Friday, September 10, 2021

What are the SMPs (Standards for Mathematical Practices)?

Raise your hand if you’ve ever had a parent say “Why is math so difficult now?!” or “This isn’t the way I learned math. It’s so complicated and confusing now.” 


Chances are that if you’re an elementary teacher, you’ve definitely heard this or maybe even thought this yourself.


The Common Core Math standards can not effectively be taught without a focus on the Standards for Mathematical Practices (SMPs). Understanding the SMPs will enable you to better be able to shift your teaching practices from a focus on content (the standards) to a focus on application and true understanding. The SMPs are actually the heart and soul of the Common Core Standards.


You might be thinking:


Think of the SMPs as the process which one must take to learn their content standards. In order for students to be truly proficient with their content standard, they must be able to apply, communicate, make connections, and reason about the math content. This differs from how you (or your students’ parents) learned math because back in the day, proficiency was measured by a correct answer or one's ability to carry out a computation (based off of rote steps). 


These practices can’t be learned in a quiet math classroom filled with drill and kill activities/worksheets (think back to when you were in school). This level of thinking must be developed in classrooms filled with thoughtful conversations and hands-on explorations about math concepts. Your ability to ask thought-provoking questions is what will truly be the change in your math classroom.


Let’s take a look at Standards 1-4:


Standard 1: Make Sense of Problems and Persevere in Solving Them


In short, what is expected is exactly what the standard says. Students will be able to understand the problem-solving process and know how to navigate the process from start to finish. They have a variety of strategies and know how to go about solving a problem. Last but not least, students don’t give up at the site of a challenging problem. They have the tools in their “toolbelt” to power through and figure it out on their own. 


How do I get my students to be able to do this?

  • Focus classroom activities and discussions on students’ thinking rather than on the correct answer

  • Do not rely on oversimplified methods to teach concepts, such as keywords (I saw the word altogether so I added).

  • Pose students with problems that push students to apply their understanding of math content and allow them the opportunities to explain their process of solving.

  • Provide students with opportunities to explore complex problems that include multiple approaches to solving. Allow them opportunities to share all of these different approaches. 

  • Praise student efforts, put value on their persistence and process on solving rather than praising the correct answers.

  • Create a supportive and nonthreatening classroom environment where discussions of confusion points are encouraged. Openly discuss these confusion points and include insights on ways to simplify problems and move through confusion. 

  • Acknowledge the efficiency of particular strategies but also celebrate individual, reasonable approaches. 


Standard 2: Reason Abstractly and Quantitatively


Standard 2 addresses the importance of building a strong understanding of numbers. When students are given a problem, they are able to represent the problem using numbers, symbols, and diagrams (abstractions). Students must see the connection between the problem situation and the abstract representation (equations). Once the equation is solved, students should refer back to the context of the problem to evaluate if the answer makes sense. 


How do I get my students to be able to do this?

  • Ask students to identify and describe the data in the problem.
  • Model building appropriate equations to solve problems.

  • Use diagrams to model math situations to make it easier to see what is happening in the problems. Can students draw a diagram to show a word problem for 3 x 5?

  • Frequently ask “what operation makes sense?” or “How should we build an equation to match this problem?”

  • Ask students to write a word problem to go with a given equation.

  • Consistently ask students to explain equations or diagrams, connecting them to the problem scenario (e.g., What does the 6 represent in our equation 6 x 3 = 18?)

  • Ask students to label answers by referring back to the problem to determine what the quantity (solution) represents. 

  • Ask students if the quantity makes sense when referring back to the problem (e.g., Does 3.5174 buses make sense?)

  • Discuss building appropriate equations to solve problems (are there more than one equation that could be used to solve this problem?) 


Standard 3: Construct Viable Arguments and Critique the Reasons of Others


This standard means that students are able to come up with a correct answer and also explain WHY it’s correct. In addition, they’re able to listen to the justification of others, or even look at how a problem may have been solved, and identify any misconceptions or misunderstandings that the person may have had. They are able to communicate their thoughts to others. 


How do I get my students to be able to do this?

  • Don’t just accept an answer from a student, follow up with questions such as “why?” or “How do you know?” 

  • Encourage students to use math vocabulary in their justifications

  • Use probing questions such as “Does that make sense?”, “Why is that true?”, “Does Ronald’s way to solve this problem also work? Why or why not?”

  • Give students the opportunity to listen to their classmates' reasoning. Rather than the teacher asking clarifying questions or correcting a misunderstanding, allow the students to do this. 

  • Create a non-threatening classroom environment where students feel safe to share their arguments and know how to ask clarifying questions, and how to respectfully disagree with others. 

  • Provide students opportunities to work with error-analysis problems. 


Standard 4: Model with Mathematics


This standard encourages students to create models or visual representations of abstract math ideas. When students create models of problems, they are able to see the problem clearly and then work towards a solution. When you ask students to create math models, you are challenging them to represent their math understanding- to get it out of their heads. The power of this is that as students share their own thinking (Standard 3) and view the models of others (and listen to their thinking) they are able to gain new insights and strengthen their own understanding. 


How do I get my students to be able to do this?

  • Model the use of diagrams and drawings to represent problems

  • Encourage the use of manipulatives

  • Encourage students to create simple diagrams to show problems

  • Encourage students to come up with multiple ways to model a given problem

  • Have students justify why they chose to use a given model

  • Ask students to interpret models of their classmates

  • Have students share out about the models they created and why


I hope that this post was helpful in learning a little about what the practices are and why they are important.


Be sure to come by next week, where I will be sharing the last 4 Standards for Mathematical Practices with you.





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