The pandemic outbreak of COVID has resulted in a very different life for the time being. Some of those things I cherish, and this is one of those ….
My Math Curriculum
I was nominated to be the Math teacher for Naiya since the “shelter-in-place” began. I started out by looking at Singapore math 1A / 1B methodologies and combining it with Montessori manipulative objects to begin to work on some fundamental concepts:
- Sequencing: Gain familiarity wit the sequences of numbers in their written form and in their quantity form
- Basic Operations: Understand what basic operations meant and implement them in a variety of ways from fingers, to beads, to “moving objects,” etc.
- Counting By: Gain familiarity with basic “counting by” structures such as counting by 2’s evens, counting by 2’s odds, counting by 5’s, and counting by 10’s.
- Word Problems: Take a word problem and translate it into a math equation or manipulative and then solve it
Throughout all of this I insisted on being able to identify numbers in two ways “Our Way” and “English.” So if I write the number 65, might say “sixty-five,” but then I ask, “how do you say that ‘Our Speak'”, and she would say “six-tens five.”
Today’s Lesson
Naiya had been getting better at solving “easily grouped” subtraction equations. So something like 65 - 20 she could just take “6 ten bars” and then take away “2 ten bars” and arrive at the answer. However, she was having a difficult time with “easily grouped” addition equations, even though she could do smaller numbers on her fingers easily. So “What is 5 + 2” is an equation she could do on her fingers, but when I’d ask her to solve an equation like “What is 25 + 10” using beads, she struggled with how to transpose the process she could easily perform on her fingers to beads. My sense is, from watching her, all of the “saying different numbers” (two-tens five plus one-tens) then gets her confused about how many ten bars am I counting and how which number am I looking for a bar with that quantity (e.g. the five bar in the equation above).
We started off the lesson today doing “easily grouped” addition because I noticed yesterday that it was challenging, even though getting the subtraction of the same quantities was straightforward for her. The lesson began with her feeling frustrated and not knowing “what to do with the bars,” she disconnected and started humming (which isn’t uncommon). I asked her to re-focus and try again … then I asked her if she wanted me to do the process and explain to her as I went. She said, yes … so I began going through the process …
It must have been the 2nd or 3rd equation that I was doing and then it was like a supernova went off in her mind … her eyes got wide, her face brightened, and she said, “Daddy, I get it. Ask me an equation.” I wrote down the following equation: I wrote down “45 + 20 = “.
Then she stood up and she starting tapping her finger into the air, like she was counting beads on a bar. First she. created the “45” out of 4 ten-bars and then the five bar and then — also in the air — she created the “20” out of two ten bars. She then said, “one, two, three, four (counting the imaginary ten bars in the first. group she had made in the air) , five, six (counting the other two ten-bars she had made in the second group in the air) … six-tens five!”
I couldn’t believe it … I was completely speechless. I wanted her to manipulate beads to solve the problem but she was able to visualize all of it in the air in front of her and then literally “count out the solution.” I wrote down another equation “26 + 30 =” and she did it again, the exact same process, putting two imaginary groups of beads in the air, and then counting . “5 tens-six!”
Reflection
This has been weeks of working one-on-one with Naiya. Putting many different problems and processes in front of her, seeing where she struggles, and figuring out ways to re-frame those problems or shift the way something is presented. Today’s breakthrough solidifies for me many things:
- Learning is not linear (yet again, thank you Robert). I watched a cognitive leap today that would have made Poisson blush
- How important tailored curriculum is. Every child is different and it’s taken me weeks to really understand what Naiya does well and what she needs to work on. I can only imagine what it’s like in crowded schools that are understaffed with children who feel shamed / boredom / fear / insert-the-word-here-that-turns-off-your-prefrontal-cortex. I genuinely believe that technology has the potential to fundamentally shift this landscape, but we have yet to even scratch the surface.
- I feel like I had the opportunity to witness a miracle today … I wonder if teachers to have similar experiences to this. If so, I can understand how fulfilling it could be to see this in different children.