I recently worked with the children in my class on BASE 5. I say BASE 5 because that was what I introduced the base work on. I was, once again, surprised how well this abstract concept, of using a different base, became something rather simple and logic for the children. How come?
I think it was the link to their well-known ‘base’ they work on- Base 10.
The sheer knowledge of how to do an exchange (carry over, what they all do on a daily-basis, is implanted in them, therefore, the act of using a different base is a simple logical frame-work.
I need to add that I do, meanwhile, work in 6th grade (elementary) yet 1st grade of the IBMYP programme. These two do overlap yet regarding heir age, 11 to 13, their reasoning mind is well developed (at least on an analytical side) therefore their wider understanding of the concept at hand is given and the time is right o confront them with this kind of lessons.
So I introduced the topic by readdressing the decimal system, making the link to the wooden hierarchical material, the families (simple, thousand, million) and directed them to the all known place values in the decimal system. A nice brief recap of what they know, bringing them back to where they come from. All felt secure and confident, that they remember all of this.
After the introduction was done, we went to the lace vales of base 5. Since the concept was understood within the decimal system, it was logic for them that instead of multiplying each number by ten, we multiply by 5;
1 – 5 – 25 – 125 – 625 = place values of base 5
All that was clear and the links were made.
The concet was understood and hence we established that in base 5, we only have 5 numbers. Vice versa, in base 10 we have 10.
Base 5 = 01234
Base 10 = 0123456789
All that was clear, and the addition exercise in base five presented no difficulty; Instead of exchanging at ten, we exchange at 5. Keeping in mind that five is an illegal number such as 6 7 8 9.
With some we went onto transforming base 5 to base 10.
There, all the knowledge of multiplication and division comes in action and need to be applied.
All in all, I need to say that this lesson was/is a fantastic manner o introduce something new yet all the known need to be applied and repeated; I can recommend to not wait too long to introduce to 11/12 year old children. It wraps it up very nice with something exciting and new.
Where to start in Geometry? What age is the right one? How much does one need to pay attention to language? Again I think that children can and need to be trained in their visual understanding and additionally one can add the right words to what they see and obsreve. The earlier they learn to be able to express what is in front of them the better it is.
I see it now in the last year of elementry and in the first years of secondary how hard it is ti express properly and clearly what they see and most of all, what they have to do or are doing. SO language is essential and will help them to describe and explain…
If you can explain it, you know how to do it…
THINK INTERDISCIPLINARY 🙂
Geometry applied in the right way is a fantastic tool to train logical thinking. already at an early stage, children can see and understand patterns. Often it is underestimated how a young brain can already understand structures infront of him or her.
So Geometry can help to train the brain. used in the right way, children will see this as something pleasing… geometry is esthetics. The eye likes symmetry and equal parts. One feels safe when the structure is even, balanced and logic. So children of all ages have comfort within geometry and if applied and shown right, it can be and is a springboard I.e. fractions.
One should n ‘ t be scared to use metal insets and let the children explore. What are they able to create? What kind of symmetries will they make? One can halp to givr certain guidelines, like no crossing lines, the iset needs to always touch another line that was drawn, etc. The younger, of course, the simpler and for older children one can add a compass or ruler,… the options are countless.
I personally think that geometry is not given the right amount of attention in a classroom. I think as well that often the right connections, the interdisciplinary links are not made, yet one clearly does not go without the other.
I do agree that math has a very high standing and that it is important, yet when one would allow the children to dwell for longer periods of time in the geometrical realm; they will, and I mean all, profit on the long run.
gives the right to make mistakes!!