The Common Core State Standards for Math actually include two types of standards: the content standards and the standards for mathematical practice. The content standards define the specific skills that are to be mastered at each grade level. For example, multiplication, division, and fractions are all content standards for 3rd grade. The standards for mathematical practice, however, outline how students go about doing the math. They are skills, based on the NCTM process standards, which students should utilize on a daily basis, regardless of the content being taught. In other words, they should be embedded into daily math instruction, rather than taught in isolation. Too often, however, teachers focus their attention and energy on the content standards and neglect the mathematical practices, resulting in students with only a surface-level understanding of the math they are doing.
So what are the standards for mathematical practices, and how can teachers go about incorporating them into their lessons? Let’s start by taking a look at the standards:
- Make Sense Of Problems And Persevere In Solving Them—understand the meaning of the problem, determine entry point, analyze information, plan a solution pathway, apply problem-solving strategies, check for reasonableness
- Reason Abstractly And Quantitatively—make sense of quantities and their relationships in problem situations, use different properties of operation and objects with flexibility, create a coherent representation of the problem at hand
- Construct Viable Arguments And Critique The Reasoning Of Others—justify conclusions, communicate them to others, and respond to the arguments of others
- Model With Mathematics—apply known mathematics to solve problems arising in everyday life, society, and the workplace
- Use Appropriate Tools Strategically—consider the available tools when solving a mathematical problem
- Attend To Precision—communicate precisely to others using clear definitions, meaning of symbols, and computational accuracy
- Look For And Make Use Of Structure—discern a pattern or structure
- Look For And Express Regularity In Repeated Reasoning—look for general methods and shortcuts, maintain oversight of a process while attending to details
Click here to grab a bookmark listing the mathematical practices and keep it with you while planning.
Now that we know what they look like, here’s my secret for embedding them into your instruction…talk less!! That’s right. You talk less, and let your students talk more. To increase the capacity of our young mathematicians, we need to deliberately plan ways for them to communicate, both orally and in writing, about the math they are doing. The “turn and talk” strategy is great for increasing student participation and engagement during a whole group lesson. Simply present an idea, or better yet ask a great question, and then have your students “turn and talk” to a partner. Routines like this one send the message that all students are expected to communicate their mathematical thinking, and it also gives students a safe forum for trying out new ideas. If you’re looking for visual aids on the Mathematical Practices for your classroom, check out my primary and intermediate poster sets.
Love the bookmark and love your suggestion of talking less. I will be sharing this post and the bookmark with the teachers I work with. It is a simple but very effective suggestion. Thanks for sharing!
The Math Maniac
My pleasure, Tara! I think the bookmark is a great tool to have at planning. 🙂
Love your bookmark and your ideas! Just returned from an NCTM interactive institute and you are echoing exactly what they are saying and teaching about the practices. 😉 I love the graphic at the top of your post as well…thanks for a great post!
Craft of Teaching
Ooh, I really wanted to go to that institute, Nichole, but I was already committed to a different conference. I’ll be it was great!
Thank you for this post and the bookmark! As a language arts teacher returning to math this year, this will be very helpful for me!
Glad you came back from the Dark Side! Ha ha. 🙂
What a great find! You really know what are talking about and have some fantastic resources! Thanks for doing what you do. I’m a new follower 🙂
Thanks, Ashley! Glad you find my blog useful 🙂
This is SO true! I use the turn and talk all the time!!! Thanks Donna!
My pleasure, Amy! 🙂
Love this…thank you so much for sharing! I so agree with you on that the student participation level is an important factor. I teach my students ‘whole brain teaching’ at the beginning of the year and they really buy into it. If you haven’t heard of it, check it out!
Whole brain teaching is AWESOME!! 🙂
Love these! My whole school will be using them this year!
Yea! Glad to hear it’s something useful. 🙂
I am new to the bogging world…but I thought the information on your page is great. I especially was interested with the information you have on CCSS. We are making the switch to CCSS and I want to be informed about every aspect of them. I also love the bookmark and posters on Mathematical Practices. I will use and share this site with my colleagues. Thank You.
Welcome to the blogosphere, Adela! So much good information to be found. 🙂
This information was very helpful and relevant to my teaching. I also agree that if we do not embed mathematical practices with CCSS our students will attain “surface level” learning. Thank you for sharing the bookmark and posters on mathematical practices.
We’ve been doing “surface level” for too long, I’m afraid, Sonia! I hope this language, and discussing the mathematical practices as “habits”, will help us take math instruction to a whole new level!
This visual really helps clear things up! I’ve been going to and doing all the ELA CC training and presenting for my school. Trying to get all of that info to stay clear in my head plus present it to the other teachers left little room for what is going on in math! I really tuned out often when our math teacher/presenter started his math talk. I’ve heard all those terms but never really took them in. Just the color coded Venn and bookmark helped more than a whole faculty meeting worth of talking!
Thanks so much!! I’m glad I was able to present a fuzzy concept in a way that’s more clear. 🙂
Thanks for doing what you do. I’m a new follower .I so agree with you on that the student participation level is an important factor. I teach my students ‘whole brain teaching’ at the beginning of the year and they really buy into it. If you haven’t heard of it, check it out!
Do you have anything like this for the TX TEKS and the Process Standards? Have you presented on this topic? I’d like to do a quick pd on embedding the TEKS process standards into math instruction and would like help with any info or activities you have used. Thanks so much for sharing your knowledge with us!
I’m a fifth grade math teacher in Ohio. I’m a huge believer in designing instruction so my students understand math and the reasoning behind the strategies I teach.
One standard that I’ve struggled with is 5.nbt.7: dividing decimals by whole numbers and wholes numbers divided by decimals.
When I begin teaching this concept, I initially have students use base ten blocks to model making equal groups. We then progress to using place value charts and partial quotients to model a decimal divided by a whole number.
Im wondering if there are any other strategies you might suggest besides teaching the “standard” algorithm?
Sounds to me like you’re using a great variety of strategies! The only thing I might recommend is having students using reasoning/estimating techniques to think about reasonableness. Check out this post for more info and to download a freebie!