Welcome back! I’ve always loved heading back to school in January because it’s an opportunity for a new start. I can teach new procedures and routines and I can introduce new teaching strategies and ideas. It’s also a great time to refocus on my curriculum and begin preparing for end of the year assessments. With this in mind, this month, I’m sharing ideas for teaching with the Common Core mathematical practice standards. And, for my Texas readers, I will be correlating them to the mathematical process standards of the TEKS.
The mathematical practice standards are included in each grade level’s Common Core State Standards. They include important processes, practices, and proficiences that are important for the development of every successful mathematician. These standards were derived from the work of The National Council of Teachers of Mathematics, NCTM, and The National Research Council.
For today’s Transformation Tuesday, I want to focus on Mathematical Practice Standard 3: Construct Viable Arguments and Critique the Reasoning of Others. An excerpt for this standard, from http://www.corestandards.org/Math, is provided below.
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.
This standard correlates with Texas Mathematical Process Standard TEKS 1G which states, “display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.” (Source: Texas Education Agency)
Activities which require students to critique the thinking of others provides a unique opportunity to better understand where a student is in the learning process and provides a glimpse into how a student has internalized a skill. Today’s idea is a modified version of my “Who’s Correct?” strategy that focuses on distinguishing correct logic from incorrect logic and identifying flaws in the thinking of others.
Here’s how to get started: For this activity, choose two ways to reason about the answer to a question or a problem. Then present the reasoning. Have students write about whose reasoning is correct and any flaws they may have found in the thinking of the presented arguments. Students should justify their thinking in pictures, words, or numbers.
This activity makes for a great journal task or formative assessment tool. In fact, this activity can be used as a quick exit ticket in order to assess student understanding of the day’s lesson and make decisions for the next lesson.
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?
Once your students are comfortable with the strategy, begin infusing their own work into the activity and have the class critique their classmates’ reasoning. (No names of course!) It’s a powerful way to help students develop better communication skills and learn from each other.
This is such a versatile strategy that it can be used with any content and with any age group. Add it to your lesson plans and give it a try this week!