Heads Up:  An Anatomical Investigation


Having students collect and analyze data to explore connections and detect patterns is an ideal way to implement the NCTM Standards (NCTM, 1989).  A context is present with the student-collected data allowing measurements to have meaning.  These projects allow the Standards to be applied as students build mathematical understanding and confidence (Edgerton, 1993).  Students expand their mathematical power by reflection, reasoning, and communication of findings.  Data on anatomical measurements provides a rich, rewarding, and sometimes surprising investigation.

Anatomical relationships can be explored among people, for different animals, and even across species.  Similar investigations can be performed on plants using comparisons suggested at the end of this article.  This article describes an investigation involving the skulls of various animals and has been tried with groups ranging from elementary age through adult.


Figure 1

 Home-Made Caliper


Students began the activity by making a caliper.  An example of a home-made caliper can be found in Figure 1.  A short narrow stick, like a chopstick or Popsicle stick, is fastened at one end of a longer, flat stick.  Door trim, a ruler, or furring strips will do.  A scale is added to the longer stick if it lacks one, using arbitrary units if desired.  A second short, narrow stick is attached so it can slide parallel to the first short stick or it can be hand-held onto the scale for measurements so that a sliding mechanism need not be invented.  Students practice using their calipers until proficiency is established.

Comparisons of personal anatomical measurements allow students to begin the consideration of relationships.  Students can measure width and height of their heads then stand in ascending order of the ratio of the measures.   Students will see the natural variability of people as well as the relationship between their ratios and appearances.  Measurements and comparisons continue until students understand the use of the caliper and the meaning of the derived ratios.  Some other comparisons to try would be thumb versus index finger, wrist versus palm, and nose versus ear.

Animal skulls are then distributed for measurement.  Have students measure the distance from tip of snout to back of skull and width of eyes (between the centers of the sockets).  See Figure 2.  Skulls can be traded for groups to check measurements.  Have students find the ratio between the skull length to the eye width.  Record the values in a table, like the one in Figure 3.  Students take an animal skull they have measured and stand in ascending order of the skull's ratio.  A wide variety of animal types should turn up a surprising result if your class' analysis is similar to our experience.  Animals with similar diets have similar ratios even though the animals themselves differed greatly in size!

Figure 2

 

Measuring Skulls


 
Figure 3

Animal         Skull Length (S)           Distance between Eyes (E)              Ratio of S:E

Squirrel                  24                                            18                                              1.333

Beaver                    29                                            20                                              1.450

Cougar                  38                                            26                                              1.462

Bobcat                    24                                            16                                              1.500

Beaver                    88                                            48                                              1.833

Muskrat                 35                                            19                                              1.842

Mt.Beaver              42                                            22                                              1.909

Beaver                    81                                            40                                              2.025

Beaver                    26                                            12                                              2.167

Muskrat                 36                                            16                                              2.250

Muskrat                   2.5                                           1                                              2.500

Muskrat                   2.5                                           1                                              2.500

Muskrat                 13                                              5                                              2.600

Mt.Beaver              14                                              5                                              2.800

Bear                        43                                            13                                              3.308

Bear                        52.5                                         14                                              3.750

Coyote                   96                                            24                                              4.000

Coyote                   38                                              8                                              4.750

 


Sample Data Table



Our groups found the general groupings of cats, rodents, bears, and dogs.  Figure 3 shows data gathered by fourth-grade students.  Their findings suggest an anatomical relationship related to their biological family.  The rodents had a wide span and had the cats within the grouping.  Our measurements also grouped the cats, but below the rodents.  The adjacent grouping of cougar with bobcat, the bears, and the coyotes was compelling even with the apparent "error" in the fourth-grade data!  It is interesting for students to propose, at this point, why this could be true.

Variations of this investigation are possible, and necessary, to extend to other domains and to cover the possibility of the unavailability of animal skulls.
There are five scale drawings of animal skulls included with this article if you want to try this activity but do not have enough animal skulls.  Whatever variation you try, it will demonstrate to you and your students the wonder of Nature and the connectiveness of mathematics.



References

 

Edgerton, R. T.  (1993).  Apply the Standards with project questions.  Mathematics Teacher, 86, 686-689.

 

NCTM.  (1989).  Curriculum and Evaluation Standards for School Mathematics.  National Council of Teachers of Mathematics, Reston, VA.


Richard T. Edgerton, Ph.D.

Seattle Public Schools

rtedgerton@seattleschools.org



Figure 4

 

Muskrat

 

Beaver

 

Cougar

 

Fox

Scale Drawings of Animal Skulls

Reprinted with permission of Bryan Glass, Ph.D.



The author wishes to gratefully acknowledge the assistance of Donna Buck in the preparation of this article and Bryan Glass, Ph.D. for the use of his skull sketches.