Thank a Teacher!

It’s that time of year again, when everyone can smell the freedom of summer. The students begin to get antsy, and teachers stress and work intensively to make it to the end zone. I always feel like it should be an easy slide home, but it always proves to be just as hectic as the beginning of the year. Now is the time to thank teachers for their hard work. I have heard complaints before about how other jobs do not get the same type of accolades, so why should teachers? My response is as follows:

People deserve and perform better through positive recognition of their efforts and work. It’s amazing how far a few kind words and a token of gratitude can go. All people who show exemplary dedication to their work deserve this recognition. This includes mothers  and fathers (who yes, get a different day), and employees in all different fields. So why do I celebrate my son’s teachers? They are the ones who take care of him when I am not there. They give him the support he needs to grow and flourish, teach him lessons about life, and are an integral part of his experiences. A good teacher can have a profound effect on a child. With the proper guidance from both school and home, my son will develop solid foundations as he grows up. His teachers are my partners, parenting from a different perspective.

As a teacher, I know how much of myself goes into my students. It is not just about reading, math, and writing. There are daily lessons about becoming caring human beings, about demonstrating tolerance and love, and about dealing with difficulties and conflicts. Teaching is not just about improving the minds of America’s tomorrow. Tightly woven within the job is supporting impressionable young scholars’ social, emotional, and mental well-being. It is both exhausting to worry about 30+ students, and exhilarating to see their successes.

My son and I made this craft to give his teacher, but also a heartfelt personal note from me along with a gift. I wrote the poem thinking about what his teachers have done for him this year. First we traced his hands on a piece of construction paper and I added a heart. Then I cut out the hands and saved them for later. We used a sponge to paint pink and white to cover a white piece of construction paper. Then I put the cut out hands and heart on top of the page and we sponge painted with purple on top. When we were finished, we just peeled off the hands. After it dried, I glued down the poem and a picture of my son. This page went into a class book along with a page of his drawings.

The notes I get from students and parents help carry me through the rough times. They remain special even as they have moved on in their lives. I encourage you to take some time to think about your child’s teacher from this year. What has that teacher uniquely done that has made a difference for your child?

Subitizing: More Than Meets the Eye

Subitizing is a relatively new concept for me. Sadly, it is not an integrated part of the mathematics curriculum yet. Therefore, children often have little experience with subitizing. When I first learned about this concept, I thought it pertained only to kindergarten, first grade, and struggling students beyond those years. However, I have now seen that children of all ages benefit from subitizing.

What is subitizing, and why is it important? Clements and Sarama (2009) define two types of subitizing. The first, perceptual subitizing, pertains to the ability to both perceive intuitively and simultaneously the amount in small number sets. No counting is neccessary, you just know the amount when you see it. Children develop the prerequisite skills for perceptual subitization at a young age. According to Clements and Sarama, children begin naming collections of 1, 2, and 3 from ages 1-2. By age three, children can also create collections made of 1-3 objects, sometimes 4. Perceptual subitization up to a collection of 4 occurs at age four, and the recognition of sets of 5 develops at age five. To encourage the development of perceptual subitizing, parents and teachers should play snapshot games where children see an organized picture of dots, squares, and other simple geometrical shapes organized in a linear fashion for couple of seconds, then determine the number.

The second type, conceptual subitizing, relates to the ability to instantly see the parts, and join them together to make a whole. For example, given the picture of five arranged with three and two dots, a conceptual subitizer would see 3 and 2, and know that makes 5. Again, no mathematical operations may be consciously enacted, but rather, an instant recognition that the parts make that whole. As children progress, subitizing helps with the visualization of operations and mental math. Conceptual subitizing to five and ten begins at age five. By age six, children are able to conceptually subitize to 20. At this age, five and ten-frames are helpful organizers for promoting subitizing at these higher levels. Skip and counting and place value with subitization begin at age seven, and by age eight, children see multiplicative relationships, such as 5 groups of 10, and 4 groups of 3, which makes 50 and 12, so 62 dots. As you can see, children benefit from subitizing activities well into third grade and beyond. Below is a table to organize these milestones in subitizing.

Trajectory of Subitizing

Age	Type of Subitizing	Example
1-2	Precursor to subitizing: Name small collections up to 3	I see two grandmas.
3	Precursor to subitizing: Create small collections up to 3 or 4	I can count three crackers.
4	Perceptual up to 4	**** I see four stars.
5	Perceptual to 5	***   I see five stars.    **
5	Conceptual to 5	***  I see three and two **   stars. There are five stars
5	Conceptual to 10	* * * * * * * I see 3, 3, and 1, which makes 7.
6	Conceptual to 20	* * * * * * * * * * * * * I see 5, 5, and 3, so that makes 13.
7	Conceptual with place value and skip counting	I saw tens and twos, so 10, 20, 30, 32, 34.
8	Conceptual with place value and multiplication	I saw groups of tens and fours, so 5 tens makes 50, 4 fours makes 16, so 66.

All information adapted from Clements and Sarama (2009)

I encourage you to try out subitizing with your students or children. Where are they in their development? I have seen eight year olds that are conceptual with place value and multiplication, and 14-year olds who are at perceptual to 4. Experiences with numbers, both counting and visualizing, are crucial for number development, regardless of the age. Once foundations are set, subitizing can be used to teach more complex topics. I have used both subitizing and arrays to develop understanding of multiplication, algebraic properties, and division. If you are new to teaching Common Core, then my new unit on teaching multiplication using subitizing and array cards may be just for you! These cards are intended to be part of a program that also includes problem solving. You can check out my 17 page free download to see for yourself!

Clements, D.H., Sarama, J. Learning and Teaching Early Math The Learning Trajectories Approach (2009). Routledge: New York, NY.

Your skills are so fine

My mom would like to take the credit for my son’s exemplary fine motor skills, and if truth be told, she is probably right. As an occupational therapist, my mother looked at play time very differently than the average person. Sure, she let my son have free play, but she also crafted games and activities that would help promote his dexterity. When my son was a baby, he spent a lot of time on the mat laying down. To entertain him, my mom would slowly tear paper towels and blow on them so they danced above my son’s head. He would shriek with delight, and it wasn’t long before he began taking the paper towels and shredding them to pieces too. Everyday, he would become engulfed in bits of this snow. Sure, it was entertainment, but you know what? He was able to hold a tripod grip on any writing utensil by the age of 2, and to be honest, I never showed him how.

Developing Fine Motor Skills: Pumpkin Pegs

So here is a fun activity for working on fine motor  that I am ripping off of a few preschools that I looked at. You can use a pumpkin of any size. Kids can draw on the pumpkins with washable markers and hammer in pegs. For younger kids, it is helpful to make some holes as starters. You can have some fun with it and make the pegs hair and draw a face on your pumpkin, or just doodle and write “words” like my three year old did!

Check out the preschool tab to get a FREE download of activities you can do with your child or students to promote fine motor skills and tool control!