I teach a math methods class for special education teacher candidates at UCONN. During a lesson on an instructional strategy on making math meaningful, I experienced an epiphany of sorts. The students were partaking in a discovery lesson in which they rotated through using four different types of manipulatives (photo below, left). They would follow directions, take photos to document their work, and then the class would rotate to the next manipulative. Two were intuitive and easy to follow, one less so, and the integer chips (red and yellow below) were foreign to several students. This mirrored the energy and attention given to a computer based discovery lesson involving matching that I also conducted. Sandwiched in between was use of my beloved PowerPoint slides (below right) in which I shared key points about meaning making. At the start I shared that I would present for less than 10 minutes, which apparently was still too long for several of them.
My point is not to be critical but to share how I am stepping back to reflect on how this anecdote reflects a broader issue. Social media, not technology in general, appears to be changing how humans learn as the formative years of the younger generations are immersed in social media.
We all know at a visceral level from our Pandemic experience that the technology itself is not nearly enough to grasp the focus of our students at a level that intellectually engages them, as opposed to engaging them with activity that is often conflated with meaningful learning. (Most of us have experienced the phenomena of an activity that the students were actively completing but at the end did not appear to learn much.)
It occurs to me that the act of learning has profoundly changed because students have all the information in the world at their fingertips (article above lightly speaks to the depth of this). They learn about each other including what they had for breakfast or what they saw at the mall. They inform and teach each other about common interests and have a broader exposure to new ideas and interests. The article cited below speaks to “learning procedure…not restricted by time and space.” That statement alone speaks to how profoundly the younger generations learn and how they view the act of leaning.
I read a comment in a teacher Facebook group posted by a college instructor who was bemoaning the engagement and effort of his math classes. This led to a broader discussion about technology as a means of engaging the students. To me it appears to be #morethantechnology and I would like to learn from others about this topic.
NOTE: I don’t believe having students exchange Tweets and Snaps about curriculum topics is enough. People share and consume information in an on demand setting, including us older folks in our ancient Facebook groups and listservs. I think we have to make the information more engaging in a substantive fashion…but how?!
In education, math especially, there exist a learning situation I call the patting head and rubbing belly phenomena. In this phenomena students are presented a math problem that consists of several steps they know how to do and then maybe one or two additional steps that are new. Adding the additional step is like adding the task of patting your head while you rub you belly. Many students will struggle with this.
Adding one additional math step to a sequence of steps that are prior knowledge or the students seems so simple. What actually can happen is the entire effort becomes challenging. This is true for all types of math, whether it is the general curriculum or life skills/consumer math.
This phenomena plays out in life skills math or consumer math in a stealthy manner because the steps or tasks seem so simple. For example, many of us have worked with a child or student who was learning to count money. When learning about a nickel or a quarter, the coin name and value are easily identified. Once both are introduced, many students confuse the two and may even freeze while attempting the work with the coins.
There is an ABA based process for addressing this using a task analysis and chaining in which steps are worked on in isolation before connecting (chaining) the steps together (and not all of them at once until the end). One related strategy to help implement this approach is through scaffolded handouts in which the steps are enumerated and the structure of the handout isolates the tasks. I have used this approach for 1 to 1 correspondence up to AP Statistics (see below).
When working out a draft of an IEP, I suggest having the task analysis and chaining explicitly identified in the accommodations page and ask for an example of what this looks like (using an example math topic).
Human senses are bombarded by external stimuli: smells, images, sounds, textures and flavors.
We have a filter that allows only some of these stimuli in. We focus on the ones that are most interesting or relevant to us.
Our working memory works to make sense of the stimuli and to package it for storage. It is like a computer, if there is too much going on, working memory will buffer.
The information will be stored in long term memory.
Either it will be dropped off in some random location and our brain will forget the location (like losing our keys)
Or it will be stored in a file cabinet in a drawer with other information just like it. This information is easier to find.
Analogy to Classroom Learning
Here is an analogy to what happens during school instruction. You are driving down the street, like the one shown below.
There is a lot of visual stimuli. The priority is for you to pay attention to the arrows for the lanes, the red light and the cars in front of you. You have to process your intended direction and choose the lane.
Other present stimuli may be filtered out because it is not pertinent to your task: a car parked off to the right, the herbie curbies (trash bins), the little white arrows at the bottom of the photo. There is extraneous info you may allow to pass through your filter because it catches your eye: the ladder on the right or the cloud formation in the middle.
Maybe you are anxious because you are running late or had a bad experience that you are mulling over. This is using up band width in your working memory. Maybe you are a relatively new driver and simple driving tasks eat up the bandwidth as well.
Impact on Students
For students with a disability that impacts processing or attention, the task demands described above are even more challenging. A student with ADHD has a filter that is less effective. One with autism (a rule follower type) may not understand social settings such as a driver that will run a red light that just turned red. Another with visual processing issues may struggle with picking out the turn arrows. Their brain may start to buffer, like a computer.
Learning is not a singular threshold to be met. There are different levels of learning – a continuum (see photo below taken from the book Teaching Mathematics Meaningfully).
A student demonstrating proficiency (fluency) is far different from a student simply showing some level of understanding (acquisition). I remember learning to drive a car with a stick shift. During acquisition (initial understanding) I was looking down at the pedals and the stick shift as I thought through the steps. It is not surprising that many students who only show acquisition of a math topic soon forget it. Despite this, the acquisition stage is often were math in schools resides.
This extends beyond math fact fluency to all math topics and the students should take the next step and demonstrate maintenance. To do this, I recommend that a curricular based assessment be given a couple of weeks after a student initially showed what is considered mastery – the student successfully performing problems aligned with a given math objective.
Below is a excerpt from the book with an explanation of the topics. I use this text in the math for special ed courses I teach at different universities.