## Thinking Math In Elementary Schools

By Jeanne DeJong

Count to 100 by ones and by tens. Tell and write time in hours and half-hours using analog and digital clocks. Add up to four two-digit numbers using strategies based on place value and properties of operations. Partition shapes into parts with equal areas, and express the area of each part as a unit fraction of the whole. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Add, subtract, multiply and divide decimals to hundredths.

Each of these is a content standard from the North Carolina Common Core Curriculum in math. Content standards describe what mathematical skills a student is to be proficient in at the end of a particular grade level. Students are taught how to “do” math through procedures and algorithms.

But that is not all that math is. Students in the Transylvania County Public Schools are also becoming math “thinkers.” Through the Eight Standards of Mathematical Practices, students are being asked to tackle math problems with an “I can puzzle it out” attitude. And the habits that this attitude develops will prepare our students for the challenges of the 21st century world. Here is a summary of the mathematical practices from an elementary (K-5) age lens:

1 — Make sense of problems and persevere in solving them. Keyword, “persevere.” I can make a plan. I do not jump to an answer. I explain the problem to myself. I organize the information I have and ask questions like: What is given? What is the question I need to answer? What prior knowledge do I have to help me? I carry out my plan. I stick with it and keep working and monitor what I am doing. I change my plan if it is not working. I ask myself “Does it (my answer) make sense?” I evaluate what worked and did not work.

2 — Reason abstractly and quantitatively. I can take numbers and put them into real world problems to help me understand them better. I pay attention to the units involved in a problem, feet, seconds, meters, etc. I can take numbers out of a word problem and work with them mathematically.

3 — Construct viable arguments and critique the reasoning of others. I can communicate my mathematical methods using examples, drawings, diagrams and actions. I can listen and critique other students’ mathematical reasoning with my own. I can ask questions to help my understanding and identify mistakes.

4 — Model with mathematics. I can recognize math everyday, everywhere. I can estimate in order to make complex problems easier. I can represent math using symbols, concrete models, pictures, words and real-world situations.

5— Use appropriate tools strategically. I have a math toolbox (a certain former BMS math teacher made sure his students had a toolbox). I know how to use math tools. I know when to use math tools. I ask myself, “Did the tool give me an answer that makes sense?”

6 — Attend to precision. Keyword, “precision.” I calculate accurately and efficiently. I can correctly use math symbols, vocabulary and units of measure. I can communicate my mathematic ideas through speaking, writing, reading and listening.

7 — Look for and make use of structure. I see how numbers are organized and put together as parts and wholes. I can understand how spaces are organized and put together as parts and wholes.

8 — Look for and express regularity in repeated reasoning. I see number patterns. I notice when calculations are repeated. I can find more efficient methods and short cuts.

Mathematics is not just about an answer; it is about the process of getting to the answer. Students in the Transylvania County Public Schools are using the Eight Standards of Mathematical Practices from the North Carolina Mathematics Curriculum to become math thinkers, puzzling out the methods that get to the answers. These practices are the foundations that will help students in future mathematics courses, and ultimately in the world of “puzzle solving” that is everyday life.

* (Jeanne DeJong is a fifth grade teacher at Brevard Elementary School.)*