Wednesday, September 28, 2011

Constructivism and Constructionism - How do we build knowledge?

Constructivism and constructionism both have their places in our classrooms, and recognizing the strengths and weaknesses of each theory can assist in helping our students learn and retain knowledge. Technology, when incorporated with either approach, can facilitate the learning to higher levels that would otherwise be unobtainable.
Each person relates to new knowledge by actively constructing their own meaning based on prior experiences. Dr. Michael Orey uses the example of a chair (Laureate, 2011); specifically, how each of us has had different experiences with a chair. Since our experiences are different, therefore, our detailed definitions of that chair will be varied. Recognizing these differences in our students' prior learning can be used to our advantage if we can learn, recognize, and adapt our classrooms to the prior knowledge. For example, since I teach mathematics, my students have learned to multiply. However, they are split, about in thirds, to the method in which they learned to multiply. Some have used the traditional column method, some have used partial products, and others have used the lattice method. Each method has its own strengths and weaknesses, but if they are examined closely, each is really just putting the numerical place order in a different location. The students cling to their own methods, so I put them in groupings to teach their method to the other students who have a different method. By doing a compare and contrast exercise, they quickly discover the similarities between all three. Some students actually are angry that the methods are so similar, because they believed their way to be the best.
With constructionism, the students best learn when they build an external artifact or something they can share with others (Laureate, 2011). An example of this creation and expansion is given in Using Technology with Classroom Instruction That Works (Pitler, Hubbell, Kuhn, & Malenoski, 2007); specifically an exercise that gathers and compares the pH of various water sources. The students gather data, which is eased and facilitated by using a pH probe hooked to a computer. The data is then entered, sorted, and graphed using a spreadsheet. The graphs allow an easy comparison of rain water, stream water, distilled water, and tap water. The students created the charts, so they had a real investment in the presentation and comparison of the data. The spreadsheet allowed the students to create the graphs in a reasonable time, so the effort and knowledge was spent on the analysis of the graph as opposed to the creation of the graph. The students are then judged on their analysis as opposed to the drawing. This comparison is the higher level knowledge skill, so the time is better spent.
I am lucky enough to incorporate several constructionist projects during my school year. One such project where my students can build something they can share with others is to spend a virtual million dollars creating their home of their future. The students use a spreadsheet to build a table which adds, subtotals, taxes, and then totals the prices of the items the students buy in their home. There are eight categories, including  a house, transportation, electronics, food, clothing, and miscellaneous items. The students must spend as close to one million dollars without going over. The spreadsheet facilitates the learning by eliminating the tedious repetition of multiplying, subtotals, and adding to get a total. The students add in hyperlinks to websites to prove the prices of their items, and at the conclusion of their project, must present their new house and its items to the class. When I am introducing the project, the students are more affected by the presentation portion. When they realize their work is going to be shared, the quality of their work improves. This gives the student a sense of accomplishment and pride, while showing the current beliefs and understandings to those around them. The students also construct a collage of their purchased items, along with their total. These collages, along with a printed copy of their spreadsheet, get displayed.
The use of the spreadsheet helps to overcome many challenges, both from the student and from the teacher. By using a spreadsheet, the need to check for correct arithmetic is eliminated. As long as the cell formulas are set up correctly, the totals will sum correctly. The students can then concentrate on finding items that meet the categories. The first pass through the items rarely comes within several hundred-thousand dollars of the million, so the students need to change items, prices, quantities, or a combination of them. Instead of being a boring addition exercise, the students concentrate on correct hyperlinks, ranging the prices to more closely meet the million. Within a few iterations, many students can even get within one dollar. After a little teamwork and brainstorming, a few students find a way to add a sticker, which costs a penny, to get the exact amount. Using the Internet for locating items expands their choices far beyond any newspaper or catalog. Besides allowing the students to find an item with the prices they are looking for, their choices allow me as a teacher an insight to their world, their wishes, and dreams. It is a project that is fun, assimilating the learning into the project.
I would like to take full credit for this project, but I cannot. One of my fellow teachers and I swapped a lesson idea, so I totally stole this from her. Because I stole it, I am duty-bound to share the rubric and a sample spreadsheet with anyone who wants it, as long as they keep paying it forward. The project I shared with the other teacher also uses presentation and collaboration. The students must construct a scale model of a famous landmark, such as the Eiffel Tower or the Space Needle in Seattle. The students do a web-quest to find pictures and dimensions of their building, and then they use scale factors to size their models. We use the Smartboard to project the image of the real landmark onto the scale model to judge the accuracy of the model. The comparison of the models is usually pretty close. The calculator and Internet allow the students to concentrate on the construction of the models rather than computing the dimensions.
Todd Deschaine

Laureate Education, Inc. (Producer). (2011). Program seven: Constructionist and constructivist learning theories [Video webcast]. Bridging learning theory, instruction and technology. Retrieved from
Pitler, H., Hubbell, E., Kuhn, M., & Malenoski, K. (2007). Using technology with classroom instruction that works. Alexandria, VA: ASCD.

Wednesday, September 21, 2011

Cognitive Learning and Adapting Instructional Strategies

There is a close relationship between cognitive learning and instructional strategies, specifically in areas that use technology. One of the aspects of cognitive learning is the inability to have more than seven thoughts in a person's short term memory. The more distractions, the less likely that knowledge will pass from short-term to long-term memory and be retained. Using technology can reduce or eliminate distractions, so it can be useful in areas that we may not fully appreciate. One example that is close to my heart is using Microsoft Excel to help with lower level mathematics skills so that the student can look higher and attain higher learning. Karen Casselman spoke of technology helping to facilitate learning by eliminating the tedious repetition (Laureate, 2011). Instead of concentrating on addition, the students allowed Excel to perform the addition, and then they could concentrate on the higher level knowledge of the lesson, in her case trending. It is important to note that Casselman's students did set up the spreadsheet formulas in Excel. Since the students are using their short-term memory to add, they cannot hope to achieve trend analysis. I did a similar exercise with my middle school students when we went through a unit on perimeter, and the results were much better with the use of a calculator, because the students needed to learn about perimeter rather than adding numbers.
Using rubrics is not new to most teachers and not new to the students. We use Excel for rubrics, which allows for the automatic calculation of the students' grades for a project. The rubric can be printed; however, the students get additional points if they use the electronic version. I read this suggestion in a section of Using Technology with Classroom Instruction That Works (Pitler, Hubbell, Kuhn, & Malenoski, 2007) that deals with organizers. The base rubric has some consistencies, such as scores for grammar, citing sources, creativity, and organization. Each new rubric then gets specific entries; for instance, a biography on a mathematician would have a section for biographical completeness, whereas a mathematics dictionary would have a different section, for number of entries. The students, and the teacher, concentrate on the content of the rubric as opposed to the scoring.
Another section in Using Technology with Classroom Instruction That Works concentrated on note-taking. I was pleasantly surprised that they advocate teacher-created notes especially in this age of word-processing. It hit close to home for me, and brought back my college years. I initially struggled in calculus, and visited my professor to get help. He was sympathetic, and sought a solution. After a brief discussion, he suggested that I was paying more attention to taking notes than following the material. He told me to continue to attend his first period class to take notes, but then return to another section of the course he taught later in the day and do nothing but pay attention. My understanding went through the roof, and my grades returned. I attempted to implement the teacher notes with my classes two years ago, and it met with limited success. Several students felt as if they did not need to pay attention because the notes were already written. The students did not feel like they had input to their notes. As a bit of more information, I am part of a program called AVID, and we utilize Cornell Notes as our method of note-taking. So we reached a compromise. Some of the notes had the headings pre-entered so the students would enter their own notes. Other sections would be the opposite, where the notes were already there, forcing them to determine the main topic. When examples are shown, the students are still fully responsible for their entries.
Overall, cognitive learning, or the limitations of attentions may throttle the information retained. However, with some simple realignments and ideas, we can refocus the students to higher level thinking by eliminating the distractions. Technology can assist by eliminating the tedious tasks, allowing the students to attain higher levels of thought analysis. If we can get one of the slots of short-term memory of our students, hold onto it, and turn it into a conduit for knowledge to flow into long-term memory, then the use of technology, cognitive learning, and instructional strategies can work in a symbiotic way rather than be mutually exclusive.
Do you have any more ideas on how to focus the students to higher levels of learning? If they pertain to mathematics, I would enjoy your contribution to this blog.

Laureate Education, Inc. (Producer). (2011). Program six: Spotlight on technology: Virtual field trips [Video webcast]. Bridging learning theory, instruction and technology. Retrieved from
Pitler, H., Hubbell, E., Kuhn, M., & Malenoski, K. (2007). Using technology with classroom instruction that works. Alexandria, VA: ASCD.

Wednesday, September 14, 2011

Combining Effort, Behaviorism, and Technology in Our Classrooms

Effort is typically a very difficult item to measure. Each person has a different self-measure of their amount of effort, and the corresponding result of that effort. A student may truly feel like they did all they possibly could to study for a test, but still score poorly. Another student, who scored higher, may not feel like their effort was enough. If it is possible to tangibly measure both efforts, it might just result that the student who believed they studied a lot had lower effort than the other student. Making the intangible effort measureable may be difficult; however, an example rubric of effort might be used to acclimate each student to the various levels of effort. Along with the use of a spreadsheet to record and track the efforts over a period of time brings the overt effort measurement along with a covert technology skill into the classroom. Students can track and then see the correlation between effort and test scores. Although the rubric only works if the students are honest and forthcoming in their self-analysis, some anonymous graphs would be a great starting point.
One section of the effort spreadsheet is homework. I assign homework from Monday through Thursday, and it should take an average of about 20 minutes to complete. Some nights will take longer, other nights might be quicker. The effort rubric breaks down the homework into four categories, the highest described as "I attempt all problems on every homework assignment, even if I think some of my answers might be incorrect. I refer to my class notes while doing homework". The lowest category, which by no means reflects the lowest possible effort, reads "I miss many homework assignments and skip many answers, particularly those problems that appear long or difficult. I almost never refer to my class notes when doing homework" (Pitler, H., Hubbell, E., Kuhn, M., & Malenoski, K.,2007). These guidelines add some actual examples of what to do and what not to do in order for the students to accurately judge themselves. The response from a student that they really tried can then be challenged, and corrections made to increase and improve the effort.
Effort should not be wasted on repetitive activity. The classroom of our past may have been one of endless worksheets and drills. It may have been tedious and boring, but most adults remember their multiplication tables because of the system of rewards that was in place. Accurate memorization resulted in high tests scores, which led to a better education. Failure to memorize led down a more serious and negative path. Educators in the past knew, and practiced behaviorism. They rewarded the good - good behavior, good grades, good citizenship; and punished the bad. In today's classrooms behaviorism still exists, although the teachers and students may not realize it is actually happening. Teachers use the approach of positive punishment to address uncooperative students, even when using contracts, listing rules, and stating consequences. This enables the students to act, and the teacher to react in the appropriate manner to the student behavior. Ironically, it seems like the students are providing the stimulus and the teachers follow with the result. A student calls out or gets out of their seat, so the teacher addresses them. It is the tail wagging the dog. Contrary to this practice, unwanted behavior that goes unrewarded will eventually be extinguished (Orey, 2001). The students receive no attention, so they may eventually stop the unwanted acts.
Technology, according to Orey, is used too often to remediate rather than to discover (Laureate, 2011). Computer tutorials may be fine to learn a program, but many educational programs do not develop knowledge, they simply reinforce. I have watched students use computer programs which repeat questions until they are answered correctly. The students might acquire the knowledge, but repetition occurs and the students learn to correctly answer the question from remembering the correct answer when they got it wrong on a previous attempt. There are software programs that require non-repetitive skills to reach a goal, which may be more of a challenge by requiring application of the knowledge for success. Other technology tools can be useful to vary the way knowledge is received. The use of videos, responders, laptops, and Smartboards all serve to keep the level of student engagement at a high level, which obviously enhances the learning process. However, a Smartboard that is used to show multiple problems quickly becomes a high priced white board.
Returning to repetition, homework and its place in the modern classroom, I think that repetition is sometimes necessary, especially when the introduction of the knowledge is weak. Although the drilling approach to learning may have a place, it ceases to be effective when overused. The repetition must also be creative and in varied contexts to necessitate the learning (Smith, 1999). Some knowledge is difficult to engrain, and students do need to develop and memorize, when it is in an appropriate context and on a limited basis. This may be why our parents had multiplication tables drilled into their minds until the knowledge became second nature. Varying the approach to teaching, with discovery, engagement, and appropriate repetition to secure the knowledge is an effective manner of transferring knowledge.
I hope you get a slight amount of insight into my classroom. Thanks for reading!

Laureate Education, Inc. (Producer). (2011). Program four: Behaviorist learning theory [Video webcast]. Bridging learning theory, instruction and technology. Retrieved from

Orey, M. (Ed.). (2001). Emerging perspectives on learning, teaching, and technology. Retrieved from
Pitler, H., Hubbell, E., Kuhn, M., & Malenoski, K. (2007). Using technology with classroom instruction that works. Alexandria, VA: ASCD.
Smith, K. (1999). The behaviourist orientation to learning. In The encyclopedia of informal education. Retrieved from

Saturday, September 10, 2011

Understanding the Brain Function for Better Retention of Knowledge

            Students are models of diversity, their cultural backgrounds, religions, families, and economic stature all contribute to the individuality of each student. The learning styles of students can be just as diverse, with the style diversity distributed amongst intrapersonal skills, interpersonal skills, tactile, musical, visual, and auditory learners. The brain, research has discovered, is constructed of a unique biological series of components. These components allow the brain to develop, strengthen, and change, thus creating a learning and retention tool.
Personal Theory and Practice
            Research, specifically that presented by Wolfe in her video Understanding The Brain, show that the brain uses connectors, called synapses, to connect memories and experiences. These synapses can be strengthened by repetition, and can also weaken with non-use. The initial connection seems to be a key to learning and the retention of memories. We all have vivid memories, easily recalled, that puzzle us as to why we retain such a memory. On the other extreme, some knowledge is elusive, and seems impossible to recall even after using all types of memory retention strategies.
            My personal theory is that the strength of the initial connection, or memory, is crucial to long-term retention. If the initial connection is powerful and deep, we cannot help but retain this knowledge. However, if the connection is so vague or does not exist, then the memory has little chance of connection through the synapse. Once the connection is made, I fully agree with Wolfe that the synapse must be used in order to strengthen the connection. I do not believe that unused connections will sever; however, they do become so weak and irrelevant that their path is not used.
            Discovery makes the initial connection powerful. If a person, in our case a student, finds the knowledge on their own, the initial connection is comparatively deep compared to a the knowledge that is forced or presented. These are the light bulb moments that are often followed by the sounds of students realizing that they just "got it". Imagine a time when we find a short-cut on the road or computer, and wind up having a revelation; specifically, this revelation is a powerful connection. If a student discovers the material with some facilitation, as opposed to lecture, the knowledge is more likely to be retained over a longer period of time. Both strong initial connections, as well as those developed with use, move knowledge into an understood position of knowledge. An example of this is multiplication tables. Some students can see the groups of sizes, while others need repetition. The end result of both, however, is that most high school graduates can easily recall a multiplication product without having to work it out in their heads. People simply know that two times five equals ten; they do not need to use mnemonics, picture recollections, or paper to recall a simple fact.
            I also believe that the mind can be made to retain knowledge by repetition, which can be used to develop the synapses, retaining the knowledge. If an initial connection is weak, it can be strengthened to a point where the knowledge is retained. This method would require some work that would be more likely found in a classroom of a previous century, with worksheets, tables, and endless drilling of facts.
            My classroom is a combination of discovery and development. Since I believe discovery is powerful, I attempt to have students discover knowledge. There does come a time where knowledge is so crucial that it needs to have moved into the second nature portion of memory. I do not believe that this should be done with all facts, but used sparingly to assure that it can remain a powerful tool. Using a previous example, multiplication tables are so important that they must be second nature. Their use throughout life, applying to many other fields or study, merit the effort and time to assure that the person can recall the answers without conscious thought.
            Each student learns in their own manner, and targeting the most efficient manner for the group may be a self-eliminating process. If a teaching method is directed specifically to one student, other students may be at a disadvantage. If our students are diverse, so should the learning methods we employ in our classrooms, developing the brain's connections in a variety of ways. Research, along with common sense, shows the brain changes, develops, heals, and adapts based on sensory inputs. Varying those inputs, i.e. our teaching methods, may provide the best overall method for the obtaining and retaining knowledge to our students.