There is compelling evidence (Reynolds, 1992 and Sfard, 1994) that imagery plays a significant role in mathematical reasoning and that mathematicians use imagery in powerful ways (Hadamard, 1949; Nunokawa, 1994; Sfard, 1994). Mathematics is not just a subject of logic and reasoning, but it is one that is laden with imagery.
Doing activities such involving tangrams (and other similar manipulatives such as pentominoes, dot cards, etc.) gives students a chance to develop their spatial sense in mathematics.
This past Wednesday the students in all of my math classes at Charlie Lake School did tangram art. I provided students with a set of tangrams die-cut from construction paper along with patterns for creating a variety of shapes. Over the years I have collected a variety of tangram patterns in books, but these days many patterns are readily available on the Internet. Put together on the hall bulletin board, the students’ tangram pictures make a delightful display.
When I have enough time, I prefer to have students (especially older ones – maybe not my grade 2’s) cut their own sets of tangrams from 10 cm squares of construction paper, but as my classes run on a fairly tight schedule on Wednesdays, I went with the pre-cut sets. (Download instructions for cutting a set of tangrams from a square here.)
I have found it interesting to observe that some students who struggle with symbolic notation in math “shine” when it comes to visual/spatial activities. I have also observed the reverse to be true: students who easily manipulate numbers cannot always move things in space so easily.
Although students sometimes perceive such as activities as “art” or a day away from doing “real math”, these kinds of activities actually build their ability to use imagery, thus building their math sense.
I encourage you to use some visual spatial activities with your students – of any age and grade level!