I had this student in my class once years ago that struggled so much in Math. He was a year behind. I worked really hard with him and he received extra support. 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. He had moved forward by a year each time which was a good thing, but would it help him in the long run? Time will tell but there are a few things that I know now that I could have done to help him understand Math, not just “do Math”.
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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.
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 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. If you like something more colorful you can try something more like these:
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 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 at other stages of Math learning more at the 2nd and 3rd grades, as well as looking more closely at everyday Math learning through problems and practice and math talks. What kinds of things do you see in your classroom that students struggle with in Math?