- 6th Grade
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