By Brooke Powers
It seems like it was yesterday that I was sitting in hours of professional development in the year leading up to the adoption of the new Kentucky Academic Standards for Mathematics in 2010, learning all about the 8 Mathematical Practices that were to be included as part of my instruction on a daily basis.
The math practices are considered the behaviors that all teachers should try to elicit from their students in order to help make them stronger mathematicians and problem solvers. Those behaviors include:
- 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; and
- Look for and express regularity in repeated reasoning.
I won’t lie, in the beginning I met the new information with the occasional eye roll and the belief that I had too much on my plate with new standards and content that went deeper than I had taught before. In the six years since I sat in those initial meetings, my thoughts have completely changed regarding the implementation of these practices in my classroom.
Rather than treating the mathematical practices as simply a checklist to mark off as done or not done, I now incorporate them daily to improve student engagement and interest in my class. We focus on a different math practice each day to get us ready for a day of learning and as a result, I have seen students grow both as mathematicians and grade-level content.
In this two-part article series, I am going to highlight how I am able to utilize classroom routines and warm-ups to elicit the behaviors categorized in the 8 Math Practices.
Reason abstractly and quantitatively
Each day, we do an estimation challenge from Estimation 180. This amazing resource provides more than 200 days’ worth of real world estimation problems that spark student interest and generate discussion about what is a reasonable estimate. The site also provides a work along, where students must defend their reasoning.
Besides just the reasoning and number sense provided by the estimation activities, I love the focus that we have been able to place on finding the percent of error. Percent error is such a big part of the 7th-grade standard and is very valuable in students being able to reason with percentages. At the end of the first nine weeks of school, 97 percent of my students had already demonstrated mastery of this standard with no formal teaching other than what comes along with the estimation activity.
Look for and make use of structure
The kids’ favorite day is probably Tuesday, when we bring out the website Which One Doesn’t Belong. This amazing site features mathematical puzzles where students are given four geometric shapes, numbers or graphs and have to come up with reasons as to why one of them doesn’t belong.
My favorite part of this activity is that there are multiple entry points for learners at all levels, so it comes already differentiated. Students can say something as simple as “the fourth shape doesn’t belong because it is the only one shaded in” to something as complicated as “the third shape doesn’t belong because it is the only shape sitting on a vertex and not a side.”
Construct viable arguments and critique the reasoning of others
Each Wednesday finds my classes answering a question from Would You Rather.
This free site provides tons of great ambiguous questions with no right answer. Students must pick a side and justify their reasoning with mathematics. After some individual think time, we spend time sharing both our choices and our reasoning and have some really deep mathematical discussions as a result.
With questions ranging from would you rather have $100,000 to spend on a MLB or NFL payroll to which slice of pizza you would rather eat, these deep questions will engage your students in this rich math practice while improving student engagement.
Each of the activities takes about 5 to 10 minutes of class time, but gets the kids in the room and ready to learn about math while engaging them in one of the eight mathematical practices. The use of these strategies has totally transformed my classroom and made my students more excited about being mathematicians. I have no doubt that intentionally focusing on the math practices would do the same in your classroom!
Brooke Powers is an education blogger and 7th-grade teacher at Beaumont Middle School (Fayette County). You can read more about providing students a real-world and engaging math experience on her blog by clicking here.
Nice article Brooke. You are using the Common Core Practices to develop critical mathematical habits of mind. Well done!