Targeting the standards for mathematical practice while teaching means incorporating instructional strategies that encourage students to make sense of mathematics! In the beginning of my teaching career, however, I was so focused on WHAT mathematics I would be teaching that I overlooked HOW my students would engage with this content. I often overlooked process standards, because I didn’t know how to explicitly teach them. However, during the switch from state standards to Common Core standards, I was introduced to Standards for Mathematical Practice. Still, I didn’t understand how I could develop these habits in my 4th grade students.
Countless workshops and professional developments later, and I was able to identify 9 key instructional strategies that helped me balanced the WHAT and the HOW of mathematics! In other words, I knew the content that needed to be covered, but I also knew how to design opportunities where my 4th grade mathematicians were DOING mathematics instead of memorizing rules and procedures.
My class looked like a madhouse at times and sounded like a circus, but the rich mathematical ideas my students came up with were worth it. It kind of made my job easier, because they were responsible for noticing relationships, justifying their answers, and questioning their peers. Looking back, I can see how the standards for mathematical practice really helped my students take ownership over their own learning!
What are the Standards for Mathematical Practice?
The Common Core Standards outline math habits that students should develop while attending school. These 8 Standards for Mathematical Practice are:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
Why are these standards important?
The standards for mathematical practice are important, because they teach students how to think like a mathematician! Part of mathematics deals with memorizing facts, but the magic really happens when you notice patterns across these math facts, generalize these patterns, and use them to create or evaluate new mathematical ideas.
In fact, this is the critical thinking we want our kids to develop in their early years, because it will help them become leaders in STEM!
Math Instructional Strategies
There are many instructional strategies that can help you target the standards for mathematical practice. Over the years, I’ve seen my kids come alive and engage with mathematics in exciting ways with just a few simple tweaks here and there. So, I decided to put a list of my favorite strategies, because SHARING IS CARING! 🙂
1. Ask non-routine problems.
One way to grow mathematicians in your class is to ask non-routine problems often!
It’s fine to explore a problem of the day, but sometimes these are review problems. I find value in these problems, but sometimes we need to push it a little further and add variety. My favorite inspiration for designing non-routine problems is to think about WHO uses math in their DAILY LIFE and in their WORK life. Then I create tasks that put students in that role!
For instance, a math unit can emphasize the mathematics that occurs during the school day. It could be calculating how much money we would need to serve breakfast and lunch in the cafeteria. Or, students could think about how the principals made a master schedule for each grade level. This could be the perfect context for time elapsed!
Going further with the scheduling idea, you might start by asking students if they like their schedule. I’m sure they’d wish recess was longer at the very least! A math challenge might be to create a new schedule for their grade level and pitch a proposal to the school principal for next year. Depending on how difficult you want to make the task, you could even explain that if your grade level changes then other grade levels may have to change as well. Students could work in groups to examine different grade level schedules.
What’s powerful about this is students feel like they helped create the math problem! They identified a “problem” in their school community and used math to get to the bottom of it!
Helping kids mathematize their surroundings is critical, interesting, and most of all rich! It definitely wouldn’t be a simple word problem they can use keywords to solve. Also, it prepares students to participate fully in their community as they grow older. It shows that math is meaningful and necessary and hopefully they’ll think it’s fun, too!
The first practice in the standards for mathematical practice focuses on persevering through problem solving and making sense of problems. Using math in real-world problem solving will definitely help students develop this habit.
2. Encourage students to use and reflect on multiple representations.
Three standards for mathematical practice focus on representations:
- Model with mathematics
- Use appropriate tools strategically.
- Attend to precision.
Using multiple representations is key for developing these thinking practices! Having kids reflect on concrete manipulatives, pictures, and abstract representations at the same time can allow them to make powerful connections! Using multiple representations can help students develop number sense, become more flexible with operations, and understand how place value relates to the algorithms they frequently use.
Putting students in the position to decide what manipulatives will be useful when solving a specific problem is also important. Sometimes, students carry out a procedure with manipulatives. How can we create opportunities for them to explore mathematics by using these objects as tools!
For instance, if students have just started a fraction unit, w e might consider letting them choose three manipulatives that can be used to show three different fractions like: 1/2, 3/4, and 7/10. Well, kids may gravitate towards fraction bars or fraction circles, but pattern blocks and cuisenaires are options, too. Perhaps, creating a manipulative scavenger hunt for fractions would be helpful in helping them try different tools and examine their usefulness.
Students who think outside the box may make a connection between base ten blocks and fractions. Realizing that the ten rod can be used to represent 1/10th of a flat or that the unit blocks could be 1/10 of the rod and 1/100 of a flat is an important discovery! This prepares students to connect fraction and decimal concepts later on.
3. Ask students to find more than one solution.
To be a mathematician, is to love efficiency! Kids get better at problem solving by revisiting problems and coming up with different solutions. When they think about the pros and cons of their strategies, they can decide which one was most efficient and tuck it away to use on future work!
For example, if students were solving the following problem:
Jaime has 12 bags of marbles. If there are 435 marbles in each bag, how many marbles does she have?
Students could use open number lines, place value blocks, or the algorithms to show how you could add all the marbles in the bag or realize that multiplication could be another strategy. After trying all these strategies, students might determine multiplication is most efficient.
I think that the biggest advantage to having multiple solutions is the opportunity to reflect. The opportunity to realize that some mathematical strategies are more efficient and less time-consuming is beneficial for students.
Also, realizing that multiplication and addition are connected to each other so they are both valid strategies is helpful if students who need a back-up strategy when solving a multi-digit multiplication problem.
4. Allow students to share solutions in a variety of ways.
When students share their solutions, this is another opportunity to reflect on different methods and identify efficient strategies. However, this is also a chance to step outside of their own thinking and try out someone else’s strategy. This is a chance for students to identify what makes a solution or a strategy valid.
- Is a solution valid because another student got the same solution as me?
- Is a strategy valid if they could have gotten the same solution as me?
- Are their multiple solutions that work, because they all satisfy the conditions of the problem?
What do you think your students might say to these questions? Would they ask different questions?
Several standards for mathematical practice are at play here! Critiquing the reasoning of other definitely comes to mind! Can you think of any other ways that sharing solutions and strategies might help students engage in the practices?
5. Introduce students to math talk moves.
Sometimes our students need help turning their thinking into words or simply learning how to argue in mathematics. Less yelling, more critiquing. Am I right?! One way to do this is to give them sentence stems that help with math talk.
Introducing students to sentence stems that target the standards for mathematical practice is key. Participating in math conversations can be uncomfortable for some students if they have never done it before. Talking about mathematics in meaningful ways may not come naturally if students are used to learning it procedurally. But, help is on the way!
Ten of my favorite sentence stems are…
- I know my answer makes sense, because…
- I noticed that…
- I am confused by…
- I solved the problem differently than you, because…
- Our answers are similar/different, because…
- I agree/disagree with you, because…
- What would happened if we…
- What I heard you say was…
- Can you explain how?
- I would like to add on to…
These talk moves align with most of the standards for mathematical practice, too! It’s a win-win!
6. Actively listen.
Okay! We’ve let the kids take over the chat, right?! Now, the fun part begins. Visit groups, station, or individual kids and listen for GOLDEN NUGGETS! They’re out there. TRUST ME!
A big part of teaching mathematics is staying alert and listening to the new ideas students come up with. During one-on-one sessions, small-group interactions, and whole-group interactions, your job is to facilitate and ask students with cool ideas about math to share. Since students can’t be everywhere in the class when they’re working in small groups, we have the advantage. We can float from group to group and witness the diverse ideas that come about.
Once I let students talk more and more, I noticed their explanations got better and better!
7. Highlight different student strategies.
Bringing students together to share ideas is crucial (See tip 4)! During whole-group discussion, think about who had a novel idea that needs to be shared with the group based on what you head while visiting groups and different students.
Whole group discussions are perfect opportunities for student to critique reasoning, create models, and attend to precision. The work you’ve done behind the scenes can really shine here. For instance, you can choose to let kids randomly share ideas, or you can purposefully select ideas that you think NEED to be shared. For instance, you can ask students to present in order from least complex to highly complex. You could also choose to highlight a group that had a unique approach. In some cases, these students may not have finished the problem, but their classmates can help them apply their strategy to the problem.
Another option is to choose two polar opposites and get them to compare what is similar and different between their strategies.
You might even call a group that got the problem wrong. Too often, we are afraid of crushing dreams, but kids should learn early on that mistakes are learning opportunities and an unavoidable part of life. Thanking them for their bravery to get up and share how they used to think about the problem is important. I always tell my students that their hard work will always make us better mathematicians!
I think it’s interesting that students know it’s perfectly fine to revise a writing assignment, but somehow math is less forgiving. Revision applies to math, too! You can always change your answer as long as you have a good reason to!
For more information on how to sequence your class discussion, here’s a book recommendation that I absolutely love.
8. Use read alouds to spark discussion.
Books can be more than a launch, though. You can design great tasks around them as well. In the past, I’ve used Two of Everything to teach multiplication and patterns. In the story, when objects are dropped in a magic bowl, the bowl doubles the amount. So, when reviewing the two times tables I use this book, but then I extended it to:
- 2-digit by 1-digit multiplication
- 3-digit by 1-digit multiplication
- 4-digit by 1-digit multiplication
- 2-digit by 2-digit multiplication
I make sure that the problems I come up with have have 2 or 22 as one of the factors so my students can concentrate on understanding the concept of multiplication. We make sure to use different representations like base-10 blocks, pictures, area models, and so on.
For justification and reasoning skills, Which One doesn’t belong can set you up for a year-long math routine. I personally like to use this book at the beginning of the year and have kids justify their answer. This sets up my expectations for math class! This also helps students form a habit of deciding whether they agree with their classmates’ explanations.
I love that each page has four shapes, and each shape could be the shape that doesn’t belong as long as your reason pans out. This book shows kids that there can be more than one answer, and they can agree with someone’s solution even when it’s different than theirs.
I use the same setup as a warmup in my class. Instead of only focusing on shapes, I use it with different numbers (primes, composites, fractions, decimals, whole numbers, etc.). I’ve also shown four different pictures of money and ask students which one doesn’t belong. My kids love this warm up, because they get to chat with friends. They also get to feel like a successful mathematician right when class starts!
There are so many great books that can help you launch math lessons, and these math read alouds deserve to be a part of every classroom library!
Integrating literacy and mathematics should not be overlooked. There are too many AWESOME books that connect to math topics to leave them out! A few of my faves are The Greedy Triangle, Two of Everything, and Which One Doesn’t Belong?
9. Praise Hardworkers!
Let’s face it! Kids begin to hate math earlier and earlier, because they have more bad experiences than good experiences with it. 🙁 To avoid this, let’s transform how we praise them! Instead of the fastest mathematician, praise the thoughtful mathematician, the inquisitive mathematician, or the perseverant mathematician!
This is a quick and simple way to teach students to persevere through problem solving and develop a can-do attitude towards mathematics. The standards for mathematical practice focus on this in the first practice and for me I think this is one of the most important standards we have!
The Big Idea Behind the Standards for Mathematical Practice
Let’s Chat!
I hope this information was helpful for you. I’m curious to know your thoughts on how you might apply these ideas in your own classroom, especially in the midst COVID-19 and distance learning activities! Leave a comment below, I’d love to hear from you!
Which Standards for Mathematical Practice do you feel most confident about teaching? Which math instructional strategies are you excited about trying in your class?
Made4Math
