Geometry as a springboard to math

When there is a first combination … you will find a second combination.

I been thinking that these combinations are ideal ways to introduce a child in primary to various terminologies, words, language. One can apply terminologies found in algebra, explain the concept of variables with the pictures you see on the board. In that case the word sum could be brought to the child’s attention, that this word is linked to an addition, introducing the word quotient and product. For visual children this can be a good tool to give them these words. By experience a 10,  11 and 12 year old can by times struggle with word problems hence to a non-understanding of the terminologies they have in front of them.

These important words are often neglected because of the drive of having the right result or answer.

Of course there are millions of ways to give ‘the words’ to a student, yet within the Montessori material is so much that can be used for things, topics, facts and ideas but one doesn’t dare to do.

Another example…

I can explain (within the chapter of equations) what it means to maintain balance. It is visual, clear and attractive. ‘whatever is done on one side of the equal sign must also be done on the other side’;This board could be my introduction. Later one also can use a scale to let the children explore.

I will continue my investigation of the vabulous variety within the Montessori material, wher and how to apply the given in different topics of mathematics.

Chris

Combinations

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 🙂

 

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Geometry as a tool to strengthen logical thinking…

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.

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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.

Chris

RULER and COMPASS

G´day y´all,

This is a book that was offered to me by a friend at school. I need to say that it is a interesting and fascinating booklet. “Practical Geometrical Constructions”. Indeed the things you are shown are flabbergasting and have a solid ´WOW`effect. It is an interesting guide for Nomenclature, that you can use additional to your Nomenclature that is available in a Montessori classroom. I need to say that for a lower elementary child, the handling of a compass is often challenging enough (and that  does by times last until secondary) yet this could be something that the teacher can construct, next to a small group of children, like a presentation, to show what is possible to construct.

I think it is fascinating. It could be a springboard for exploration along regular polygons, equilateral triangles etc. The designing of shapes with a compass can and is indeed a special sort of art. Plus, there is no better way to explore and learn those different names of shapes and all the additional terminologies that need to be known within the geometrical realm.

I can recommend that little book. It is a sweet little addition to your albums and other resources.

bildschirmfoto-2016-12-04-um-19-53-22Here you can see the ISBN number in case you are interested.

Geometry as a window to your inner self

The three fundamental shapes in geometry

screen-shot-2016-09-18-at-13-19-42The relationships between these three shapes are fascinating and endless. Just like your inner self.

The complexity of these geometrical shapes, the simplicity is challenging.

This shape is an ideal springboard for students to start a geometrical experience and is opening doors throughout the chapter. One can link various aspects and relations to these three objects, this picture. The nomenclature has its beginning in this image and can be transposed to further aspects. Once the right language, terminologies are in place, furthermore can be given, built upon, extracted and created to proceed deeper.

Even the use of tools that are needed for geometry can be introduced by creating this image. Ruler, protractor, compass and pencil are needed to create. These tools will be following the students throughout their career and be needed all the time.