Mathematics and Society - OS X Lion Server

DIDACTICSTEACHING VIA PROBLEM SOLVING32have students paraphrase a word problem (as mentioned before, paraphrasing also helps (to force an "active" reading as opposed to a recitation of words).Nelson's workcited above suggests that having students write mathematical sentences for given diagrams,pictures or graphs might also be worthwhile.Robertson [1975] has describedsome translation work with balance set-ups, as in the diagrams below.S Ga·· H... c: ...f' = (2. xm) ... 3~QTRAlJ5LATIOl\l :..ITRAI\lSLATIOI0 : t. dU2 TRI\I0SLATIO~: Yl>l'cLgTELL-THE-ACTIONWANTED-GIVENGUESS-AND-CHECK~There does seem to be evidence that writing equations for word problems is aproductive approach (e.g., see Lerch and Hamilton, 1966).how to teach students to write theseequations.There are at least threeapproaches to teaching the writing ofequations for word problems: (a) thesentence-that-tells-the-action approach,(b) the wanted-given method, and (c) theguess-and-check technique.approaches.What is not so clear isWAYS TO CHOOSE EQUATIONS:Let's use the following word problem to illustrate theJan bought a ball glove. Then she decided to buy a ballfor $2.98. In all she spent $16.93. How much did theglove cost?A student who is using the sentence-that-tells-the-action approach is to imagine thestory (bought glove, then bought ball for $2.98, paid $16.93) and write the mathematicalsentence that reflects the action of the story (n + 2.98 = 16.93).Althoughthe resulting equation may not itself indicate what calculation to perform (as inthis example), the method does give an equation which is an accurate "portrayal" ofwhat happened in the problem. [Hartung, 1959] Under the wanted-given approach, thestudent is to determine what is wanted (the cost of the glove) and what is, given (thecost of the ball and the total cost) and then to decide how to get the "wanted" fromthe "given" (16.93 - 2.98 = n). Here the calculation necessary to solve the problemis indicated, but the equation does not "describe" what went on in the problem (theequation 16.93 - 2.98 = n implies that something was removed). With the guess-andchecktechnique, the student guesses the answer (e.g., $15) and then checks it ((15 + 2.98 ~ 16.93). If the guess checks, fine; if not, the student substitutes a 'variable for the guess and solves the resulting equation (n + 2.98 = 16.93).(