Problems and "That Other Stuff": Types of Chemical Content Catherine Middlecamp and Elizabeth Kean The University of Wisconsin-Madison, Madison, WI 53706
The emphasis in many general chemistry courses is on solvine .. .nroblems. A varietv of techniaues have been oroposed for tearhing students the skills of problem solving ( 1 5 ) . Problem sol\.ine. however. does not stand in isolatiun from chemical content. students must command specific chemical knowledge in order to solve a chemical problem in a meaningful way. T o quote Greeno, a prohlem-solving expert, "All problem solving is based on knowledge"(6). T o quote a student, "To solve problems, we have to learn all that other stuff." What is the nature of "that other stuff' that we teach in introductory chemistry courses? How should students go about learning it? In this paper, we will describe three types of chemical content, learning strategies for each type, and methods of teaching students to use the appropriate strategies. The Content Hierarchy All content is not alike. I t is useful to conceptualize chemical content as consisting of facts, concepts, and rules. The rationale for distinguishing between types of content is to highlight the different learning (and teaching) processes involved with each. Our intent is for students and teachers alike to develop different strategies for working with different types of content. We do not expect that all content will neatly fit into these categories, nor is it of great importance exactly what the categories are. Of importance is that differences exist. Facts, concepts, and rules are hierarcharical as listed, with each one becoming increasingly complex and with the learning of one being dependent on the ones before it. The figure pictures the hierarchy, with the most basic and simple facts a t the bottom and problems at the top. Thus, facts, concepts and rules make up the foundation of knowledge on which the abilitv to solve chemical oroblems rests. Examoles of the different types of content taken from the chemic'al topics of acids and bases are given in Table 1.
Chemical Facts Chemical facts are statements about how the world is and how the world will he represented. Examples of facts include descriptions and names of chemicals, as well as names given to chemical ideas and relationships. I t is a fact that chlorine is a pale, yellow-green gas. Nitric acid is the name of the chemical HN03; this is a fact because chemists have agreed that it shall be so. Chemical facts usually cannot be "figured out". They describe reality or conventions on which people agree. Chemical Concepts Chemicalconcepts are ideas about matter. Each concept is represented by a single word or phase that has the same meaning as the whole chemical idea. For example, "acid", "base", "titration", and "endpoint of a titration" are concepts. Each of these words or phrases can he substituted for the idea i t represents. Chemical concepts are complex; they have many parts and are interrelated with other concepts. Chemical concepts may also be developed during a course, with new parts and meanings added periodically. For example, the concept of an acid may initially be taught as a class of compound that can he recognized from its formula (acid formulas begin with the chemical symbol H). Later, the teaching of Br$nsted/Lowry or Lewis acids, classification of acids as weak or strone. -. the DH . scale. weak acid eauilihria. organic acids and their reaction, etc., will enlarge and profoundly alter what students know about acids. Chemical Rules Chemical rules are generalizations about how things usually behave or relate. Typical chemical rules include the following: how a class of chemicals behaves ("All nitrate salts are soluble.") how the properties of a substance vary ("The solubility of gases in liquids decreases with an increase in temperature.")
.
Table 1. Different Types of Chemlcal Content Types of Contern
t
t
Complexity
I CONCEPTS
I Content hierarchy.
FACTS
Examples from AcidIBase Chemistry
Facts
Sulfuric acid = H&04 Sulfuric acid is a strong acid. Sulfuric acid is found in car baneriar.
Concepts
acid strong acid pH indicator
Rules
Acids react with bases to form selts. All hydroxides are soluble except. .
Problems
Draw lhe Lewis dot structure for NH3. Find me pH of 0.20 M HCI if 15 mL of 0.30 M nitric acid is mixed with 20 mL of 0.30 M ootassium hvdmxide. find. . .
.
Volume 65
umber 1
January 1988
53
. .
how two or more concepts are related ("The pressure and volume of an ideal gas are inversely proportional.") how chemicals will he represented ("In net ionic equations,the farmuals of weak acidsand bases will be written as molecular species.")
Since rules are generalization that are true only in a specific context, tbey often have restrictions andlor exceptions. Rules depend on prerequisite facts and concepts. The rule, "all nitrate salts are soluble," cannot he used unless the student knows facts such as the formula for the nitrate ion and understands the concepts of "salt" and "solubility". Relating Content to Problems Although facts, concepts, and rules may be taught as ends in themselves. thev most often are taueht as a basis for problem solving. T L , the student who would be successful in solvina chemical problems has an incentive to master these types of content as prerequisites. For example, suppose the student is asked to solve the following simple problem: Given the name of a compound, calcium chloride, write its chemical formula. We designate this as a problem because it consists of sequential action (decisions and operations) that take the solver from the initial state (the name) to the goal state (the formula). To solve this problem, one must: 1. Racugnize the cumpound as ionic 2. Recall the rule9 that govern formulas of ronic rompuundi :I. Recall the chrmiral symbols for the element^ ~akiumand rhlorine 4. Write the chemical symbols correctly, with the metal symbol written first 5. Determine the charges on the ions by locating the elements on the periodic chart using the rule relating charges to group membership 6. Recall the rule that ionic compounds contain the minimum equals numbers of positive and negative charges 7. Apply the previous rule to determine number of calcium and chlorine atoms 8. Use subscripts to display how many of each ion are present, omitting the subscript for a single ion.
-
..
The ability to solve this problem, indeed, any chemical problem, depends on the facts, concepts, and rules. Failure to learn and use correctly this knowledge results in failure to solve the problem. Learning Processes for Different Types of Content Different mental processes are required for the mastery of each type of content. Students need the skills of memorization for learning facts, classification for mastery of concepts, and application for rule usage. In this section we briefly summarize these skills, referring the reader to the literature for more extensive information. Learning Processes for Facts Students need to he able to recall factual information quickly and accurately. Memorization is the deliberate process by which facts are placed in long-term memory. Typical memorization tasks in introductory cbemistry courses include the names and corres~ondinasvmhols for selected elements, names, and formulas for poiyitomic ions, common names of chemicals, etc. Sets of rules that are based on chemical behavior (e.g., solubility rules) also may need to be memorized. Students need powerful enough memorization strategies to learn a large number of chemical facti in a relatively short oeriud oftime. Manv.general studvskills hooksdesrribe how to memorize (7,8). Strategies useful for memorizing chemical content include workine activelv durine memorization. looking for patterns in ihe material, chunking material into loeical/manaeeable blocks.. . ~ r a r t i r i n arecall. and wrendinememorization over time (9).
-
54
Journal of Chemical Education
Learning Processes for Concepts Each topic in general cbemistry requires the mastery of manv concepts. Not onlv must the concept word/~hrasebe learned, hut the idea that the concept represents must be learned, often an idea totally new to the student. I t is not uncommon for 20 or more cdncepts to he introduced in the course of a one-hour lecture. Small wonder that some students perceive chemistry to be a language course! Concept mastery begins with finding an adequate definition for the conceot. This mav nor he straiehtforward. since more than one deiinition for ;concept maybe presented in a course. each one useful in a different context. Moreover. finding the definition is but the beginning of understanding the concept. Manv c o n c e ~ t consist s of a set of characteristics that fori the basis for identifying examples and nonexamples of the concept class. For example, as students study the concept "acid", they must developcriteria that enable them to identify which compounds are acids and which are not, either from the behavior of the compound in the lab or by identification of the formula of the compound. Finallv. ., it does students little eood to learn conceots in isolation. I t is the relationship among concepts that allows students to use concents in problem solvine. Thus, students must be able to relate aci& to other types of ibnic compounds (such as bases and salts), . . to identifv strona vs. weak acids, toknow when "acidness"is an important issie, etc. To develop these relationships, students can use activities such as conEept mapping, outlining, and drawing "tree diagrams" (10-13). Learning Processes for Rules As with learning concepts, learnhg rules requires more complex thought processes than memorization. Principles and laws. mathematical formulas. era~hs-these are but some of the methods of presenting rules. When confronted with one of these, the student must first recognize what rule is involved. Then, in order to understand the rule, the learner must have a precise understandina of the underlvina facts and concepts. Next, the student must find out when t6e rule does and does not apply, particularly noting exceptions to the rule. If possible, the rationale or cause of a rule also should be sought out, because this will make the rule easier to remember. Ultimately, rules are taught so that they may be applied to both familiar and novel situations. Students mav need to generate fur themselves criteria for drtrrmining when a rule should b e a ~ ~ l i cAdditionalls, d. the\ musl ~racliceavu1\~inr .. . the rule so that its use is smooih and facile; Finally, the rules taught in introductory courses are often simplifications of chemical or physical behavior. No sooner is a rule given than modifications and refinements may be added. For example, the following rule may he taught: "The ionization energy of elements increases to the top and right of the periodic chart." This rule may be used for predicting the relative ionization energies of elements from their position on the periodic chart. However, students may soon he confronted by the reversal of expected magnitude of the first ionization energies for the elements nitrogen and oxygen. Studentsmay then need togenerate anew rule that accounts for unusually high ionization energies when the electron removed is from a filled or half-filled shell (14). Teachlng Different Types of Content Introductory chemistry courses are not organized by facts, concepts, rules. and ~rohlems.teachine each in turn as the foundatibn for the next. ~athe;, tbey are organized by topic, buildina- from simple topics to more comnlex ones. For a given topic, facts, concepts, rules, and problems are taught together. For example, umhen teaching the topic of acids, the instructor may snlw a titration problem. In the process, the cuncept of indicators may he introduced, along with some factual information about specifir indicators. Similarly,
rules for determining the pH at the end of a titration may he presented in the course of (lcscrihing the titration process. It is nut likelvthat thiscurrent oreanizationofcour~es will change. At present, there is no evidince that other methods of oreanizine information would lead to better learnine. However, one consequence of this organization is that both students and teachers tend to treat all content as if it were alike. Students may feel that all they need to do is memorize the information presented, ignoring the need to develop concepts and rugs and to use the learning processes described in the previous section. Faculty, likewise, may he unaware of the options open to them, in presenting different types of content. In this section, we describe some options that faculty can exercise when teaching types of content. Teachhg Facts-Issues To Consider How explicit to be about what students must know. Suppose you present the following factual material in a lecture on nuclear chemistry: % natural abundance for
isotopes of uranium
Definitions which attempt to be simple and incisive often leave loop-holes,so that some of the things which the definition should exclude are allowed to creep in, and so that some of the things which really belong are excluded. Definitions which endeavour to leave no loop-holesoften become so general or so complex as to be quite valueless for the purpose of enabling someone to recognize the thing which is defined.Sometimes such definitions consist of terms which themselves need to he defined before the original definition can he understood. Definitions, then, tend to be either helpful and inaccurate, or accurate and unhelpful. We recommend that the use of "incomplete but helpful" definitions be legitimized in general chemistry courses. How to use examples and nonexamples when teaching. Another option is that of defininga concept by example. The following is a part of a set of lecture notes on the free radical chlorination of an alkane: Chlorination is a chain reaction. 1. Initiation
-
CI2
2C1.
(C1. is a free radical)
2. Propagation
Should your students learn these facts? You as the instructor may or may not expect students to memorize such information. But in teaching, you must choose (explicitly or by default) whether to tell your students which facts are worth knowine. How much to describe representations. Factual material describes svstems of re~resentation.For examde, there are alternate ways of writkg isotope symbols used in nuclear equations:
How manv of these should vou Should vou exoect ? present? . students to pick them up, as necessary, perhaps 6 y reahing the text? Do vou want to teachstudents to handle the change of represent&ions without warning or explanation? How much contextlrationale to present. Lastlv, instructors decide whether to include or omit factual ma&rial that gives context or a rationale for studying a topic. Faculty struggle with how much time to devote t o discussing wh; chemists are interested in a topic, since time spent on that means less time for actuallv discussine the tooic. Whv. .. for example, do we expect students to learn about colligative properties? What physical manifestations lead to the theoretical descriptions of these properties? Without context or rationale, students mav lose interest in the tooics. . . studvine them purely to satisfycourse requirements but without intrinsic motivation.
-
Teaching Concepts-Issues To Consider Which definition to choose. The teaching of a chemical concept often begins with the presentation of a definition. But the instructor must choose a definition from a numher of possibilities. As an illustration, look at the following definitions of the concept of a mole: Definition I: "A mole is the amount of a auhstnnce conraining as many elemenrary units as there are atmn inernrtly 12 p. of the varhon-I?isorope (kc'," (13,. 1)cfinirion2: A rn& ir a counting unlt; i t dearrihwthe number of aromic or mulccular particlei contarned in a sample ot a suhstance. The first definition is accurate but may not enable the student to comprehend what the mole actually is how it will be used. The second definition is incomplete, but perhaps more functional for the student. The definition paradox has been well stated by Berry (16):
+ CH, .CH, + CI, C1.
-
-
3. Termination
.CH,
+ CI.
.CH,
+ HC1
CH,Cl+ C1.
-
CH,CI
In this instance, the students were left with the job of determining the criteria for recognizing an initiation, propagation, and termination step (e.g., a termination step contains two free radicals as reactants and produces a molecular species as the product). Inferring the defining concept attributes from small numbers of examnles in a hieh-level skill and may he beyond many introductbry chemisGy students. Concept mastery means the ability to classify examples and nonexamples correctly. Thus, the numher and clarity of examples and nonexamples provided for classification practice are important. Examples are often provided in text and homework problem sets. Nonexamples are almost never pointed outto students, even in the cases of mutually exclusive concepts, in which an example of one concept is automatically a nonexample of the other. For instance, NaCl is an example of an ionic compound, and thereby a nonexam~ l ofe a covalent com~ound. What relationships to prouide among concepts. Finally, faculty have the option of drawing relationships among concepts or ignoring those relationships. Classroom teaching tends to be linear: content follows content, each topic discrete from the next. Should the lecturer provide aframework that ties concepts topether? Possibilities for this include short overviewsat thebeginning or short summarizations at the end of a topic. For example, after introducing compounds, element:, molecules, and atoms, you could po&t out the categories that are mutually exclusive: elements and compounds, molecules and atoms. However, elements can be made up of atoms or of molecules, etc. During a lecture presentation of a topic, faculty can also help students to organize material. For example, a student's notes from a lecture on alkanes included the following remarks: Less dense than water Nonpolar Water insoluble Volume 65 Number 1 January 1988
55
This information was simply stated by the instructor, with nosummarizing label. It was left to thestudents to figureout that these were some chemical and physical prop&ies of alkanes. Without the ability to categorize information into useful chunks. the student mav attemnt to learn the required conceptual information by rote memorization, with little clue as to the meaning of the information. Teaching Rules-issues To Consider Whether to label a rule explicitly as such. Should you identify a ~ i e c eof content as a rule? Rules come in manv guises:-mathematical formulas and graphs as well as prose statements. It can be time-consuming to point out all the rules that you teach. For example, here is a rule: "Any atom with atomic number greater than 83 is radioactive." This statement efficientlv summarizes a set of facts known about elements with Z > i 3 . This rule directs the student, when confronted with a h e a w element. to classifv it as radioactive and to look for the decay process that the element employs. When students learn rules, they must be prepared to do something with the rule, that is, to apply it. Again, as with concepts, if students do not recognize rules, they may be content to memorize the rule, unaware of the need to apply the rule. Whether to explicitly point out applications of a rule. Should you identify the specific applications of a rule? Again, theanswer to thisquestion depends on what youwant students to be able to do and how you expect them to have the skills to do it. For example, suppose you present a plot of the number of neutrons vs. the number of protons for stable isotopes, in order to illustrate the "belt of stability". From this, students could extract a rule as to which elements are likelv to be stable if thev have eaual numbers of neutrons and protons. They couldthen a p i l y this rule to isotopes to predict the mode of decay. When applications are not presented by teachers, students may not be able to anticipate them without some examples (e.g., "Would you expect C-14 to be stable? If not, what radioactive mode of decay is likely?") Suggestion for Improving Students' Abillty To Learn Neither lectures nor textbooks can possibly present "everything" that a student might need to know. Incomplete content oresentations are esneciallv common in lectures. where timeis constrained. The studen& have the job of sorting out the different tvDes of content and mastering them accordingly. When content is presented in abbreviated form, that is, when rules are presented without applications, the student must recognize what is missing and supply it. Instructors can take certain steps to improve the learning abilities of students for different types of content. We include the following suggestions: 1. Point out the existence of differnet types of content. For the strong student, this will bring into consciousness what helshe already knows. For the weaker student, this will provide the start of the differentiating process that leads to mastery. 1. Model appropriate learning processes. At the outset of a course, model the learning processes appropriate for different twes of content. Teach students the useful auestions that thev m;st ask in order to master each type of content. For exampli, develop one of the early concepts completely, explaining the necessity of being able to recognize examples and nonexamples. Hand out a tree diagram that shows a possible set of relationships between a number of related concepts that you have just taught. As the course progresses, provide less and less structure and information. Point out how your teaching has changed and how vou have movided students with tools for independent learning. 3. Diagnose students'diffieulties with types of content. When students come to you for help in learning material or after a poor exam performance, learn to recognize what errors students have
56
Journal of Chemical Education
table 2. Errors Students Mlghl Make with Dmerent Types of Content
TYDBof
Content
Facts
Errors Student Mioht
Make
Trying to reason out facts Mat are known by
memrlzatlon. Trying to reason out facts that can be reasoned out but are more efficiently used if memorized
Concepts
Trying to memorize a concept.
being able to recognize examples or nonexamples. Not knowing how the concept relates to oUmr concepts. Making an enor in using a rule usin0 the rule In the wrono conten srlpping or mlxlng ~p steps in a ru e Formu at ng an 'nconect ru e from ns.ff cient data Not recognizing the type of problem. Using the wrong algorithm to solve the problem. Not being able to figure out a method to salve s problem. Making an enor while solving the problem-what kind of enor? Nd
Rules
Problems
..
made with different types of content. Tahle 2 lists examples of types of errors that students might make in the topic of acidbase chemistrv. When workine with students. tm to reconstruct Did &dents memorize fact incorrecttheir thoueht .. brocesses. . Ig
