Sequencing comes into play in multiple areas of math, so it’s important to make sure which aspect of sequencing you are thinking about or learning about.
- Counting to 100 and back to 1 by ones
- Naming Days of the Week, Months, Continents, etc.
- Skip Counting and Coin Sequences
- Addition and Multiplication Facts
- Multi-Step Procedures (like long division)
- Following Multi-step Directions
- Solving Word Problems
To keep it really interesting, the reasons why sequencing is difficult can vary! I’ll address the reasons with each aspect of sequencing.
Let’s start with counting to 100 by 1’s. This is a great example of a math task that is conceptually fairly straightforward, as long as students have 1-to-1 correspondence, but can be very difficult to execute despite that understanding. This is one of those skills that can have a deep impact on learning. If you have trouble counting up, learning addition can be very challenging.
A student who is struggling with counting might sound something like this:
“One, two, three, um, one, two, three, four, five, um, six, seven, um” Starts building up some momentum, “One, two, three, four, five, six, seven, eight, nine, ten, umm…”
Expressive Language: A student who is having difficulty counting because of expressive language issues will benefit from hearing someone else count with them while using objects to count. For students who are having a particularly difficult time with producing the names of numbers, I will write the names on base-ten blocks to help support the process of learning to count.
Word Retrieval: A student might know the counting sequence well and all the names for the numbers, but when they go to grab the word, it’s not there. You know that feeling when a word is on the tip of your tongue, but you can’t quite find it? Imagine that happening every day, throughout the day. Assuming the student can read, writing out the words for the numbers can help support this student. You could write them out on a list off to the side, or list them in order. Practicing naming the numbers out of sequence will also help.
Auditory Memory: Remembering the days of the week, counting, multiplication, and the seasons can be difficult due to weak auditory memory. This also shows up in writing, when a student can only remember part of a sentence that they are trying to write. Auditory memory can be improved simply by practicing sequences, recalling sentences from memory (start at a manageable level and then make it longer over time), and by listening to simple tunes and reproducing them on a piano. If this seems to be exceptionally hard, I usually recommend that parents consult with an audiologist.
Attention: If a student is losing their place in the sequence because they start talking about something else, or pause and lose track, give them something physical to count. The physical stimulation is usually enough to keep their attention on the task. Adding in a metronome can also help. You set the speed to match the rate at which the student is counting.
Processing Speed: For student who can count to 100 but slowly and laboriously, I use a number sheet in rainbow colors and have them alternate from naming the colors to naming the number, and then combine that with a metronome at a pace that matches their counting. I’ll sometimes add in a wiggle board as well, so they have to keep track of the rhythm while balancing. This engages many senses at once and makes it so challenging that once you take away the wiggle board and the metronome, counting seems easier!
Working Memory: If a student has trouble switching between the tens place, “18, 19, . . . .20” and then zips through the 20’s until “29……30!” then I encourage them to practice counting by tens, and then focusing in on “19, 20. 29, 30. 39, 40…” until it becomes more automatic. This is not something I’ll spend a lot of time on unless there is such a significant delay that they start to derail completely.
Once a student can easily count up to 100 and understands how the numbers repeat at each new set of ten, I have them practice counting down from 100 to 1. That’s a significantly harder task!
I scaffold this process by making sure they can easily count down from 10 to 1, then 20 to one. Then 100 to 0 by tens. And then we combine it all. Some students need extra support at first. Sometimes I hold my fingers up to keep track of the 10’s, or I give them a quiet verbal cue for the next lower ten. I have worked with some students who consistently need to figure out the lower ten before starting with the nine. For instance, they might say “…94, 93, 92, 91, 90, 80, 89, 88, 87…” – as long as I know they are just cueing themselves, I chalk that up to an effective strategy.