Science, Math

MULTICULTURALISM IN MATHEMATICS, SCIENCE, AND TECHNOLOGY: READINGS AND ACTIVITIES, Thom Alcoze et al; Addison-Wesley Publishing, 800-227-1936; 1993, 204 pags, worksheet blackline masters, large wall map, oversize paperback, $34, Grades 7 - 12, 0-201-29417-6

. This is a workbook that contains 37 units of very short readings about the lives and achievements of Black, South American, and Oriental scientists, as well as a few anonymous "ancient cultures" historically-recorded achievements. These last include 5 Native American units. Each of these is followed either by a hands-on science experiment, usually (but not always) using apparatus that can be inexpensively constructed, or by collection of data and doing calculations or math problems of a type related to those discussed in the reading. Lists of material requirements -- often incomplete -- are given in the teaching notes at the end of the book. Each unit is to be photocopied and handed out to students. Teaching notes for each unit at the back of the book mention the cpurses each unit would be an appropriate supplement to (Algebra II, any lesson on human circulatory systems; asny lesson sequence discussion the solution of linear equations), and necessary prerequisites. Notes also include "additional background" and "extension ideas".

In the book's introduction, teachrs are urged not to "look for material from specific cultures represented in his or her classroom" but to use experiences from all cultures represented "to give students a truly global perspective." Unfortunately, this would only be practical if the units were all for elementary students having a single teacher, who could fit them in with different subjects or topics. But at the secondary level, there will be 2-5 different teachers involved -- earth science, life science, health (perhaps), pre-algebra, Algebra I, II, and gometry. The topics do not form a unified course, they are a mish-mash, with widely varying math requirements from 5th grade to secoind-year algebra. Only a handful could be used with any of the typical grade 7 - 12 math or science courses. Global perspective isn't possible. Science and mathmatics are inherently global, they are unified disciplines with coherent, logical structures Trying to use this book for "a course in multicultural science" would rsult in confused students who would have learned little of value at the end -- in particular little of the methods and ideas that actually make science and mathmatics global, usable by anyone willing to learn it. But there are many other problems with this book that.

An inexplicable problem with the whole book is the absence of a bibliography. In no case is the "reading" more than a few paragraphs, sometimes about th life of the scientist or mathematician whose work is related to student activities. For the anonymous cultural activities, almost anyone teaching them would want more information, which won't be easy to find. An example of this is the Inca quipu or counting-cords. Another example is one of the Navajo lessons, on pine pitch as an antiseptic. This is known to virtually every tribe (and was known to northern European peoples in ancient times, too), so there is no reason to restrict it to Navajo, and mention only desert-growing pines. It is mentioned that one possible source of pine pitch might be steaming knots in pine boards; this will not work for purchased cured lumber.

The hands-on science part of this lesson requires pre-prepared agar culture dishes, and a source of staphylococcus aureus bacteria. These are indeed orderable by some people (from Carolina Biological Supply, for example). However Federal Health Service regulations prohibit their shipment to high schools, preparatory schools and individuals, because they are potentially dangerous pathogens. Only colleges or medical research labs are deemed to have sufficient knowledge (and equipment) to use them safely in research. Thus it is astounding that these pathogens would be specified for an experiment that might be done by 7th graders. The book is downchecked for this reason: that on first read-through, I found an unsafe experiment which cannot be legally (or safely) performed in any high school. This maks any science book unacceptable.

That glaring safety error also makes me suspicious that many of the lessons may never have been tried in actual classroom conditions. ! Instructions do not mention obtaining culture disk kits (which include control disks and a disk to be saturated in the test antibiotic -- pine pitch); these are $4.75. Actually a safe experiment might be done with Carolina Biological Supply's Antibiotic Production Kit, which includes tube cultures of 4 micvroorganisms, 40 sterile Petri dishes, 6 bottles of antibiotic assay agar, 2 inoculating loops, 6 sterile bags, and autoclave (disposable) bag ($60 for a kit for a class of working in pairs). Then you're all set if you have a local source of fresh pine pitch (don't bother trying to steam pine boards from the local lumber yard). The textbook also fails to mention that micro-cultures require expensive lab apparatus not usually found in high schools: a micro-culture incubator, and real sterilization with an autoclave (not holding something in a cigarette lighter for 10 - 15 seconds!). Of course I have no idea if the pine pitch shows a measurable difference in growth of the non-pathogenic microorganisms that can safely be used in school science conditions. The pine pitch "experiment" has all the signs of never having been carried out by anyone. It was thought up by the science writers, sitting around a University professor's lab, perhaps, but not actually done in any high-school situation. The failure to note the illegal and unsafe character of the proposed experiment at a high-school lab level is simply inexcusible, and also means that the identified "reviewer" cannot be trustd to have performed any of the experiments described.

In other cases, I found inaccuracies or omissions. For example the "experiment" part of Chi Shih-Chieh's mathematical experiments makes some conbinations of beans, rice, and corn grains and asks "wqhich of the above combinations provides a person's complete protein needs?" As it happens, there is plenty of information about protein complementarities to be found in Frances Moore Lappe's Diet for a Small Planet, where studnts would learn about the several different types of amino acid contained in different foods, and ratios of foods (including beans with grains) that provide "complete" protein needs. But there is no information about this anywhere in the book in hand. The question about proteins comes from off the wall.

Th tile page lists an Alsce Johnson, Detroit Public Schools, as "reviewer". Mr. or Ms. Johnson does not appear to have been bothered by the fact that (s)he could not legally obtain the pathogens prsecribed for the pine-pitch experiment, and it is unlikely the Detroit public schools have microbial incubators or autoclaves. (Nor has (s)he noticed that other experiments are undoable following the procedurs described.) Just because staph is such a well-known pathogen (having mutated so as to be resistant to most antibiotics, it is now posing huge health problems in all hospitals), I find it totally incredible that none of the 13 writers and one reviewer raised any questions about its use in grades 7 - 12 science classes. It took me about 1 minute to discover that obtaining the pathogen would be illegal, all I had to do was consult a science supply catalog.

That's one example of the fact that whoever uses this book had better have a lot of knowledge besides the missing cultural knowledge that might have at least been findable if there were bibliographies for each unit, and a big university library with many rather technical sources was nearby. Another example of hands-on student work that is inadequately presented is the Zuni floodplain desert irrigation method.

The improvised stream table's measurements are only given (in centimeters!) for "box bottoms that hold 4 cartons of soft drinks" 4 of which are assembled. any school science labs have stream tables, ranging from small, cheap plastic ones to large elaborate controllable tables. There is no way to translate the improvised apparatus into measurements for the experiment. Does this experiment not work with the clean sand, recommended for use on stream tables (because the write-up here specifies "clay soil") or what? Clay soil is not necessarily readily available, and is likely to be full of roots and other plant materials if just dug in the schoolyard, and is very messy to work with, which is why school lab stream tables use clean sand. At the end of this experiment an "extension" is described, tlling students to get really scientific and cmpare the efficiency of the several kinds of different irrigation/dam designs. To "control" variables, they are suppposed to weigh the clay soil before filling the stream tray, and measure the amounts of water poured on and runoff.

But there is no mention of measuring the soil that will be carried off, and with clay soil, that will be quite a bit, especially since there is no way to control the rate of flow. Too, while students are supposed to analyze and compare "efficiencies" of different little dam systems, there is no definition of what constitutes efficiency. If one infers that the moste fficient dam design retains the most water in the soil of the tray, a dam all the way across from top to bottom, that holds back all water in the soil, is more efficient than any other design (although not practical for actual desert flood plain agriculture). An uncrollable variable which has more effect on the results than anything else is rate of flow of water from the punctured gallon jug. (A wooden pencil cannot punch a plastic milk-bottle as students are instructed to do. The pencil will break. This is an experiment I did just now.)

The Zuni unit is the last in the book, and the most frustrating. Probably a very interesting reading, both on the modern long-term ecological flood plain irrigation project would be fascinating reading -- just as the all-too-brief unattributed quote from some description of it is.

Inadequate in a different way is a 2-lesson unit on "the Native Americans". The reading here starts with a couple of unattributed rephrases (the first apparently from Black Elk Speaks) from a Lakota saomebody who's described as "a Native-Aermicn elder and teacher of the Chippewa nation": (for th writers' info, that's Ojibwe or Anishnaabe, and thre are dozens of tribes!). These worthies say (respectively) that circles and round things are important and that we are allr elated because we're all children of Mother Earth. From this we look at circular atomic orbitals, at a cutaway diagram of the earth comparing its innards (which were not known to any indigenous peoples) to parts of mammalian bodies, and thence to some zany worksheet activities that purport to be picking out ecosystems (by naming pictures of plants and animals). In other words, we go from vague native mentions of circles to a contention that this has something to do with atomic orbitals on the one hand or cycles that might be diagramed as circular. Lesson 2 (Native agriculture), but fails to mention that the teacher will need to procure corn varieties, and that the use of the recommended shoe box as planter will result in very rapid collapse of wet cardboard. This experiment is doable (though not in the way of the write-up) with several caveats: namely that to obtain viable corn seed in "several varieities" you must generally look to a scientific supply house, and available seed corn combos have been prepared for genetic experiments. The little shoebox "planters" shown, aside from the fact they'd fall apart, are not large enough for corn planters. Waterproof corn planter seed flats for corn growth experiments are aoubt $45 for 10, and each water differential in the proposed experiments must be done in a different planter. Corn takes a while to sprout and grow, and often will not do so in ordinary classroom conditions, where heat is shut down evenings and weekends.

In general the "book" experiments, which are usually mathematical, mostly do seem to be viable, though some are just wrong. For example, a proposd "geometry experiment" purports to use Eratothenese's method of measuring distances on the surface of the spherical earth by using angles drawn on a flat disk with continents drawn on it. It is asserted that this is "a process of indirect measurement similar to that used by Eratosthenes". That's just false, and there are various other problems with the whole discussion. In the discussion of 19th-century Russian mathematician Sonya Kovalevsky, there is no reason at all to call "aexes of symmetry" "lines of symmetry", it appears to be just a bit of baby-talk left in. In what could have been a good discussion of symmetries and trnsformations in the context of Navajo rugs, the author of that unit does not appear to actually know anything about this area of geometry. Also, the author appears to know nothing of the history of what are now considered traditional Navajo rugs. The bold geometric patterns ar not traditional -- the traditional weave was a kind of twill. With the coming of anyline (chemical) dyes at the end of the 19th century, bright bold, gemoetrics were found to sell well. Far from being considered individual works of art, traders, who had monopoly control on weavers' rugs imposed the pattersn they found to sell well, and these were quite standardized, not "individual works of art". A weaver didn't draw her pattern on a piece of paper, becuase she had memorized the several patterns she knew in terms of weaving instructions. Earth colored dyes were switched to when traders learned they could sell such rugs for more money. Only in recent years has there been an outgrowth of individual artistry and a rediscovery of traditional plant-based dyes. Most rugs for the tourist trade are still quite standard in pattern, and one weaving family will stick to the patterns it collectively knows usually, i.e. "Navajo weavers seldom, if ever repeat a rug pattern a second time" is not true for the majority. The most individual rugs are the so-called pictorials, which are not symmetric-geometric patterns, but pictures of life on the reservation.

In the Maya numbers section, the simple base-20 addition exercises will work as described, but insufficient information is given for the time cycles, which require a calendar diagram (such as is used in the Sunbusrst-Wings Mayan math-science curriculum materials, from which it appears this unit-lesson may have been cribbed). Actually the worksheet exercises use several made-up short cycles, not the Mayan ones.

In the section on Black engineer Lewis Howard Latimer, I see no reason why students are supposed to cut and fold strips of aluminum foil to use to make circuits of, with batteries, instead of using wire. Since the improvised strips of foil are not insulated, there are all kinds of problems with every experiment, resulting in diagrams that suggest batteries are being held in the air, with dangling strips that supposedly don't contact anything (this is never mentioned, but I figurd they had to be doing this if in fact someone tried any of these experiments, bcause they certainly won't work if th strips of foil -- the conductors -- are laying on most surfaces). . This seems like an idiotic way to do simple electricity experiments of the type that are done in 4th and 5th grade classes using wire which is available at any hardware store.

In the teaching suggestions for the unit on Eloy Rodriguez and doing simple liquid chromatography the suggestion is given to melt an eyedropper and pull its tube out thin, instead of getting an inexpnsive micro-pipette. Unless the teacher is an experienced glassworker, this will just result in a ruined medicine dropper, all metled together, but even if the teacher is an experimenced glassworker who makes all kinds of chmistry glassware, the result will be a tubule of irregular diameter, unsuited for height measurements.

In brief, this book cannot be recommended. It appears to have been the pubisher's idea to get a few teachers together over the summer to draft something, and they then editorially polished the drafts (i.e. for spelling and grammar, not for science, accuracy, doability of expriments), It's not clear who laid out in advance the "facts about the anceints" which most teachers wouldn't know. Absnce of a bibliography for any of the lesson-units is a big hole in the usefulness of the research, especially since some of the writers apparently didn't understand what the source was getting at and presented incomplete or inaccurate rewrites, e.g. Erathostenes' earth surface measurments. Many of the experiments were obviously not done by anyone, or if they were, have not been written up in doable manner. No bibliographies are provided to find out more of the historical and cultural facts. At least one experiment is included whose performance in a school science lab is so unsafe it is (fortunately) illegal under Federal Health Regulations to ship the pathogen called for, but the teacher is unlikely to be able to obtain the pine pitch anyway to try the exerpiment with something safer, or to have equipment needed needed for doing culture (in the scientific sense) experiments.

How could this book have been in print since 1993 without some of these facts about it being discovered? I suppose schools have bought it, science or math teachers may have picked out an item or two that is workable, then put the book back on the shelf. I also suppose that the average teacher knows even less of the history of mathmatics and science than did this book's authors (and reviewers), Maybe the reading sections -- all of which are brief and inadequate -- were used as student handouts and the discussion questions (with short blanks for worksheet answers) were done, but the experiments were mostly bypassed. If this were a rough draft, 1- 2 years of work (which would requires actually working out the details for all the experiments, giving complete-with-measurements apparatus construction info, complete materials lists and supply sources and approximate costs, elimination of experiments requiring uncommon and expensive lab apparatus, etc) might make it actually usable. Currently there is no relationship between the wall poster and the book it accompanies; to the book should be added a unit on each of the people or methods shown on the wall poster map. At present, I'd have to say (with disappointment) that about all that's good about this book is its concept. Reviewed by Paula Giese