The concept map is an educational tool with great versatility. It is useful in eliciting, representing, and assessing students'understandings; and as an organizer, guide, and vehicle for developing curriculum and in the design and delivery of instruction. Additionally, the process of constructing a concept map - concept mapping - is a powerful learning strategy that is graphic in nature and forces the learner to think about the relationships between terms. This latter aspect makes concept mapping especially suited to the study of science, given that the learner may perceive that studying science means memorizing a bunch of facts.
If you already have examined or taught any of the Investigation level lessons in this unit, you noticed that concept maps are shown as part of the "overview and outcomes" section of most of these lessons. Additionally, some of these lessons specifically recommend teaching and learning activities and assessments that employ concept mapping. Each of the concept maps shown in the "overview and outcomes" section of the lessons illustrates concept relationships that are important components of the understanding that each lesson seeks to develop. We envision that these maps will serve as a flexible guide for the teacher in terms of what science content and understandings are especially important relative to the outcomes and instruction in each lesson. Accordingly, we anticipate these maps will be of use to the teacher as s/he plans and carries out instruction and assesses learning. We also anticipate that the teacher may not use the maps exactly as set forth. The teacher may embellish the map, pull out small portions of the map, revise the map, and so on. Again, these maps are not meant to explicate the only accurate understanding or a totally complete understanding of the subject matter.
The purpose of this appendix is to familiarize educators such as yourself with (a) the important components of a concept map, (b) the concept map construction process, and © various reasons and ways to use concept maps to educate your students. To do this, we have elected not to provide you with a "factual" presentation on the "what, why, and how" of concept maps. Instead we are asking that you complete a self-instructional "inductive-type" activity that puts you in the role of student/learner. This "inductive" approach is in keeping with the kind of learning (meaningful as opposed to rote) fostered by concept mapping and simultaneously provides you with experience in constructing concept maps. Experts logically recommend that educators gain experience in constructing concept maps before using them in the instruction of others.
The time required to compete the self-instructional activity will vary from about one to two hours. The actual amount of time you spend will depend on (a) how much previous experience you have with concept mapping and (b) the extent to which you engage in critical thought as you construct the maps that are a part of this activity.
After the self-instructional activity, we provide some suggested steps and approaches for you to use in introducing concept maps to your students and helping them to build competence in concept mapping. However, the self-instructional activity that follows also familiarizes you with such steps and approaches. By completing the self-instructional activity, you will formulate your own ideas on appropriate ways to teach students about concept mapping, which you can use to improve those that we offer. At the end of this appendix, we also provide you with guidance for scoring concept maps, should you choose to use them as a quantitative assessment tool.
For "part 1" of this activity, we have put you in the role of student, enrolled in a course on environmental pollution. We intentionally have chosen for concept mapping a sub-topic with which educators in developed countries are quite familiar-household waste. The learning scenario is "reading and studying" a portion of a text, followed by attending a class presentation related to the text reading. However, the scenario could be set in any of several other contexts and target different types of study materials, e.g., the course could be a workshop, the text reading a journal article, and the lecture a related video.
You are assigned to read a section of one chapter in your text on environmental pollution that deals with the content and management of household waste. To help you learn from and study the reading, the instructor has asked you to identify what you believe are the 12 most important concepts in the reading, and construct a concept map of these terms. The instructor says one of your terms should be "household waste" and this should be the focus or "most inclusive" (also called "superordinate") concept in your map.
Previous to making this assignment, your instructor has introduced you to a concept map by using one to deliver a presentation on a different topic. While doing so, the instructor provided a definition for "concept": It is an object or an event that we perceive with regularity to have certain features, characteristics, etc. A "label" is used to designate the object or event. The label is usually a noun (e.g., the object "insect" or the event "pollination") and may be qualified further by an adjective (e.g., for example "stinging insect"). A concept can also be an "attribute or characterisitic" or a "state" (state of being or existence). For example, in the statement "Insects can be beneficial," "beneficial" is an attribute of some insects. In the statement "The water is polluted," "polluted" is a state that the water is in. The "labels" for attributes and states are often adjectives and verbs.
You complete the reading assignment, highlighting what you believe are important points and ideas as you go along. After you have finished reading and highlighting, you construct your map by proceeding through the five steps outlined below.
Step 1: Select the concepts. You review material you have highlighted and identify what you believe are the 12 most important concepts - the concepts you believe are most central to an understanding of this topic. You make a list of these concepts, which turns out to be as follows:
household waste paper drinking water
yard waste solvents food
landfills compost non-food
recycling incinerators economic incentives
Step 2: Cluster the concepts. Your instructor has already given you one of the 12 concepts to be used as the "most inclusive" or "superordinate" concept in your map: household waste. You now proceed to rank or cluster the remainder of your 12 concepts from "most inclusive/general" to "least inclusive/most specific." Your list turns out like this :
Most inclusive: somewhat specific Most specific
food econonomic incentives solvents
non-food recycle paper
landfill drinking water
incineration yard waste
compost
What might be another useful way to cluster these concepts? There is another way to cluster concepts to facilitate construction of concept maps: This will become apparent later in the activity, at which point we will return to this thought.
Step 3: Position Superordinate Term and Begin Linking Concepts. You begin to construct a concept map of these terms. You start by writing the superordinate concept of "household waste" at the top of a blank sheet of paper. You enclose this term in a box or circle:
At this point, you may decide to write each of the remaining concepts on very small "sticky notes", which can be moved about on the blank sheet of paper as opposed to writing each concept directly on the blank sheet. The reason for this is that you may want to rearrange your concepts while making the map and the "stickies" will save some erasing and rewriting.
Regardless of whether you choose to use stickies or not, there are two different ways you can proceed in constructing the map. You make the decision to proceed by mapping the concepts in one at a time, linking them as you go along. What might be another way to proceed? (We will come back to this question later in the activity.)
As a first step in mapping in the remaining concepts, you select from your list one relatively inclusive/general concept that, in your thinking, is closely related to the superordinate term. You select "non-food." You must formulate the word or words that accurately describes, according to your text reading, the relationship between the superordinate concept and the concept related to it. We call these the "linking words." The learner (mapper) should try to be "economical" in formulating these links. In other words, the mapper should avoid being "wordy." Linking concepts is the most important aspect of concept mapping. This requires a good deal of "critical thinking."
You decide upon the linking words "can be" and use this phrase to link the two terms, as shown on the next page.
As mentioned above, two concepts linked together form a relationship. You may think of this relationship as an "idea." Another name used to describe a relationship between two concepts is "proposition." So, "household waste can be food" is a proposition. The linking words in a proposition often are or include verbs, but may also be or include other parts of speech, e.g., prepositions, conjunctions, and adjectives. Your choice of linking words depends on the type of relationship that you want to construct. What type of relationship is "household waste can be food?"
It is an "inclusion" or "instance" type of relationship. What other linking words may be used for "inclusion/instance" type relationships?
Here are a few examples of linking words used to describe inclusion type relationships: composed of, contains, includes, has part, and such as. As you are in the process of selecting and mapping the previous two terms, you (quickly) realize that "household waste" also can be "non-food" and add this to the map:
The map now shows two propositions: "household waste can be food" and "household waste can be non-food." A concept map is very dynamic: The mapper often will make changes in linking words and reorganize parts of the map during the map construction process. Such changes and reorganization frequently become necessary in order to add new concepts and construct new relationships, and to represent how the learner now understands the subject matter. Herein lies the real study benefit of concept mapping, a point which we will return to near the end of this activity.
Step 4: Finish Mapping in All Concepts. You continue to make the map grow by relating additional concepts from your list to concepts already on the map. You continue with the more "inclusive" terms first, working your way down to the most specific terms until your concepts are "mapped in."
Before you examine an example of a map (shown on next page) containing all of these concepts, you should try your "mind" at drafting a concept map of these terms on a separate sheet of paper. We have not included the actual textbook reading from which this list of important concepts was derived. However, you are familiar with these concepts and various relationships between them, so just use your existing knowledge to construct the map. Please read the two notes that follow before you start.
In regards to this concept map, please note the following:
Let's return now to the question posed earlier in Step 3: Is there another way, other than placing and linking the concepts one by one, to begin constructing the concept map? What is your thinking on this question now (then see what follows for an idea)?
The other way to begin constructing the concept map is first to arrange all of the concepts on a sheet of paper, referring to your clusters and thinking about how they are related as you do the arranging. If you had chosen this method to initiate map construction, your initial map might look like the one shown previously (or the one you constructed), but without the links. The more inclusive/general concepts would be closer to the top of the paper and the more specific concepts lower on the page. Concepts that are closely related would be located nearer to each other on the paper than concepts that are less related. Once you are satisfied with the spatial arrangement of all the concepts, then you begin to link them, using linking lines and words that describe their relationship. If you follow this method of initiating concept map construction, what do you think might happen to your arrangement of concepts once you start to link them?
Contrast the map you actually constructed with the one shown previously. Do the two maps differ at all in terms of the basic types of relationships that are illustrated?
Recall that the first relationship "household waste can be food" was an "inclusion" type relationship. Inclusion or instance type relationships can also be thought of as a relationship that illustrates classification. Is there another inclusion or classification type of relationship in the map shown on the previous page?
What other basic types of relationships are shown in the map on the previous page or in the map that you constructed?
Being cognizant of basic types of relationships can help the mapper think critically and elaborate to expand the map. Two other basic types of relationships now shown in the map on the previous page are (a) cause and effect or action, e.g., "solvents can contaminate drinking water" and (b) process, e.g., "economic incentives encourage recycling" or "household waste is disposed via landfills". Another broad type of relationship not yet shown on the map is characteristic, e.g., has property, feature, function, or attribute. Other types of relationships can be temporal (e.g., follows, precedes), similar or dissimilar (e.g., opposite, same, in contrast to), and quantitative (e.g., greater than, equal to).
Given that your map is undoubtedly different from the map shown on the previous page, does that make your map wrong?
Suppose two individuals are experts on and know equally as much about the set of terms being mapped. Would the maps constructed by these two individuals be the same?
We will discuss answers to these questions later in this activity under the heading "Individualistic nature and accuracy of concept maps."
Step 5. Now, you study your map to see if there are any other relevant relationships that should be illustrated between terms on the map. Such relationships, if they exist, will usually take the form of cross-links. Cross-links are relationships that exist between two concepts or two propositions in different vertical segments of the concept map. A cross-link can be thought of as a special and oftentimes more powerful type of proposition. Cross-links help to integrate a concept map into a cohesive whole.
When terms in different vertical segments are linked together to form a relationship, an arrow is used to show the direction of the relationship. One cross-link that can be established in the map illustrated earlier in this activity follows:
Cross-links can be constructed at any point in the mapping process. The idea of cross-links is introduced at this point in this activity simply as a matter of convenience. In other words, the learner need not wait until all terms are mapped in order to search for cross-links. In fact, the learner will often "see" cross-links when only some of the terms have been mapped. Such cross-links may be forgotten if not mapped in at that point.
Based on your common knowledge of these terms and the relationships illustrated in your map, do you see some obvious cross-links that can be made? While thinking about this, it is useful to keep in mind the basic types of relationships, e.g., "characteristic" and "cause and effect."
If so, construct one or two cross-links on your map: Draw in the link and write in the linking word(s) which describe the relationship. Don't forget the arrow(s)!
On the next page reappears the map from the previous page, but now it includes three cross-links.
Now, let's return to the thought introduced previously in Step 2: that there is another way to cluster concepts before you begin to construct the concept map. Please examine the map shown above or the one you have been constructing: What other method of clustering may have facilitated linking the concepts?
The other method of clustering concepts is to group them according to their interrelatedness. Five example interrelated clusters of the concepts to be mapped are shown below. Please examine the cluster to the far right: food is not a type of yard waste and these concepts are not directly linked in the map shown previously. However, they are interrelated because both can be cross-linked to compost. Please also note that in this method of clustering, a single concept may appear in more than one cluster. For example, paper appears in the first two clusters shown below. This type of clustering may be used in addition to or instead of clustering according to "degree of inclusiveness".
economic incentives nonfood solvents landfills food
recycling paper landfills incineration yard waste
paper solvents drinking water compost
compost yard waste
The day after you completed the above reading and concept map on household waste, you attend a class presentation on the same topic. In this presentation, your instructor elaborates on the reading, as described below.
She discusses the many forms of paper waste, which includes packaging from food and non-food items, and magazines. She emphasizes that about one-half of the waste in landfills is in the form of paper. She discusses some problems with the disposal of waste (be it from households or elsewhere) in landfills and incinerators. For example, she explains how many landfills are reaching capacity and new ones are very expensive to build because of the safety regulations (etc.) now in place. She goes on to discuss some problems associated with incineration: It contributes to air pollution, although emissions are substantially reduced through filters or other mechanisms; and it results in an ash that must be disposed of and which can contain certain metals at levels considered hazardous to the environment.
Based on this presentation, you decide to expand your map to include four or five more terms and propositions as well as more cross-links. "Try your mind" at expanding your map now! After you are done, take a look at the next page. It illustrates the previous map of the original 12 concepts, expanded to include some of the concepts and relationships from the above presentation.
Part 2: Potential Benefits of Concept Mapping as a Study Tool
Based on your reading and experience to date with concept maps/mapping, what do you believe are some benefits a person could derive from using concept mapping as a study tool?
You may have mentioned that concept mapping will facilitate remembering and recalling key points and ideas from assigned readings, class notes, and so on. You also may have mentioned reasons for this. For example, concept mapping helps the learner integrate new information with what the learner already knows; it helps the learner interrelate, think critically about, and elaborate on these key points and ideas. Another reason that concept mapping facilitates recall is that, like the learning strategy of outlining, concept mapping is helpful in organizing one's thoughts. In your thinking, how is concept mapping superior to outlining ?
Concept maps have at least two "thinking/learning" advantages over outlines:
Does a concept map remind you of any other graphic visuals you have encountered or made in the study of science? What are some?
In answering the above question, you may have recalled studying or making various diagrams, such as one of the circulatory system, a food web, or a food chain. Perhaps you recalled a cyclic diagram, such as one portraying the water or the carbon cycle. Or, you may have recalled a flow chart illustrating certain procedures or events. Scientists, science teachers, and science writers frequently make use of such visual images, such as diagrams of cycles and pathways, flow charts, and graphs in order to illustrate ideas and processes. These images are efficient means through which scientific information can be represented and communicated. A concept map is an excellent addition to this collection of types of visual images.
Concept mapping is highly congruent with the learning theory of constructivism, which says an individual actively constructs his/her knowledge and in a manner which relates new information to what s/he already knows (i.e., the individual's past learning). A concept map constructed by an individual reflects to some degree how that individual stores the knowledge in memory. Therefore, a concept map may be thought of as a form of external memory that can be "held in place", studied, and reorganized as necessary to become more meaningful to the individual. A concept map extends the limited capacity of "working" memory!
Furthermore, the act of concept mapping is believed to be similar to the process humans actually use to construct knowledge. Concept mapping will facilitate meaningful learning. Concept mapping is a "constructivist" learning strategy that will help individuals link (relate) new information to what they already hold in memory.
Earlier, questions were posed about the similarity and accuracy of concept maps constructed from the same set of terms but by two different individuals. An individual's memory structure is somewhat unique: We say memory structure is idiosyncratic. Since a concept map attempts to parallel this structure, it is highly unlikely that any two individuals would use all the same linking words or organize the map identically, even if they were both experts and knew equally as much about the topic. For example, in the map we have focused on in this appendix, the relationship "household waste reduced via economic incentives" could employ another and equally correct linking phrase: "contained through." In terms of organizing the map, an individual may decide to place "compost" directly below (and linked to) "yard waste," and subsequently cross-link "recycling" with "compost."
The map shown previously uses two concepts to categorize types of household waste: food and non-food. In your thinking, what are other concepts that could be used to categorize appropriately household waste?
Your answer to the above question might have included concepts such as "organic," "paper," "metal," "plastic," "glass," "hazardous," and "miscellaneous." The reading that these concepts were drawn from may have included such concepts, and they are appropriate categories for houshold waste.
How about accuracy? Quite obviously this is a concern central to the use of concept maps as a tool to assess learning. Certainly an individual can have misunderstandings or incomplete understandings about a topic. So, relationships shown in a concept map can be inaccurate or limited relative to "state of the art" knowledge in the subject under study or an instructor's expectations. For example, "landfills have a limitless capacity" is not accurate; and "food can be used for composting" represents a limited understanding relative to "food some which can be used for composting" (e.g., meat and fat traditionally are not recommended for the compost pile!)
Also, the content of a student-prepared concept map, taken as a whole, can be incomplete/limited according to the expectations of an instructor. For example, an instructor may provide students with 10 or so concepts and assign them to construct a concept map that shows how these concepts are interrelated, according to a recent topic of class study. Here, the instructor probably will be looking for the presence of certain propositions and cross-links. The instructor also may decide to give students only three or four "seed" concepts and to have students identify and map in what they understand to be the other six or seven very important concepts. Here, the instructor will be looking for the presence of certain concepts and relationships. Still, the instructor needs to recognize the idiosyncratic nature of learning and understanding, and be open to "accept" concepts and propositions that have very similar semantic meanings or have parallel wording.
Additionally, given that concept maps really are a way for students to "show what they know," the instructor might find that some students' maps go considerably beyond what the instructor expected, and illustrate considerable insight and critical and creative thought. When possible, the instructor should consider such insight and creativity in assessing students.
In order to pull together and summarize the various concepts and relationships discussed about concept maps and concept mapping in parts 1 through 3 of this self-instructional activity, we have constructed a concept map of the topic "concept map." This concept map attempts to synthesize a broad understanding of "concept map" by interrelating 15 concepts central to this topic. Before you examine this map (on the next page), "try your mind" at constructing such a map on a separate sheet of paper. Doing so will result in a greater personal learning gain than if you only look at the map we have constructed. Briefly review parts 1 through 3 and select the 15 (or so) concepts that you believe are most central to an understanding of "concept map."
After finishing your map, contrast it with our example. Your selection of concepts as well as the relationships you draw undoubtedly differ somewhat from the ones we have included in our concept map. Based on this comparison, perhaps you will decide to modify or expand your map because you now believe you omitted one or more very important concepts or omitted or did not show accurately one or more relationships. Alternatively, in your thinking you may decide that we did not show one or more very important concepts or concept relationships! Regardless of the changes made to either map, your map still will look different than ours. As stated earlier, personal constructs of meaning are somewhat "idiosyncratic."
Teaching Students the "What, Why, and How" about Concept Maps
If you completed the previous self-instructional activity or have taught students how to concept map in the past, you already have thoughts and past experiences on how to (a) initially expose students to the idea of a concept map as well as (b) help them develop competence in concept mapping. Your ideas may be superior to those we set forth below. Several of the strategies and ideas we recommend using here are similar to those we employed in the self-instructional activity. Accordingly, we sometimes will refer you to components of the self-instructional activity instead of reiterating what is already contained herein. The self-instructional activity highlighted one important use of concept mapping: as a study tool. In what follows, we pinpoint various other instructional uses of concept maps/mapping, which include the following:
Conveying Content. One good way to "introduce" students to the idea/visual of a concept map is to use one in presenting some science content. This fits with one of many possible instructional uses of concept maps: to convey knowledge in a given domain subset. To avoid overwhelming students, this introductory concept map should not include a great number of concepts or cross-links. Let's say you wanted to introduce students to "concept maps" in the last Foundation/Awareness level lesson. The first Investigation lesson ("The Atmosphere") actually suggests a concept map as a presentation strategy for the content of this lesson. So, after reviewing the lesson, you could modify as desired the concept map shown within the lesson and use it to present to the students key concepts and relationships and/or to summarize content at the end of the lesson. Ideally, you would construct some of the concept map in front of the class as you present the material as opposed to showing students a map that is entirely preconstructed. Additionally, you could solicit their input on concept relationships for the map: This is discussed in more detail in a subsequent paragraph.
Advance Organizer. A veteran physical science teacher who helped develop and field-test this GAC curriculum introduced her students to concept mapping at the beginning of the school year. She had students complete a text reading on "what is" physical science, and used their responses to various questions to construct in front of the class a concept map of what constitutes physical science. As such, this concept map served as an advance organizer for the topic of physical science and upcoming study. She also used this concept map to introduce students to the important idea that interrelationships exist amongst terms in their text readings on physical science. Thinking about concept interrelationships helped students understand why the authors of their text chose to include certain terms. She posted a large copy of this advance organizer concept map on the bulletin board for reference during the school year.
You might decide that you would like to provide students with an advance organizer concept map of the content of the Investigation lessons, before starting the first Investigation lesson. Accordingly, you could pull from across the various Investigation lessons several concepts that represent the breadth of various topics to be studied. The concept maps shown in each lesson provide a quick reference for this purpose. In addition to providing a broad overview, another important quality of an advance organizer is that it helps students relate what they already know to the new information. So, as you select concepts for this presentation, you will want to include a few with which students have some familiarity.
The last lesson (number 11) at the Foundation/Awarness level presents a concept map that can serve as an an advance organizer for the Investigation level lessons. Some of this concept map appears below; a couple of additional concepts (smog and ozone "hole") with which students are going to be familiar are included.
As suggested previously, instead of showing students all of the concepts already mapped in, you may want to construct the map as you go along. This will model for students the map construction process. By so doing, you simultaneously would be introducing them to the graphic visual of a concept map and as well as how to construct a map.
Probe Pre-instructional Understandings. At some point, you also may want to ask students to help you map in some of the concepts. In addition, you might ask students to cite what they believe to be a few additional concepts related to the topic, and to help you map them in. This will engage students and help them relate further the upcoming Investigation lessons material to what they already know. However, such engagement also will elicit their exisiting understandings, and likely will surface some misconceptions (perhaps a better term here is "alternative conceptions").
Using a concept map to elicit students' pre-instructional understandings is another utility of the concept map tool. You will need to make a decision in advance regarding how you will handle any alternative conceptions. For example, you may decide to alter as needed any alternative conceptions in order for the growing concept map to explicate only what is scientifically appropriate. Alternatively, you may decide to map in any alternative conceptions that students provide and tell students that "we may change" what is up here as we study and learn more about GAC. A large copy of this concept map on a portable blackboard or large sheet of paper (or giant dry erase board, if your school can afford it!) could remain visible somewhere in the classroom and you could revisit it from time to time. You might let students decide when this map should be revisited by simply telling them to let you know when and how they believe this map should be changed. The map can serve as a stimulus for ongoing discussion throughout the lessons, and as such, help students to see connections across the lessons.
Their are several ways to go about developing student competence in concept mapping. Regardless of what you choose to do, it is important to stress to students that concept mapping is a learning strategy "that works" for many students. You may be wondering how the veteran physical science school teacher referred to above went on to develop concept mapping skills in her students. She began by giving students concept maps that were partially completed. The first map they received contained all of the links and linking words (which she referred to collectively as the connecters), some of the concepts, and empty boxes for the remainder of the concepts. A concept list appeared at the bottom of the map, from which students could choose concepts to place in the empty boxes. The next concept map the students received was like the previous, except that it did not have a concept list: Students had to come up with their own concepts to place in the empty boxes. Students graduated from this situation to a concept map that contained the concepts but no connecting words (which they had to derive and place), and finally, to a situation where they prepared an entire map "from scratch." What follows are some recommendations given by various expert sources on how to develop student competence in concept mapping.
Begin with Familiar Concepts. No one becomes an "accomplished mapper" overnight, although most students can pick up the basics rather quickly. The key in beginning to develop mapping skills in students is to use a subject matter for mapping with which all students are quite familiar-topics where students can use their existing knowledge to readily think of valid relationships, and accordingly, be successful in their initial attempts at mapping. Recall that we used the content area of "household waste" in the self-instructional activity for teachers.
A concern voiced by another one of the teacher-authors of this curriculum is that this early exposure be enjoyable to the students-that they have some fun doing the mapping. She suggested that "fun" topics would be family or foods associated with different occasions (e.g., holidays, picnic, sports event, movie). The topic of foods also could deal with mapping typical foods served for breakfast, lunch or dinner. Additionally, this teacher suggested that "school" would be good a good topic. For the topic of school, the concept list might include the following:
school principal subjects science
students custodians english
teachers classroom math
Regardless of your choice of topic, you should keep the list of concepts to 10 or so. Place the concept list on the board and explain to students that these words or terms are called concepts. Then, explain the nature of concepts (see step 2 of the self-instructional activity set forth earlier in this appendix). To help students understand that any given concept has certain characterisitics, features, and/or qualities about it that we perceive with regularity, pick a concept from the list and ask students to describe it or to tell what it is. For example, if you chose the concept "subject", students might cite different examples of subjects, tell you that a subject is something we learn about, or that some subjects are harder or more interesting than others. Having the students describe the concept "teacher" might be especially fun for the students and lead to some interesting discussion! Additionally, you might show students pictures, items, etc., that are clearly not examples of the concept you are dealing with and ask them "Is this a ______?" How do you know this is not a ________?" For example, if teacher was the concept you were examining, you might show pictures of people identified by uniform (or otherwise) as being in a different occupation (e.g., a chef or a policeman). If a certain type of breakfast food, such as cereal, was the concept, you could show examples of waffles or toast.
Tell students that our knowledge of the qualities, characterisitics, and features of the concept allows us to determine what is and is not an appropriate example. Our memory stores these concepts, and everything we know about them. Our memory allows us to learn new information about these concepts and "link" this new information to the concepts. This new information includes how one concept that we know about may be related to another concept that we know about. We are going to learn a technique that will help us learn and remember new information about concepts. This technique is called concept mapping.
Relating Concepts. For the concepts you have listed on the board in the above example, tell students that you know they are familiar with all of these concepts. Each of the concepts, in one way or another, is related to one and usually several of the other concepts listed. Suppose you have chosen "school" and the related concepts cited above as the topic. Cite and write on the board a couple of short phrases that describe the relationships between any two "school" concepts, e.g., "subjects can be math," "subjects taught by teachers," "students study subjects," or "school needs custodians." Then ask students to write a few of their own phrases and have vounteers put their example phrases on the board.
Review the above example phrases and ask the students: "What is the purpose of the word or words between the concepts, i.e., what does this word(s) do?" Explain the nature of the linking words and what constitutes a proposition (see self-instructional activity, step 3). You may want to point out examples of different types of relationships, e.g., instance or classification, cause and effect, and process (see self-instructional activity, step 4). You also may find that students identify more readily with the term "connecter" to signify collectively the linking lines and linking words.
Tell students that it is possible to draw a map illustrating the concepts and their relationships (or connections). If you have already introduced students to a concept map as described previously under "the first exposure," make reference to this earlier example of a concept map. Tell students that the concept map we will make will be on the topic of school (or another topic of the teacher's choice). Since school is our focus concept, it goes at the top of the paper. As described in steps 3 and 4 of the self-instructional activity, there are several ways to proceed at this point. You could have the students help you cluster the concepts into groups according to level of inclusiveness and/or degree of relatedness. Each student (or several small groups of students) might have at his/her desk a pad of small sticky notes or cards on which the concepts are written and they could form clusters on their own first. You might have each of the concepts written on a small piece of acetate for the purposes of clustering and moving about on an overhead projector, and later linking them. Alternatively, you could use large sticky notes that are visible to the class, and a blackboard or dry-erase board.
Adapt and employ the materials and procedures from the self-instructional activity (steps 2-4) as you see fit in teaching students how to construct a first draft of a concept map from the list of concepts about school. You might want to get the students started by mapping in three or four concepts, and then have each student or small group of students map the remaining ones on their own. Subsequently, students can refer to their maps in helping you construct a class map. Make sure to point out that there are many possible correct relationships between these concepts and that different students will come up with different connecting words to describe the many different relationships. Furthermore, no two students will organize their map exactly the same. One of the teacher-developers of this GAC curriculum who used concept maps extensively in her classroom described this flexibility aspect of concept mapping as a "freedom thing" for her students:
The thing that they really like . . . and that I think it is really important to tell the kids, at least in my opinion, [is] that there is no right concept map. [T]here are 28 kids in here and you are going to organize this 28 different ways, but as long as your connecters are right, then it is okay with me. As long as whatever you put in there is a correct relationship, that is okay with me. And I think that gives kids a little bit more of a comfort level that they can do it.
Asking for Other Related Concepts. Once an initial map is constructed, you may want to ask students for other concepts, not on the list, that they "see" as being related to concepts now in the map. Subsequently, make the map grow by having small groups of students or the entire class map them in.
Cross-link Concepts. Introduce the idea of a cross-link and draw in one or two (see the self-instructional activity, step 5). Again, you may want students to think a bit and map some cross-links in small groups, and then refer to their small group map in helping you construct more cross-links on a class map. You also may want to refer to these "cross-links" as connecters, but connecters that contain arrowheads-and that drawing in the arrowhead is especially important if the connection goes sideways or upwards.
Assign Concept Mapping. To build competence in mapping, give assignments that require students to employ this tool. For example, students could concept map the 10 or 15 most important concepts in a reading from their science book or shown in a video. Students can use concept maps in cooperative and collaborative learning groups. For example, in the "jigsaw" cooperative learning strategy where students meet in expert groups and plan a lesson to teach other students (see Investigation lesson 7), a concept map can be constructed by each expert group to help them decide what science content is really important to teach others. Collaborative learning can occur when each individual draws a map of a given set of concepts and then individuals meet in small groups to negotiate one small group map (see Investigation lesson 14). This engages students heavily in "talking science". They get practice using a science vocabulary and explaining to others how they understand certain subject matter.
An incentive for getting students to concept map is to have students include them in a portfolio (e.g., several maps on the same topic over time). Additionally, assessments of their understanding should include reference to their concept maps. If tests are given, include test items that require students to draw concept maps or that students likely will do better on as a result of drawing previous maps. Such test questions generally examine for higher order learning outcomes, e.g., analysis and synthesis as opposed to knowledge and comprehension. The last section of this appendix explains various ways to score concept maps as a quantitative assessment of understanding.
Concept maps are considered to be an alternative form of assessment. Concept maps also have various characterisitics of authentic assessment. What follows does not cover all of the parameters on which concept maps can be scored. For additional information, a reference list is provided at the end of this appendix.
This is one parameter applicable to the assessment of "free form" (described below) concept maps and essay questions. It is also useful in assessing the knowledge student's have gained from assigned readings as well as class lectures and presentations. It generally is not applicable when the instructor "provides" all (or most) of the concepts to be mapped.
Free-form maps. Here, the instructor provides only the superordinate (and possibly a few additional "seed") concepts. The student is expected to identify the majority of relevant concepts to be mapped. The number of relevant concepts identified by students is simply counted or a more complex system can be used where concepts are scored according to their inclusiveness: Broad, inclusive, theory-level concepts (e.g., greenhouse effect) receive more "points" than concepts with less inclusiveness and more specificity, such as those that state specific examples (e.g., carbon dioxide, as an example of a greenhouse gas).
Essay Questions. The instructor writes an essay question and then prepares an answer key for that question in the form of a concept map. This "answer key" (referent) concept map explicates the concepts that the instructor is looking for in the "desired" response. Students receive "credit" only for concepts they cite that are part of the expert map, with the option of giving credit for up to a certain number of additional relevant concepts. This referent concept map has greater utility in scoring students answers to essay questions based on the concept relationships contained therein. See the section below on "number of valid propositions."
Readings and Lectures/Presentations. The self-instructional activity in this appendix illustrated the selection of concepts from readings and presentations. For more information on this, obtain the reference by Mason listed at the end of this appendix.
This parameter is always examined in the assessment of concept maps. It is applicable regardless of whether the concepts to be "mapped" have been identified by the student ("free form" mapping as described previously) or provided by the instructor. Here, the instructor simply checks each proposition for validity, i.e., is the relationship shown scientifically correct or is it inappropriate (does it illustrate a misconception)? If the concepts are provided by the instructor, an expert map can be prepared by the instructor as a guide for checking validity of propositions. In some cases, the instructor may want to check for the presence of specific (as shown in the expert map) valid propositions in the concept map. Propositions can be weighed equally (e.g. one point each) or differently according to the degree of importance ascribed to the relationship by the instructor. Scoring procedures for assessing the validity of propositions are given in various references cited at the end of this appendix (e.g., see Novak and Gowin and Mason).
This parameter provides for assessment of the extent to which the concepts in a concept map are progressively differentiated. A branch is established when a concept at one level in the concept hierarchy is related via valid links to two or more concepts at the next (subordinate) level in the concept hierarchy. For example, in the first "household waste" concept map shown previously in this appendix, there are only two instances of branching: (1) Household waste (first level) is progressively differentiated to economic incentives, food, non-food, landfills and incineration (all at the second level); and (2) Non-food (second level) is progressively differentiated to paper, yard waste and solvents (all at the third level). The third concept map shown on household waste contains three additional instances of branching (see incineration, landfills, and paper). Again, instances of branching can be weighted equally (e.g., one point each) or differently at the instructor's disgression. (See the reference by Vargas and Alvarez at the end of this appendix)
This parameter allows for assessing maps based on the degree of integrative reconciliation: Meaningful connnections are established between two concepts in different vertical segments of the concept hierarchy. Cross links are propositions in that they show via a labeled link a valid relationship between two concepts. However, they typically (but not always) illustrate a more comprehensive understanding, because they connect different segments of propositions in the concept hierarchy. Therefore, they may be weighted more heavily than propositions in determining a score for the concept map. Novak and Gowin (see reference at the end of this appendix) provide ample detail on assessing concept maps on the parameter of cross-links.
Some authorities (e.g., see Novak and Gowin) discuss the inclusion of "examples" in concept maps. The instructor may request that students include examples of specific concepts in their maps for two reasons: (a) to facilitate the "anchoring" of the concept in the student's cognitive structure and (b) to assess whether or not the student can identify types of objects, events, and so on that the concept label represents (e.g., "panda" or "grizzly" are each examples of the concept "bear").
Some authorities recommend that if examples are requested by the instructor, students should not box them in when placed in their map. However, examples of a given concept can be concepts themselves (e.g., "panda" is a perceived regularity in an object, yet is an example of a type of bear). Additionally, relationships can be established between an example of one concept and an example of another concept (e.g., "panda eats bamboo", where bamboo is an example of a plant or type of wood). Therefore, requesting that specific examples of concepts be treated differently than the concepts that they are examples of may be confusing to students and may limit progressive differentiation and integrative reconciliation within a concept map.
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