We have been trying to ascertain where Lily’s comprehension of a few foundational mathematical aspects are, in order to have an idea of some upcoming activities and explorations.
She seems to really enjoy Odd Squad and Peg+Cat still, and has gained some relevant and important understanding of concepts from these shows.
1) Rounding: She understands the concept and seems to use the skill in every day life sometimes, however, she doesn’t quite seem to see its actual value when it comes to quickly assessing value for the purpose of convenience. It seems this remains beyond her concrete grasp just yet.
2) Place value seems to be understood, at least consistently through the thousand place. She also has an awareness of places to hundredths. She doesn’t see the value in this exercise/presentation except when wanting to add multi digit numbers, which we are working on mental math development to facilitate.
3) Multiplication is solid in as far as concrete sets, exponential progression, and the value/purpose. We will find a way to encourage intake of basic facts for memorization.
4) Doubles and basic singe digit addition has taken root, as has skip counting by 2, 3, 4, 5, 10, and 2/4/8/16/32/64/128/etc… thanks to Tom and Angela.
5) Subtraction concepts seem to be taking shape. Sometimes Lily uses counting up, other times she seems to be able to remove amounts in chunks, but either way, the concept is solid.
6) Division and fractions seem to be well understood. Lily can demonstrate dividing a whole into as many parts as desired, has a quick response when asked to half a whole, including when a number halved results in a mixed number, and seems to successfully be able to split just about any amount into a requested or desired amount of even sets. She demonstrates an understanding of 1/2, 1/4, 2/3, 6ths, 8ths, and exponential dividing.
7) Exponential multiplication is understood and can be demonstrated when she sees the relevance to something that interests her.
8) Monetary denominations seem to be well understood, but at this point, money in a given amount has little relevance or interest for her. She is beginning to learn the concept of necessary amount, more than enough/change, and the need to make choices of purchases based on conscious consideration. Perhaps in the next year these concepts may become more relevant for her, in which case, she has a solid foundation to draw upon.
9) Basic and advanced geometry concepts have taken, um, shape.
Lils enjoys working with shapes, has a solid concept of spatial relationship and reasoning, and manages tangible and virtual dimensional manipulation with ease. Lily has successfully taken a fun “test” in which she had to determine which aspect of a given shape, when options are rotated or otherwise modified, is missing. https://www.123test.com/spatial-reasoning-test/ & https://www.fibonicci.com/spatial-reasoning/test/
Fibonicci, as well as fractals have held her interest for the last year.
10) Lily has a good understanding of the power of 0. She recalls ten through trillion, by tens/hundreds/thousands/hundred thousands well. She has some sense of the magnitude of the larger amounts.
11) Recognition of space, area, diameter, and how to figure some of these, in certain instances, has been demonstrated and self initiated in some instances. She often has to take/generate measurements for the various projects she undertakes building, including sewing projects.
12) Time: Lils is aware of the 12 vs 24 hour, am/pm, and projection/subtraction of time. She is able to explain what time an alarm would ring if set to go off after a number of hours, based on a given set time. For instance, if she goes to sleep at 10pm and needs to be awake at 8am, she is able to indicate how many hours she would have slept. Also, if asked to indicate what time she would wake if she’d gone to bed and needed ___ hours of sleep, she can reliably indicate what time she’d wake.
I expect there is more to this list, but this is a good start. Over the coming weeks, I will add video and other materials as she presents opportunities, for the purpose of demonstration of her understanding and functional use of mathematically related concepts.
The drawing/painting was created the day following our trip to the ASU planetarium, in which we saw the preview of Robert’s “Fractal Explorations”, which Russ wrote music for (and/or just for the planetarium in general). She genuinely seemed to enjoy the show, which is sort of rare, and was clearly inspired to create her own representation of what she saw in the presentation. She named this painting, “Iterations of Autumn”.
