## Number Sense and Math Reasoning Inventory

I have two children of my own. Often, they end up becoming guinea pigs when it comes to math instruction (or just about anything). As a secondary teacher, I feel qualified to teach integration, quadratic functions, or any other topic beyond Algebra 1. When my son brought home his first set of flash cards from school, I was at a loss. The only tool up my sleeve was memorization by repetition. Needless to say, we spent many hours drilling and crying (ok, I was the one crying). My younger son watched and didn’t speak, but he was absorbing. Little ones are like sponges and sometimes that is not good.

A few days after the flashcards disappeared, my then 6-year-old said, “Mom, I know why 3 x 5 is 15.” I was curious. His response shocked me. He explained that if he counted by three’s 5 times, he would end at 15. He also told me that he could do it the other way and count by five’s 3 times. Of course, I knew this, but in my pursuit to push my older son to memorize faster, I skipped the understanding. What my 6-year-old was developing was number sense.

One of the complaints I most often hear from high school teachers is that students do not have number sense. I’m not sure how you measure number sense or how to teach it, but you know it when you see it and you definitely know when it is lacking. I need students to understand that 3/4 – 1/4 is 1/2 without having to perform an algorithm. Sometimes I think we become too engrained in teaching algorithms without understanding. My hope is that the new common core assessments will force teachers to fix this.

Recently a colleague introduced me to a website, Math Reasoning Inventory, that encourages formative assessment for understanding and building number sense. Maybe some of you already use it and can offer feedback. I have not seen anything like it in mathematics before and am excited about how this could change elementary mathematics education. The site encourages teachers to conduct interviews with the students on mathematics problems. The focus is not only the correct answer, but how a student achieved that answer. For example, if a student is asked to calculate 7000 – 70, using a standard algorithm would be considered an inappropriate strategy. I have to say I love this! Students forget algorithms and cute tricks, but true number sense and understanding will always work. I encourage you to look at the website and provide feedback below. I would love to have students at the secondary level who had been evaluated with this method.

Number sense is hard to define and harder to assess, but I believe that the Common Core will help us achieve what is so necessary for mathematical success.

I tend to see a lot of focus on one-on-one time with students performing interviews to solve problems and things like that. How do you think a good teacher would go about making time for one-on-one interviews with all students and not leave the others to fend for themselves? I’m very interested in this whole thing!

– Grant Yost

Grant,

I love that you read my blog! I think it is so important to have one on one time with students, but it is difficult to schedule. One way we are experimenting with this year is having an upperclassmen in the room who is working as a class assistant. He or she could lead the class or help small groups while the teacher works with students one on one. Another way that I have done this in the past is to assign an individual activity in the computer lab and work with students one on one while the other students are engaged. I think elementary teachers do this well. I’m always amazed with my son’s teacher and how she creates centers and one of the centers is working with her one on one. She empowers the students to be leaders in each center. For example, Tyler is the ‘technology’ leader this year. If a student has a question or problem with technology during center time, they ask Tyler and not the teacher. This enables her to work uninterrupted with a student or small group. I think we as high school teachers need to adopt this idea and try to make it work in our classrooms.

Amber