When it doesn't add up

     So this week kicked off the first Professional Development Community meeting (PLC) of the school year. The content area focused on Math so I led the discussions for each grade level PreK-5. One of the areas at the core of the meeting was about the importance of student's conceptual understanding of numbers. Two weeks before the first PLC, I went to teacher's classrooms to find out what they felt were big issues with math; here's what they shared:

• Students don't know their basic math facts
• Fluency and concepts of numbers is a problem 
• Students have a limited understanding of place value
• Fractions (use of visual models) are a struggle at the upper grades

  The cause of each of these issues is deeply rooted in NUMBER SENSE. According to Howden (1989), "number sense is a student's ability to have good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms”.
     In summary, students come to school having prior knowledge of numbers (i.e. knowing telephone numbers, seeing speed limit signs on the streets, seeing money exchanged at the grocery store, etc.) Where the connection happens is when lessons or activities are taught in a way that builds upon what students already know. This is what gives them the opportunity to develop number sense.
I visited a 3rd grade classroom recently. The students are being introduced to multiplication and division, so they were sitting on the carpet in a large circle during the part of the lesson I observed. Each of them had a whiteboard and marker. The teacher posed the question "there are 19 students in this class. Each has 3 pencils. How many pencils are there?" She gave students time to solve the problem while moving around to observe them at work. 
     I noticed that most of them drew pictures along with an equation (19 circles and 3 dots in each circle). After hearing several students share their answer, the teacher asked "who solved  this problem another way?"...notice, she never said whether the answer was correct or not. One student shared his work: "There are 19 of us in class, but I know that 20 is one more than 19, so I made 20 groups of 3, which equals 60. Then I took one group of 3 away
20 x 3=60
60-3=57
That's how I knew that there are 57 pencils". Again this is what the idea of number sense means. So I challenge you to continue to build on what students already know and less on the what we believe they don't know. When that happens, you will see them develop into better problem solvers. 
Until next time...go out there and be GREAT!

 Looking for ideas to promote Mathematical Thinking in your classroom or at home? Check out the websites listed below!
mathbeforebed.com/
​https://www.youcubed.org
https://mrorr-isageek.com/
​
Reference
Howden, H. (1989). Teaching number sense. Arithmetic Teacher, 36(6), 6-11.
Number Talks: Whole Number Computation by Sherry Parrish

​
​
​
​
​