Here you will find a collection of resources I have on some foundational skills:
- 1-to-1 Correspondence
- Subitizing Patterns and Quantity Sense
- Visual-Spatial Relationships
- Rapid Automatic Naming
You’ll notice these areas may need to be supported by an Occupational Therapist (OT) or Speech and Language Therapist (SLP). For the most part, I don’t reference age ranges because by about 7 or 8 years old, these skills are assumed to be fine in the classroom and aren’t looked at. I have met adults who struggle with these skills. But, if you have a student who is struggling to learn math, it’s worth checking these out. From 4-7 years old, it should be fine to work on developing these skills as long as you aren’t pushing into a place of frustration and anxiety.
I would love to hear any recommendations you have in these areas. Please try to categorize them based on the four areas (or add a category of your own!)
When you count objects one-by-one, in theory, you say a number each time you touch an object. For students who struggle with counting, organization, impulsiveness or tracking, this can present a challenge.
Activities for 1-to-1 Correspondence
For younger kids, I start with larger objects. For seven years and up, I use paper clips because they are a little harder to work with. I put out a pile of objects and watch how they count.
- Is the counting synchronized to the movement? Do they double count because they are counting faster than they can move? Or are they under-counting because they are moving faster than they can count?
- Do they keep the objects organized? Is the miscount due to losing track of what they have and haven’t counted yet?
- Are they randomly counting and moving objects?
- Once they can count smaller and smaller objects, can they count dots? Do they lose track visually? Do they need to tap or make marks with their pencil?
- Do they have the physical and organizational requirements for 1-to-1, but are struggling with the language of counting?
If they are having issues with 1-to-1 correspondence, I have them recount a pile of of objects until they get the same number twice in a row. I usually don’t show them how to improve, they have to work it out for themselves.
One exception to that rule is if their frustration level is getting too high because they are doing their best and just can’t control their motor movements well enough. An OT referral might be the next step. Or, if the language ability is the issue, then I focus on supporting language development. More on that later!
Subitizing Patterns and Quantity Sense
At the most basic level, subitizing is hardwired. We can recognize from 1 – 4 objects without counting. That’s why we have special words for first, second, and third – but switch to fourth, fifth, sixth, etc. And why early counting has the words “one, two, many” as the names for numbers. From there, you can leverage subitizing and pattern recognition to develop quantity sense. Students who have trouble memorizing addition and subtraction facts likely struggle with subitizing patterns and quantity sense. In a nutshell, they struggle with taking parts into a whole. They may also struggle with memorizing sight words. Visual memory plays a role in all of this as well, but we’ll get to that down the road.
Back to quantity sense, I have worked with kids who can’t reliably count the fingers on one hand at the age of seven.
Me: Count your fingers on one hand.
Student: “One, two, three, (skip a finger), four”. I have four fingers on one hand.
Me: Awesome. Let’s count again.
Student: “One, two, three (double count a finger), four-five, six”.
Me: How many fingers do you have on one hand?
It does not phase them in the slightest that they have different numbers of fingers on the same hand. This is my favorite example of issues with quantity sense. A student who has issues counting, but has strong quantity sense, will recognize that they counted wrong. A student with quantity sense issues may have memorized that they have five fingers on their hand, but not care that they counted four and six.
Activities for Subitizing Patterns and Quantity Sense:
There is a great app for the ipad to practice this skill: Subitize Tree
And, I have been working with a lovely developer to design a game that develops quantity sense using Mayan Numbers. It’s in very early stages, but feel free to take it for a spin: Mayan Numbers Drill or Mayan Numbers Matching
This is another area that might lead to an OT referral. I am not an OT so I still need to sort out the difference and relationships between visual-perceptual, visual-motor, and visual-spatial, but what I do know is that one of the most easily overlooked fundamental areas of learning math is this visual realm.
Some of the more obvious ways it shows up is in handwriting and organization on the page, Cartesian graphing, and copying shapes. If you want to check this one, have a student copy a dot design and see what they see. And ask them to draw a square on grid paper. This might not happen to everyone, but most of my students will draw something like a 5 x 6 “square”. I ask them how they know it’s a square and they tell me the sides are the same length. I ask them to count the the length of their sides, and they discover the error. Obviously, any of us could misdraw a square. I am sharing this to illustrate how someone can understand a definition but not be able to demonstrate the meaning.
Activities for Visual-Spatial Relationships
This pinterest has some great examples of what your student might find challenging. I use this types of images as an assessment and as an activity. I don’t just look to see if a student can do it, but what strategies they use, how much erasing is needed, and how frustrating the activity is.
Here is a massive collection of activities from Your Therapy Source. I have not used this particular resource, but it is an OT’s collection. You can make example activities if you are trying to figure out which one will benefit your student before purchasing. The overall look is pretty young, so if you are working with an older student, it might not be the best choice.
I also love to use Critical Thinking Company’s Building Thinking Skills. I don’t follow the grade-level recommendations. I use the first few pages of each section as an assessment. And, for a language boost, where it says to write information, you can have students give answers verbally instead. Also, I do have to provide more foundational work for students who can’t complete the activities as written in the book.
Rapid Automatic Naming
Rapid Naming is the ability to look at an object or number and call it by name without hesitation. Difficulty with rapid naming contributes to issues with learning to count and vocabulary in math, and contributes to issues with reading.
If you like to read research, here’s a study that showed “… counting and RAN were powerful predictors of arithmetic and reading fluency.”
Activities for Rapid Automatic Naming
I have developed a series of activities to work on RAN and processing speed but need to put together the directions before making them available. Let me know if you’re interested and I’ll speed things up!