I’ll admit it, and I’ve even said it myself: “Until Little Johnny shows me mastery of this skill….I can’t extend him.” However, I would now like to go back and apologize to Little Johnny and all those students that I didn’t offer extensions to, because I wrongly thought they should show me mastery of a previous skill first. Today I hope to convince teachers who are still saying this, that it is not too late to change!
I have been frustrated this year because my own son learns differently and seems to struggle with written output. That being said, he has demonstrated that he is quite able to do math. In Grade 1, they were working on adding and subtracting to 20 and yet Oliver has demonstrated to us that he can perform up to 3 digit addition and subtraction already. So at our last parent-teacher interview, we asked the teacher what kind of extensions would be available for kids like Oliver and we received the typical answer, “Until he can show me he can do this (see picture below), I can’t extend him….”. We were heart-broken, and at the time, I didn’t have the right words to explain why he should be extended. But now I do! So if you are a parent with a child who learns differently, now you will too!
Today, I hope to convince you (and Oliver’s teacher!) with 3 simple arguments, that this way of thinking is obsolete!
A. There is more than one way to skin a cat!
Oliver’s writing output is minimal and as a result it would take weeks for him to show you that he knows his 10 facts. His teacher even admitted that his written work fills the ‘to be completed’ bin at school. This means he will never be extended, never experience a productive struggle and may tap out of math class altogether.
The above task demonstrates Oliver’s extreme laziness (or his ingenuity?!). He was obviously given choice (yay!); however, he chose the easiest way out (5+0, 4+0, 0+0!!). I would have used real dominoes and removed most of the ones with zeros so that students like Oliver were forced into a productive struggle. Another way to extend would be to include some dominoes from the 12 by 12 set, or even suggest some students to add two dominoes together. These are all ways to differentiate the task, but today I want to talk about how to differentiate the product.
Teachers who take the time to use alternate ways for students to show what they know, will be able to see the strengths of more of their students. Differentiating product is essential in assessment, even in math, and especially in primary. Watch what happens when I do the same task that the teacher was doing, but allow Oliver to show what he knows in different ways (i.e. differentiate the product). By offering multiple ways for him to show what he knows, I can see clearly that Oliver knows his 10 facts and is in fact, ready and able to be extended.
B. Quality over quantity!
There is no benefit to having a child do the same type of question 50 times. If they can do it correctly a few times, it is far more beneficial to see if they can transfer the skill to a different type of question; or to see if they can problem solve using that skill. In other words, why not find more creative ways to get them to practice. If the goal is to add and subtract to 20, an extension would be to bring in problem-solving. Ken-kens are a great way to still have fun, build fluency and not drill to kill. Here’s an example. Click here for my earlier post on Ken-Kens.
C. Don’t deny students access to extensions!
A great way to extend is with problem-solving. A favourite go-to for me is the NCTM’s Math Forum Problem of the Week questions. Built with low floor, high ceiling, wide walls in mind; they are a great way to engage your students with mathematics, reinforce concepts learned in the classroom, and bring in real problem-solving in an authentic way. And they have problems for primary! Here is an example of a problem that Oliver worked on that shows transference of the skill of addition. He chose to use counters to solve this one, and I acted as scribe to record his final answer, since written output appears to have been holding him back in math previously.
Universal design for learning (UDL) means using tasks with low floor, high ceiling, wide walls. By giving students more interesting access points, you not only engage them, but you can see whether they have the basic skill, while extending those that need it at the same time. Low floor means all students can access it; high ceiling means the task can be extended; but now teachers, I beg you, please add wide walls! Ask yourself: how inclusive is my task and how might I provide multiple pathways to get from the low floor to the high ceiling? The only drawback…you might be shocked to see what your students can do!
I know we are teaching in a different time right now because of COVID-19 and home-learning has brought on some challenges. However, we need to still remember that there is more than one way to skin a cat! Differentiation should still be a part of our practice. We can still get creative about how to offer low floor, high ceiling, WIDE WALL tasks. Below are some resources that might help you get you started. Oh and I think you should know, Oliver’s teacher recognized his need and has been extending him, even before I wrote this. Thank you Mrs. S! So which students in your class need extensions? Perhaps they all do!
Here are some resources to get you started:
Differently Wired by Debbie Reber
Inclusion Strategies with Shelley Moore
Remote Learning Activities K-8 (designed by Fawn Nguyen for RSD)
National Council of Teachers of Mathematics: Problems of the Week (subscription required)