The development of early number sense is critical for children to be able to understand math in later years. There are important developmental skills that all students needs in order to conceptually understand math. If there are gaps in these skills, we need to use intervention in order to fill the gaps so that the child can move forward in their numeracy learning.
I had this student in my class once, years ago who struggled so much in Math. He was a year behind when I met him in September. This child received extra help outside the classroom as well as the lessons in class that were very hands-on. I had him for two years in a row as part of a looping situation. At the end of the 2 years, he was still a year behind. While that made me disappointed, I did realize that he had moved forward by a year each time which was a good thin, but there were learning gaps. I think he made such good progress because we did a lot of hands on learning. What I think I could have done to help him understand Math more and not just “do Math” was to be able to identify the learning gap and target those skills.
Numeracy is different than Mathematics. Mathematics is a body of knowledge and numeracy is the ability to use this knowledge to reason and apply Mathematics knowledge to everyday life. It is not the quantity of Math knowledge that one has that is important, it is the ability to “see” math and use it to function in day to day life.
Our students need to touch Math and understand quantity. It is critically important that teachers help students develop number sense as a initial skill in their numeracy development. While most initial number sense is developed in the Pre-K, K, and 1st grades, it is developmental and must be nurtured. Whether students have number sense in K or older, the importance is that their learning is hands on and conceptual in nature.
Jo Boaler (Professor of Math at Stanford) explains the importance of this in this video where she talks about compression in learning. Watch it here.
In order to effectively develop number sense in your students, they need lots of hands on practice counting, subitizing and decomposing numbers.
Counting is one of the important early number sense skills that students learn and use to find out “How Many?” Knowing how to count to 10 is memorization and is an abstract concept. A more concrete measure is to apply their understanding of 5 by counting and using 1-1 correspondence. Young students need TONS of practice counting. There are many things that they can count – simple things like beans or buttons or rocks. Count all the things! Often times, we stop having children count too soon.
When figuring out 5 + 3, does your student count the first 5 fingers out then continue counting 3 more or do they subitize 5 and count on 3 more? Subitizing refers to a student’s ability to instantly recognize a number without counting it like in the case of one hand is 5. Formatively assessing this will help you know what skills they need to work on next. Eventually, students stop looking at and needing their fingers because they can subitize. Subitizing is one skill that our students need in order to develop number sense. So is it okay for students to use their fingers when they are figuring out a problem? Absolutely!
According to research, using your fingers gives students a visual not only to look at but also in their brain. The important thing here is that you can observe students working on Math whole class or more closely in a small group and you can use these observations to determine at what stage your student is currently at and what they will need to move forward in their learning. A great way to practice subtilizing is with 10 frames, dominoes and dice. Dice are handy because they can be used for Math games which reinforce subtilizing while having fun. Kids don’t even know they are learning! (It’s so much better than a math drill, don’t you think?) I don’t know what it is about dice but I just love them! Do you? My favorite dice are the dice within dice set.
When kids can subitize, it makes learning how to add and subtract much easier. Another important element of early number sense is when students are able to decompose, that is, take a whole number and identify the parts. ie. 5=2+3 . As students become more numerate, they apply this to larger numbers. ie. 25=20+5
As your students are learning and growing with practice in these early number sense skills, they are building a confidence in their Math ability. It is so important to develop this early confidence so that they don’t “fear” Math like many adults do. Many of us did not learn this way, rather we learned processes and memorized formulas. No wonder Math fear developed in many people over the years. With hands on lessons and practice, our students will be more engaged in their learning and inspired to learn more.
It is also important for students to be constantly thinking about Math in real life scenarios because there is Math everywhere! In future posts, I will be looking more closely into breaking down the math progressions so that you can more easily identify where your students are at. Knowing this will help you to target the skills they need and fill in any learning gaps you may see. While many of these skills are built in preschool and 1st grade, some students in 2nd, 3rd or beyond may not have learned these important skills. What kinds of things do you see in your classroom that students struggle with in Math?
Due to the popularity of this post, I wanted to elaborate on some of these concepts discussed here and provide some activities to help you teach number sense. I have added a new number sense post to the blog with more detail on teaching number sense and tips for intervention for those students showing learning gaps.
You can find the new post here or by clicking this image.