Check out the other posts in this series! Perceptual Part 2, Figurative Part 3, Initial Number Sequence Part 4, Intermediate Number Sequence Part 5, Facile Number Sequence Part 6.
Get the full overview in one place! Presented at the Making Math Moments Summit, you can get the full presentation here!
Counting is Tricky
Counting is a lot trickier than people think.
Because it has been so long since most adults have learned to count, they don't realize how long it takes and the nuances of becoming an efficient and accurate counter.
To become a good counter, students need to:
Know the forward number sequence (verbal)
Have a one-to-one correspondence, and have the concept of cardinality- or knowing that the number they said is how many are in the collection
Know the symbolic representation or numeral and know that the symbol indicates the number of objects
Use that information to solve problems
The reason you learn letter sounds is to use them for the purpose of reading, you learn the aspects of number to solve problems.
It’s common to see that some students may know the number sequence but not have one-to-one correspondence or have one-to-one correspondence but do not know the number sequence or understand the concept of cardinality.
To help students become amazing counters, each of these areas needs to be practiced together to develop a well-rounded idea of numbers and number sense. This becomes even more important as they get older and if they don't have number sense everything in math becomes more difficult for students to access and use that knowledge to solve problems.
What is an Emergent Counter
If you have a student who is still learning to count items that they can see, they are emergent counters. They may be:
getting stuck on the number words or sequence
have trouble matching numbers to objects
have difficulty identifying the number symbols/numerals and knowing what quantity the numeral represents
What do I look out for?
There are some things you might see students do to let you know that this is where your students are:
Skipping numbers when counting or saying numbers out of order, ex. 1,2,6,4,10,7, 6
Saying more than one number when counting objects
Using their finger to hover over the objects they should be counting AKA “hover finger”
Saying more than one number for object
Might recognize some but not all common dot patterns like those on a dice face or finger patterns, (tell you without counting how many fingers you are holding)
How can I help students in this stage of counting?
Number Sequence and Rote Counting
The number sequence is knowing the order in which numbers are said. Knowing this leads to an understanding that each new number is one more than the previous number. When starting to learn the number sequence, students don't yet really attach a meaning to the words, but they do need to learn them.
I’ll be honest, repeating the number sequence can be dry, and often the students who need to recite the sequence may be nonparticipants when the whole class is counting.
My top two number sequence activities are movement counting and counting by 10’s skip counting song so students can eventually count to 100.
Movement Counting- As we count to the 100th day of school, I reveal a decade at a time on the 100s chart and we choose a movement we do for each decade we count.
Counting Songs- When singing a different area of the brain lights up, so if your students are having trouble remembering the number sequence, try singing it or incorporating counting songs as brain breaks
You can listen to this Rote Counting Episode on Apple Podcasts or Spotify or read this Rote Counting post to learn more about some routines and activities you can do to support rote counting with your students.
Developing one-to-one correspondence
One-to-one correspondence is the ability to match one object in a group to another. Counting refers to the understanding that each object gets one number value.
So what can we do?
Give students LOTS of opportunities to count items, practice the number sequence, and give them strategies to track their counts.
At this stage of counting, your students may require activities that let them just match items without counting to support the idea that one item goes or “matches” For example if I give a student a large printout of a dice face, they would have to put one counter on each dot. Eventually, they start to match one item to one number as they learn the number sequence with number sense routines and activities listed above.
Activities for One-to-One Correspondence
Matching Mats
Some students need to practice matching one object to an item without numbers so matching mats are perfect for that!
Pop It Task Cards
Do your students love pop its too? These task cards are great for engagement, and again working on matching items. With these cards, students will have to make a matching design on their Pop-It.
Play-Doh Mats
At this stage of counting, students may also need to work on their fine motor skills. Play doh mats with numbers and places to make a set to match the number are a great way to do double duty!
Counting Mats
These counting mats grow with your students! They can start by counting on the themed 10 or 20 frame mats, then move on to problem-solving in small groups!
You can read more about one-to-one correspondence in this blog post and some activities for one-to-one in this one.
You can get more information about the types of counters from the Learning Trajectories website.
Keeping Track of Counting Progress
It can be easy for students to get frustrated with counting as it is a combination of skills that need to be developed together in order for them to become proficient and efficient counters.
One way I found a lot of success in tracking students' counting progress is with a visual goal-setting and counting sheet. Since I taught Spanish Immersion it is available in English and Spanish. It has a quick progress tracker so I can quickly check the numbers they know and the numbers they are still working on.
It goes beyond just counting and includes goals for:
✅Identifying numbers to 20
✅Counting to 100
✅Writing numbers to 20
✅Counting objects to 20
✅Subitizing numbers
✅Decomposing number to 10
✅Number before and after
The best part is that these big goals are broken down into smaller bite-sized goals so your students can build their confidence and momentum throughout the year!
You can take a closer look at this visual goal-setting and counting sheet in this post!
Commentaires