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We can and often do use this basic right triangle function a2 =b2 +c2 in deck building to be sure that we are placing the deck sides at right angles to the building by using what my carpentry teacher (Bernie Campbalik) called the 6-8-10 rule. From one corner of where the deck will be bolted to the building (or from the end of the deck ledger already bolted in place, measure six feet in from one end of the ledger and mark that point. Then measure eight feet out from the building along your proposed deck side joist and mark that point on the inside of the joist. Now measure the distance between point 1 and point 2 - a diagonal line between the deck side joist and the ledger board. Move the side joist as necessary to make the diagonal line exactly 10 feet and you are guaranteed that the side joist is at a perfect right angle to the building - a nice way to decide how to locate deck corner post piers. For a different and interesting use of triangles and plane geometry to convert stair slope in degrees to tread depth and riser height see Calculate stair tread depth or riser height from stairway slope in degrees.
The geometry approach to calculating stair rise and run over rough terrain when you have only two measurements works correctly provided you know enough triangular geometry to convert between your sloped-line measurement (the hypotenuse of the triangle) and the triangle's other sides that form the rise & run dimensions. In a geometry or trigonometry text you'll see that when we refer to the angle ab we mean the angle formed at the intersection of lines a and b, or in this case the lower left angle in our sketch. Geometry teaches that if we know three pieces of data about a right triangle (one side length and two angles, or two side lengths and one angle) we can obtain all of the other data about a triangle - all of its angles, and the actual lengths of all of its sides.
Our carpenter's square at left is one such tool, though there are some neat level tools that, placed on a slope, will simply give you the angle directly as a readout.
If you don't think this whole sine-cosine process is absolutely horrible for field use in building a set of stairs then we're not on the same planet. A generalized example of the explanation below is given at ROOF SLOPE DEFINITIONS where we explain that you can easily convert any slope (roof, road, or stair) into rise or run distances using the Tangent function.
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The Illustrated Home illustrates construction details and building components, a reference for owners & inspectors. Our recommended books about building & mechanical systems design, inspection, problem diagnosis, and repair, and about indoor environment and IAQ testing, diagnosis, and cleanup are at the InspectAPedia Bookstore.
The dozer comes in many sizes, The smallest is a mini dozer, just a little bigger than a garden tractor not weighing more than two thousand pounds. Larger machines can weigh up to 40 tons, and are used for land clearing, rough grading, large excavation sites, roads, forestry, and pond building.
Dozer’s use tracks to move, on top of the tracks are grousers, a thin raised area the width of the track.
If a person is looking to clear land, make a mountain out of a mole hill, or pond building then a dozer is the way to go. I have a 450C case dozer, live in the mountians with steep grades, is there any way to keep the dozer from sliding when plowing snow on steeping grades? I never used a dozer for plowing after that, it is a helpless feeling until you get traction again.
It was a pleasure to be able to work with a "real person" who has hands on pond experience and is willing and able to answer questions (or research the answers) related to the products I was interested in.
Another characteristic of concept maps is that the concepts are represented in a hierarchical fashion with the most inclusive, most general concepts at the top of the map and the more specific, less general concepts arranged hierarchically below.
A final feature that may be added to concept maps is specific examples of events or objects that help to clarify the meaning of a given concept. Concept maps were developed in 1972 in the course of Novaka€™s research program at Cornell where he sought to follow and understand changes in childrena€™s knowledge of science (Novak & Musonda, 1991). In addition to the distinction between the discovery learning process, where the attributes of concepts are identified autonomously by the learner, and the reception learning process, where attributes of concepts are described using language and transmitted to the learner, Ausubel made the very important distinction between rote learning and meaningful learning. The material to be learned must be conceptually clear and presented with language and examples relatable to the learnera€™s prior knowledge. As noted above, it is important to recognize that because individuals vary in the quantity and quality of the relevant knowledge they possess, and in the strength of their motivation to seek ways to incorporate new knowledge into relevant knowledge they already possess, the rote-meaningful distinction is not a simple dichotomy but rather a continuum. Another important advance in our understanding of learning is that the human memory is not a single a€?vessela€? to be filled, but rather a complex set of interrelated memory systems.
While all memory systems are interdependent (and have information going in both directions), the most critical memory systems for incorporating knowledge into long-term memory are the short-term and a€?working memory.a€? All incoming information is organized and processed in the working memory by interaction with knowledge in long-term memory. This means that relationships among two or three concepts are about the limit of working memorya€™s processing capacity. It should be noted that retention of information learned by rote still takes place in long term memory, as does information learned meaningfully; the difference is that in rote learning, there is little or no integration of new knowledge with existing knowledge resulting in two negative consequences. Therefore, to structure large bodies of knowledge requires an orderly sequence of iterations between working memory and long-term memory as new knowledge is being received and processed (Anderson, 1992). There are obvious differences between individuala€™s abilities, and some of these have been explored by Gardner (1983).
While it is true that some students have difficulty building concept maps and using these, at least early in their experience, this appears to result primarily from years of rote-mode learning practice in school settings rather than as a result of brain structure differences per se.
To illustrate how difficult it can be for individuals to modify their ideas, especially if they learn primarily by rote, we cite the example of interviews done by the Private Universe Project (PUP) at Harvard University (Schneps, 1989). As indicated earlier, we defined concept as a perceived regularity (or pattern) in events or objects, or records of events or objects, designated by label.
As defined above, concepts and propositions are the building blocks for knowledge in any domain.
While there is value in studying more extensively the process of human learning and human knowledge creation, this is beyond the scope of this document.
In learning to construct a concept map, it is important to begin with a domain of knowledge that is very familiar to the person constructing the map. A good way to define the context for a concept map is to construct a Focus Question, that is, a question that clearly specifies the problem or issue the concept map should help to resolve. Given a selected domain and a defined question or problem in this domain, the next step is to identify the key concepts that apply to this domain. It is important to help students recognize that all concepts are in some way related to one another. Students often comment that it is hard to add linking words onto the a€?linesa€? of their concept map.
Finally, the map should be revised, concepts re-positioned in ways that lend to clarity and better over-all structure, and a a€?finala€? map prepared.
Thus, we see that concept maps are not only a powerful tool for capturing, representing, and archiving knowledge of individuals, but also a powerful tool to create new knowledge. The software allows the user to link resources (photos, images, graphs, videos, charts, tables, texts, WWW pages or other concept maps) located anywhere on the Internet or in personal files to concepts or linking words in a concept map through a simple drag-and-drop operation.
CmapTools provides extensive support for collaborative work during concept map construction.
Through the storing of concept maps in CmapServers, CmapTools encourages collaboration among users constructing the maps.
The extensive support that CmapTools provides for the collaborative construction of concept maps by groups, whether they are at the same location or in distant locations, has encouraged the increasing use of collaboration during map building. A Concept Map-Centered Learning Environment CmapTools provides a variety of features that make it possible for teachers to use concept maps for a variety of the tasks that students perform (CaA±as & Novak, 2005). A concept map-centered learning environment implies that concept maps are used throughout the development of a learning unit or module. Just as there are many possible uses of concept maps within the classroom activities, there are a variety of a€?starting pointsa€? for the construction of the initial concept maps by students. Each student can construct the initial concept map individually, giving the teacher feedback on the level of understanding of every student. The concept map can also be a class effort, using a projector, where all students give their opinion and participate in the construction of the map.
Likewise, the starting point from which the map is constructed can vary depending on the expected previous understanding by the students, the difficulty and novelty of the topic, and the teachera€™s confidence in mastering the topic. We refer to a list of concept waiting to be added to a concept map as the parking lot of concepts. Figure 11 is an a€?expert skeletona€? concept map that corresponds to the same topic as the a€?parking lota€? in Figure 10. The use of a€?expert skeletona€? concept maps is a research topic we are pursuing, and for which we dona€™t have as much experience as with the focus question and parking lot starting points. It is important to note that the a€?expert skeletona€? concept maps should be built by an expert on the topic. We foresee a program of using a€?expert skeletona€? maps to scaffold learning beginning with the development of a series of concept maps in a discipline, starting with the most general, most inclusive ideas and then gradually moving to more specific concept maps that will guide the learners. Learners can also engage in laboratory or field studies that will add important concrete experiences needed for developing fuller meanings to concepts, and sometimes the excitement that comes with discovering new ideas or relationships.
The extent of materials and ideas that can be built into knowledge structures using a€?expert skeletona€? concept maps, CmapTools, and WWW resources far surpass what any textbook or any teacher could provide.
In 1966, Bobbs-Merrill published an elementary science textbook series, The World of Science, written largely by Novak with the objective of introducing basic science concepts to elementary school students and teachers.
Obviously, it would be a very deficient science program that did nothing more than have students copy and do some building on the a€?expert skeletona€? concept maps provided for grade two, or for any other grade.
A pilot program effort is already in progress in Italy, where Giuseppe Valittuti (2004) and his colleagues are now working to translate The World of Science books into Italian. The greatest challenge we may expect is to change the school situational factors in the direction of teacher as coach and learner from the prevailing model of teachers as disseminator of information.
We might expect some oppositioin to implementation of the New Model of Education from individuals who believe that "inquiry" learningis the only way to improve education.
There is an enormous job of teacher education that needs to be done before the New Model can be implemented in schools.
We are now beginning to see in many science textbooks the inclusion of concept mapping as one way to summarize understandings acquired by students after they study a unit or chapter. Using concept maps in planning a curriculum or instruction on a specific topic helps to make the instruction a€?conceptually transparenta€? to students.
One of the uses of concept maps that is growing at a fast rate is the use of concept maps to capture the a€?tacita€? knowledge of experts. While we expect that interviews, case study analyses, a€?critical incidenta€? analyses and similar techniques will have value in extracting and representing expert knowledge, it is likely that the end product of these studies might still be best represented in the form of concept maps, perhaps with some of the interview data and other information presented through icons on maps. At IHMC we continue to be very active in the area of capturing and representing expert knowledge (Coffey et al., 2002). In this paper we have tried to present the theoretical foundations and the origins of what we call concept maps.
We also wish to use this document as a foundation for further experimentation, critique, and dialogue regarding the use of this tool. Why not start by assessing your own strengths?  Great leaders not only help their employees to identify and apply their strengths, but they know what their own strengths are and they use them to serve others.
Using a calculator and it's square root function, and the most basic knowledge of geometry is not enough - we also need a table of sine and cosine values, functions readily found these days online.
It's not really that bad if we just realize this is simple plane geometry that defines the relationships between a right triangle (that means one angle of the triangle is set at 90 degrees) and the lengths of its sides.
For any stairway of a given angle or slope (say 38 degrees in your case) the ratio of run (x) to rise (y) will remain the same. Well it's easier to use a scientific calculator and just ask for the Tangent of a known angle.
The tread rise (for which we are solving the equation) is the blue Y at the left of the sketch. The Horizon system runs on always-available cloud-based software for office computers, laptops, tablets, iPad, Android, & other smartphones. The text is intended as a reference guide to help building owners operate and maintain their home effectively.
It may not be fast but having good traction, stability, and low center of gravity makes the dozer suited for working on irregular land and steep slopes.
Mostly used for working in tight places, like preparing a garage for a cement floor, small trail thru the woods and dragging logs.
There are different size and styles of blades, general purpose, production, and special application. Winter time these grousers act like ice skates and the dozer can slide side ways making it dangerous loading on a trailer and or plowing snow on a sloped driveway. When ever possible work up hill or down hill, avoid traveling along the side of an incline. Push material to the ditch or house, never drive along side due to the weight and vibration of the dozer will pack the material to an extent of pushing the concrete block or walls in or having the ditch cave in possibly injuring the dozer and operator. But then depending on temps’ and snow condition the tracks can build up with snow leaving the grouser useless to bite in the ground. They include concepts, usually enclosed in circles or boxes of some type, and relationships between concepts indicated by a connecting line linking two concepts. The hierarchical structure for a particular domain of knowledge also depends on the context in which that knowledge is being applied or considered.
These are relationships or links between concepts in different segments or domains of the concept map. Normally these are not included in ovals or boxes, since they are specific events or objects and do not represent concepts. During the course of this study the researchers interviewed many children, and they found it difficult to identify specific changes in the childrena€™s understanding of science concepts by examination of interview transcripts. These are acquired by children during the ages of birth to three years, when they recognize regularities in the world around them and begin to identify language labels or symbols for these regularities (Macnamara, 1982). Concept maps can be helpful to meet this condition, both by identifying large general concepts held by the learner prior to instruction on more specific concepts, and by assisting in the sequencing of learning tasks though progressively more explicit knowledge that can be anchored into developing conceptual frameworks. This condition can be met after age 3 for virtually any domain of subject matter, but it is necessary to be careful and explicit in building concept frameworks if one hopes to present detailed specific knowledge in any field in subsequent lessons. The one condition over which the teacher or mentor has only indirect control is the motivation of students to choose to learn by attempting to incorporate new meanings into their prior knowledge, rather than simply memorizing concept definitions or propositional statements or computational procedures. Creativity can be seen as a very high level of meaningful learning, and we will discuss this further. Both direct presentation and discovery teaching methods can lead to highly rote or highly meaningful learning by the learner, depending on the disposition of the learner and the organization of the instructional materials.
The Rote-Meaningful learning continuum is not the same as the Reception-Discovery instructional continuum.
Concept maps are also effective in identifying both valid and invalid ideas held by students, and this will be discussed further in another section. Figure 4 illustrates the memory systems of the human mind, and interactions with inputs from our affective and psychomotor inputs.
The limiting feature here is that working memory can process only a relatively small number of psychological units (five to nine) at any one moment (Miller, 1956).
For example, if a person is presented with a list of 10-12 letters or numbers to memorize in a few seconds, most will recall only 5 to 9 of these. We believe one of the reasons concept mapping is so powerful for the facilitation of meaningful learning is that it serves as a kind of template or scaffold to help to organize knowledge and to structure it, even though the structure must be built up piece by piece with small units of interacting concept and propositional frameworks. While the latter are the principal elements that make up our knowledge structures and form our cognitive structure in the brain, we pause briefly to discuss other forms of learning.
So-called a€?learning stylea€? differences are, to a large extent, derivative from differences in the patterns of learning that students have employed varying from high commitment to continuous rote-mode learning to almost exclusive commitment to meaningful mode learning.
The staff of PUP interviewed 23 Harvard graduates, alumni and faculty, asking each a€?Why do we have seasons?a€? Only eleven concepts, properly organized are needed to understand why we have seasons, and one arrangement of these concepts is shown in Figure 5.
One representation of the knowledge structure required required for understanding why we have seasons.

It is coming to be generally recognized now that the meaningful learning processes described above are the same processes used by scientists and mathematicians, or experts in any discipline, to construct new knowledge. We can use the analogy that concepts are like the atoms of matter and propositions are like the molecules of matter. Since concept map structures are dependent on the context in which they will be used, it is best to identify a segment of a text, a laboratory or field activity, or a particular problem or question that one is trying to understand.
Every concept map responds to a focus question, and a good focus question can lead to a much richer concept map. These are links between concepts in different segments or domains of knowledge on the map that help to illustrate how these domains are related to one another. A a€?stringa€? map created by a fourth grade student following a class field trip to a paper mill. Therefore, it is necessary to be selective in identifying cross-links, and to be as precise as possible in identifying linking words that connect concepts.
This is because they poorly understand the relationship between the concepts, or the meanings of the concepts, and it is the linking words that specify this relationship.
When computer software is used, one can go back, change the size and font style, and add colors to a€?dress upa€? the concept map. The software not only makes it easy for users of all ages to construct and modify concept maps in a similar way that a word processor makes it easy to write text, it allows users to collaborate at a distance in the construction in their maps, publish their concept maps so anybody on the Internet can access them, link resources to their maps to further explain their contents, and search the WWW for information related to the map.
Links to these resources are displayed as icons underneath the concepts, as shown in Figure 7.
Vygotsky (1978) introduced the idea that language and social dialogue can support learning, especially when members of the social group are at about the same Zone of Proximal Development (ZPD). When maps are stored in a server on the Internet, users with appropriate permissions (CaA±as et al., 2003c) can edit shared concept maps at the same time (synchronously) or at their convenience (asynchronously).
Concept maps within this environment are likely to be used as the mechanism to determine the level of understanding students have about the topic being studied before the topic is introduced. The whole spectrum of learning activities can be integrated using CmapTools, incorporating various learning activities recorded via the software creating a digital portfolio as a product of the learning. For example, a€?How do we measure time?a€? can be given to the students as the question to answer through the construction of the concept map.
The staring point for the construction of the concept map can be a list of concepts that the teacher wants to make sure all students include in their map. The beginning of a concept map with a focus question and a parking lot with concepts to be included in the map.
An a€?expert skeletona€? concept map has been previously prepared by an expert on the topic, and permits both students and teachers to build their knowledge on a solid foundation.
Observe that in this example, some of the concepts were left in the a€?parking lota€? for the student to add to the concept map. Oa€™Donnell, Dansereau, & Hall (2002) have shown that a€?knowledge mapsa€? can act as scaffolds to facilitate learning. The intention is that the expert will be better at selecting the small number of concepts that are key to understanding the topic, and express accurately the relationships between these concepts.
But the expected final number of concepts in the map is a function of the number of concepts in the a€?skeletona€?.
For example, Figure 11 shows a a€?expert skeletona€? concept map for the sciences that encompasses key major concepts needed to understand science. An Energy transformation Cmap that could be accessed by linking it to the a€?Energya€? concept in the concept map in Figure 11, and a Photosynthesis Cmap that may be linked to it. Thus if one clicks on a concept such as a€?electrical energya€? in Figure 12 and selects one of the a€?searcha€? menu options, CmapTools will retrieve WWW resources that not only deal with electricity, but also relate to other concepts in the map. In fact, teachers supervising this kind of study are likely to learn as many new things as their students. Unlike most elementary science textbooks, this series presents in-depth instruction in basic concepts at all grade levels, including instruction in concepts dealing with the nature of science, nature of matter, energy and energy transformations. Schema showing the New Model for Education with an a€?expert skeletona€? concept map that can serve as the a€?backbonea€? for an emerging portfolio in science.
It would be important for the teacher to help students perform these activities, and similar related activities, some of which might by suggested in WWW resources. Schema showing the New Model for Education with concepts and resources added to the a€?expert skeletona€? concept map, plus a page from a World of Science book providing relevant reading and activities. Students need concrete, hands on experiences with real things and to observe real phenomena to put meaning into the concept labels provided in the concept maps and other resources.
Valittuti and his colleagues have obtained funding from the Italian Ministry of Education for teacher training and a number of elementary school teams began working with the World of Science concept maps and other resources during the 2005-2006 year. We know that we need to engage teachers and administrators in training programs that can model the new educational approaches, and we need to seek their counsel on ways to improve on the New Model for Education. Teachers need to become familiar with the use of CmapTools software and the various tools it contains. Change in school practices is always slow, but it is likely that the use of concept maps in school instruction will increase substantially in the next decade or two. Many students have difficulty identifying the important concepts in a text, lecture or other form of presentation.
A concept map prepared cooperatively by the faculty of the College of Veterinary Medicine at Cornell University to show the over-all structure for a revised curriculum. In fact, these methods continue to be highly popular with many cognitive scientists, most of whom are unfamiliar with Ausubela€™s work and the kind of epistemological ideas on which concept mapping is based.
As the CmapTools software has evolved, it has become an increasingly useful tool for this work, as illustrated by the remarkable resources on Mars prepared at NASA Amesa€™ Center for Mars Exploration (Briggs et al., 2004).
An example of a concept map that can be accessed via clicking on one of the resources attached to a concept on Figure 16.
While at first glance concept maps may appear to be just another graphic representation of information, understanding the foundations for this tool and its proper use will lead the user to see that this is truly a profound and powerful tool.
The CmapTools web site provides opportunities for lively exchanges among users and researchers.
Beth Cabrera shares the power of positivity and purpose through her research, writing, and speaking.
Typically the blade has six movements, up, down, left and right angle, and tilt where just the left or right corner can be adjusted to dig into the ground.
Use extreme caution when working along side an embankment, the embankment could let go and the dozer will slide down the hill, or the bank above the dozer could give way and bury the operator. If the approach is head on and once the machine crosses the half way point the blade will slam to the ground launching the operator in to the air. Words on the line, referred to as linking words or linking phrases, specify the relationship between the two concepts.
Therefore, it is best to construct concept maps with reference to some particular question we seek to answer, which we have called a focus question. Cross-links help us see how a concept in one domain of knowledge represented on the map is related to a concept in another domain shown on the map. This early learning of concepts is primarily a discovery learning process, where the individual discerns patterns or regularities in events or objects and recognizes these as the same regularities labeled by older persons with words or symbols. The indirect control over this choice is primarily in instructional strategies used and the evaluation strategies used.
They can be as effective as more time-consuming clinical interviews for identifying the relevant knowledge a learner possesses before or after instruction (Edwards & Fraser, 1983). However, if the letters can be grouped to form a know word, or word-like unit, or the numbers can be related to a phone number or something known, then 10 or more letters or numbers can be recalled. Second, the knowledge structure or cognitive structure of the learner is not enhanced or modified to clear up faulty ideas. Iconic learning involves the storage of images of scenes we encounter, people we meet, photos, and a host of other images. His work has received much attention in education and has served to draw attention to the broad range of differences in human abilities for various kinds of learning and performance. It is not easy to help students in the former condition move to patterns of learning of the latter type.
The PUP interviewers found that 21 of the 23 interviewed could not explain why we have seasons, a topic that is taught repeatedly in school. In fact, Novak has argued that new knowledge creation is nothing more than a relatively high level of meaningful learning accomplished by individuals who have a well organized knowledge structure in the particular area of knowledge, and also a strong emotional commitment to persist in finding new meanings (Novak, 1977, 1993, 1998).
There are only around 100 different kinds of atoms, and these make up an infinite number of different kinds of molecules.
Some important considerations for construction of better concept maps and facilitation of learning will be discussed further below.
This creates a context that will help to determine the hierarchical structure of the concept map.
When learning to construct concept maps, learners tend to deviate from the focus question and build a concept map that may be related to the domain, but which does not answer the question. These concepts could be listed, and then from this list a rank ordered list should be established from the most general, most inclusive concept, for this particular problem or situation at the top of the list, to the most specific, least general concept at the bottom of the list.
Post-its allow a group to work on a whiteboard or butcher paper and to move concepts around easily. Cross-links are important in order to show that the learner understands the relationships between the sub-domains in the map. The class identified concepts in the parking lot on the left, but this student was not successful in using many of these and her map makes little sense.
Cross-links are key to show that the learner understands the relationships between the sub-domains in the map.
In addition, one should avoid a€?sentences in the boxesa€?, that is, full sentences used as concepts, since this usually indicates that a whole subsection of the map could be constructed from the statement in the box. Once students begin to focus-in on good linking words, and on the identification of good cross-links, they can see that every concept could be related to every other concept. Clicking on one of these icons will display a list of links from which the user can select to open the linked resource. Many of the CmapServers are a€?publica€?, allowing anybody (no authorization needed) to publish their collections of concept maps and resources (CaA±as et al., 2004a). Concept maps are now beginning to be used in corporations to help teams clarify and articulate the knowledge needed to solve problems ranging from the design of new products to marketing to administrative problem resolution. The concept map can thus become an artifact around which the various activities of the learning process can be centered, as shown in Figure 8.
The maps are then developed, extended and refined as the students develop other activities on the topic and increase their understanding, possibly concluding with complex knowledge models that link resources, results, experiments, etc., and that can be used if desired as a final presentation by the students. The concept map can be constructed by students working in couples or small groups, where the teacher must pay attention to the level of participation of every student. The list of propositions on the top right window are automatically derived from the Cmap, and those with a a€?pina€? have been a€?publisheda€?. The type of focus question makes a difference in the type of concept maps that the student builds. For example, a a€?skeleton mapa€? that consists of five concepts should be expanded by the student to a map with 15 to 20 concepts. Learners can begin with such a map, add concepts from the parking lot, link digital resources and also construct more specific submaps. The program tries to figure out what the Cmap is about and prepare a query for Web search engines that will generate results that are relevant to the ideas being developed in the concept map.
Moreover, beginning with the a€?expert skeletona€? maps as starting points reduces the chance that misconceptions or faulty ideas held by learners or teachers will be reinforced and maximize the chance that they will build knowledge structures that in time remove or diminish misconceptions (Novak, 2002).
Learners would also add their own concepts to the a€?expert skeletona€? concept map, as well as resources identified in readings and from the Internet. The plan is to have four sets of schools focus on different aspects of The World of Science series and produce photos and videos of students doing projects that illustrate and utilize the various science concepts.
There is also the challenge of changing assessment practices that now rely primarily on multiple-choice tests that measure mainly rote recall of information, to performance-based tests that require students to demonstrate that they understand basic concepts and can use these concepts in novel problems solving, and that they can use Internet resources to grow and modify their concepts and learn new concepts. They also need to learn about the theory underlying concept mapping, including the ideas in this paper. Other innovative practices for assessing student understanding of subject matter are also available (Mintzes et al., 2000). The hierarchical organization of concept maps suggests more optimal sequencing of instructional material. Part of the problem stems from a pattern of learning that simply requires memorization of information, and no evaluation of the information is required. This tacit knowledge is acquired over years of experience and derives in part from activities of the expert that involve thinking, feeling and acting. We also used a€?clinical interviewsa€? in our early work, as noted above, but we found it necessary to invent a better way to represent what our learners knew and how their knowledge was changing over time.
Figure 16 shows a a€?Homea€? concept map for the knowledge portfolio that Briggs created and Figure 17 shows one of the many submaps he created. It may at first look like a simple arrangement of words into a hierarchy, but when care is used in organizing the concepts represented by the words, and the propositions or ideas are formed with well-chosen linking words, one begins to see that a good concept map is at once simple, but also elegantly complex with profound meanings.
This document itself should be a a€?livinga€? document, with revisions occurring periodically as we gain new knowledge and experiences with the use of this tool. The effects of cooperative, competitive and individualistic goal structure on achievement: A meta-analysis. The information available in brief visual presentations, Psychological Monographs: General and Applied, 74(11), 1-30. You can do this using a transit, a protractor or other angle measuring tool either by placing your angular measuring tool on the sloped surface of the stringer side a, or by actually measuring the angle formed between side a and a horizontal or level surface. We define concept as a perceived regularity in events or objects, or records of events or objects, designated by a label.
The concept map may pertain to some situation or event that we are trying to understand through the organization of knowledge in the form of a concept map, thus providing the context for the concept map. In the creation of new knowledge, cross-links often represent creative leaps on the part of the knowledge producer. The fundamental idea in Ausubela€™s cognitive psychology is that learning takes place by the assimilation of new concepts and propositions into existing concept and propositional frameworks held by the learner. This is a phenomenal ability that is part of the evolutionary heritage of all normal human beings. Instructional strategies that emphasize relating new knowledge to the learnera€™s existing knowledge foster meaningful learning.
In a related test, if we give learners 10-12 familiar but unrelated words to memorize in a few seconds, most will recall only 5-9 words. It is good that schools are recognizing that there are important human capabilities other than the recall of specific cognitive information so often the only form of learning represented in multiple-choice tests used commonly in schools and corporations. While concept maps can help, students also need to be taught something about brain mechanisms and knowledge organization, and this instruction should accompany the use of concept maps. Included in this group was a graduate who had recently taken a course in the Physics of Planetary Motion, who also believed erroneously that seasons were caused by the earth moving closer to the sun in summer and further away in the winter. Epistemology is that branch of philosophy that deals with the nature of knowledge and new knowledge creation.
There are now about 460,000 words in the English language (most of which are concept labels), and these can be combined to form an infinite number of propositions. It is often stated that the first step to learning about something is to ask the right questions. Although this rank order may be only approximate, it helps to begin the process of map construction.
This is necessary as one begins to struggle with the process of building a good hierarchical organization.
This student was a good oral reader, but she had very poor reading comprehension and was a committed rote learner (see Novak & Gowin, 1984, page 108). This also produces some frustration, and they must choose to identify the most prominent and most useful cross-links. Using CmapTools, it is possible to use concept maps to access any material that can be presented digitally, including materials prepared by the mapmaker.
When students work cooperatively in groups and use concept maps to guide their learning, significantly greater learning occurs (Preszler, 2004). Through CmapServers, users of all ages and working in many disciplines have published thousands of maps on all topics and domains. The high degree of explicitness of concept maps makes them an ideal vehicle for exchange of ideas or for the collaborative construction of new knowledge. CmapTools has a recorder feature tht allows recording and playback of steps in map construction, including identification of each contributor. The lower right window shows propositions from other participants in Soup, some of which have discussion threads attached questioning or commenting on the proposition. A question like a€?What are plants?a€? will lead to a declarative, more classificatory concept map than the question a€?Why do we need plants?a€? Experiments show that not only the focus question, but also the root concept of a concept map have a strong influence on the quality of the resulting concept map (Derbentseva et al., 2004, 2006).

Figure 10 presents the focus question and parking lot for the focus question a€?What is the structure of the Universe?a€? The student, group of students, or class is expected to build a concept map that answers the question and includes at least the concepts in the list.
If the a€?skeletona€? map contains 20 concepts, which makes it more of a complete map, the final map could be expected to contain about 50 to 60 concepts. Of course, the learner still needs to select new concepts from the material and construct new propositions on the concept map that add meanings and clarity to the map. Our plan is to use The World of Science books as a starting point for a demonstration project for A New Model for Education. There will be much feedback from classrooms helping the teams to refine their work, sharing a€?electronic portfoliosa€? using CmapTools.
There remains in the New Model plenty of room for acquisition of specific facts and procedures, but now these should be learned within the context of powerful conceptual frameworks. Since the fundamental characteristic of meaningful learning is integration of new knowledge with the learnersa€™ previous concept and propositional frameworks, proceeding from the more general, more inclusive concepts to the more specific information usually serves to encourage and enhance meaningful learning. Such students fail to construct powerful concept and propositional frameworks, leading them to see learning as a blur of myriad facts, dates, names, equations, or procedural rules to be memorized. Concept mapping has been shown to help learners learn, researchers create new knowledge, administrators to better structure and manage organizations, writers to write, and evaluators assess learning. Some interrelationships between constructivist models of learning and current neurobiological theory, with implications for science education. Alternative instructional systems and the development of problem solving skills in physics. Experiments on the effect of map structure and concept quantification during concept map construction. The magical number seven, plus or minus two: Some limits on our capacity for processing information. Concept maps and vee diagrams: Two metacognitive tools for science and mathematics education. Human constructivism: A unification of psychological and epistemological phenomena in meaning making. Learning, creating, and using knowledge: Concept maps as facilitative tools in schools and corporations.
Meaningful learning: The essential factor for conceptual change in limited or appropriate propositional hierarchies (liphs) leading to empowerment of learners. Thanks to Alan Carson and Bob Dunlop, for permission for InspectAPedia to use text excerpts from The Home Reference Book & illustrations from The Illustrated Home. Galow specializes in residential construction including both new homes and repairs, renovations, and additions.
Thanks to Alan Carson and Bob Dunlop, for permission for InspectAPedia to use text excerpts from The Home Reference Book & illustrations from The Illustrated Home. At the back end it can have optional equipment, a winch for forestry or pulling out stuck equipment and rippers, that will penetrate the ground to loosen up the hard packed dirt and rocks to make it easier for the blade to dig in. The label for most concepts is a word, although sometimes we use symbols such as + or %, and sometimes more than one word is used. There are two features of concept maps that are important in the facilitation of creative thinking: the hierarchical structure that is represented in a good map and the ability to search for and characterize new cross-links. This knowledge structure as held by a learner is also referred to as the individuala€™s cognitive structure. After age 3, new concept and propositional learning is mediated heavily by language, and takes place primarily by a reception learning process where new meanings are obtained by asking questions and getting clarification of relationships between old concepts and propositions and new concepts and propositions.
Evaluation strategies that encourage learners to relate ideas they possess with new ideas also encourage meaningful learning. The reality is that unless students possess at least a rudimentary conceptual understanding of the phenomenon they are investigating, the activity may lead to little or no gain in their relevant knowledge and may be little more than busy work.
If the words are unfamiliar, such as technical terms introduced for the first time, the learner may do well to recall correctly two or three of these. While the alphanumeric images Sperling used in his studies were quickly forgotten, other kinds of images are retained much longer. Studies by Penfield and Perot (1963), among others, indicate that regions of our brain that are activated when we hear sounds are the same regions that are active when we recall sounds.
One reason we encourage the integration of the broad range of activities represented in our New Model for Education is to provide opportunities for these other abilities to be represented and expressed. The information in the above paragraphs should become part on the instructional program for skillful use of concept maps. In fact, the earth is slightly closer to the sun when it is winter in Massachusetts, rather than in summer. There is an important relationship between the psychology of learning, as we understand it today, and the growing consensus among philosophers and epistemologists that new knowledge creation is a constructive process involving both our knowledge and our emotions or the drive to create new meanings and new ways to represent these meanings. Although most combinations of words might be nonsense, there is still the possibility of creating an infinite number of valid and meaningful propositions. We refer to the list of concepts as a parking lot, since we will move these concepts into the concept map as we determine where they fit in.
Computer software programs are even better in that they allow moving of concepts together with linking statements and the moving of groups of concepts and links to restructure the map.
This process involves what Bloom (1956) identified as high levels of cognitive performance, namely evaluation and synthesis of knowledge.
In this way, concept maps can serve as the indexing and navigational tools for complex domains of knowledge, as will be illustrated later with NASA materials on Mars (Briggs et al., 2004).
In our work with both teachers and students, small groups working cooperatively to construct concept maps have proven to be useful in many contexts. While concept maps on these public servers are only a sample of concept maps submitted by persons using CmapTools, and some do not meet our criteria of good concept maps, they nevertheless serve to illustrate diverse applications. We have also found that the obstacles deriving from personal insecurities and fear of embarrassment are largely circumvented, since critical comments are directed at the concept map, not at the person(s) building the map. Experienced concept mappers agree with researchers that the most challenging and difficult aspect of constructing a concept map is constructing the propositions; that is, determining what linking phrases will clearly depict the relationship between concepts. In this case, we are probably referring to using a relatively complete (not skeleton) map as a scaffold, expecting students to go deeper into the topic by creating several submaps that are linked to the starting point map. Here we also see a submap that might be created by a group of learners, and a sample of two resources that could be accessed via icons on the submap.
Thus, the learner or team of learners is very actively engaged in the meaning building process, an essential requirement for meaningful learning to occur.
To begin, a€?expert skeletona€? concept maps have been prepared for some sections of the grade two book and the whole of the grade four book of the World of Science entitled The Expanding World of Science. This feedback should help us to rapidly refine concept maps, techniques and approaches for improving practice of the New Model for Education.
Research (Bransford et al., 1999) has shown that factual information acquired in a context of meaningful learning is not only retained longer, but this information can be used much more successfully to solve new problems. Teachers should work collaboratively to build on some of the simpler concept maps dealing with education ideas and perhaps add resources to some of the more complex concept maps. There is nothing written in stone that says multiple choice tests must be used from grade school through university, and perhaps in time even national achievement exams will utilize concept mapping as a powerful evaluation tool. Thus, in curriculum planning, we need to construct a global a€?macro mapa€? showing the major ideas we plan to present in the whole course, or in a whole curriculum, and also more specific a€?micro mapsa€? to show the knowledge structure for a very specific segment of the instructional program. For these students, the subject matter of most disciplines, and especially science, mathematics, and history, is a cacophony of information to memorize, and they usually find this boring. In fact, the biography of one Nobel Lauriat in biology (Barbara McClintock) was entitled, A Feeling for the Organism (Keller, 1983). However, when we began to concept map the expert knowledge of a cardiologist who literally a€?wrote the booka€? on this technology, it was evident that there were concepts missing in the map and that the a€?tacit knowledgea€? of our expert was not fully expressed in his book or in our interviews.
In addition to submaps, a wide variety of digital resources can be accessed via the concept maps. Knowledge modeling and the creation of el-tech: A performance support system for electronic technicians. Carson Dunlop Associates' provides extensive home inspection education and report writing material. Propositions are statements about some object or event in the universe, either naturally occurring or constructed. Out of the necessity to find a better way to represent childrena€™s conceptual understanding emerged the idea of representing childrena€™s knowledge in the form of a concept map. This acquisition is mediated in a very important way when concrete experiences or props are available; hence the importance of a€?hands-ona€? activity for science learning with young children, but this is also true with learners of any age and in any subject matter domain. Typical objective tests seldom require more than rote learning (Bloom, 1956; Holden, 1992).
Our brains have a remarkable capacity for acquiring and retaining visual images of people or photos. While we can locate regions of the brain that are active in learning or recall of information using positron emission tomography (PET) scans, the specific mechanisms by which neurons store this information is not known.
Nevertheless, we seen the organizing opportunities afforded by associating the various activities with an explicit knowledge structure as very beneficial.
The primary reason we have seasons in latitudes away from the equator is due to the tilt of the earth on its axis toward the sun in summer resulting in longer days and more direct radiation, thus greater heating. Learners struggling to create good concept maps are themselves engaged in a creative process, and this can be challenging, especially to learners who have spent most of their life learning by rote. Some concepts may remain in the parking lot as the map is completed if the mapmaker sees no good connection for these with other concepts in the map. When CmapTools is used in conjunction with a computer projector, two or more individuals can easily collaborate in building a concept map and see changes as they progress in their work.
Concept mapping is an easy way to encourage very high levels of cognitive performance, when the process is done well.
In the early 1990s, Latin America, students using the IBM Net (before the Internet) were very successful in creating concept maps both with students in their classroom and with students in other countries (CaA±as et al., 2001). When a concept map is saved to a CmapServer, a a€?web pagea€? version of the map is also stored, so a WWW browser is sufficient to browse through all the published concept maps. Having learners comment on each othera€™s concept maps, whether they are in the same classroom or in different schools, is an effective form of peer-review and collaboration. So giving the student some of the concepts does not take away from the difficulty in the map construction, although it may somewhat limit the creativity of the student in selecting the concepts to include. The CmapTools Network may serve as a clearinghouse for some of these efforts through its Public servers in Italy and other countries. Even with the current state of technology and pedagogical understandings, it is possible for schools, states or countries to mount a New Model for Education. This is a chicken-and-egg problem because concept maps cannot be required on national achievement tests if most students have not been given opportunities to learn to use this knowledge representation tool.
Faculty working independently or collaboratively can redesign course syllabi or an entire curriculum. Nonaka and Takeuchi (1995) stress the importance of capturing and using the knowledge of corporate experta€™s tacit knowledge if a company wants to become a€?the knowledge creating companya€?. Thus, the concept map not only allowed us to represent the experta€™s knowledge, but also to find gaps in the knowledge structure we were procuring through interviews.
Paper presented at the Seventh World Conference on Artificial Intelligence in Education, Washington DC. Online concept maps: Enhancing collaborative learning by using technology with concept maps. Paper presented at the Symposium at the 11th Biennial Conference of the European Association for Research in Learning and Instruction (EARLI), Cyprus. A case study in the research paradigm of human-centered computing: Local expertise in weather forecasting.
Why minimal guidance during iInstruction does not work: an analysis of the failure of constructivist, discovery, problem-based, experiential, and iInquiry-based teaching. Propositions contain two or more concepts connected using linking words or phrases to form a meaningful statement.
In fact, the worst forms of objective tests, or short-answers tests, require verbatim recall of statements and this may be impeded by meaningful learning where new knowledge is assimilated into existing frameworks, making it difficult to recall specific, verbatim definitions or descriptions. For example, in one study (Shepard, 1967) presented 612 pictures of common scenes to subjects, and later asked which of two similar pictures shown was one of the 612 seen earlier? Other ideas for improving instruction to achieve understanding of the subject is available elsewhere (Mintzes et al., 1998). In winter, the axis of the earth points away from the sun, thus resulting in shorter days and less intense radiation. Rote learning contributes very little at best to our knowledge structures, and therefore cannot underlie creative thinking or novel problem solving. CmapTools also allows for collaboration between individuals in the same room or anywhere in the world, and the maps can be built synchronously or asynchronously, depending on the mapmakersa€™ schedules. This is one reason concept mapping can also be a very powerful evaluation tool (Edmondson, 2000). In our own classes and workshops, and in classes taught by our students and colleagues, small groups of students working collectively to construct concept maps can produce some remarkably good maps. Whenever a concept map is made with CmapTools and then saved, the maker is asked to provide a focus question, as well as key concepts for this concept map.
It does provide the teacher with insight into which concepts the student(s) had trouble integrating into the concept map, indicating little or no understanding of these concepts.
The a€?expert skeletona€? concept maps would serve as a starting point for students and teachers for each section illustrated in the book, and then students would use these Cmaps together with CmapTools to search the WWW for pertinent resources and ideas. We anticipate that an abundance of both anecdotal and empirical data will flow from these efforts in a few years. On the other hand, if state, regional, and national exams would begin to include concept maps as a segment of the exam, there would be a great incentive for teachers to teach students how to use this tool.
For example, faculty working together to plan instruction in veterinary medicine at Cornell University constructed the concept map shown in Figure 15.
This kind of problem was recognized years ago in Hoffmana€™s (1962) The Tyranny of Testing.
What is interfering with these 21 Harvard people is confusion with the common experience that when we are closer to a fire or lamp, the heat is more intense than when we are further away. As people create and observe new or existing objects or events, the creative people will continue to create new concents and new knowledge. Figure 13 illustrates one of the a€?expert skeletona€? concept maps that could be used as the starting point for building a knowledge model, preferably students working in teams and sharing ideas. Based on the solid theoretical and related research findings now available, there is every reason to be optimistic that these innovative efforts will be successful. Figure 1 shows an example of a concept map that describes the structure of concept maps and illustrates the above characteristics. Three days later, they were still 92% correct, and three months later they were correct 58% of the time.
Thus, these people have failed to recognize that this same phenomenon is not operating to give seasons on Earth. Creating new methods of observing or recording events usually opens up new opportunities for new knowledge creation.
Currently there are a number of projects in the USA and elsewhere that are doing research to see if better evaluation tools can be developed, including the use of concept maps.
Boumedine (Ed.), Proceedings of IKS 2002 - the IASTED international conference on information and knowledge sharing (pp. This and many other studies have shown that humans have a remarkable ability to recall images, although they soon forget many of the details in the images. For example, the creation of the concept mapping method for recording subjecta€™s understandings has led new opportunities to study the process of learning and new knowledge creation. Considering how often we look at pennies, it is interesting that the subjects asked to draw a penny in a study by Nickerson and Adams (1979) omitted more than half of the features or located them in the wrong place.
This is commonly observed in many, many examples of a€?misconceptionsa€? in every field of study. Some features of the latest versions of CmapTools also facilitate the use of concept maps for assessment.
We believe that integrating various kind of images into a conceptual framework using concept mapping software like CmapTools (described below) could enhance iconic memory, and we hope research on this will be done. The only solution to the problem of overcoming misconceptions is to help learners learn meaningfully, and using concept maps can be very helpful. For example, the a€?Compare concept mapsa€? tool allows the comparison of an a€?experta€? concept map for a topic with maps constructed by students, and all similar or different concepts and propositions are shown in color.

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