Links:
- Video 2008 - Sketchup Animation: Middle School Masaccio
- Video 2009 - Sketchup Cars Animation: Middle School Granacci
- Blog
- Students' Models - 3D Warehouse
- Interview
Sketchup and Math with 13-year old students
I'm an italian math teacher. I teach math to 11 through 13-year old students.
I think that Sketchup can be used in interesting ways
and with interesting results for teaching math to 13-year old students.
At that age in Italy, students have to learn the basics of
3-dimensional geometry:
parallelepids, tetrahedrons, pyramids, cylinders, cones, spheres,... volumes and surface areas.
This year (2009) I've been trying sketchup with 13-year old students.
I made them use sketchup for 1 hour a week for 16 weeks.
I think that there are a number of interesting aspects in using sketchup for math:
-
Sketchup is very easy to learn and has a very intuitive user interface that allows everybody to draw easily 3-dimensional objects.
-
Abstract concepts and objects become tangible. When you build a
pyramid to use as the roof of a house, that pyramid becomes very
palpable: you have to draw it, you have to rotate it, you have to pan
over it, you have to color it. I would say that
the objects become even more tangible than with real objects (but I
also made the children build solids using stems and plasticine).
- Children need to be focused on the construction of the object and not on the object iteself. This puts great emphasis on the process and not on the product itself, on building, for instance, a prism and not on the prism itself. I think this is a very important aspect.
Too
many times math becomes a collection of objects and a collection of
rules: math is not that, math is the ability of reasoning about
processes and relationships among objects. -
Lots and lots of math concepts and names are involved. Just to
list but a few: all kinds of solids (cubes, parallelepipeds, prisms,
pyramids, cylinders, cones,...), planes, axes, orthogonality in space
between a line and a plane, orthogonality between planes, heights,
intersections, areas and volumes, decompositions of solids,
coplanarity, parallelism, sections, rotations in space along a given
axes, symmetries, translation (shifting), scaling along a given axes,
unfoldings, ...
-
The use of computers activates interest and allows each child to work at its own pace.
I
really think that children are happy when working on a computer not
because it is just a game, but because their minds feel that they're
learning a lot. One hour on a computer drawing solids creates whole new
worlds in the child's mind. The existence of such worlds in the mind of
the children gives a solid basis for all subsequent work that may
become progressively more abstract. -
Lots of related concepts are involved. Hidden lines, shadows, transparency, perspective, vanishing points, axonometric projection, ...
-
Emotional aspect. Children get emotionally involved when the
use of a cylinder allows them to draw the wheel of their car. It is
important, i think, to let the children have those emotions and allow
them, for instance, to color the car when finished.
All these aspects allow then the following work.
-
Working in the classroom, the students are lead to organize the ideas (name of objects, volume formulas, ...).
-
When the students know sketchup they accept happily that the teacher may use it to explain something.
Here we have lots of possibilities since the teacher may use advanced
tools of sketchup to explain many ideas (volumes of rectangular and
oblique prisms, decomposition of parallelepiped in pyramids, rotation
solids, sections of solids, construction of platonic solids, ... to
name but a few).
___
Talking about Sketchup, there are various aspects of great interest:
- The inference system
of sketchup that interprets the 2-dimensional positions of the mouse as
a 3-dimensional position in space and looks for the best match of the
position of the mouse.
- The push/pull tool which strictly relates to the concept of prism.
- The follow-me tool which allows the construction of rotation solids (and much more).
___
I surely forgot some educational or some tecnichal aspects but I think that there is enough material to think about.
___
I made the students work by following some sheets I had prepared.
They worked in pairs: one reads the sheet, the other draws, then they start again switching roles.
I also made a blog during this work, where students commented and downloaded their works.
Finally, many students downloaded sketchup and worked with it also at home.
Thanks for your interest.
Links:
- Video 2008 - Sketchup Animation: Middle School Masaccio
- Video 2009 - Sketchup Cars Animation: Middle School Granacci
- Blog
- Students' Models - 3D Warehouse
- Interview
_____
About me:
- Degree in Math
- Phd in Math
- Degree and graduate studies in Information-Technology
- Graduate studies in "Math and Science Teaching"
- I've been working as a software developer and designer for some years but finally decided to work in schools.
guzman tierno