If you are a classroom teacher, you always find a student or two (maybe more), who just don’t “get” it. Marybeth (her real name is unrevealed) is mine this year. Other teachers who have known her in previous years tell me about her all the time. “She doesn’t get it, does she?” “He mom was in Special Ed.” “She should be in Special Ed.” I am thinking about the similar students while teaching in Japan. There is no place to refer students who just don’t get it. There are some toughness and consistency in their mathematical learning system. By 3rd grade, almost no students struggle with adding single digit numbers. If the plan is simple and sophisticated, I can help Marybeth before multiplication lesson starts. So, I start observing her math performance characteristics when she works in a large group, a small group, and individual work. In the addition computation routine, she is totally confident with plus ones, however, she start showing inconsistency even from plus ones. I am thinking if she is cognitively delayed corresponding the existence of objects and numerals. Maybe there are just 10 dots in her brain when she sees the number 10. In other words, she lacks the concept of grouping or relationships. There is no wonder why she feels so overwhelmed when she sees the number “145”. One hundred forty five dots are flying around in her brain! This coming week, I try to focus on strengthening the cognitive understanding of numbers under 10 with 10 frames. 10 frames are transferable to the 10 fingers, too. Another option is the abacus. I wish I had it in my class.
Soroban a.k.a. Abacus

A simple yet sophisticated plan for Marybeth has one strict rule. That is not to exceed 15 minutes for her addition and subtraction practice with her mom. I don’t want her to feel overwhelmed. I want her to feel successful. So I simply divide 15 minutes into 3 components. The first component is to improve the automatic recognition of the 10 frame for 5 minutes. Instead of recognizing one dot at time (counting one by one), I want her to recognize the numbers of dots in the 10 frame as a group. The second component is to be familiar with the combination of 5. She practices this form in one minute at time. The final component is to practice addition and subtraction in the horizontal equations. Numbers she uses are under 5.

I am pulling some resources from Japanese 1st grade practice book. My hope is for her to feel confident by completing and accomplishing her daily goal in a short amount of time. I use my Home-School Connection sheet to communicate with her mom. She seems enthusiastic when I introduced this simple yet sophisticated plan.

Marybeth spontaneously recalls numbers from 1 to 5, when I flash 10 frame cards in front of her. She can recall how many more to go to 5 on the number line. Twelve “Making 5” problems have been done in 15 seconds, 13 seconds, and today, it was 11 seconds. Her goal is 10 seconds.

Knowing her confidence and competence, I introduced to her a new game with 10 frame cards. Show one card at time with numbers from 5 to 10. Instead of just recalling, she says the number of dots like, “5 and 1 is 6” or “5 and 3 is 8”.

I noticed she counts one by one in this practice, so I suggested her goal will be 2 seconds for one card. I am trying to strengthen her number sense by recognizing them as groups, not one by one. I sent an email to her mom with an attachment of the on line game that perfectly matches with the 10 frame activities we have been practicing.

In the number line, I will introduce the activity, How Many to Go Back to 5. It was very hopeful day for me, and hopefully, she felt the same way, too.
10 Frame Practice Game

Other ideas come from Investigation. Children will develop their number sense simply by playing number games that they were supposed to have explored in Kindergarten and first grade. You can find 15 minutes every day. It is simple. Just be consistent.