Careful Looking and Language Skills
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
We see people all the time and unless two identical twins are involved we keep the different people straight in our minds. How do we do this? Without thinking about it we note that some people are tall, others short; some are thin, others heavy set; some are dark haired, some blond, some wear beards, and women typically look different from men. Using our observation skills we set down mental markers that distinguish one person from another. Yet, if we were unfortunate enough to observe a suspect at a crime and are asked by the police to give a description of the criminal, we can probably provide some rudimentary information but not enough information to guarantee that we are describing exactly one person.
Skill in geometry begins with visual discrimination skills and good language skills. We need to have the visual skills to tell how two objects are alike and how they are different, and the language skills to describe these similarities and differences.
As a warmup exercise for what is to follow obtain a physical cube (a wooden cubical block will do fine) and carry out the following exercise in the power of observation:
Look at the cube carefully and
a. Write down at least 20 properties or facts about it!
b. Compile a list of the "technical words" that you need for describing the properties of the cube that you wish to capture.
In case you have trouble locating a cube you can use the picture below to help, though having a physical cube works much better!
a. What is the name usually given to the polyhedral object below?
b. Repeat Activity 1 for this polyhedra object:
c. At what grade level do you think it proper to start getting across the ideas involved with the list of properties that you develop and the list of words that you compile?