What is subitizing?
What is "Dot Flash"?
Subitizing -- What is it? Why do we do it?
Many years ago, after attending a session at a math conference, I started flashing a collection of dots to my students. Although, they were able to tell me how many dots they saw altogether, I did not have a deep understanding of the power this activity had to enhance number sense for our young students. It was not until I was working to obtain my Masters that I unpacked my own mathematical understanding. I became so interested and intrigued that I chose subitizing as my final project to complete my Masters. Rather than just writing a paper, I wanted to provide teachers with a valuable resource so I wrote and published a professional resource for teachers titled, "The Benefits of Subitizing, Helping Early Childhood Educators". (click for more information)
After completion of my Masters, I led a group of teachers in my school through an AISI project. Our focus was to determine if subitizing daily in the early elementary years benefited students’ number sense identified in the research. We set up baselines and assessed throughout the year.
Our findings verified what the research states: if a teacher takes 5 minutes a day to engage their students in a subitizing activity, number sense is vastly enhanced. Therefore, it improves children's mathematical success.
The teacher group became so intrigued that we continued on with the project for another year. This project impacted our school enough to put money into a numeracy support project in which educational assistants worked with those students who were targeted as having challenges. The success rate was phenomenal, but unfortunately when budgets were cut the project had to be let go.
At every chance, whether it is with individual teachers or when I present to teachers at a conference or at a Professional Development Day, I incorporate learning time for subitizing. No matter if I am working with teachers or students, they are completely engaged. My students love it and if we have to miss it they are not happy campers.
What is subitizing?
For those of you unsure of what subitizing is, it is recognizing a collection of dots at a glance. It is also referred to as part-part-whole because within the larger collection are smaller collections that make the whole.
The research states that the collections be made from homogeneous dots, not fancy pictures of dogs, cats, etc. They do not state the reasons why but say it puts students’ learning at a detriment. There is also a sequence in which to organize and present the collections to our students.
We must first begin with arrays (matrixes), then move to linear arrangements, then dice arrangements and lastly scrambled arrangements. Research also states we could have some dots different colors to help children see those smaller collections within the larger collection.
Once you have a collection of dots created, either on a paper plate or on the Smart Board, you give the students 3 flashes… and it is a flash. If you show it for too long the students will do a ‘count all’ rather than visualizing and recognizing those arrangements at a glance.
The first flash is to VISUALIZE. WHAT DOES THAT ARRANGEMENT LOOK LIKE?
The second flash is to LOOK FOR SMALL GROUPS.
The third flash is to QUANTIFY (which means to add and find the sum or the total).
- Look for small groups
There are no more than 3 flashes (this is research based), so I tell my students if they didn’t see the whole collection to quantify what they did see and then when they see the collection they can determine where they made an error.
DO NOT SHOW THE COLLECTION UNTIL STUDENTS HAVE SHARED THEIR TOTAL.
Also, I do not show the collection until I have 2-4 students share how they saw the PARTS OF THE WHOLE within the 3 flashes.
If I show the collection then students start making up other ways in which they saw it. It is important they share their thinking on what was seen on the flash.
For example, for the collection of dots below, one of my students saw the sum of 10 as the parts, 4, 2, 1 and 3. This student quantified these parts as 4 and 2 is 6. Add 1 more to 6 is 7 and I know 7 and 3 make a friendly 10.
The above example gives insight into the researched based activity called Dot Flash.
The three pictures below show another researched based activity called Reproduce. It follows the same 3 steps as Dot Flash but the students reproduce the collection of dots.
They can’t start reproducing until after the second flash (this is so important because the first step of visualization is pertinent) and they must reproduce the collection exactly as they see it. I then extend the reproducing activity to help with the understanding of multiplication.
As I see understanding grow deeper I extend this learning of multiplication to using grid paper to show these arrays and we move into division. Subitizing lends itself to the learning of almost the entire primary curriculum. It is quite amazing and the best thing is that the students love it!
Subitizing can also be done with a collection of coins(money) which leads into a deeper understanding of fractions and decimals. This comes from one of the Cathy Fosnot books I read 3 years ago. It is fascinating and the concepts that can be learned from this is incredible…For example:
For money, the coins are always set up as an array/matrix and the coins must all be the same. (eg. all quarters, all dimes, etc)
You do this like the dot flash activity: The students get 3 flashes. The first flash is to visualize, the second flash is to look for small groups and the third flash is to quantify. However, they are to quantify two things, the number of coins and the value of the collection of coins.
After the 3 flashes, I ask the students to share their thinking before putting down the screen because it is important they share what they saw on the flashes.
Following this discussion was the connection of their understanding of fractions we have learned from our daily routine as well as our number line work.
Remember: All learning is CONNECTED and REVISITED Daily.
As you can see from the picture, I had a student come up to show his thinking of how he quantified the value of the coins as the fraction of one-half and that each one-half of the whole is 50 cents and two halves is the whole and has the value of $1.00.
Another student said she saw the four quarters and counted 25, 50, 75, 100. I asked her to circle each count as a part of the whole and write the fraction and value for each count. You see this displayed in the next picture below. We counted each part as one-fourth, two-fourths, three-fourths, four-fourths and then I asked so if ¼ of the whole is 25 cents, what value is ¾ of the whole.
The next picture shows a student who circled ¾ of the whole and identified the value as 75 cents.
Another student piped up and said, "I know another way to write ¼ of the whole." The next picture shows that this student circled ¼ and wrote 25/100.
This then led me to introduce equivalent fractions. The next picture shows our discussion. I asked if 25/100 is the same as ¼ and I wrote this down. Then I wrote ½ and asked if there was another fraction to mean/show the same value and many of the students could tell me 50/100. Lastly, I wrote down ¾ and asked if there is another fraction to mean/show the same value and again I heard 75/100. Very briefly, I talked about these fractions showing equivalence.
As I have mentioned previously, subitizing can impact almost the entire primary curriculum and impact the later elementary years. The simple flashing of a collection of dots and/ or money can vastly enhance our students' number sense. The best part of this is that students love it and I hear it if we have to miss subitizing in our daily routine.
I hope I have heightened your interest to learn more about subitizing and how to incorporate it into your daily instruction to enhance your students’ number sense.
I have included a free Smart Notebook file with 10 slides so you can give it a try with your students. Click here to download the file: Subitizing Freebie (please note that you need Smart Notebook software to open this file. Contact me if you have questions.)
Try it with your students
I can’t wait to hear how it goes and for you to ask me any questions that may come up as you work with your students. I will be helping anyone interested in extending their learning about subitizing through videos and webinars in the weeks to come. I also am aware of how precious the time of a teacher is and therefore, I will also have subitizing Smart Board files available for purchasing.
I look forward to hear how it is going! Leave a comment or question below.
Tiny Polka Dot Cards!
I also wanted to make you aware that Dan Finkel (MathforLove) has a new material for sale called Tiny Polka Dot Cards. I had told one of the kindergarten teachers at our school. When she checked it out on Amazon, you could only get it shipped within the States. However, there is a printable version for a cost of $5.00. She has shared this with me and looks it absolutely awesome! You would have to copy onto thicker paper and laminate but it would be worth it! Here is the link: Tiny Polka Dot Print and Play