Teachers often ask me how I teach the mathematical
In today’s post, I’m sharing how to use the mathematical practice standards to increase the rigor in your classroom and create mathematical thinkers.
Each grade level’s Common Core State Standards include the mathematical practice standards. They include important processes, practices, and proficiencies that are essential for the development of every successful mathematician. These standards derived from the work of The National Council of Teachers of Mathematics, NCTM, and The National Research Council.
Mathematical Practice Standards
MP1: Make Sense of Problems and Persevere in Solving Them
CCSS.MATH.PRACTICE.MP1: Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?”
This standard requires students to restate the question and decide how and where to start. NCTM (2014) suggest teachers use “purposeful questions to assess and advance students’ reasoning and sense-making.” In addition, George Polya (1945), attributed with establishing the basic 4-step
1. to help students solve a problem.
2. to help students develop the ability to solve future problems on their own.
While asking good questions seems easy enough, asking purposeful questions takes both forethought and planning. We must strike a balance between asking questions that give away too much and asking questions that do not give enough support to enable the student to move forward in his/her thinking. Thinking about and planning the questions to ask students while problem-solving in advance will help support their success as mathematicians. When designing instructional experiences with problem-solving, consider how your students will interpret the problem and where they might want to begin.
Read more about asking good questions here!
MP3: Construct Viable Arguments and Critique the Reasoning of Others
CCSS.MATH.PRACTICE.MP3: Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.
Activities which require students to critique the thinking of others provide a unique opportunity to better understand where a student is in the learning process and a glimpse into how a student internalized a skill. A version of my “Who’s Correct?” strategy focuses on distinguishing correct logic from incorrect logic and identifying flaws in the thinking of others. It makes a great journal task or formative assessment. Or, use the activity as a quick exit ticket.
For this activity: Choose two ways to reason about the answer to a question or a problem. Then, present the reasoning. Next, have students write to explain whose reasoning is correct and justify their thinking in pictures, words, or numbers.
As an additional activity, have students discuss what words or pictures could have been added to clarify the reasoning or make it easier to understand. Questions to help stimulate discussion include:
- What suggestions would you offer to help [name] make [his/her] explanation clearer?
- What vocabulary words can [name] use to make [his/her] explanation clearer?
- Would a picture make [name]’s thinking clearer? How?
- What else does [name]’s explanation need to include in order to convince someone else that [his/her] solution is correct?
Variation: Once students are comfortable with the strategy, include your students’ work! It’s a powerful way to help students develop better communication skills and learn from each other.
MP4: Model with Mathematics
CCSS.MATH.PRACTICE.MP4: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later.
This standard encourages us to emphasize the role of real-life mathematics in our everyday instruction. In fact, over the years, I have found it easier
Math picture books provide a great platform for connecting math content and skills with the real world. In fact, that’s what I love most about them. They allow us to present new math content and skills through the context of a real-world situation, even if the story itself is a fantasy. I often insert them into my lesson introductions or as my “engage” piece to stimulate student thinking about a skill.
While not all math picture books present concepts through the context of a story, there are many that do just that. Need some ideas? Then check out this link for ways to use math picture books in the classroom and snag a list of my favorites. The post includes a treasure trove of book ideas! You’ll find each page includes a story summary, skill connections, and guiding questions.
Using the mathematical practice standards not only increases student thinking,
Sound Off! How do you reinforce the mathematical practice standards in your classroom? Tell us about it in the comments below.
Reference: NCTM (2014). Principles to actions: Ensuring mathematical success for all. NCTM: Reston, V.A.