The Back Page: My Favorite Lesson: All Knotted Up

Our favorite lesson is a hands-on activity that helps students visually “tie” (pun intended) the concepts of rate of change and y-intercept together in a meaningful context using strings and ropes. Students tie knots in ropes of various thicknesses and then measure the length of the rope as the number of knots increases. We provide clothesline, twine, bungee cord, and other ropes found at local crafts, sporting goods, and home stores. We avoid very thin string, such as thread or knitting yarn, because the knots are small and the string length does not change enough to explore a rate of change. A variety of thicknesses is important because this allows for variability in the rates of change.

Larval Development of Cucumaria Elongata (Echinodermata: Holothuroidea)

Cucutnaria elongata Düben & Koren, collected from the Northumberland coast in January 1968, was induced to spawn in the laboratory by raising the temperature. At spawning, the animal waved its pharyngeal bulb back and forth while a thin string of gametes was discharged. The freshly spawned eggs, surrounded by a jelly coat, were at the end of the second meiotic division and the size varies from 250 to 350 μ in diameter. Oocytes in the ovarian tubules can be grouped into three stages according to their size and other morphological features. Insemination of artificially recovered eggs resulted in only a very low frequency of abnormal development up to 8-cell stage. However, over 90% fertilization was achieved by insemination of the naturally shed eggs and the development was normal. The cleavage was holoblastic and radial type. The larva hatched at post blastula stage and swam freely with its animal pole upward. A doliolaria stage with four ciliary bands and pentactula stage with five primary tentacles subsequently developed. The planktonic life at temperature 9–11 °C ended on the ninth day after fertilization. Pentactula, up to 4 months old, live underneath the mud where they are deposit feeders. The primary tentacles bearing mucus glands in the form of papillae are important in both locomotion and feeding. An outline of chronology from fertilization up to 5 months old is presented.